RU2783222C1 - Method for filtering photons from the residual radiation of coherent pumping - Google Patents

Abstract

FIELD: quantum optics.

SUBSTANCE: invention relates to the field of quantum optics and quantum information and concerns a pumping filtration method for sources of quantum states. The method involves feeding to M inputs of an N-channel interferometer, characterized by a transfer matrix U of size N by N, generated photons from M photon sources with residual coherent pumping signals from at least one laser radiation source. Coherent pumping signals when using the continuous mode are formed with the same frequency spectrum and the same polarization, and when using the pulse mode, coherent pumping pulses of the same polarization form and with matching central frequencies of their spectrum are formed, which are fed synchronously to the N-channel interferometer. The transfer matrix U is designed with the ability to focus coherent pumping input signals, including residual coherent pumping signals from photon sources, to at least one output, and output part of the photons from photon sources to the remaining outputs.

EFFECT: reducing losses during filtration, providing the possibility of filtering photons generated by multiple sources by one device and the possibility of filtering radiation when the polarization of radiation coincides with the polarization of the generated photons.

7 cl, 9 dwg

Description

The field of technology to which the invention belongs

The invention relates to the field of quantum optics and quantum information, namely to methods for generating optical quantum states of electromagnetic fields. The invention can be used in devices for quantum optical computers and simulators. The invention can also be used as an element of quantum communication networks, including quantum repeaters.

State of the art

Photon sources are used in fundamental experimental research and applied devices that process information based on quantum algorithms. The quantum states of photons that are generated by such sources are carriers of quantum information, which are converted if used in computational quantum algorithms or sent between remote subscribers if used in quantum communication algorithms.

The prior art sources of single photons based on quantum dots (US9619754B2). In such sources, a quantum dot excited by coherent optical radiation emits a single photon as a result of the transition from the excited to the ground quantum state. In this case, the central wavelength of the emitted photon is equal to the wavelength corresponding to the energy difference between the excited and ground states of the quantum dot. The frequency spectrum of the coherent radiation that excites the quantum dot must have components with wavelengths equal to or shorter than the central wavelength of the transition. When a point is excited, part of the energy of the coherent radiation is absorbed by the point.

The disadvantage of such photon sources is the presence of residual radiation of coherent pumping, which propagates along with the photon generated in it, which makes it impossible to directly use such sources in the implementation of quantum information algorithms - coherent radiation introduces noise, errors, or even disables the quantum device.

Sources of pairs of single photons are known from the prior art, using nonlinear optical interactions, disclosed in the work of S. Paesani et al., “Near-ideal spontaneous photon source in silicon quantum photonics” // Nature Communications 11, 2505 (2020). In such sources, intense coherent radiation enters a medium with a cubic nonlinearity of the optical response, where it leads to the production of pairs of photons at wavelengths below and above the wavelength of coherent radiation. The spectra of generated photons are located close to the wavelength of coherent radiation.

As in the case of single photon sources based on quantum dots, the disadvantage of such photon sources is the presence of residual coherent pump radiation, which propagates along with the photon generated in it, which makes it impossible to directly use such sources in the implementation of quantum information algorithms.

The prior art methods for filtering coherent radiation from generated photons, disclosed in the work of T.Huber et al., “Filter-free single-photon quantum dot resonance fluorescence in an integrated cavity-waveguide device” // Optica, v.7, No. 5, p. 380-385 (2020) . The method uses the difference in the polarization of the coherent radiation used to excite photon sources from the polarization of the generated photons. Coherent radiation enters and exits the source in a direction at an angle to the direction in which the photon is generated. Thus, the method makes it possible to filter coherent radiation from generated photons even in cases where the wavelength spectrum of coherent radiation overlaps with the spectrum of generated photons.

The disadvantage of this method is the unpolarized states of the generated photons, while in the implementation of quantum information algorithms it is necessary to use photons with linear polarization. To obtain linearly polarized photons from unpolarized ones, a polarizer can be used, but it leads to the loss of at least half of the generated photons.

The closest to the claimed technical solution is a method for filtering coherent radiation from generated photon signals, disclosed in the invention “Interferometer filters with compensation structure” US2020/0371287 (2020). This method uses the difference in the wavelengths of the exciting coherent radiation from the wavelengths of the generated photons. For filtering, the central wavelength of the transmission resonance of the two-channel interferometer is tuned so that it falls within the central wavelength of the generated photons. In this case, the resonance width of the interferometer is such that its spectral line does not overlap with the spectrum of coherent radiation and, therefore, the interferometer does not transmit it. As a result, the generated photons can be obtained at the output without the admixture of coherent radiation.

The disadvantage of this filtering method is the introduction of losses into the generated photon signals, which leads to a decrease in the efficiency of photon sources and, consequently, to a decrease in the efficiency of the quantum device using these sources. As the wavelengths of the generated photons approach the pump spectrum, the losses introduced by the filter increase. The disadvantage of this method is also the impossibility of its use in cases where the frequency spectrum of the exciting coherent radiation overlaps - both partially and completely - with the spectrum of the generated photons. Another disadvantage of the method is the need to use a separate filtering interferometer for each individual source, which complicates and enlarges the optical schemes. In addition, the disadvantage is the need to adjust the central resonance wavelength of each interferometer individually for each photon source, which also complicates the calibration and control of the circuit.

The technical problem solved by the claimed invention is the high losses introduced by the elements that filter the residual coherent radiation from the generated photons. Also, a technical problem to be solved is the impossibility of filtering by known methods in the case when the polarization, spatial mode and time interval of the coherent excitation pulse coincide with the corresponding parameters of the generated photons and their wavelength spectra overlap. At the same time, this resonant excitation mode seems to be the most optimal in terms of the quality of the quantum properties of photons obtained in some widely used sources, for example, based on quantum dots. The impossibility of performing resonant excitation without introducing significant losses hinders an increase in the efficiency of quantum devices using sources of this type, or even makes it impossible to implement large-scale quantum algorithms. Another technical problem to be solved is the complexity of optical circuits consisting of multiple photon sources, which is due to the need to use a separate filter device/element for each source. Filter elements increase in size and often require individual active adjustment.

Disclosure of invention

The technical result of the invention is to increase the efficiency of photon sources that use coherent optical radiation for excitation. Efficiency is increased by reducing the losses introduced by traditional methods of filtering coherent radiation. Another technical result of the invention is the possibility of filtering coherent radiation from photons generated by multiple sources with one device, which simplifies its adjustment. Also, the technical result of the invention is the possibility of filtering coherent radiation in the resonant method of excitation of sources of single photons, when the polarization of this radiation coincides with the polarization of the generated photons, and their wavelength spectra overlap.

The technical result is achieved by a pump filtering method for sources of quantum states, including the supply to M inputs of an N-channel interferometer, characterized by a transfer matrix U of size N by N, generated photons from M photon sources with residual coherent pumping signals from at least one laser source. radiation, while coherent pumping signals from laser sources when using the continuous mode are formed with the same frequency spectrum and the same polarization, and when using the pulsed mode, coherent pumping pulses of the same polarization shape are formed with the same center frequencies of their spectrum, which are fed to the N-channel interferometer synchronously ; the transfer matrix U is configured to focus input coherent pump signals, including residual coherent pump signals from photon sources, to at least one output, and output a portion of photons from photon sources to the remaining outputs.

In one of the embodiments of the method, at least one of the remaining inputs of the N-channel interferometer is additionally supplied with a coherent pump signal from at least one laser radiation source, while using the pulsed mode, coherent pump pulses are fed to the N- channel interferometer synchronously, including residual pulses of coherent pumping from photon sources.

сигналов когерентной накачки, поступающих на вход N-канального интерферометра, включая остаточные сигналы накачки от источников фотонов, на передаточную матрицу U дает заданный вектор амплитуд

, который содержит ненулевые элементы с индексами, соответствующими каналам, в которые осуществляется фокусировка когерентной накачки, а остальные элементы вектора

- нулевые:

The transfer matrix U is designed in such a way that the multiplication of the amplitude vector

of coherent pump signals coming to the input of the N-channel interferometer, including the residual pump signals from photon sources, to the transfer matrix U gives a given amplitude vector

, which contains nonzero elements with indices corresponding to the channels into which coherent pumping is focused, and the remaining elements of the vector

- null:

The coherent pump signal is focused into a subset of outputs, consisting of K outputs of an N-channel interferometer, by varying the phase shift elements until the maximum power measured in this subset of outputs is reached. In another embodiment of the invention, coherent pumping is focused by varying the parameters of the dividers included in the N-channel interferometer, or by varying the coherent pump amplitudes at the input to the N-channel interferometer.

An embodiment of the invention is possible, according to which the output signals from photon sources that have passed through the N-channel interferometer and contain photons from photon sources are subjected to conversion by the second interferometer with the number of inputs and outputs not less than the number of outputs of the first interferometer containing photons from photon sources.

The method can be implemented using a pump filtering system for quantum state sources, including at least a laser radiation source, at least one photon source, at least one N-channel interferometer configured to filter received signals from photon sources that have passed the first interferometer from residual coherent pumping signals as described above, and detectors installed at the outputs of the N-channel interferometer, the number of detectors corresponding to the number of outputs K, into which the coherent pumping is focused.

The generation of single photons in sources with excitation by laser pumping is associated with the need to filter the pump that remains after excitation. The residual coherent pump propagates along with the generated photons and, in the absence of filtering, the operation of quantum devices that implement quantum methods for processing and transmitting information is impossible. To filter residual pumping at the output of photon sources, frequency or polarization filters are introduced, which use the difference in the frequency spectrum or polarization of the pump from the spectrum or polarization of the generated photons. Filters of this type do not pass the pump, but they introduce losses into the generated photons. In this case, the closer the frequencies from the photon spectrum are to the residual pumping spectrum, the more difficult it is to filter the pumping from useful photon signals without introducing significant losses.

The present invention does not use the traditional approach with frequency or polarization filters. The invention exploits the difference in the conversion performed by a multichannel interferometer on a plurality of signals in coherent pump states and generated photons in Fock states. Thus, there is no need to use traditional filters in the circuit.

Brief description of the drawings

The invention is illustrated by drawings, where in Fig. 1 is a diagram illustrating the principle of the claimed invention. Fig. 1a illustrates the process of photon generation with excitation by coherent pumping. In FIG. Figure 1b shows the proposed scheme for filtering coherent pumping from generated photon signals.

In FIG. Figure 2 shows a diagram illustrating the proposed pump filtering method with two multichannel interferometers connected in series.

In FIG. Figure 3 shows a diagram illustrating the proposed pump filtering method with two serially connected multichannel interferometers and one photon source.

In FIG. Figure 4 shows a diagram illustrating the simplest example of the implementation of the proposed method for filtering coherent pumping.

In FIG. Figure 5 shows a scheme for filtering coherent pumping using a cascade of series-connected interferometers.

In FIG. 6 are diagrams illustrating the relationship between the coherent pumping frequencies and the frequency(s) of generated photons for different types of sources.

In FIG. 7 shows the optical scheme of a multichannel interferometer implemented in an example of a specific implementation of the claimed invention.

In FIG. 8 shows a diagram of a two-channel programmable block of the Mach-Zehnder interferometer used as a component block of a 5-channel interferometer in an example of a specific implementation of the claimed invention.

In FIG. 9 shows a diagram of an optical setup used in an example of a specific implementation of the claimed invention.

Positions in the drawings indicate:

1 - photon source,

2 - coherent pump pulse,

3 - momentum of the generated photon or photons,

4 - pulse of residual coherent pumping,

5 - multichannel interferometer,

6 - many sources of photons,

7 - set of pulses of coherent pumping,

8 - a set of photons generated by sources, and a set of pulses of residual coherent pumping,

9 - many inputs of the multichannel interferometer 5,

10 - multiple outputs of the multichannel interferometer 5,

11 - channel into which the residual coherent pumping is focused,

12 - pulse of residual coherent pumping,

13 - a set of outputs into which photons are output,

14 - state of photons,

15 - multichannel interferometer following the first multichannel interferometer 5,

16 - many inputs of the interferometer 15,

17 - set of inputs of the interferometer 15, which receives the state of photons 14 generated in the interferometer 5,

18 - many outputs of the interferometer 15,

19 - a set of channels into which photons are output after the interferometer 15,

20 - the state of the extracted photons at the outputs of the interferometer 5, which is fed to the inputs of the interferometer 15,

21 - residual coherent pumping at output 11 of multichannel interferometer 5 in a cascade circuit of several series-connected interferometers,

22 - output of the interferometer 15, into which the residual pumping is focused,

23 - residual coherent pump pulse coming out of the output 22 of the interferometer 15,

24 - two-channel divider,

25 - divider inputs 24,

26 - divider outputs 24,

27 - state at the outputs of the divider 24 in the case of two photons at its input,

28 - state at the outputs of the divider 24 in the case of one photon at its input,

29 - pumping frequency for a photon source based on nonlinear media with quadratic nonlinearity, generating pairs of photons at frequencies of 30 and 31,

32 and 33 - frequencies of coherent pumping in the case of photon sources based on nonlinear media with cubic nonlinearity generating pairs of photons at frequencies of 30 and 31,

34 - frequency of coherent pumping for a source based on a quantum emitter,

35 is the frequency of generated photons in the case of a source based on a quantum emitter,

36 - two-channel programmable unit as part of a multi-channel interferometer,

37 - coherent pump signals applied to the inputs of a 5-channel programmable interferometer used in a specific technical implementation of the invention,

38 - focused power signal into one output channel of a 5-channel programmable interferometer used in a specific technical implementation of the invention,

39 - static balanced dividers as part of two-channel programmable blocks 36,

40 - variable elements of phase shifts as part of two-channel programmable blocks 36,

41 - integral optical element of a directional divider that implements a static balanced divider,

42 - variable phase shift element,

43 - laser generating coherent pumping,

44 - laser power splitter 43,

45 - source of single photons based on a quantum dot,

46 - programmable 5-channel interferometer,

47 - optical radiation detector capable of detecting intense coherent laser signals,

48 - superconducting detectors of single photons,

49 - computer that controls the conversion of a 5-channel interferometer,

50 - electrical lines through which the computer 49 controls the interferometer 46,

51 - electrical lines through which the signals from the detectors of single photons 48 arrive at the computer 49,

52 - area of convergence of 5 waveguides in the integrated optical chip of the power splitter,

53 - waveguide, through which the radiation from the laser 43 was started.

Implementation of the invention

The invention is based on the use of photon sources excited by coherent optical radiation.

For a more unambiguous understanding of the essence of the claimed invention, the main terms and definitions used in the present description are presented below.

A photon source or simply a source is an element or device that generates electromagnetic signals described by quantum states with one certain number of photons or a superposition of a finite number of states, each of which has a certain number of photons. The invention concerns sources excited by coherent optical radiation, which is usually generated by lasers. Photon sources have two stationary energy levels that describe the stationary states of electrons or holes. The transition from the upper ( radiating ) state to the lower ( ground ) state is accompanied, depending on the type of source, by the generation of one or several photons simultaneously. To excite the source, it is irradiated with coherent radiation, for example, from a laser. Coherent radiation used to excite photon sources can be pulsed or continuous.

In the case of resonant excitation, the central wavelength of radiation is equal to the central wavelength of the emitted photon, which corresponds to the difference between the energies of the emitting and ground states of the source. In the case of nonresonant excitation, the central wavelength of the spectrum of the exciting radiation differs from the central wavelength of the spectrum of the emitted photon. With non-resonant excitation, an auxiliary level/levels can be used that have more energy than the radiating one. In this case, an auxiliary level is excited, the excited state from which subsequently passes to the emitting level, from which the photon is generated. Energy levels with energies higher than those of the main one may not be stationary, but virtual.

Coherent pumping or simply pumping is a coherent electromagnetic field that is used to excite a source to generate a photon or photons. The invention concerns pumping characterized by a coherent state. The properties of electromagnetic states in a coherent state and in a state with a certain number of photons are different - the effect of the same electromagnetic signal converter on signals prepared in two states is different.

The invention deals with electromagnetic signal converters. The converted signals are fed into the input channels of the transducer , and the converted signals are output from the output channels of the transducer . The method of encoding information into channels is set by the converter. Each input channel of the transducer is characterized by a set of values of the degrees of freedom of the electromagnetic field, which must have the input signals coming to its input. Two electromagnetic signals, characterized in that the corresponding sets of degrees of freedom differ in at least one value, can be generated and measured independently of each other. In order to be able to feed signals to the input of the transducer independently of each other, the sets of degrees of freedom values corresponding to the set of input channels must not have coincidences.

Spatial modes, frequency modes, temporal modes and polarization modes are used as the degrees of freedom of the electromagnetic field. Two different transducer channels are characterized by two different sets of field degrees of freedom, which must differ by at least one value. For example, when spatially encoding channels, the signals at the input and output of the converter must enter/exit in different spatial modes.

Linear N-channel conversion is the conversion of electromagnetic signals between N channels, the effect of which on coherent signals can be described by a linear law:

- число каналов преобразования,

- комплексные амплитуды когерентных сигналов, поступающие на вход преобразования,

- комплексные амплитуды преобразованных сигналов на выходе преобразования. Здесь индексы

и

принимают значения от 1 до

и обозначают номера канала, к которым относятся амплитуды. В (1) комплексные коэффициенты

формируют матрицу

размерности

, которая и определяет конкретное линейное преобразование. Выражение (1) может быть представлено в матричном виде: where

- number of conversion channels,

- complex amplitudes of coherent signals arriving at the input of the transformation,

- complex amplitudes of the converted signals at the conversion output. Here the indices

and

take values from 1 to

and denote the channel numbers to which the amplitudes belong. In (1) complex coefficients

form a matrix

dimensions

, which defines a specific linear transformation. Expression (1) can be represented in matrix form:

и

- столбцы, составленные из амплитуд сигналов на входе и выходе преобразования, соответственно. Число каналов преобразования

характеризует размерность преобразования.where

and

- columns composed of the amplitudes of the signals at the input and output of the transformation, respectively. Number of conversion channels

characterizes the dimension of the transformation.

, которая связывает друг с другом столбец амплитуд на выходе преобразования со столбцом на его входе (см. выражение (2)). The transformation transfer matrix or simply the transformation matrix is called the matrix

, which relates to each other the amplitude column at the output of the transformation with the column at its input (see expression ( 2 )).

An N-channel linear converter or a linear N-channel device or a linear N-channel interferometer or simply an interferometer is any device that performs a linear N-channel conversion of electromagnetic signals. An N-channel converter has N input and N output channels.

A multichannel interferometer is an N-channel interferometer with N>=3.

By focusing coherent pumping in the present invention is meant tuning the transfer matrix of a multichannel interferometer in such a way that the coherent pumping power supplied to its inputs comes out of a subset of its outputs. Thus, the photons emerging from the remaining outputs of the multichannel interferometer do not contain an admixture of coherent pump states.

, либо же состояние бифотонов

. Т.к. на возбуждение источника в общем случае расходуется не вся энергия накачки, после взаимодействия с источником остается когерентный импульс с временным профилем 4.On FIG. 1 is a diagram illustrating the present invention. Fig. 1a schematically illustrates the generation of photon quantum states by a photon source with coherent pumping. In it, a pump pulse with a time profile 2 arrives at the photon source 1, which excites the source. An excited source emits a light pulse with profile 3, which differs from coherent pumping in that its quantum state generally represents only one component with a certain number of photons or a superposition of a finite number of states with a certain number of photons. For example, depending on the type of source, either a single photon is generated

, or the state of biphotons

. Because In the general case, not all the pump energy is spent on excitation of the source; after interaction with the source, a coherent pulse with a time profile of 4 remains.

или других состояниях фотонов, которые отличаются от когерентных (в зависимости от типа источников). Сгенерированные в источниках импульсы вместе с импульсами остаточной накачки поступают на часть входов интерферометра 5. После возбуждения источников остаточные импульсы накачки и синхронные с ними импульсы когерентных сигналов 8 поступают на входы 9 интерферометра 5. Вместе с когерентным излучением на вход интерферометра 5 поступают также и сгенерированные фотоны.On FIG. Figure 1b shows the proposed scheme for filtering coherent pumping from generated photon signals. Several photons are simultaneously generated in the scheme, for which several photon sources are used simultaneously. The interferometer 5 is used to convert the coherent pumps and generated signals. A plurality of photon sources 6 are simultaneously excited by coherent pump pulses 7, as a result of which they generate signals in single-photon or bi-photon states

or other states of photons that differ from coherent ones (depending on the type of sources). The pulses generated in the sources, together with the residual pump pulses, arrive at a part of the inputs of the interferometer 5. After the sources are excited, the residual pump pulses and pulses of coherent signals 8 synchronous with them arrive at the inputs 9 of the interferometer 5. Together with the coherent radiation, the generated photons also arrive at the input of the interferometer 5 .

The interferometer converts the coherent pump pulses and the generated photon states. As a specific transformation of the interferometer 5, one is chosen such that the total coherent pump power supplied to all input channels of the interferometer is focused into a subset of the set of output channels 10. Without loss of generality, the description of the operating principle of the present invention will be assumed that the interferometer 5 focuses the pump into one output channel. On FIG. 1b, the focusing channel is the first upper channel 11 with the temporal pump profile 12 emerging from it. pump and photons, pumping can be applied to channels that do not receive photons from sources. For these reasons, there is a significant likelihood of generating photon signals at the outputs 13 that are not pumped. That is, the converted signals 14 output from the channels 13 are not noisy by the coherent pump 12.

On FIG. 2 shows a diagram illustrating the proposed pump filtering method, which is supplemented by another interferometer 15. Interferometer 15 performs the transformation of the filtered states of photons after the interferometer 5. Interferometer 15 has a plurality of input channels 16, some of which 17 receive filtered signals 14. The interferometer 15 performs state transformation photon signals 14, as a result of which, at its outputs 18, photon signals are converted into a form that may be more convenient for further applications. In particular, photons after the interferometer 15 can only be localized in a subset 19 of the set of output channels 18, which consists of a smaller number of channels than the original set of channels 13, the states of which are output after the filtering interferometer 5.

интерферометра, которая будет выполнять фокусирующее действие. Так, если амплитуды когерентных импульсов накачки на входе в интерферометр характеризуются столбцом комплексных чисел

, где

- комплексная амплитуда сигнала на входе в интерферометр с индексом

, а

означает транспонирование, то амплитуды когерентных сигналов на выходе из интерферометра задаются столбцом

. Для заданных амплитуд накачки на входе

(включающих как остаточные, так и дополнительные импульсы накачки) передаточная матрица интерферометра

, выполняющая фокусировку накачки в один выходной канал, например, с индексом

, получается решением уравнения:The performance of the proposed scheme is determined by the possibility of focusing coherent signals into one or a subset of channels without residual conversion into channels 13, which are used to obtain filtered photon states. It is known that for any configuration of amplitudes of coherent signals at the input to the interferometer, it is always possible to select the transfer matrix

interferometer, which will perform the focusing action. Thus, if the amplitudes of coherent pump pulses at the input to the interferometer are characterized by a column of complex numbers

, where

is the complex amplitude of the signal at the input to the interferometer with the index

, a

means transposition, then the amplitudes of coherent signals at the output of the interferometer are given by the column

. For given pump amplitudes at the input

(including both residual and additional pump pulses) interferometer transfer matrix

, which performs pump focusing into one output channel, for example, with the index

, is obtained by solving the equation:

имеет только один ненулевой элемент с индексом m. Уравнение (3) всегда имеет решение для передаточной матрицы

. Таким образом, многоканальный интерферометр всегда можно настроить на фокусировку когерентных сигналов.where is the column

has only one nonzero element with index m. Equation (3) always has a solution for the transfer matrix

. Thus, a multichannel interferometer can always be tuned to focus coherent signals.

(

). В данном случае фокусировка всей мощности накачки в один выходной канал возможна, если передаточная матрица интерферометра имеет следующие элементы:The following are some examples that explain the proposed method in more detail. For one photon source and an N-channel focusing interferometer, we consider the case when the profiles of the frequency spectra and polarization of the input pump pulses coincide, and they arrive at the interferometer synchronously, and the amplitudes of all pump pulses are the same:

(

). In this case, focusing the entire pump power into one output channel is possible if the interferometer transfer matrix has the following elements:

,

) - это известная матрица, выполняющая дискретное преобразование Фурье (S.A. Fldzhyan, M.Yu. Saygin, S.P. Kulik, “Optimal design of error-tolerant reprogrammable multiport interferometers” Optics Letters v. 45, No 9, p. 2632-2635 (2020)). Используя линейное преобразование

, можно рассчитать амплитуду на выходе 1-го канала интерферометра:

, тогда как на остальных выходных каналах

(

), подтверждая тем самым возможность фокусировки накачки. Таким образом, в этом примере, мощность накачки, поступающей на все входные каналы интерферометра с передаточной матрицей

, выходит из одного выходного канала.(

,

) is a well-known matrix that performs a discrete Fourier transform (SA Fldzhyan, M.Yu. Saygin, SP Kulik, “Optimal design of error-tolerant reprogrammable multiport interferometers” Optics Letters v. 45, No 9, p. 2632-2635 (2020 ) ). Using Linear Transform

, we can calculate the amplitude at the output of the 1st channel of the interferometer:

, while on the other output channels

(

), thereby confirming the possibility of pump focusing. Thus, in this example, the pump power supplied to all input channels of the interferometer with a transfer matrix

, comes out of one output channel.

зависит от числа поступающих фотонов (числа источников фотонов) и от их расположения относительно входных каналах интерферометра. В качестве конкретного примера состояний фотонов на выходе интерферометра

, фокусирующего всю мощность накачки, рассмотрен случай, когда имеется только один источник фотонов, способный генерировать одиночный фотон. Фиг. 3 иллюстрирует данный пример (изображены только импульсы генерируемых однофотонных состояний). Если входной канал интерферометра, на который поступает фотон, имеет индекс

, то состояние на выходе есть суперпозиция:Distribution of generated photons in the output channels of the interferometer

depends on the number of incoming photons (the number of photon sources) and on their location relative to the input channels of the interferometer. As a specific example of photon states at the interferometer output

focusing the entire pump power, we consider the case when there is only one photon source capable of generating a single photon. Fig. 3 illustrates this example (only the pulses of generated single-photon states are shown). If the input channel of the interferometer, to which the photon arrives, has the index

, then the output state is a superposition:

- квантовое состояние с одним фотоном в выходном канале с индексом

. В состоянии (5) вероятность появления фотона в каждом выходном канале равна

, а в вероятность появления фотона в состоянии 20 в оставшихся N-1 каналах (со 2-го по N-й) равна

. Т.е., имеется доля вероятности появления однофотонного импульса 21 в выходном канале 11, куда сфокусирована вся мощность накачки, равная

. Т.к. компонента 21 не используется для приготовления квантовых состояний фотонов, то случай попадания фотона в этот канал является его потерей, т.к. отфильтрованными от накачки являются состояния в выходных каналах с 2-го по N-й. Таким образом, вероятность прохождения одиночного фотона через фильтрующий интерферометр равна

. Квантовое состояние фотона на выходе является смешанным и описывается оператором плотности:where

is a quantum state with one photon in the output channel with index

. In state (5), the probability of a photon appearing in each output channel is

, and in the probability of the appearance of a photon in state 20 in the remaining N-1 channels (from the 2nd to the Nth) is equal to

. That is, there is a fraction of the probability of the appearance of a single-photon pulse 21 in the output channel 11, where the entire pump power is focused, equal to

. Because component 21 is not used to prepare the quantum states of photons, then the case when a photon enters this channel is its loss, because pump-filtered are the states in the output channels from the 2nd to the nth. Thus, the probability of a single photon passing through the filtering interferometer is

. The quantum state of the photon at the output is mixed and is described by the density operator:

- состояние с 0 фотонов во всех каналах с индексами от 2 до N,

- состояние суперпозиции одного фотона со 2 по N-й выходной каналы. Из вида состояния (6) следует, что в каналах с индексами с 2 по N будет выходить фотон в состоянии

с вероятностью

; с вероятностью

в этих каналах фотона не будет.where

- state with 0 photons in all channels with indices from 2 to N,

- the state of superposition of one photon from the 2nd to the Nth output channels. It follows from the form of state (6) that in channels with indices from 2 to N, a photon will emerge in the state

with probability

; with probability

there will be no photon in these channels.

, распределенном по N-1 каналам (2…N), преобразовать в фотон, выходящий из одного, можно воспользоваться дополнительным преобразованием, которое осуществляет интерферометр 15 с числом каналов N-1. Для этого выбирают передаточную матрицу

интерферометра 15 таким образом, что она удовлетворяет уравнению:

, где

- столбец, составленный из коэффициентов разложения состояния

,

- столбец, имеющий все элементы нули за исключением одного, индекс которого соответствует каналу, куда должен быть преобразован фотон. На Фиг. 3 фотон сосредоточен в одном выходном канале 22. Таким образом, импульс фотона 3 от источника 1 преобразуется в импульс фотона 23 с вероятностью

. Очевидно, что потери фотона в рассматриваемой схеме можно уменьшить (повысить вероятность прохождения фотона

), если увеличивать число каналов

интерферометра 5.In order for a photon to be in a state

, distributed over N-1 channels (2…N), can be converted into a photon coming out of one, you can use the additional transformation that the interferometer 15 performs with the number of channels N-1. To do this, select the transfer matrix

interferometer 15 so that it satisfies the equation:

, where

- a column composed of the coefficients of the decomposition of the state

,

- a column that has all elements zero except for one, the index of which corresponds to the channel where the photon should be converted. On FIG. 3 photon is concentrated in one output channel 22. Thus, the momentum photon 3 from source 1 is converted into a momentum of photon 23 with a probability

. It is obvious that the loss of a photon in the scheme under consideration can be reduced (increase the probability of a photon passing through

), if you increase the number of channels

interferometer 5.

состояния

на выходных каналах When implementing the example, when more than 1 photon arrives at the input of the focusing interferometer 5, the probability distribution of possible photon configurations is not equally probable, as in the case of 1 photon - the configuration probabilities depend on the indices of the input channels to which these photons arrive. The probabilities of realizing different photon configurations at the output of the N-channel interferometer are reduced to calculating the probability amplitudes

states

on output channels

обозначает выходное состояние фотонов с распределением по каналам, задаваемым вектором

, где

- число фотонов в канале с индексом j, вектор

обозначает конфигурацию фотонов на входе в интерферометр:

. Суммирование в (7) производят по всем возможным конфигурациям фотонов M, распределенным по N модам. Число всех конфигураций дается сочетанием из N по M. Число фотонов на выходе должно быть равно числу фотонов на входе, поэтому

. Амплитуды в состоянии

рассчитывают по формуле (S.Aaronson, A. Arkhipov, “Computational complexity of linear optics”, arxiv:1011.3245 (2010)): where

denotes the output state of photons with a distribution over channels given by the vector

, where

- number of photons in the channel with index j, vector

denotes the configuration of photons at the input to the interferometer:

. The summation in (7) is performed over all possible photon configurations M distributed over N modes. The number of all configurations is given by a combination of N through M. The number of photons at the output must be equal to the number of photons at the input, so

. Amplitudes in state

calculated by the formula ( S.Aaronson, A. Arkhipov, “Computational complexity of linear optics”, arxiv:1011.3245 (2010) ):

- перманент матрицы

, которая получена из передаточной матрицы

интерферометра отбором строк и столбцов в соответствии с векторами

и

: строка с индексом j берется

число раз (если

, то она не берется), столбец с индексом I берется

число раз. Также в (8) введены обозначения для факториалов:

,

. Вероятность реализации конфигурации фотонов, описываемой вектором

, при входной конфигурации

, дается

.where

- matrix permanent

, which is obtained from the transfer matrix

interferometer by selecting rows and columns in accordance with the vectors

and

: the string with index j is taken

number of times (if

, then it is not taken), the column with index I is taken

number of times. Also in (8) the notation for factorials is introduced:

,

. The probability of realizing the photon configuration described by the vector

, with input configuration

, is given

.

поступает 2 фотона, по одному в каналы с индексами

и

(входное состояние:

, т.е.

, а остальные

). Множество возможных состояний фотонов на выходных каналах представляет собой все комбинации 2 фотонов, распределенных по N каналам. Расчет вероятностей конфигураций фотонов с помощью формулы (8) приводит к следующим выражениям:It is possible to implement the method when the input of the focusing interferometer with the transfer matrix

2 photons arrive, one at a time into the channels with indices

and

(input state:

, i.e.

, and the rest

). The set of possible photon states on the output channels is all combinations of 2 photons distributed over N channels. The calculation of the probabilities of photon configurations using formula (8) leads to the following expressions:

и

(

;

), и for configurations containing photons in different channels with indices

and

(

;

), and

(

).for configurations with 2 photons in one output channel with index

(

).

. Вероятность потери сразу двух фотонов

.Assuming, as in the previous example, that the loss of photons is related to the probability of their passage to the first output channel into which the coherent pump is focused, we can calculate the losses in the considered scheme with two photons. Using formulas (9) and (10), the probability of losing one photon is

. The probability of losing two photons at once

.

пространственными каналами. Фиг. 4 иллюстрирует две схемы с минимально возможным числом источников и каналов, которые используют двухканальный делитель 24. В общем виде передаточная матрица элемента делителя принимает вид:The simplest case, in which the proposed method works, uses a single divisor with

spatial channels. Fig. 4 illustrates two circuits with the smallest possible number of sources and channels that use a two-channel divider 24. In general, the transfer matrix of the divider element becomes:

описывает его коэффициент прохождения по мощности

и коэффициент отражения

, а угловой параметр

описывает разность фаз между входными каналами. Фиг. 4а поясняет преобразование делителем двух импульсов когерентной накачки 4а и 4б, которые поступают на его входы 25. Если импульсы накачки поступают на делитель синхронно (в одном временном окне), их частотные спектры и поляризации совпадают, то всю их мощность можно сфокусировать в один из двух выходных каналов 26. Используя (3) и обозначая амплитуды когерентных импульсов через

и

, условие фокусировки в один канал принимает вид:

, которое разбивается на два уравнения:

и

. Решение уравнений всегда существует, если

и

. В рассматриваемом примере существует два способа выполнения фокусировки накачки. Во-первых, если амплитуды когерентных импульсов заданы и имеется возможность варьировать параметры делителя

и

, то их можно выбрать таким образом, чтобы удовлетворить условию фокусировки. Во-вторых, если заданы параметры делителя и

и имеется возможность управления мощностями и амплитудами накачек, то их можно подобрать таким образом, чтобы удовлетворить условию фокусировки.where is the angular parameter

describes its power transmission coefficient

and reflection coefficient

, and the angular parameter

describes the phase difference between input channels. Fig. 4a explains the conversion by the divider of two coherent pump pulses 4a and 4b, which arrive at its inputs 25. If the pump pulses arrive at the divider synchronously (in the same time window), their frequency spectra and polarizations coincide, then all their power can be focused into one of two output channels 26. Using (3) and denoting the amplitudes of coherent pulses through

and

, the condition of focusing into one channel takes the form:

, which breaks down into two equations:

and

. The solution of the equations always exists if

and

. In the example under consideration, there are two ways to perform pump focusing. First, if the amplitudes of coherent pulses are given and it is possible to vary the parameters of the divider

and

, then they can be chosen in such a way as to satisfy the focusing condition. Second, if the divisor parameters and

and it is possible to control the powers and amplitudes of the pumps, they can be chosen in such a way as to satisfy the focusing condition.

Fig. 4b illustrates the transformation of two single photons (3a and 3b) generated by two sources (1a and 1b) arriving at the inputs 25 of the divider 24. If the photons are indistinguishable, i.e. have the same spectra, polarization and synchronously arrive at the inputs 25, then the state 27 at the outputs 26 can be calculated using formulas (8) and (11):

и

находят из условия фокусировки импульсов накачки в выходной канал с индексом 1. Квантовое состояние фотонов на выходе канала 2, в котором отсутствует импульс когерентной накачки, является смешанным и задается оператором плотности:In (12) the divisor parameters

and

is found from the condition of focusing pump pulses into the output channel with index 1. The quantum state of photons at the output of channel 2, in which there is no coherent pump pulse, is mixed and is given by the density operator:

The average number of photons coming out of the channel with index 2, which is described by the state ( 13 ), is equal to 1. Thus, in the simplest scheme shown in Fig. 4b, when filtering the residual coherent pump, half of the photons are lost.

Fig. 4c illustrates the case when the inputs 25 of the divider 24 are supplied with one photon 3a from one source 1a. State 28 at the outputs of the divider 24 has the following form:

, таким образом, потери в случае, изображенном на Фиг. 4в, составляют

.The probability of finding a photon in the output with index 2 is

, thus the loss in the case shown in FIG. 4c, make up

.

The proposed method for filtering coherent pumping can be implemented using a cascade of interferometers connected in series, as shown in Fig. 5. In such schemes, the next first programmable interferometer 5a focuses the coherent pump 4 arriving at its inputs into the output 11a. The remaining unfiltered pump coming out of the remaining outputs of interferometer 5a, together with the state of photons 14a, enters the inputs of the next interferometer 5b. In this case, the corresponding inputs of the interferometer 5b are connected to the outputs of the interferometer 5a. Interferometer 5b performs additional filtering of the coherent pump, which it focuses into output 11b. On each interferometer, the pump is filtered, which is not fed to the inputs of the following interferometers - filtered pump signals 12a, 12b, and 12c in FIG. 5. The scheme can include as many interferometers as necessary for an acceptable level of pump filtering, i.e. the power level of the coherent pump output from the last 5v interferometer must be much lower than the photon power in the 14v state. Cascade circuits consisting of several filtering interferometers can provide a better level of coherent pump filtering compared to circuits containing a single interferometer 5. For example, in the case when one interferometer does not allow a high level of filtering due to interferometer design limitations and / or alignment accuracy its parameters.

, где

- центральная частота накачки, а

и

- центральные частоты генерируемых фотонов. В зависимости от частотной дисперсии в среде, в которой реализуют процесс СПР, которая зависит от центральных частот, поляризации и пространственных мод, источники могут генерировать фотоны, как с отличающимися частотами, так и с совпадающими частотами. При этом поляризации и/или пространственные моды генерируемых фотонов могут отличаться или совпадать.There are several types of photon sources in which the present invention can be used. On FIG. 6 are diagrams illustrating the relationship between the coherent pumping frequencies and the frequency(s) of generated photons for different types of sources. The diagram shown in Fig. 6a corresponds to sources of photon pairs based, for example, on the effect of spontaneous parametric scattering (SPS). The SPR process proceeds in a medium with quadratic optical nonlinearity. In such sources, photons from intense coherent pumping with a center frequency of 29 decay into pairs with center frequencies of 30 and 31. In this case, the relation is valid:

, where

is the pump center frequency, and

and

are the central frequencies of the generated photons. Depending on the frequency dispersion in the medium in which the SPR process is implemented, which depends on the central frequencies, polarization and spatial modes, the sources can generate photons, both with different frequencies and with the same frequencies. In this case, the polarizations and/or spatial modes of the generated photons may differ or coincide.

и

и частоты генерируемых фотонов

и

удовлетворяют следующему соотношению:

. Для реализации источника такого типа необходимо среда с кубической нелинейностью. В общем случае, частоты и поляризации всех волн накачек и генерируемых фотонов могут, как совпадать, так и отличаться.In FIG. Figure 6b shows a diagram illustrating the ratio of center frequencies for photon pair sources with two pumps with center frequencies of 32 and 33. Pump frequencies

and

and frequency of generated photons

and

satisfy the following relation:

. To implement a source of this type, a medium with cubic nonlinearity is required. In the general case, the frequencies and polarizations of all pump waves and generated photons can either coincide or differ.

. На Фиг. 6г изображена диаграмма, соответствующая нерезонансному возбуждению источника одиночных фотонов. В таком случае

.In FIG. 6c is a diagram illustrating the relationship between the pump center frequency 34 and the generated photon 35 for single photon sources based on quantum emitters, such as quantum dots. Sources of this type can generate at most one photon at a time. The diagram illustrates the resonant method of source excitation, in which the center frequency of the generated photons coincides with the center frequency of coherent pumping:

. On FIG. 6d shows a diagram corresponding to non-resonant excitation of a source of single photons. In this case

.

, общее число двухканальных блоков в универсальных схемах, упомянутых выше, равно

. Кроме этого, схемы универсальных интерферометров содержат независимые

фазовых сдвигов, располагаемые сразу после входов или перед выходами в интерферометр. Таким образом, общее число элементов фазовых сдвигов в универсальных интерферометрах должно быть не меньше

.The programmable interferometers 5 used in the invention for filtering the coherent pump may have different architectures. A universal method for implementing multichannel programmable interferometers by combining two-channel transformations with each other is known, proposed in the works of M. Rack et al., “Experimental implementation of any discrete unitary operator” // Phys. Rev. Lett. T. 73, No. 1, S. 58 (1994) and V.R. Clemens et al., “Optimal design of universal multiport interferometers” // Optica, vol. 3, no. 12, p. 1460 (2016). This method makes it possible to construct arbitrary linear transformations by connecting two-channel transformations to each other and by appropriate choice of the parameters of these two-channel transformations. The essence of the method lies in connecting one after another a plurality of transformation layers, each of which contains a plurality of two-channel blocks that operate independently of each other. Each of the two-channel blocks in the composition of a large multichannel interferometer can be controlled by setting the values of the phase shifts on the elements. Each of the blocks contains 2 elements of variable phase shifts. In the case when the number of channels in the interferometer is equal to

, the total number of two-channel blocks in the universal circuits mentioned above is

. In addition, the schemes of universal interferometers contain independent

phase shifts located immediately after inputs or before outputs to the interferometer. Thus, the total number of phase shift elements in universal interferometers should not be less than

.

Non-universal programmable interferometers can be used to filter coherent pumping. An example of a programmable 5-channel interferometer that is capable of filtering coherent pumping is shown in FIG. 7. The interferometer consists of 8 two-channel blocks 36. In FIG. 7 illustrates the case when coherent pump signals 37 are fed to all inputs 9 of the interferometer. Transfer matrices of two-channel units 36 can be adjusted in such a way as to focus the entire power 38 of coherent signals into one output 11.

On FIG. 8a shows a diagram of the Mach-Zehnder interferometer (MZI) - an optical element that is a programmable two-channel unit 36. The MZI consists of two static balanced dividers 39 and two variable phase shift elements 40. Setting the values of the phase shifts 40 determines the MZI transfer matrix. On FIG. 8b shows a diagram of the integrated optical implementation of the MCI, which performs the conversion between two spatial channels implemented in the form of two single-mode waveguides. In this implementation of the IMC, the elements of static dividers 39 are implemented in the form of directional dividers 41 - areas of convergence of two waveguides before the connection between them is realized (A. Snyder, J. Love "Theory of optical waveguides" // Radio and Communication 1987). Variable phase shift elements 40 are implemented in the form of integrated optical elements 42. The elements change the refractive index of the material near their location near the waveguide section in such a way that a phase shift is introduced in this section. For example, a thermo-optical, electro-optical, or piezo-optical phase shift element can be used.

The pump filtering method is carried out as follows.

), который выполнен с возможностью изменения его передаточной матрицы U. Выбирают подмножество из K выходов N-канального интерферометра, в которые будет осуществляться фокусировка когерентной накачки. Сигналы с этих выходов подают на детекторы, измеряющие мощность. Для выбранного интерферометра число каналов K выбирают исходя из возможности фокусировки накачки - мощность когерентной накачки на остальных выходах должна быть минимальной и удовлетворять требованиям. В качестве критерия можно использовать мощность когерентной накачки, проходящей в оставшиеся N-K выходы интерферометра, которая должна быть намного меньше, чем мощность фотонов на этих выходах.1. To filter the coherent pump from M sources, the signals from their outputs are fed to the inputs of an N-channel interferometer (

), which is configured to change its transfer matrix U. A subset is selected from the K outputs of the N-channel interferometer, into which the coherent pumping will be focused. Signals from these outputs are fed to detectors that measure power. For the selected interferometer, the number of channels K is chosen based on the possibility of pump focusing - the coherent pump power at the remaining outputs should be minimal and satisfy the requirements. As a criterion, one can use the coherent pump power passing into the remaining NK outputs of the interferometer, which should be much less than the photon power at these outputs.

N-канального интерферометра программируют таким образом, чтобы мощность, измеряемая на K его выходах, выбранных для фокусировки накачки, была максимальной. Для этого варьируемые элементы сдвигов фазы интерферометра меняют таким образом, чтобы измеряемая мощность накачки в K выходах была максимальной. При использовании последовательности из нескольких интерферометров, изображенной на Фиг. 5, выполняют программирование всех интерферометров с достижением максимума мощности в выходах 11а, 11б, … 11в.2. Focusing transfer matrix

The N-channel interferometer is programmed in such a way that the power measured at its K outputs, chosen for pump focusing, is maximum. To do this, the variable elements of the phase shifts of the interferometer are changed in such a way that the measured pump power in the K outputs is maximum. Using the sequence of multiple interferometers shown in FIG. 5, all interferometers are programmed with the achievement of maximum power in outputs 11a, 11b, ... 11c.

The proposed method for filtering coherent pumping can be implemented with interferometers using spatial coding. In such systems, a waveguide or a spatial mode of free space can act as a channel. In optics, waveguide structures forming spatially encoded circuits can be implemented as an integrated optical circuit, which can be fabricated using planar lithography technology ( L. Chrostowski, M. Hochberg, Silicon Photonics design: from devices to systems // Cambridge Univ. Press , 2015 ) or by 3D technology such as laser printing ( IV Dyakonov et al., Reconfigurable photonics on a glass chip // Phys. Rev. Applied, vol. 10, 044048 (2018) ). As phase shift elements in such circuits, 1) thermo-optical elements can be used, which change the phase incursion of the waveguide section when an electric current is passed through them due to its heating, 2) electro-optical elements, which change the phase incursion when a voltage is applied due to changes in the concentration of electrons and / or holes in the waveguide section, and 3) a piezo-optical element that changes the phase shift of the signal propagating in the waveguide under the action of an electrical voltage, which causes mechanical stress in the waveguide section, which changes its refractive index.

линий образует множество каналов всего преобразования. В качестве амплитуды сигнала, распространяющегося по частотному каналу, выступает комплексная амплитуда соответствующей частотной компоненты. Стоит заметить, что использование частотной кодировки каналов многоканального преобразования позволяет использовать для передачи и преобразования один пространственный канал - один волновод, одну пространственную моду свободного пространства. Для осуществления взаимодействия между частотными каналами предложено использовать набор преобразований модуляции частотных каналов, которая наводит на каналы зависящую от времени фазу, профиль которой можно подбирать, и формирователь импульсов.The claimed invention can also be implemented in systems with frequency coding channels. In this case, non-overlapping frequency lines of the electromagnetic field spectrum act as discrete channels. Each line is assigned a channel number, so a set of

lines form a set of channels of the entire transformation. The amplitude of the signal propagating along the frequency channel is the complex amplitude of the corresponding frequency component. It is worth noting that the use of frequency coding of multichannel conversion channels makes it possible to use one spatial channel for transmission and conversion - one waveguide, one spatial mode of free space. To implement the interaction between frequency channels, it is proposed to use a set of frequency channel modulation transformations, which induces a time-dependent phase on the channels, the profile of which can be selected, and a pulse shaper.

Multichannel systems with frequency channels are most widely used in optics, in particular, in quantum optics. The claimed invention can be implemented by analogy with the system described in the work of H.-H. Lu et al., Electro-optic frequency beam splitters and tritters for high-fidelity photonic quantum information processing, Phys. Rev. Lett., vol. 120, 030502, 2018), which demonstrates in practice the implementation of the Hadamard transform for one frequency channel and the tritter transform for three frequency channels. To implement the invention can be used fiber optic equipment, which is standard for telecommunications wavelengths in the region of 1550 nm. For modulation, electro-optical modulators and a pulse shaper, which are standard components of telecommunications equipment, can be used. In addition to fiber-optic telecommunication components, their entire set can also be implemented using integrated optical circuits, since all necessary elements were demonstrated. For example, an integrated optical pulse shaper is demonstrated by KA McKinzie et al. InP integrated pulse shaper with 48 channels, 50 GHz spacing amplitude and phase control, 2017 IEEE Photonics Conference (IPC), 197-198 (2017) . Integrated optical modulators have been available for manufacturing in integrated optical design for a long time ( K. Ogawa, Integrated silicon-based optical modulators: 100Gb/s and beyond, SPIE Press, ISBN: 9781510625815, 2019 ).

, интерпретируется как сигнал в канале

, а амплитуда импульса интерпретируется как амплитуда сигнала в канале с этим индексом. Как и в случае с частотным кодированием, при временном кодировании используют одиночный пространственный канал, который может представлять собой волновод или пространственную моду свободного пространства. Для осуществления взаимодействия между каналами в этой схеме необходимы линии задержки и динамически варьируемые делители.The claimed invention can also be implemented in systems using time coding. In this case, non-overlapping time intervals act as discrete channels. Each time interval is assigned a channel number. An impulse of an electromagnetic signal located in a time interval with a certain index

, is interpreted as a signal in the channel

, and the pulse amplitude is interpreted as the signal amplitude in the channel with this index. As with frequency coding, temporal coding uses a single spatial channel, which may be a waveguide or free space spatial mode. To implement the interaction between channels in this scheme, delay lines and dynamically variable dividers are needed.

In particular, the claimed invention can be implemented by analogy with the multi-channel time-coding scheme presented in KR Motes et al., Scalable boson sampling with time-bin encoding using a loop-based architecture // Phys. Rev. A, vol. 113, 120501 (2014), which proposes a versatile multi-channel circuit based on fiber delay loops and reconfigurable two-channel dividers, are standard components found in telecommunications, for example. Multi-channel transform blocks can be implemented using multiple nested delay loops and constant dividers, while variable phase shifts can be implemented using dynamically programmable phase modulators or phase shifts.

Specific Implementation Examples

МГц, 2) разветвитель мощности лазерного излучения 44, который распределяет когерентные сигналы от лазера на 5 пространственных каналах, выполненный в интегрально-оптическом исполнении, 3) источник одиночных фотонов 45 на основе квантовой точки, генерирующий фотоны на длине волны 918.8 нм (центральная длина волны излучения лазера была специально подстроена для резонансного возбуждения источника фотонов), 4) программируемый 5-канальный интерферометр 46, выполненный в интегрально-оптическом исполнении, 5) детектор оптического излучения, способный регистрировать интенсивные когерентные сигналы лазера 47, 6) 4 сверхпроводниковых детектора одиночных фотонов 48, 7) компьютер 49, управляющий преобразованием 5-канального интерферометра через электрические линии 50 и обрабатывающий сигналы с детекторов, которые поступают на него по электрическим линиям 51.To test the feasibility of the proposed invention with the achievement of a technical result, an optical installation was assembled, shown in Fig. 9. The main elements of the setup are: 1) a pumping laser 43 generating pulses at a central wavelength of 918.8 nm with a duration of ~100 fs and a repetition rate

MHz, 2) a laser power splitter 44, which distributes coherent signals from the laser to 5 spatial channels, made in an integrated optical design, 3) a single photon source 45 based on a quantum dot, generating photons at a wavelength of 918.8 nm (central wavelength laser radiation was specially tuned for resonant excitation of the photon source), 4) a programmable 5-channel interferometer 46, made in an integrated optical design, 5) an optical radiation detector capable of detecting intense coherent laser signals 47, 6) 4 superconducting single photon detectors 48 , 7) computer 49, which controls the transformation of the 5-channel interferometer through electric lines 50 and processes the signals from the detectors that come to it through electric lines 51.

As a programmable interferometer 46, which performs filtering of the residual coherent pumping, an integrated optical chip was used, created using femtosecond laser printing technology, which makes it possible to manufacture both planar and three-dimensional integrated optical circuits. Details of the fabrication technology used can be found in IV Dyakonov et al., “Reconfigurable photonics on a glass chip,” Phys. Rev. Applied, vol. 10, 044048 (2018) . To create an integrated optical circuit chip, a quartz workpiece in the form of a rectangle with a length of 12 cm, a width of 5 cm and a thickness of 0.5 cm was used. Interferometer 46 had 5 channels, and its circuit was made with the mutual arrangement of elements shown in Fig. 7. Two-channel blocks of Mach-Zehnder interferometers 36 in the integrated optical circuit of the interferometer 46 are implemented according to the design shown in FIG. 8b, where directional splitters are implemented using waveguide convergence regions.

At the first stage of manufacturing a programmable interferometer chip 46, passive waveguide structures are created in the volume of the workpiece, forming a static optical circuit, which is a directional dividers connected to each other. The beginnings and ends of the waveguides are brought to the opposite ends of the glass blank to enable the introduction and removal of optical signals.

To implement programmability, phase shift elements were fabricated on the chip, with the help of which interferometers were reconfigured. The phase shift elements used the thermo-optical effect. The elements of variable phase shifts were metal strips located above the sections of the waveguides on which it was necessary to implement these elements. When voltage was applied to the elements, the corresponding sections of the waveguides were heated, as a result of which the refractive index of the glass in this area changed, thus causing a phase shift relative to unheated sections.

To split the coherent radiation from the laser 43 between 5 spatial channels, an integrated optical chip of the splitter 44 was manufactured using femtosecond laser printing technology, the scheme of which is shown in Fig. 9b. To create an integrated splitter chip, a quartz billet in the form of a rectangle with a length of 12 cm, a width of 5 cm and a thickness of 0.5 cm was used. The splitter circuit consists of 5 waveguides and includes an area of convergence of these waveguides laser, which was fed to one waveguide and distributed between closely spaced waveguides. The beginning and end of one waveguide 53, into which radiation from the laser was fed, were brought to the opposite ends of the chip, while for the remaining waveguides only the output ends were brought to the end in order to output radiation from the chip. The input of pump radiation from the laser is carried out through an optical fiber. The output of the separated coherent radiation from the outputs of the splitter chip is also carried out through optical fibers. The distance between the waveguides in the coupling region and the length of the coupling region were selected in such a way as to realize a uniform distribution of the coherent pump power between the 5 output channels.

A single photon source was used in the optical setup. The source was a quantum dot in a microcavity located in a cryostat and maintained at a temperature of 4 K ( SE Thomas et al. “Bright polarized single-photon source based on a linear dipole” // Phys. Rev. Lett., vol. 126, 233601 ( 2021) ). The cryostat had a transparent window for the possibility of planting coherent laser pumping and outputting generated single-photon signals at a central wavelength of 918.8 nm. The pulsed radiation from the laser coming out of one channel of the splitter was fed through an optical fiber to an optical telescope located near the cryostat window, which focused the pump radiation into the photon source; the generated photons with residual pumping were also output through the telescope. A resonant pumping scheme was implemented in the setup - the central wavelength of the pumping laser pulses corresponded to the central wavelength of the generated photons (see Fig. 5c).

Radiation from 5 outputs of the programmable interferometer arrived at the detectors. One detector 47 was capable of detecting intense radiation from the laser. The electrical current from the detector is proportional to the measured power of the optical signal entering the detector. The 4 remaining detectors 48 had sensitivity at the level of single-photon signals. The arrival of one photon at the detector led to an electrical impulse, which arrived via one of the 4 electrical lines 51 to the computer 49. Superconducting detectors were used as detectors of single photons. The signals from the 4 outputs of the programmable interferometer were fed into the detectors. The detection efficiency for single photons was ~85%. Electrical signals from all 5 detectors were fed to a personal computer. The same computer controlled the programmable interferometer by setting the voltages on the thermo-optical elements to phase shifts. The computer program processed the signals coming to the computer from the detectors.

To connect the optical elements of the optical setup, single-mode fibers were used that preserve the polarization of optical signals.

Гц, а мощность, поступающая на детектор 47, составляла

нВт.To demonstrate the operation of the claimed invention using the created installation, the interferometer 46 was first adjusted to “focus” the entire pump power into the output 47 with the photon source not working. To turn off the photon source, the central wavelength corresponding to the radiative transition of the source was tuned relative to 918.8 nm to the short-wavelength region, so that laser pumping could not excite the source. The wavelength detuning was made by local heating of the source, which was performed by applying voltage to a diode located next to it. The computer searched for the configuration of voltages applied to the phase shift elements in the interferometer 46, which corresponds to the maximum electric current coming from the detector 47. a fraction of the pump can still pass into the channels in front of the photon detectors 48 due to inaccurate tuning of the interferometer according to the signal from the detector 47, then more precise tuning of the interferometer 46 was carried out in order to improve the quality of the “focusing” of the pump power into the channel in front of the detector 47. For this, tuning was carried out phase shift voltage, which minimized the count rate from single photon detectors 48. As a result of adjustment, the photo count rate of detectors 48 was

Hz, and the power supplied to detector 47 was

nW.

кГц.Next, the photon source was turned on by adjusting the wavelength corresponding to the radiating transition to resonance with a pump wavelength of 918.8 nm. As a result, at the output of single photon detectors 48, an increase in the photocount frequency (total frequency on all detectors 48) was observed, which amounted to ~220 kHz. Because Tuning the wavelength of the radiative transition, including a photon source, leads to the absorption of a photon from coherent pumping, and it could also be accompanied by a change in the optical properties of the microresonator and quantum dot, one more substring of the interferometer 46 was carried out. During tuning, the goal was to reduce the frequency of photocounts of photon detectors 48. After tuning, the photocount frequency decreased and amounted to

kHz.

нВт., поступавшей на детектор 47, как мощности отфильтрованной накачки, а частоты фотоотсчетов

Гц (полученной на этапе без работающего источника фотонов) как частоты отсчетов фотонов когерентного излучения, которое не удалось отфильтровать подстройкой преобразования интерферометра 46. Был проведен пересчет мощности излучения из единиц Вт в единицы фотоны/с:

, где

Дж*с - постоянная Планка,

м/с - скорость света в вакууме,

нм - длина волны накачки. Средняя мощность сфокусированного когерентного сигнала на детекторе 47 составила

1/c. Таким образом, оценка для коэффициента фильтрации накачки составила

. Здесь

- эффективность детекторов одиночных фотонов.Based on the results of the experiment by the claimed method in the implementation described above, an estimate was made of the value of the filtration coefficient. The average power of optical radiation was calculated

nW, which arrived at detector 47, as the power of the filtered pump, and the photocount frequencies

Hz (obtained at the stage without a working photon source) as the frequency of counting photons of coherent radiation, which could not be filtered out by adjusting the conversion of interferometer 46. The radiation power was recalculated from units of W to units of photons/s:

, where

J * s - Planck's constant,

m/s is the speed of light in vacuum,

nm is the pump wavelength. The average power of the focused coherent signal at detector 47 was

1/c. Thus, the estimate for the pump filtering coefficient was

. Here

- efficiency of single photon detectors.

МГц. Условия возбуждения источника были такими же, как и в эксперименте с интерферометром 46. Таким образом, оценка для потерь равна

.It is also possible to evaluate the total losses introduced into single-photon signals generated by the source, all the way from the output of the fiber that outputs photons from the source, to the interface of the fiber with the input to the interferometer 46, the losses in this interferometer, the interface of its outputs with fibers connected to the detectors 48. For this purpose, the average rate of photocounts was measured directly at the exit of the fiber that extracts photons from the source. She made

MHz. The source excitation conditions were the same as in the experiment with the interferometer.46 Thus, the loss estimate is

.

Thus, the invention makes it possible to increase the efficiency of photon sources using coherent optical radiation for excitation. Efficiency is increased by reducing the losses introduced by traditional methods of filtering coherent radiation. In addition, the invention makes it possible to perform filtering of coherent radiation from photons generated by multiple sources with a single device, which simplifies its tuning. Also, the advantage of the proposed invention is the possibility of filtering coherent radiation with the resonant method of excitation of sources of single photons, when the polarization of this radiation coincides with the polarization of the generated photons, and their wavelength spectra overlap.

Claims (10)

1. Pump filtering method for sources of quantum states, including: - supply to M inputs of an N-channel interferometer, characterized by a transfer matrix U of size N by N, generated photons from M photon sources with residual coherent pumping signals from at least one laser radiation source, at the same time, coherent pumping signals from laser sources when using the continuous mode are formed with the same frequency spectrum and the same polarization, and when using the pulsed mode, coherent pumping pulses of the same polarization shape are formed with the same center frequencies of their spectrum, which are fed to the N-channel interferometer synchronously; the transfer matrix U is configured to focus input coherent pump signals, including residual coherent pump signals from photon sources, to at least one output, and output a portion of photons from photon sources to the remaining outputs. 2. The method according to claim 1, characterized in that at least one of the remaining inputs of the N-channel interferometer is supplied with a coherent pumping signal from at least one laser radiation source, while using the pulsed mode, the pulses coherent pumping is fed to the N-channel interferometer synchronously, including residual coherent pumping pulses from photon sources; 3. The method according to claim 1, characterized in that the transfer matrix U is designed in such a way that the multiplication of the amplitude vector

coherent pump signals coming to the input of the N-channel interferometer, including the residual pump signals from photon sources, to the transfer matrix U gives the given amplitude vector

which contains nonzero elements with indices corresponding to the channels into which the coherent pump signal is focused, and the remaining elements of the vector

- null:

4. The method according to claim 3, characterized in that the focusing of the coherent pump signal is carried out in a subset of outputs, consisting of K outputs of the N-channel interferometer, by varying the phase shift elements until the maximum power measured in this subset of outputs is reached. 5. The method according to claim 3, characterized in that the focusing of the coherent pump signal is carried out by varying the parameters of the dividers that make up the N-channel interferometer, or by varying the amplitudes of the coherent pump signals at the input to the N-channel interferometer. 6. The method according to claim 1, characterized in that the output signals from the photon sources that have passed through the N-channel interferometer and containing photons from the photon sources are subjected to conversion by the second interferometer with the number of inputs and outputs not less than the number of outputs of the first interferometer containing photons from photon sources. 7. A pump filtering system for sources of quantum states, including at least a laser radiation source, at least one photon source, at least one N-channel interferometer configured to filter received signals from photon sources that have passed the first interferometer, from residual signals of coherent pumping by the method according to claim 1, and detectors installed at the outputs of the N-channel interferometer, while the number of detectors corresponds to the number of outputs K, into which the coherent pumping is focused.

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