GB2477961A

GB2477961A - Measuring photon correlations in photons emitted by a source

Info

Publication number: GB2477961A
Application number: GB1002890A
Authority: GB
Inventors: James Dynes; Zhiliang Yuan; Andrew W Sharpe; Andrew James Shields
Original assignee: Toshiba Research Europe Ltd
Current assignee: Toshiba Europe Ltd
Priority date: 2010-02-19
Filing date: 2010-02-19
Publication date: 2011-08-24
Anticipated expiration: 2030-02-19
Also published as: GB2477961B; GB201002890D0

Abstract

Apparatus and method for measuring photon correlations from a photon source. Light from photon source 101 passes through a beam-splitter 103, a variable attenuator 213 and onto first photon number resolving detector 201 to produce a first output signal indicating the number of photon arrival events detected with an accuracy of one photon. Similarly light reflected from beam-splitter 103 passes through variable attenuator 311 and onto a second photon number resolving detector 301 to produce a second output signal. The apparatus further comprises a discriminator 303, 305 for each output signal, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events. The apparatus further comprises a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminators and produces a measure of the correlation of the photon source. The coincidence circuit may measure the time delay between photon arrival events. The photon detection stage may include avalanche photon detectors. The apparatus may form part of a quantum communication system.

Description

I

Photon Correlator and Method of Measuring Photon Correlation The present invention is concerned with the field of characterising light sources. More specifically, the present invention is concerned with measuring the 2 and higher order correlations of a photon source.

The need to characterise a photon source and specifically measure correlations in photons emitted by the source is becoming more and more important. The photon sources which are of most interest are laser diodes and single photon sources which operate in the telecoms wavelength range of 1100 -l700nm and visible wavelength ranges of 300-llOOnm. In the field of quantum key distribution, high order photon correlations threaten security. Therefore, characterisation is required for quantum communication systems based on weak coherent pulses and quantum communication systems based on non-classical photon sources, e.g. semiconductor quantum dots and parametric down conversion. This characterisation may also be used for non-classical state preparation for quantum computing/ quantum logic, as described in, for example, W. Vogel, Phys. Rev. Lett. 100, 013605 (2008).

Previously, methods of measuring correlations in light sources to the nth correlations g(n) have used beam splitters and n single photon detectors where n is an integer of 2 or more. Examples of these methods are: Multi-meander superconducting nanowire detectors (SSPD Correlator); and Time-multiplexed intensity Correlator (TMD).

These systems which can measure higher order correlations at near-infrared wavelengths are unsuitable for practical application. Their disadvantages are: 1. Significant equipment complication due to the need for n -1 beamsplitters and n detectors. When using lnGaAs avalanche photodiodes as detectors (wavelength range 1300-l700nm) the measurement time can be intolerably long due to low single photon efficiencies (10% per detector).

2. Can only operate at liquid Helium temperatures; very low single photon efficiency and low maximum count rate (80MHz).

3. Instead of spatial multiplexing, multiplexing is achieved temporally. However, the setup is only suitable for photon sources with low repetition frequencies (<100kHz).

Most systems rely on either spatial-multiplexing or time-multiplexing to divide input photon signals into slots. Photon correlations are then derived from events arriving in given slots.

The present invention at least partially addresses the above problems and in a first aspect provides an apparatus for measuring photon correlations from a photon source, the apparatus comprising a photon detection stage, wherein at least two output signals are outputted from said photon detection stage, where each output signal indicates the number of photon arrival events detected with an accuracy of one photon, the apparatus further comprising a discriminator for each output signal, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events, the apparatus further comprising a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminator circuits and produces a measure of the correlation of the photon source.

The present invention uses photon number resolving detector(s) rather than usual single photon detectors.

The present invention uses either a photon number resolving detector or a plurality of photon number resolving detectors. Here, the output of the detector(s) is proportional to the number of incident photons (number of photon arrival events).

Photon arrival events are binned into photon number slots by a circuit that discriminates the detector output voltage. The discriminator circuit can either be a threshold type or a window type. The binned photon number events can then be used for deriving photon correlations.

The present invention has the following advantages: 1. Uses fewer detectors and beamsplitters -therefore cheaper and more corn pact.

2. Can measure higher-order correlations than existing systems.

3. Works with sources at high repetition frequency.

4. Can tolerate high photon count rates, which results in reduced integration times.

5. Synchronized to external clock.

6. Photon source repetition frequency not limited.

7. Low timing jitter. This means photon sources with short coherence times can be used with the Toshiba Photon Correlator.

8. Operates at ambient temperatures with thermoelectric cooling (i.e. does not require cryogenic cooling).

9. Uses standard fabrication technology so relatively cheap.

In the simplest case with one photon number resolving detector, correlations can be realized up to order n, where n is the photon number resolving capability of the detector. N may be any interger greater than or equal to 2. In a preferred embodiment, n is equal to or greater than 3. In a further preferred embodiment, n is greater than or equal to 4.

The present invention may be configured with a photon detection stage which comprises a single photon detector and a splitter which is configured to divide the output of said photon detector into two output signals. Alternately, the photon detection stage may be configured with multiple photon detectors and a beamsplitter to divide the input signal between the two photon detectors. In general, it is preferred that there will be just two photon detectors, but more photon detectors are possible.

In both of the above arrangements, it is possible to achieve an arrangement where one discriminator is set to pass a signal corresponding to n photon arrival events and a second discriminator is set to pass a signal indicating a single photon arrival event.

In a different arrangement, one discriminator may be set to indicate x photon arrival events and a second discriminator may be set to indicate y photon arrival events. In this situation, x+y = n, i.e. the correlation which is desired.

In this arrangement, the discriminator circuit will determine that n photon arrival events have occurred when the output from both discriminators is coincident.

In a preferred arrangement, the two discriminators pass the same number of photon events. This has the advantage that both detectors are sampling at the same avalanche voltages. This means that they should have similar efficiencies and this should reduce errors in the calculations.

When there are a plurality of photon detectors, preferably, there will just be two as an aim of the invention is to reduce the number of photon detectors required while still allowing high order correlations to be preformed. However, it should be noted, the invention could also be implemented using three or more detectors in the photon detection stage.

The present invention can be used to determine very high order correlations since it is possible to set the discriminator to measure these high order photon arrival events which is turn allows a higher order correlation to be measured and processed.

The coincident circuit can measure the time delay between photon arrival events.

In a preferred embodiment, the photon detector or photon detectors will be gated using avalanche photo-diode detectors. These detectors will also preferably comprise means to isolate the avalanche signal from the output using a self-differencing detection circuit. Such self-differencing detectors are discussed in GB 2 447 254.

However, in a preferred embodiment, the seif-differencing circuit will comprise a signal divider to divide the signal from the detector into two parts and an electrical line to delay one of the parts relative to the other and a signal difference to output the difference between the two parts. It is this differenced signal which is output from the detector which may then be passed through a discriminator.

The detector may further comprise a means to balance the strength of the two parts.

The detector may further comprise a means to vary the length of the delay. In a further embodiment, the detector further comprises an amplifier(s) to amplify the output of the self-differencing circuit(s).

Preferably the detectors are gated at a frequency> 100MHz.

In a preferred embodiment, a variable attenuator is provided to adjust the photon flux impinging on the photon detection stage.

The present invention may also comprise a plurality of neutral density filters configured to adjust the photon flux impinging on the detection stage.

The present invention may further comprise a cooler to lower the temperature of the avalanche photodiode(s).

In a further embodiment, means are provided to couple light to the APD through an optical fibre.

The present invention may be used to characterise a continuous wave (CW) or pulsed source. If it is used with a pulsed source, then preferably the gating of the photon detectors is synchronised with the pulsed source.

If the source is continuous, then the photon detector is preferably free running.

However, a gated detector may be used, preferably, such a gated detector will have gating period which is shorter than the coherence time of the source.

In a further aspect, the present invention provides an emitter for a quantum communication system, said emitter comprising a photon source, an encoder for encoding quantum information on photons outputted from said source and an apparatus for measuring photon correlations from said photon source as described above in accordance with the first aspect of the present invention.

The above quantum source could be used with any quantum communication system.

In a third aspect, the present invention provides a quantum communication system comprises an emitter and a receiver, said emitter comprising a photon source and an encoder for encoding quantum information on photons outputted from said source, said receiver comprising a decoder configured to decode said encoded photons and at least one photon detector, the system further comprising an apparatus for measuring photon correlations as described above in accordance with the first aspect of the present invention. In the third aspect, the photon measuring apparatus may reside in either the emitter or the receiver In a fourth aspect, the present invention provides a method for measuring photon correlations from a photon source, the method comprising: detecting the output of the source using a photon detection stage, wherein at least two output signals are outputted from said photon detection stage, where each output signal indicates the number of photon arrival events detected with an accuracy of one photon, passing each output signal through a discriminator, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events; receiving the output signals which have passed through the discriminators in a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminators and produce a measure of the correlation of the photon source.

The present invention will now be described with reference to the following preferred, non-limiting embodiments in which: Figure 1 is a schematic of a photon correlation apparatus useful for understanding the present invention; Figure 2 is a schematic of a photon correlator in accordance with an embodiment of the present invention based on one photon number resolving detector; Figure 3 is a schematic of a photon correlator in accordance with a further embodiment of the present invention with two photon number resolving detectors; Figure 4 is a schematic of a photon number resolving detector for use in a photon correlator in accordance with an embodiment of the present invention; Figures 5a to 5c schematically illustrates three types of photon source employed to test the photon correlator described in figure 3, figure 5a is a multi mode InGaAs laser, figure 5b is a pulsed distributed feedback laser operating at slightly above its threshold and figure 5c is a pulsed distributed feedback laser operating at well above its threshold; Figure 6 shows DFB laser output characteristics as a function of laser intensity level for the photon sources of figures Sb and 5c; Figure 7 (a) shows two plots of the probability distribution reflecting the statistics of the avalanche peak height of the self differencirig output VSd, for the two photon sources shown in 5a and 5b, figure 7b shows plots of the theoretical probability distribution reflecting the statistics of the avalanche peak height of the self differencing output VSd, for two photon sources; Figure 8 shows a plot of the coincidence counts as a function of photon number resolving detector relative temporal delay for a photon correlator in accordance with an embodiment of the present invention based on two photon number resolving detectors; Figure 9 shows a plot of the correlation value, as a function of 305 discrimination level for the photon correlator in accordance with an embodiment of the present invention based on two photon number resolving detectors, figure 9b shows the results for the source of figure 5c in more detail; Figure 10 shows a plot of the simulated correlation value as a function of discriminated photon number state, for a photon correlator in accordance with an embodiment of the present invention; and Figure 11 shows a schematic of a quantum communication system with a correlation stage in accordance with an embodiment of the present invention.Figure 1 shows a known photon correlator which is useful for understanding the present invention, In Figure 1, photon source 101 is typically attenuated down to the single photon level.

Its output first impinges on first beamsplitter 103. First beanisplitter 103 is a 50:50 photon transmittance/reflection beamsplitter. Photons which are transmitted through first beam splitter are directed to second beamsplitter 105. Photons which are reflected by first beam splitter 103 are directed towards third beamsplitter 107. Both second beamsplitter 105 and third beamsplitter 107 are 50:50 beamsplitters.

Second beamsplitter 105 directs transmitted photons towards first single photon detector 109 and directs reflected photons towards a second single photon detector 111. The single photon detectors are configured to register a photon arrival event by creating a macroscopic electrical pulse.

Third beamsplitter 107 directs transmitted photons to third single photon detector 113 and reflected photons to fourth single photon detector 115.

The four single photon detectors 109, 111, 113 and 115 send their output signals via channels 117, 119, 121 and 123 to four channel photon timing card 125.

Electrical channels 117, 119, 121 and 123 are connected to a four channel photon timing card, 125. The photon timing card 125 serves to register the arrival times of the single photon detector macroscopic electrical pulses and thus by extension register the photon arrival times at the four single photon detectors. Typically a time stamp will be allocated for each photon arrival time.

Furthermore, photon timing card 125 comprises electrical discriminators for each of the four channels. Discriminators are used to separate electrical noise from true macroscopic electrical pulses caused from photon arrival events. However, there will always be some underlying noise from the single photon detectors which cannot be removed. This is due to single photon detector dark counts.

Photon timing card 125 stores the photon timestamps in a memory. Photon timestamps are used to build up a temporal correlation histogram. The function describing the temporal photon correlation histogram is referred to as the 4 photon correlation function. Of special interest is the normalized fourth order photon correlation function, g(4) at time zero: (a÷a4) g(4)= 4 (1) Here â and a refer to the photon creation and annihilation operators respectively.

The numerator of (1) is measured experimentally by summing photon arrival events from all four single photon detectors that arrive in coincidence at relative time delay At = 0 over a given timing window, eg. 1 second. These events correspond to correlated detection events. The electrical channel lengths, 117, 119, 121 and 123 need to be taken into account.

These coincident photon arrival events with At = 0 are extracted by examining the photon arrival event timestamps. This can be performed by a processor on board photon timing card 125 or by an external computer.

The denominator of (1) is measured experimentally by summing all photon arrival events which are coincident but with a relative time delay At!= 0. These events correspond to independent single photon detection events. To satisfy the condition of independence, the coherence time t of photon source 101 must be smaller than L\t.

Again, these coincident photon arrival events L\t!= 0 are extracted by examining the photon arrival event timestamps. This can be performed by a processor on board photon timing card 125 or by an external computer.

The resulting normalized fourth order photon correlation function, g(4) characterizes the fourth order correlation properties of the photon source 101 under test.

Measurement of g(4) permits distinguishing between photon sources with different photon number statistics.

Higher order correlation measurements, g(n) where n > 4 can be realized by generalizing prior art apparatus in Figure 1 with n -I beamsplitters and n single photon detectors. Equation (1) generalization in these cases is: (aa) g(n) (2) (ââ) Figure 2 shows a photon correlation apparatus in accordance with an embodiment of the present invention, a photon correlator based on one photon number resolving detector.

As for figure 1, photon source 101 is typically attenuated to the single photon level.

The output of photon source 101 may be directed through variable attenuator 213 which will be expfained in more detail later. The photons are then directed into photon number resolving detector 201. Photon number resolving detector 201 produces an electrical output which is proportional to the incident number of photons. Therefore, it is possible to determine if a single photon has impinged on detector 201 or if two photons or three photons etc. Therefore the detector can distinguish between a single photon arrival event, a two-photon arrival event, a three photon arrival event etc. The electrical power signal output by photon number resolving detector 201 is then split using power splitter 203. Power splitter 203 divides the signal into two outputs, the first output is directed towards discriminator 205 and the second output to discriminator 207. The discriminators allow portions of the electrical signal corresponding to n-photon events to be selected where n is the photon number. The output 209 refers first discriminator 205 and the output 211 of second discriminator 207 are provided to timing card 125. However, it should be noted that in this case, it is possible to just use two channel photon counter as opposed to a photon timing card.

In this embodiment, window discriminators 205 and 207 will be set to pick out different incident photon numbers. For example, window discriminator 205 can be set to pass only 4 photon events and window discriminator 207 can be set to pass only 1 photon events.

Photon timing card, 125, can collect these window discriminated photon arrival events via the two electrical channels 209 and 211.

In this way, the 4 photon correlation function, g(4), as referred to in Equation (1), can be evaluated. Window discriminator 205 passes events proportional to and window discriminator 207 passes events proportional to (&a).

Nevertheless, care must be used in evaluating g(4) as the photon number resolving detector efficiencies for different photon number will in general be different. Proper characterization of the photon number resolving detector, 201, efficiency as a function of photon number should be carried out before correlation measurements are performed.

Higher order correlation measurements, g(n) where n > 4 given by Equation (2) can be realized by adjusting the window discriminator 205 to select those electrical signals which originate from n photon events. g(n) can be measured up to flmax, where flmax 15 the maximum photon number resolving capability of the detector, 201.

Variable attenuator, 213 can be used to tune the intensity of photons impinging on the detector. In prior art Figure 1, the intensity of photons impinging on the detectors must be kept at a low level, usually 1u <<1. With the new art, the intensity of impinging photons can be much higher resulting in elevated photon coincidence rates and therefore reduced integration times.

Figure 3 depicts a photon correlation apparatus in accordance with a further embodiment of the invention. The photon correlator is based on two photon number resolving detectors.

The apparatus comprises a first beamsplitter 103 which is a 50:50 beamsplitter i.e. a 50:50 probability of transmittance/reflectance. Photons which are transmitted through beamsptitter 103 then pass through variable attenuator 213 and into first photon number resolving detector 201. The output of photon number resolving detector 201 is then passed through discriminator 303.

The discriminated output is then passed through channel 307 to timing card 125.

Photons which have been reflected by first beamsplitter 103 are then passed through second variable attenuator 311 and directed onto second photon number resolving detector 301. Second photon number resolving detector 301 produces an electrical output which is proportional to the incident number of photons. This output is then passed into discriminator 305. The output of discriminator 305 is then passed along channel 309 to timing card 125.

Electrical window discriminators, 303 and 305, are used to select n photon events.

Ideally, window discriminators will be set to pick out different or the same incident photon numbers. For example, window discriminator 303 can be set to pass only 2 photon events and window discriminator 305 can be set to pass only 2 photon events.

Photon timing card, 125, can collect these window discriminated photon arrival events via two electrical channels 307 and 309.

In this way, the 4 photon correlation function, g(4), as referred to in Equation (1), can be evaluated. Coincident photon arrival events with At = 0 measures photon arrival events proportional to (aa) and coincident photon arrival events with At!= 0 measures events proportional to(a+2a2).

A new correlation function (4) is formulated: (a÷4a) (4) 2 2 (3) (a+2a2) g(2) Hence g(4) defined in Equation (1) is related to the quantity,(4) if the second order correlation, g(2) is measured. The second order correlation is given by (cf. Equation (2)): /+22 aa g(2)=: " 2 (4) Adjusting the window discriminators, 303 and 305, to select only one photon events translates to coincident photon arrival events with At = 0 measures photon arrival events proportional to (a+2a2) and coincident photon arrival events with At!= 0 measures events proportional to(ââ).

An attractive feature of this setup is the possibility of loss independence, i.e.: there is no requirement to characterize the efficiencies of the photon number resolving detectors, 201 and 301. This loss independence only holds if the window discriminators select exactly n photon events.

Usually, photon number resolving detectors, 201 and 301, will be identical and therefore possess the same photon number resolving capability, flmax This means the setup in Figure 3 can measure photon correlations up to g(2nmax).

Higher order correlation measurements, g(n) where n > 4 given by Equation (2) can be realized by adjusting the window discriminators 303 and 305 to select those electrical signals which originate from n photon events. Generalizing Equation (3): 2 g(n) (4) 2 2) g(3i Figure 4 shows a preferred form of photon number resolving detectors 201 and 301 to be used in photon correlators in accordance with an embodiment of the present invention.

A capacitor 401 and inductor 403 comprise a bias-tee 405 by which to combine an AC modulation voltage, Vac, 407 from an AC voltage source 409 and fixed DC bias VdC, 411 from a DC bias source 413 for form an avalanche photodiode (APO) bias voltage V3pd, 415. In the preferred embodiment this APD bias voltage 415 is applied to a Indium Gallium Arsenide (InGaAs) based APD 417, although the APD material type is not limited to lnGaAs; it could be silicon or germanium depending on the wavelength sensitivity desired.

The photocurrent induced by an avalanche arising from photon detection results in a voltage across a series resistor 419, which corresponds to an output voltage, V0Lj, 421.

Large periodic capacitive response resulting from high speed operation of APD conceals any weak avalanches, so a self-differencing circuit is employed 423, comprising a signal divider 425, two electrical lines 427 and 429 and a signal differencer 431 The APD output voltage, 421 is input into signal divider 425, which divides the signal into two closely equal components. A potentiometer 435 is used to balance the dividing ratio and further equate the two components. Since one of the electrical delay lines 427 is longer than the other 129, one of these components will necessarily be delayed.

The delay is selected to be an integer number of gating periods T supplied by the AC voltage source 431, and the delay line 427 is chosen to be adjustable in order to tune the delay independently of T. When these two signals are input into a signal differencer 431, they are subtracted one from the other and the strong periodic capacitive response is largely cancelled leaving behind a weak seif-differencer output voltage, VSd, 433. It is common to use a 1GHz low-pass filter 437 and linear amplifier 439 to further improve the quality of Vd, 433.

This allows weak avalanches to be revealed in the seif-differencer output, VSd, 433. The amplitude of these weak avalanches is dependent on photon number.

Figure 5 depicts the three types of photon source which were used to test the photon correlator of Figure 3.

In Figure 5a, the source comprises a pulsed multi-mode lnGaAs laser, 501. Laser 501 displays intensity fluctuations due to operation slightly above laser threshold. Such fluctuation manifests experimentally as photon bunching. The degree of bunching is accentuated by use of a filter 503 which selects a mode close to a wavelength of 1550nm. Filter 503 will have a bandwidth smaller than the spectral mode spacing of laser 501. Typically the source of 5a is also attenuated to the single photon level.

A pictorial representation of source of figure 5a optical frequency spectrum is also shown. A number of modes, 505, with different intensities (vertical axis) are depicted as a function of optical frequency (horizontal axis). The filter selects the mode, 507, as shown by the dotted rectangle.

The source of figure 5b comprises a pulsed distributed feedback type laser operating at a wavelength of 1550nm operating slightly above laser threshold, 509. Typically the source of figure 5b is also attenuated to the single photon level.

Similarly to the source of figure 5a, in the source of figure 5b there will be intensity fluctuations and hence photon bunching, although the intensity fluctuations will not be as strong as the source of figure 5b and hence photon bunching will not be as strong.

A pictorial representation of source of figure 5b optical frequency spectrum is also shown. A single mode, 511, is depicted as a function of optical frequency (horizontal axis).

The source of figure 5c comprises a pulsed distributed feedback type laser operating at a wavelength of l55Onni operating well above laser threshold, 513. Typically the source of figure 5c is also attenuated to the single photon level.

Similarly to the source of figure 5b, there will be intensity fluctuations for the source of figure 5c and hence photon bunching although the intensity fluctuations will not be as strong as the source of figure Sb so the photon bunching will not be as strong.

A pictorial representation of the optical frequency spectrum of the source of figure Sc is also shown. A single mode, 515, is depicted as a function of optical frequency (horizontal axis).

Figure 6 depicts the intensity of a distributed feedback laser, as referred to in Figures 5b and Sc, output as a function of laser driving intensity.

Two different regimes are shown. Regime 1 comprises data up to point 601 and corresponds to the laser below lasing threshold. Regime 2 comprises data beyond point 601, and the data exhibits a sharp increase in optical output power which is the signature of lasing.

Slightly above threshold, 603, the laser is slightly unstable. Data point 603 corresponds to photon source of Figure Sb.

Well above threshold, the laser is expected to exhibit a well-stabilized output. Data point 605 corresponds to photon source of Figure 5.

Figure 7 a) depicts the experimentally measured avalanche statistics, arising from the avalanche probability plotted as a function of the self-differencer output, Vsd for an embodiment of a photon number resolving detector based on an lnGaAs APD as described in Figure 4.

The APD is gated with AC modulation comprising a square wave with a frequency of 1GHz and amplitude Vac 6-7V. A DC bias of VdC -52V is also applied.

The probability distributions are plotted for two photon sources, 5130 (701) and 5001 (703). Both probability distributions were obtained from around 10 million samples, accumulated in real-time using a fast digital oscilloscope.

When excited with photon source 5130, the avalanche voltage distribution shows a number of distinct peaks, trace 701.

Peak at photon number n = 0, OmV, corresponds to the 0-photon contribution from gates in which no photon was detected. The width of this feature is attributed to a residual component of the capacitive response of the APD, due to the imperfect cancellation of the self-differencer circuit.

Peaks at photon numbers n »= 1 correspond to avalanches arising from the absorption of different photon number states, n of the incident light field.

The avalanche voltage distribution can be satisfactorily modeled assuming the photon number distribution of the source is Poissonian with a mean detected photon flux, 2.6, Figure 7b), trace 705.

Each photon peak, n »= 1 is assumed to be Gaussian and to reflect the statistical broadening, the widths of the photon peaks are scaled as relative to the 1-photon peak width. The areas of each photon peak are proportional to the expected Poisson photon number distribution probabilities and up to n = 5 photon number states are employed in the simulation. The main features of the experimental trace 701 are reproduced.

The ability to detect differences in the photon statistics for dissimilar photon sources is now illustrated. The photon source was substituted with photon source 5001. Here the average detected photon flux was similar to before with 1u 2.8.

Photon source 5001 gives rise to a rather different avalanche voltage distribution, trace 703. The 0-photon peak is higher than for the laser source operating well above threshold, indicating the presence of more vacuum states. Conversely there is a suppression of the 2-photon and 3-photon number states.

Photon source 5001 is expected to exhibit intensity fluctuations due to operation close to lasing threshold. Such fluctuation is manifest experimentally as photon bunching.

Bunching can be viewed as a departure from the statistical independent statistics of a Poissonian source. The degree of bunching is accentuated through selection of a single mode by filtering.

The mathematical form of the photon number distribution for this particular case is not known precisely, so we choose an analytic photon counting distribution function, p(n), representing a linear superposition of an amplitude stabilized field with mean photon number p and a narrowband random noise field with mean photon number /J,: p(n) 4 1 ____ exp1- l1FiI-n;1;- 2 (}+dUfl1+IUfl) I l+/4,)J (5) Here F1 is the confluent hypergeometric function of the first kind.

Equation (5) is valid when the intensity fluctuations are small. The following relations fix /-and /J, from experimentally measurable quantities, namely average detected photonflux, p=/J+/J andg(2)=/i,(p+2J1)//-C+l.

Using 1u 2.8 and g(2) = 1.2 (the value of g(2) is corroborated experimentally by an independent measurement of g(2)), the resulting modeled avalanche distribution is depicted in Figure 7 b), trace 707. There is clear qualitative agreement with the experimental avalanche distribution.

For both types of photon source, the theoretical avalanche distribution is overestimated for strong avalanche heights. This is possibly due to the quenching effect of the APO series resistance causing large avalanches from photon number states with n> 5 to be reduced in size.

Thus for approximatelyn »= 4 the avalanche distribution is likely to be made up from a greater number of photon number states than what would be expected from a simple linear model. The linear model supposes a linear avalanche voltage dependence on photon number, as indicated by the positions of the dotted lines in Figure 7.

Figure 8 depicts a typical coincidence counts histogram as a function of photon number resolving detector relative delay, At for the photon correlator setup using APD based two photon number resolving detectors, as described in Figures 3 and 4.

The arrangement will be the same as a conventional arrangement used to measure a second order correlation function g(2) if the photon number resolving function is disabled.

By setting the discrimination level at -300mV, a value far greater than single photon signals, for both detectors 201 and 301, the measurement gives a correlation result that is different from g(2).

The photon source of Figure 5a is used.

At zero time delay (At -0) a prominent correlation peak, 801, is observed due to photon bunching.

At non-zero time delays (At!= 0) smaller correlation peaks, 803, are observed.

To distinguish the correlation from conventional g(2), the correlation is defined as the ratio of peak height at At = 0 to the average height at At!= 0 encapsulates the degree of correlation measured and is consistent with Equation (4).

Figure 9 depicts photon correlations, as a function of photon number resolving detector discrimination level of discriminator 305, for the photon correlator using APD based two photon number resolving detectors, as described in Figures 3 and 4.

For all measurements in Figure 9, photon number resolving detector discrimination value, 303 is held fixed at -300mV.

For different discrimination levels of discriminator 305, correlation plots similar that depicted in Figure 8 are collected and the correlations, evaluated. Figure 9 plots the resulting correlations, (traces 801, 803 & 805) as a function of 305 discrimination level for the three photon sources of figures 5a (801), 5b (803) and 5c (805).

All three sources give rise to > 1 even at the lowest discrimination level used. As the discriminator level is tuned to higher levels, increases in all cases.

This can be readily understood in terms of elevated photon bunching through higher order correlations. The order correlation is the expectation of the joint detections of n photons correlations. For photons that are indistinguishable and statistically dependent, there is a factorial increase of the available permutations of photon amplitudes as n rises. At higher discrimination levels, higher photon number states feature more markedly than lower photon number states and the correlation is therefore expected to be higher than for lower photon number states.

This is in direct contrast to what would be expected for the case of statistically independent photons. In this case the photon statistics are Poissonian and no bunching is possible for any order of correlation.

The photon source of figure 5c shows the least amount of correlation; this is expected for a laser source operating well above threshold with largely Poissonian statistics.

for the source of figure 5c attains -1.3 at the very highest discrimination level employed as shown in figure 9b.

Operating the same laser close to threshold the source of figure 5b shows a marked increase in correlation which is due to increased intensity fluctuations leading to increased photon bunching.

The source of figure 5a displays the highest correlation values; attaining 45 for these measurements. Intensity fluctuations for this source are by far the highest of all sources under test.

Figure 10 depicts the simulated correlations as a function of photon number resolving detector discrimination level of discriminator 305, for the photon correlator using APD based two photon number resolving detectors, as described in Figures 3 and 4.

To connect the measured data to the usual normalized correlation functions eg. g(2), can be formulated in a similar fashion to Equation (4).

The coincidence peak at At 0 is proportional to the correlation (aflh2)a(''2))whereas the peaks at At!= 0 are proportional to (a2 afl2 at') Here n refers to the photon number state sampled by discriminator i and the expectation of the operators is taken over the density matrix of the incident photon field given by the linear superposition of an amplitude stabilized field and a narrowband random noise field, Equation (5).

We have: +n2) g-, ça+fn2a'2)(a2' a'7' However, Equation (6) corresponds to the case of only post-selecting individual detected photon number states, i.e.: using window discriminators. To incorporate the fact that threshold discriminators are used in the experiment it is necessary to integrate over all photon number states greater than the lowest allowed photon number state.

Therefore is re-written as: umax (+(fll+fl2)a(flI+fl2))p(n)p(n) (7) max )(a'ai)p(ni)p(n2) fli M Here p(n1)refers to the n photon number state detection probability. We stress that completely characterizes a photon source up to 2m and represents all possible joint detections.

All three photon sources under study feature different photon number statistics which is incorporated in the model through the mean photon numbers,u and 1u,. These mean photon numbers are derived from the total average photon number 1u and g(2). For the sources 5001, 5009, & 5130, g(2) = 1.2, 1.075 & 1.001 respectively.

Avalanche height self-limiting due to the APD series resistance is likely to distort the linear avalanche voltage dependence on photon number for high photon number. We can incorporate this fact by increasing flmax for the detectors.

Figure 10 shows, for the photon sources of figure 5a (1001), figure 5b (1003) and figure 5c (1005) plotted with photon number resolution up to flm = 7. The x-axis is plotted on a logarithmic scale to emphasize the avalanche self-limiting. for all sources shows a similar growth and dependence to that observed experimentally, qualitatively confirming our underlying model.

The simulations indicate that correlations up to n = 14 can be measured. The correlation can be related to the usual normalized correlation function g(14) via Equation (7), provided correlations for n < 14 are measured as well which is straighiforwardly achieved in the above arrangement.

Figure 11 shows a quantum communication system with a photon correlation stage of the type described above.

Quantum communication systems are well-known in the art and the detail of such a system is well outside the scope of this application. In its most basic form, a quantum communication system comprises an emitter 1021 which sends photons over cable 1022, or through free space, to receiver 1023.

The emitter comprises a photon source 1025 which output photons into encoding means 1027. Encoding means 1027 may be phase encoding means, for example an interferometer, a polarisation encoding means etc. In the system of figure 11, a further stage 1029 is provided. Stage 1029 is a photon correlation stage which is of the type described with reference to figures 2 to 10. Photon correlation stage 1029 is configured that it may be switched to receive the output of photon source 1025 to measure its degree of correlation Thus, the photon correlation stage used when it is desirable to characterise the source and then switched off when the system is being used to send a key.

The correlator may be provided before the encoding stage 1027, as an alternative to the encoding stage or after the encoding stage.

Receiver 1023 comprises a decoding stage 1033 and a detector 1031. A correlation detection stage 1035 is also provided to check the correlation of the photon source 1025.

The photon source may be correlated offline and there will be no need to provide correlation in situ in either of the emitter or the detector. In practice, a correlation stage will either be provided in the emitter or receiver 1023. However, for completeness, a correlation stage is shown in both the emitter 1021 and receiver 1023.

Claims

CLAIMS: 1. An apparatus for measuring photon correlations from a photon source, the apparatus comprising a photon detection stage, wherein at least two output signals are outputted from said photon detection stage, where each output signal indicates the number of photon arrival events detected with an accuracy of one photon, the apparatus further comprising a discriminator for each output signal, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events, the apparatus further comprising a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminators and produces a measure of the correlation of the photon source.
2. An apparatus according to claim 1, said coincidence circuit being configured to measure an nth order correlation, where n is an integer of at least 2, where a discriminator is configured to indicate n photon arrival events or where two or more discriminators pass output signals which indicate numbers of photon arrival events and where the sum of the number of photons in the photon arrival events equals n.
3. An apparatus according to claim 2, wherein a first discriminator is configured to pass an output signal which indicates a single photon arrival event and a second discriminator passes an output signal which indicates a n photons arrival event.
4. An apparatus according to claim 2, wherein a first discriminator is configured to pass an output signal which indicates a n photons arrival event and a second discriminator is configured to indicate a n-rn photons arrival event where m is an integer and is less than n.
5. An apparatus according to claim 4, wherein n/2 is an integer and mn/2.
6. An apparatus according to either of claims 4 or 5, wherein the coincidence circuit determines the correlation using when both discriminators pass photon arrival events and when one discriminator recognises a photon arrival event.
7. An apparatus according to any preceding claim, wherein the photon detection stage comprises a photon detector and a splitter configured to divide the output of said photon detector into two output signals.
8. An apparatus according to any of claims 1 to 6, wherein said photon detection stage comprises a beam splitter configured to divide the output of a photon source between first and second photon detectors, wherein the first photon detector outputs one of said output signals and the second photon detector, another of said output signals.
9. An apparatus according to either of claims 7 or 8, wherein said photon detector or photon detectors are avalanche photon detectors.
10. An apparatus according to any preceding claim, wherein the discriminators set a discrimination window which selects a set number of photon arrival events.
11. An apparatus according to any preceding claim, wherein the coincidence circuit measures the time delay between photon arrival events.
12. An apparatus according to claim 9, comprising means to isolate the avalanche signal from the output using seif-differencing detection circuits.
13. An apparatus according to claim 12, wherein the self-differencing circuit comprises a signal divider to split the signal into two parts, an electrical line to delay one of the parts with relative to the other and a signal differencer to output the difference between the two parts.
14. An apparatus according to any preceding claim, further comprising a variable attenuator to adjust the photon flux impinging on the photon detection stage.
15. An apparatus according to claim 18, further comprising a plurality of neutral density filters configured to adjust the photon flux impinging on the photon detection stage.
16. An apparatus according to any preceding claim, wherein a detector in said photon detection stage is a gated photon detector and the source is a pulsed source, and wherein the gating of the detector is configured to synchronise with the pulsed source.
17. A an apparatus according to any of claims 1 to 15, wherein a detector in said photon detection stage is a free running photon detector and the source is a continuous source.
18. An emitter for a quantum communication system, said emitter comprising a photon source; an encoder for encoding quantum information on photons outputted from said source and an apparatus for measuring photon correlations from said photon source in accordance with any of claims 1 to 15.
19. A quantum communication system, said system comprising an emitter and a receiver, said emitter comprising a photon source and an encoder for encoding quantum information on photons outputted from said source, said receiver comprising a decoder configured to decode said encoded photons and at least one photon detector, the system further comprising an apparatus for measuring photon correlations from said photon source in accordance with any of claims I to 15.
20. A method for measuring photon correlations from a photon source, the method comprising: detecting the output of the source using a photon detection stage, wherein at least two output signals are outputted from said photon detection stage, where each output signal indicates the number of photon arrival events detected with an accuracy of one photon, passing each output signal through a discriminator, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events; receiving the output signals which have passed through the discriminators in a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminators and produce a measure of the correlation of the photon source.Amendment to the claims have been filed as follows CLAIMS: 26 1. An apparatus for measuring photon correlations from a photon source, the apparatus comprising a photon detection stage, wherein at least two output signals are outputted from said photon detection stage, where each output signal indicates the number of photon arrival events detected with an accuracy of one photon, the apparatus further comprising a discriminator for each output signal, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events, the apparatus further comprising a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminators and produces a measure of the correlation of the photon source.2. An apparatus according to claim 1, said coincidence circuit being configured to measure an nth order correlation, where n is an integer of at least 2, where a discriminator is configured to indicate n photon arrival events or where two or more discriminators pass output signals which indicate numbers of photon arrival events and where the sum of the number of photons in the photon arrival events equals n.3. An apparatus according to claim 2, wherein a first discriminator is configured to pass an output signal which indicates a single photon arrival event and a second discriminator passes an output signal which indicates a n photons arrival event.4. An apparatus according to claim 2, wherein a first discriminator is configured to pass an output signal which indicates a m photons arrival event and a second discriminator is configured to indicate a n-rn photons arrival event where m is an integer and is less than n.* ** _*. * * s-5. An apparatus according to claim 4, wherein n/2 is an integer and m=n/2. *S S..6. An apparatus according to either of claims 4 or 5, wherein the coincidence *. circuit determines the correlation using when both discriminators pass photon arrival events and when one discriminator recognises a photon arrival event.7. An apparatus according to any preceding claim, wherein the photon detection stage comprises a photon detector and a splitter configured to divide the output of said photon detector into two output signals.8. An apparatus according to any of claims I to 6, wherein said photon detection stage comprises a beam splitter configured to divide the output of a photon source between first and second photon detectors, wherein the first photon detector outputs one of said output signals and the second photon detector, another of said output signals.9. An apparatus according to either of claims 7 or 8, wherein said photon detector or photon detectors are avalanche photon detectors.10. An apparatus according to any preceding claim, wherein the discriminators set a discrimination window which selects a set number of photon arrival events.11. An apparatus according to any preceding claim, wherein the coincidence circuit measures the time delay between photon arrival events.12. An apparatus according to claim 9, comprising means to isolate the avalanche signal from the output using self-differencing detection circuits.13. An apparatus according to claim 12, wherein the self-differencing circuit comprises a signal divider to split the signal into two parts, an electrical line to delay one of the parts with relative to the other and a signal differencer to output the difference between the two parts. sII.. .** 14. An apparatus according to any preceding claim, further comprising a variable attenuator to adjust the photon flux impinging on the photon detection stage.III15. An apparatus according to claim 1, further comprising a plurality of neutral density *r*. filters configured to adjust the photon flux impinging on the photon detection stage.16. An apparatus according to any preceding claim, wherein a detector in said photon detection stage is a gated photon detector and the source is a pulsed source, and wherein the gating of the detector is configured to synchronise with the pulsed source.17. A an apparatus according to any of claims 1 to 15, wherein a detector in said photon detection stage is a free running photon detector and the source is a continuous source.18. An emitter for a quantum communication system, said emitter comprising a photon source; an encoder for encoding quantum information on photons outputted from said source and an apparatus for measuring photon correlations from said photon source in accordance with any of claims 1 to 15.19. A quantum communication system, said system comprising an emitter and a receiver, said emitter comprising a photon source and an encoder for encoding quantum information on photons outputted from said source, said receiver comprising a decoder configured to decode said encoded photons and at least one photon detector, the system further comprising an apparatus for measuring photon correlations from said photon source in accordance with any of claims I to 15.20. A method for measuring photon correlations from a photon source, the method comprising: detecting the output of the source using a photon detection stage, wherein at least two output signals are outputted from said photon detection stage, where each output signal indicates the number of photon arrival events detected with an accuracy of one photon, passing each output signal through a discriminator, said discriminators being configured to pass output signals which indicate a predetermined number of photon arrival events; receiving the output signals which have passed through the discriminators in a coincidence circuit configured to measure the coincidence rate using the outputs of the two discriminators and produce a measure of the correlation of the photon source.