CN111443548B - Nonlinear photonic crystal and two-photon frequency and path super-entanglement generation method thereof - Google Patents

Nonlinear photonic crystal and two-photon frequency and path super-entanglement generation method thereof Download PDF

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CN111443548B
CN111443548B CN202010313789.1A CN202010313789A CN111443548B CN 111443548 B CN111443548 B CN 111443548B CN 202010313789 A CN202010313789 A CN 202010313789A CN 111443548 B CN111443548 B CN 111443548B
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CN111443548A (en
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息朝祥
丁译洲
何广强
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Shanghai Jiaotong University
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    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/353—Frequency conversion, i.e. wherein a light beam is generated with frequency components different from those of the incident light beams
    • G02F1/3544—Particular phase matching techniques
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/355—Non-linear optics characterised by the materials used
    • G02F1/3551—Crystals
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/355—Non-linear optics characterised by the materials used
    • G02F1/3558—Poled materials, e.g. with periodic poling; Fabrication of domain inverted structures, e.g. for quasi-phase-matching [QPM]
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/35—Non-linear optics
    • G02F1/353—Frequency conversion, i.e. wherein a light beam is generated with frequency components different from those of the incident light beams
    • G02F1/3544—Particular phase matching techniques
    • G02F1/3548—Quasi phase matching [QPM], e.g. using a periodic domain inverted structure

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Abstract

The invention provides a nonlinear photonic crystal capable of directly generating double-photon frequency and path super-entanglement, wherein the nonlinear photonic crystal adopts 5% MgO-doped LiNbO under the conditions of room temperature and I-type phase matching (e → o + o)3And (4) crystals. The pump light is normally incident to the surface of the nonlinear photonic crystal along the positive z direction, and signal light and idle light are generated after interaction, wherein the signal light and the idle light meet the frequency and path super-entanglement relationship. The nonlinear photonic crystal and the two-photon frequency and path super-entanglement generation method thereof provided by the invention are simulated, and the verification proves that the nonlinear photonic crystal can generate the maximum entangled state, and other parameter processes are effectively inhibited, so that the super-entangled state with higher quality is generated.

Description

Nonlinear photonic crystal and two-photon frequency and path super-entanglement generation method thereof
Technical Field
The invention relates to a nonlinear photonic crystal design technology in the technical field of quantum entanglement generation, in particular to a nonlinear photonic crystal and a two-photon frequency and path super-entanglement generation method thereof, which is a nonlinear photonic crystal design scheme for directly generating two-photon frequency and path super-entanglement.
Background
Quantum entanglement is an important feature of the quantum world and describes a property of association between particles or groups of particles that is not limited by distance. Quantum entanglement is an essential quantum resource for many applications in quantum information processing, and is widely used in quantum key distribution, quantum invisible state transfer, quantum entanglement exchange and relay, quantum precision metering and the like.
Super-entanglement is a high-dimensional quantum entanglement and refers to the simultaneous quantum entanglement between particles or groups of particles in two or more dimensions. Compared with a common quantum entanglement source, the super-entanglement source has larger application, can realize complete distinction of four Bell states, realizes a single-photon double-quantum-bit CNOT gate, realizes a double-quantum-bit exchange gate and the like. In addition, super-entanglement can improve the performance of many quantum applications, such as enabling more secure quantum key distribution, enabling super-dense encoding, and the like.
In 2002, m.genoevea and c.novero designed sources of polarization and temporal super-entanglement; in 2003, a Chen soldier professor and the like designed a super-entanglement source of polarization and path; the university of science and technology team in Puji of 2019 prepares a super-entanglement source of photon orbital angular momentum and polarization.
The standard technique for effectively creating entanglement is to create a Spontaneous parametric down-conversion (SPDC) process under the influence of the second-order nonlinear polarization coefficient of the nonlinear medium. Spontaneous parametric down-conversion refers to pump light (frequency is omega) in second-order nonlinear photonic crystalP) Interacts with nonlinear crystal to generate signal light (frequency is omega)S) And idle light (frequency omega)I) Was first discovered in 1970 by two scientists, Burnham and Weinberg. Because of the second-order nonlinear polarization coefficient chi in the nonlinear photonic crystal(2)Is very small, the intensity of the input pump light should be sufficiently large in order to guarantee the conversion efficiency of the optical spontaneous parametric down-conversion process. In the second-order nonlinear crystal, pump photons interact with the second-order nonlinear photonic crystal according to a certain probability, and then the pump photons are annihilated to generate new signal photons and idle photons, wherein the energy of the signal photons and the idle photons comes from the annihilated pump photons. The implementation of the spontaneous parametric down-conversion process must satisfy the energy conservation condition (ω)P＝ωS+ωI) It is not necessary to satisfy the conservation of momentum condition
Figure BDA0002458702960000021
The conversion process under the spontaneous parameters can also be realized when the momentum conservation condition is not completely satisfied, but the efficiency is extremely low, and the conversion efficiency of the conversion process under the spontaneous parameters can be maximized only when the momentum conservation condition is completely satisfied, that is, the nonlinear parameter process has perfect phase matching. The optical spontaneous parametric down-conversion process is currently the main method for preparing photon entanglement sources, mainly because it is stable,the generated optical signal is high in intensity, and the generated photon pairs have entanglement characteristics.
Quasi-phase matching (Quasi-phase matching) is a general method for solving phase matching conditions, and can well solve the phase matching problem in the SPDC process. The idea of quasi-phase matching is to adjust the structure of the nonlinear photonic crystal so that the nonlinear coupling coefficient of the nonlinear photonic crystal varies periodically. On a nonlinear crystal, periodically inverting the optical axis of the crystal according to the position of the crystal, so that the nonlinear coupling coefficient of the crystal is also periodically inverted along with the position of the crystal, and the process is also called periodic polarization of the crystal, and the periodically polarized crystal can compensate the nonzero wave vector adaptation quantity of the parametric process
Figure BDA0002458702960000022
Figure BDA0002458702960000023
The method can thus effectively increase the efficiency of the parametric process.
However, the prior art does not design a two-photon frequency and path super-entanglement source, and does not directly construct the two-photon frequency and path super-entanglement source by utilizing a nonlinear photonic crystal.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a nonlinear photonic crystal and a two-photon frequency and path super-entanglement generation method thereof.
The invention is realized by the following technical scheme.
According to one aspect of the invention, a nonlinear photonic crystal capable of directly generating two-photon frequency and path super-entanglement is provided, and the nonlinear photonic crystal selects LiNbO with MgO doping under the conditions of room temperature and I-type phase matching3And (4) crystals.
Preferably, the room temperature is 20-25 ℃.
Preferably, the polarization property of the class I phase matching condition is e → o + o, i.e. one e optical photon is converted into two o optical photons.
Preferably, the doping amount of MgO is 5%.
Preferably, the quasi-periodic lattice structure of the nonlinear photonic crystal is: in a set coordinate system, the thickness L of the nonlinear photonic crystal in the z direction satisfies L ═ m pi/delta kzWhere m is a non-negative integer,. DELTA.kzIs the modulus of the phase adaptation quantity in the z-axis direction. Second-order nonlinear polarization coefficient chi of nonlinear photonic crystal(2)Along the direction of the x axis and is inverted at a specific position of the x axis to realize a second-order nonlinear polarization coefficient chi(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)The-1 domains alternate with a designed law.
According to another aspect of the present invention, there is provided a two-photon frequency and path super-entanglement generating method of the nonlinear photonic crystal described in any one of the above, comprising:
the pumping light is normally incident to the surface of the nonlinear photonic crystal along the positive z direction, and the pumping light wave vector
Figure BDA0002458702960000031
And a unit vector parallel to the y-axis constitute a pump light plane,
Figure BDA0002458702960000032
amount of phase adaptation in the x-axis direction provided perpendicular to a nonlinear photonic crystal
Figure BDA0002458702960000033
And
Figure BDA0002458702960000034
and generating signal light and idle light after interaction, wherein the signal light and the idle light meet the frequency and path super-entanglement relationship.
Preferably, the quantum state | ψ > of the frequency and path super-entanglement relationship is expressed as:
Figure BDA0002458702960000035
in which the subscript S represents the signal light, i.e. photon transmissionThe transmission path is above the pump light plane, and subscript I represents idle light, namely the photon transmission path is below the pump light plane; theta1,SIndicating signal light at an angle theta1In the case of emission, θ1,IIndicating idle light at an angle theta1In the case of emission, θ2,SIndicating signal light at an angle theta2In the case of emission, θ2,IIndicating signal light at an angle theta2In the case of emission, ω1,SIndicating the frequency of the signal light as omega1Condition of (a), ω2,IIndicating an idle light frequency of omega2Condition of (a), ω2,SIndicating the frequency of the signal light as omega2Condition of (a), ω1,IIndicating an idle light frequency of omega1The case (1).
Preferably, the nonlinear photonic crystal satisfies multiple quasi-phase matching conditions, and can simultaneously generate multiple matched spontaneous parametric down-conversion processes.
Preferably, the quasi-phase matching conditions are four, which are:
(1)
Figure BDA0002458702960000036
(2)
Figure BDA0002458702960000037
(3)
Figure BDA0002458702960000038
(4)
Figure BDA0002458702960000039
in the formula (I), the compound is shown in the specification,
Figure BDA00024587029600000310
is a frequency of omegaPThe wave vector of the pump light of (1),
Figure BDA00024587029600000311
at an angle theta1The frequency of the emergent light is omega1Of (2) a signalThe wave vector of the light is then,
Figure BDA00024587029600000312
at an angle theta1The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure BDA00024587029600000313
at an angle theta1The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure BDA00024587029600000314
at an angle theta1The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure BDA00024587029600000315
at an angle theta2The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure BDA00024587029600000316
at an angle theta2The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure BDA00024587029600000317
at an angle theta2The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure BDA00024587029600000318
at an angle theta2The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure BDA00024587029600000319
and
Figure BDA00024587029600000320
for the amount of phase adaptation in the x-axis direction,
Figure BDA00024587029600000321
is the phase adaptation amount in the z-axis direction;
accordingly, the four matched spontaneous parameter down-conversion processes are: one frequency of omegaPThe pumping light photons are converted into a frequency omega by the nonlinear photonic crystalSAnd a signal light photon of frequency omegaIThe conversion process satisfies the energy conservation omegaP＝ωS+ωI。
Preferably, the z-axis phase-adaptive quantities in the four matched spontaneous parameter down-conversion processes have the same modulus values and opposite directions, so that the four spontaneous parameter down-conversion processes have the same efficiency, and further the maximum degree of super-entanglement is generated.
Compared with the prior art, the invention has the following beneficial effects:
1. the nonlinear photonic crystal and the two-photon frequency and path super-entanglement generation method thereof select 5 percent MgO-doped LiNbO under the conditions of room temperature (20 ℃ to 25 ℃) and I-type phase matching (e → o + o)3The crystal is designed to be capable of being matched with four spontaneous parameter down-conversion processes at room temperature, so that the frequency and path super-entangled photon pair can be directly generated when only one beam of pump light is injected without a heating furnace.
2. The nonlinear photonic crystal and the two-photon frequency and path super-entanglement generation method thereof provided by the invention can independently design the structure of the nonlinear photonic crystal, so that the nonlinear photonic crystal simultaneously meets a plurality of (the invention meets four) spontaneous parameter down-conversion processes, which are needed for designing a quantum super-entanglement source.
3. The nonlinear photonic crystal and the two-photon frequency and path super-entanglement generation method thereof provided by the invention are simulated, and the design scheme can be verified to generate the maximum entangled state and effectively inhibit other parameter processes, so that the super-entangled state with higher quality can be generated.
4. The nonlinear photonic crystal and the two-photon frequency and path super-entanglement generation method thereof provided by the invention combine multiple disciplines such as quantum optics, nonlinear optics, crystal optics and the like, and solve the problem of nonlinear crystal design in the process of preparing the two-photon frequency and path super-entanglement.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic diagram of a two-photon frequency and path super-entanglement source design based on a nonlinear photonic crystal in an embodiment of the invention.
FIG. 2 is a diagram illustrating four quasi-phase matching conditions that can be satisfied by a nonlinear photonic crystal capable of generating two-photon frequency and path super-entanglement according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of a quasi-periodic lattice structure of a nonlinear photonic crystal capable of generating two-photon frequency and path super-entanglement in accordance with an embodiment of the present invention.
FIG. 4 is a graph of the spatial Fourier transform spectrum of a quasiperiodic lattice of a nonlinear photonic crystal producing two-photon frequency and path super-entanglement in one embodiment of the present invention.
Detailed Description
The following examples illustrate the invention in detail: the embodiment is implemented on the premise of the technical scheme of the invention, and a detailed implementation mode and a specific operation process are given. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.
The embodiment of the invention provides a nonlinear photonic crystal capable of directly generating two-photon frequency and path super-entanglement, wherein the nonlinear photonic crystal is selected from MgO-doped LiNbO under the conditions of room temperature and I-type phase matching3And (4) crystals.
As a preferred embodiment, the room temperature refers to the working temperature of the nonlinear photonic crystal design, and is 20-25 ℃, and further preferably, the room temperature is 25 ℃.
As a preferred embodiment, the polarization property of the class I phase matching condition is e → o + o, i.e. one e photon is converted into two o photons.
In a preferred embodiment, the amount of MgO is 5%.
As a preferred embodiment, the quasi-periodic lattice structure of the nonlinear photonic crystal specifically includes: according to the coordinate system defined in FIG. 1, the nonlinear photonic crystal has a length of 3.947cm in the x-direction, a width of 1cm in the y-direction, and a thickness L in the z-direction satisfying L-m pi/Δ kzWhere m is a non-negative integer,. DELTA.kzFor the modulus of the quantity of phase adaptation in the z-axis direction, Δ kz＝0.04μm-1. Second-order nonlinear polarization coefficient chi of nonlinear photonic crystal(2)The second order nonlinear polarization coefficients χ were achieved by inverting along the x-axis direction specified in FIG. 1 at the specific positions listed in Table 1(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)The-1 domains alternate in a designed pattern (fig. 3 is a schematic diagram).
Based on the nonlinear photonic crystal provided by the embodiment of the present invention, the embodiment of the present invention provides a two-photon frequency and path super-entanglement generation method of any one of the above nonlinear photonic crystals, including:
as shown in FIG. 1, the pumping light is normally incident to the surface of the nonlinear photonic crystal along the positive z direction, and the pumping light wave vector
Figure BDA0002458702960000051
And a unit vector parallel to the y-axis constitute a pump light plane,
Figure BDA0002458702960000052
amount of phase adaptation in the x-axis direction provided perpendicular to a nonlinear photonic crystal
Figure BDA0002458702960000053
And
Figure BDA0002458702960000054
after interaction, signal light and idle light are generated, and the signal light and the idle light meet the frequency and path super-entanglement relation.
As a preferred embodiment, the quantum state | ψ > of the frequency and path super-entanglement relationship is expressed as:
Figure BDA0002458702960000055
in the formula, subscript S represents signal light, that is, the photon transmission path is above the pump light plane, and subscript I represents idle light, that is, the photon transmission path is below the pump light plane; theta1,SIndicating signal light at an angle theta1In the case of emission, θ1,IIndicating idle light at an angle theta1In the case of emission, θ2,SIndicating signal light at an angle theta2In the case of emission, θ2,IIndicating signal light at an angle theta2In the case of emission, ω1,SIndicating the frequency of the signal light as omega1Condition of (a), ω2,IIndicating an idle light frequency of omega2Condition of (a), ω2,SIndicating the frequency of the signal light as omega2Condition of (a), ω1,IIndicating an idle light frequency of omega1The case (1).
As a preferred embodiment, the pump light wavelength is 775 nm.
In a preferred embodiment, the signal wavelength is 1700nm and the idle wavelength is 1424.3 nm; accordingly, Δ kx1＝0.2801μm-1，Δkx2＝0.3185μm-1Wherein, Δ kx1Shows the amount of phase adaptation in the x-axis direction in FIG. 2
Figure BDA0002458702960000061
A modulus value of (d); Δ kx2Shows the amount of phase adaptation in the x-axis direction in FIG. 2
Figure BDA0002458702960000062
The modulus value of (a).
As a preferred embodiment, the nonlinear photonic crystal meets various quasi-phase matching conditions, and can simultaneously generate a plurality of matched spontaneous parametric down-conversion processes.
As a preferred embodiment, as shown in fig. 2, the quasi-phase matching conditions are four, which are:
(1)
Figure BDA0002458702960000063
(2)
Figure BDA0002458702960000064
(3)
Figure BDA0002458702960000065
(4)
Figure BDA0002458702960000066
in the formula
Figure BDA0002458702960000067
Is a frequency of omegaPThe wave vector of the pump light of (1),
Figure BDA0002458702960000068
at an angle theta1The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure BDA0002458702960000069
at an angle theta1The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure BDA00024587029600000610
at an angle theta1The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure BDA00024587029600000611
at an angle theta1The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure BDA00024587029600000612
at an angle theta2The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure BDA00024587029600000613
at an angle theta2The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure BDA00024587029600000614
at an angle theta2The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure BDA00024587029600000615
at an angle theta2The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure BDA00024587029600000616
and
Figure BDA00024587029600000617
for the amount of phase adaptation in the x-axis direction,
Figure BDA00024587029600000618
is the phase adaptation amount in the z-axis direction;
accordingly, the four matched spontaneous parameter down-conversion processes are: one frequency of omegaPThe pumping light photons are converted into a frequency omega by the nonlinear photonic crystalSAnd a signal light photon of frequency omegaIThe process satisfies the energy conservation omegaP＝ωS+ωI。
As a preferred embodiment, the z-axis phase-adaptive quantities in the four matched spontaneous parameter down-conversion processes have the same modulus value and opposite directions, so that the four spontaneous parameter down-conversion processes have the same efficiency, and further the maximum degree of super-entanglement is generated.
As a preferred embodiment of the method according to the invention,
Figure BDA00024587029600000619
modulus value of (Δ k)z＝0.04μm-1；θ1＝0.1741rad，θ2＝0.1982rad。
The technical solutions provided by the embodiments of the present invention are further described in detail below with reference to the accompanying drawings.
The embodiment of the invention provides a two-photon frequency and path capable of being directly generatedThe super-entangled nonlinear photonic crystal is 5% MgO-doped LiNbO at room temperature (preferably 25 ℃) and under the conditions of I-type phase matching (e → o + o)3And (4) crystals.
As shown in fig. 1, the two-photon frequency and path super-entanglement generation method of the nonlinear photonic crystal is as follows: pump light (frequency of omega)PE light) is normally incident on the surface of the nonlinear photonic crystal along the positive z direction, and the pump light wave vector is perpendicular to the phase adaptation amount provided by the nonlinear photonic crystal along the x-axis direction
Figure BDA0002458702960000071
And
Figure BDA0002458702960000072
generate signal light (with frequency of omega) after interactionSO light) and idle light (frequency ωIO light), the signal light and the idle light satisfy a frequency and path super-entanglement relationship.
In the embodiment of the invention, the wavelength of the pumping light is 775 nm.
As shown in fig. 2, the nonlinear photonic crystal employs four quasi-phase matching to generate four spontaneous parametric down-conversion processes; wherein the content of the first and second substances,
the four quasi-phase matching conditions are respectively as follows:
(1)
Figure BDA0002458702960000073
(2)
Figure BDA0002458702960000074
(3)
Figure BDA0002458702960000075
(4)
Figure BDA0002458702960000076
in the formula
Figure BDA0002458702960000077
Is a frequency of omegaPThe wave vector of the pump light of (1),
Figure BDA0002458702960000078
at an angle theta1The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure BDA0002458702960000079
at an angle theta1The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure BDA00024587029600000710
at an angle theta1The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure BDA00024587029600000711
at an angle theta1The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure BDA00024587029600000712
at an angle theta2The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure BDA00024587029600000713
at an angle theta2The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure BDA00024587029600000714
at an angle theta2The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure BDA00024587029600000715
at an angle theta2The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure BDA00024587029600000716
and
Figure BDA00024587029600000717
for the amount of phase adaptation in the x-axis direction,
Figure BDA00024587029600000718
for the amount of phase adaptation in the z-axis direction, the modulus Δ kz＝0.04μm-1。θ1＝0.1741rad，θ2＝0.1982rad。
The conversion process under four matched spontaneous parameters is as follows: one frequency of omegaPThe pumping light photons are converted into a frequency omega by the nonlinear photonic crystalSAnd a signal light photon of frequency omegaIThe process satisfies the energy conservation omegaP＝ωS+ωI。
The nonlinear photonic crystal can simultaneously match the four spontaneous parameter down-conversion processes. The non-linear process occurs as long as the periodic polarization of the crystal can compensate for the momentum mismatch in the x-direction, while the mismatch in the z-direction only affects its conversion efficiency. In the case of fig. 2, all four processes have momentum mismatch in the z-direction, and therefore, the efficiency of the non-linear process will be lower than otherwise. In the present embodiment, ensuring that the mismatch along the z-axis has the same magnitude but only opposite direction, the efficiency of the conversion process will be the same for the four spontaneous parameters, which means maximum super-entanglement.
In the present embodiment, the preferred wavelength of the signal light is 1700nm, and the frequency of the idle light is about 1424.3 nm. Accordingly, Δ kx1＝0.2801μm-1，Δkx2＝0.3185μm-1Wherein, Δ kx1Shows the amount of phase adaptation in the x-axis direction in FIG. 2
Figure BDA0002458702960000081
A modulus value of (d); Δ kx2Shows the amount of phase adaptation in the x-axis direction in FIG. 2
Figure BDA0002458702960000082
The modulus value of (a).
As shown in FIG. 3, the quasi-periodic lattice structure of the nonlinear photonic crystal hasThe body is as follows: according to the coordinate system defined in fig. 1, the nonlinear photonic crystal preferably has a length in the x direction of 3.947cm, a width in the y direction of 1cm, and a thickness L in the z direction satisfying L ═ m pi/Δ kzWhere m is a non-negative integer,. DELTA.kzFor the modulus of the phase adaptation quantity in the z-axis direction, preferably Δ kz＝0.04μm-1. Second-order nonlinear polarization coefficient chi of nonlinear photonic crystal(2)The second order nonlinear polarization coefficients χ were achieved by inverting along the x-axis direction specified in FIG. 1 at the specific positions listed in Table 1(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)The-1 domains alternate with a designed law.
As shown in fig. 4, which is a spatial fourier transform spectrogram of a quasiperiodic lattice, it can be seen that the fourier coefficients of the two dominant frequencies of the quasiperiodic lattice are very close, preferably 0.398 and 0.3979, respectively.
The frequency and path super-entangled quantum state | ψ > of the nonlinear photonic crystal thus obtained is expressed as:
Figure BDA0002458702960000083
in the formula, subscript S represents signal light, that is, the photon transmission path is above the pump light plane, and subscript I represents idle light, that is, the photon transmission path is below the pump light plane; theta1,SIndicating signal light at an angle theta1In the case of emission, θ1,IIndicating idle light at an angle theta1In the case of emission, θ2,SIndicating signal light at an angle theta2In the case of emission, θ2,IIndicating signal light at an angle theta2In the case of emission, ω1,SIndicating the frequency of the signal light as omega1Condition of (a), ω2,IIndicating an idle light frequency of omega2Condition of (a), ω2,SIndicating the frequency of the signal light as omega2Condition of (a), ω1,IIndicating an idle light frequency of omega1The case (1).
Table 1 shows the inversion rule of the second-order nonlinear polarization coefficient of the nonlinear photonic crystal generating the two-photon frequency and path super-entanglement according to an embodiment of the present invention.
Figure BDA0002458702960000091
Figure BDA0002458702960000101
Figure BDA0002458702960000111
Figure BDA0002458702960000121
Figure BDA0002458702960000131
Figure BDA0002458702960000141
Figure BDA0002458702960000151
Figure BDA0002458702960000161
Figure BDA0002458702960000171
Figure BDA0002458702960000181
The above embodiments of the present invention provide a nonlinear photonic crystal and two-photon frequency thereofAnd a path super-entanglement generation method, wherein the nonlinear photonic crystal adopts 5% MgO-doped LiNbO under the conditions of room temperature and I-type phase matching (e → o + o)3And (4) crystals. In the two-photon frequency and path super-entanglement generation method, the wavelength of the pumping light is 775 nm. Pump light (frequency of omega)PE light) is normally incident to the surface of the nonlinear photonic crystal along the positive z direction, and signal light (with frequency of omega) is generated after interactionSO light) and idle light (frequency ωIO light), the signal light and the idle light satisfy a frequency and path super-entanglement relationship.
By simulating the nonlinear photonic crystal and the two-photon frequency and path super-entanglement generation method thereof provided by the embodiment of the invention, the technical scheme provided by the embodiment of the invention can be verified to generate the maximum entangled state, effectively inhibit other parameter processes and generate the super-entangled state with higher quality.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.

Claims (8)

1. The nonlinear photonic crystal capable of directly generating double-photon frequency and path super-entanglement is characterized in that the nonlinear photonic crystal adopts MgO-doped LiNbO under the conditions of room temperature and I-type phase matching3A crystal;
the quasi-periodic lattice structure of the nonlinear photonic crystal is as follows: in a set coordinate system, the thickness L of the nonlinear photonic crystal in the z direction satisfies L ═ m pi/delta kzWhere m is a non-negative integer,. DELTA.kzA modulus value of a phase fitting amount in a z-axis direction; second-order nonlinear polarization coefficient chi of nonlinear photonic crystal(2)Along the direction of the x axis and is inverted at a specific position of the x axis to realize a second-order nonlinear polarization coefficient chi(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)The crystal domains of-1 alternate with a designed law;
the quantum state | ψ > of the frequency and path super-entanglement relationship is expressed as:
Figure FDA0002998557500000011
in the formula, subscript S represents signal light, that is, the photon transmission path is above the pump light plane, and subscript I represents idle light, that is, the photon transmission path is below the pump light plane; theta1,SIndicating signal light at an angle theta1In the case of emission, θ1,IIndicating idle light at an angle theta1In the case of emission, θ2,SIndicating signal light at an angle theta2In the case of emission, θ2,IIndicating signal light at an angle theta2In the case of emission, ω1,SIndicating the frequency of the signal light as omega1Condition of (a), ω2,IIndicating an idle light frequency of omega2Condition of (a), ω2,SIndicating the frequency of the signal light as omega2Condition of (a), ω1,IIndicating an idle light frequency of omega1The case (1).
2. The nonlinear photonic crystal of claim 1, wherein the room temperature is 20-25 ℃.
3. The nonlinear photonic crystal according to claim 1, wherein the type i phase matching condition has a polarization property of e → o + o, i.e. one e optical photon is converted into two o optical photons.
4. The nonlinear photonic crystal according to claim 1, wherein the amount of MgO doped is 5%.
5. A two-photon frequency and path super-entanglement generation method of the nonlinear photonic crystal according to any one of claims 1 to 4, comprising:
the pumping light is normally incident to the surface of the nonlinear photonic crystal along the positive z direction, and the pumping light wave vector
Figure FDA0002998557500000012
And a unit vector parallel to the y-axis constitute a pump light plane,
Figure FDA0002998557500000013
amount of phase adaptation in the x-axis direction provided perpendicular to a nonlinear photonic crystal
Figure FDA0002998557500000014
And
Figure FDA0002998557500000015
and generating signal light and idle light after interaction, wherein the signal light and the idle light meet the frequency and path super-entanglement relationship.
6. The method for generating two-photon frequency and path super-entanglement of a nonlinear photonic crystal as claimed in claim 5, wherein the nonlinear photonic crystal satisfies a plurality of quasi-phase matching conditions, enabling a plurality of matched spontaneous parametric down-conversion processes to occur simultaneously.
7. The method for generating two-photon frequency and path super-entanglement of a nonlinear photonic crystal according to claim 6, wherein the quasi-phase matching conditions are four, respectively:
(1)
Figure FDA0002998557500000021
(2)
Figure FDA0002998557500000022
(3)
Figure FDA0002998557500000023
(4)
Figure FDA0002998557500000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002998557500000025
is a frequency of omegaPThe wave vector of the pump light of (1),
Figure FDA0002998557500000026
at an angle theta1The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure FDA0002998557500000027
at an angle theta1The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure FDA0002998557500000028
at an angle theta1The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure FDA0002998557500000029
at an angle theta1The frequency of the emergent light is omega1The wave vector of the idle light of (1),
Figure FDA00029985575000000210
at an angle theta2The frequency of the emergent light is omega1The wave vector of the signal light of (1),
Figure FDA00029985575000000211
at an angle theta2The frequency of the emergent light is omega2The wave vector of the idle light of (1),
Figure FDA00029985575000000212
at an angle theta2The frequency of the emergent light is omega2The wave vector of the signal light of (1),
Figure FDA00029985575000000213
at an angle theta2EmittingFrequency of omega1The wave vector of the idle light of (1),
Figure FDA00029985575000000214
and
Figure FDA00029985575000000215
for the amount of phase adaptation in the x-axis direction,
Figure FDA00029985575000000216
is the phase adaptation amount in the z-axis direction;
accordingly, the four matched spontaneous parameter down-conversion processes are: one frequency of omegaPThe pumping light photons are converted into a frequency omega by the nonlinear photonic crystalSAnd a signal light photon of frequency omegaISaid conversion process satisfies the energy conservation ωP＝ωS+ωI。
8. The method as claimed in claim 7, wherein the z-axis phase-adaptive quantities of the four matched spontaneous parameter down-conversion processes have the same mode values and opposite directions, so that the four spontaneous parameter down-conversion processes have the same efficiency, thereby generating the maximum degree of super-entanglement.
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