CN111562708A - Nonlinear photonic crystal and two-photon frequency and discrete path super-entanglement generation method - Google Patents
Nonlinear photonic crystal and two-photon frequency and discrete path super-entanglement generation method Download PDFInfo
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- 239000004038 photonic crystal Substances 0.000 title claims abstract description 75
- 238000000034 method Methods 0.000 title claims abstract description 67
- 230000008569 process Effects 0.000 claims abstract description 40
- 239000013078 crystal Substances 0.000 claims abstract description 28
- 239000013598 vector Substances 0.000 claims description 44
- 238000006243 chemical reaction Methods 0.000 claims description 30
- 230000002269 spontaneous effect Effects 0.000 claims description 23
- 238000005086 pumping Methods 0.000 claims description 21
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- CPLXHLVBOLITMK-UHFFFAOYSA-N magnesium oxide Inorganic materials [Mg]=O CPLXHLVBOLITMK-UHFFFAOYSA-N 0.000 abstract description 7
- 239000000395 magnesium oxide Substances 0.000 abstract description 7
- AXZKOIWUVFPNLO-UHFFFAOYSA-N magnesium;oxygen(2-) Chemical compound [O-2].[Mg+2] AXZKOIWUVFPNLO-UHFFFAOYSA-N 0.000 abstract description 7
- GQYHUHYESMUTHG-UHFFFAOYSA-N lithium niobate Chemical compound [Li+].[O-][Nb](=O)=O GQYHUHYESMUTHG-UHFFFAOYSA-N 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 4
- 239000002245 particle Substances 0.000 description 4
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- 239000002096 quantum dot Substances 0.000 description 2
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- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000007429 general method Methods 0.000 description 1
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Abstract
The invention provides a super-entanglement generation method of two-photon frequency and multiple pairs of discrete paths based on a nonlinear photonic crystal. The nonlinear photonic crystal selects 5% magnesium oxide (MgO) doped lithium niobate (LiNbO) with a two-dimensional structure under the conditions of room temperature and I-type phase matching (e → o + o)3) And (4) crystals. The nonlinear photonic crystal and the method for generating the super-entanglement of the two-photon frequency and the multiple pairs of discrete paths thereof provided by the invention are simulated, and the invention is verified that the nonlinear photonic crystal can generate the maximum entangled state, other parameter processes are effectively inhibited, and the super-entangled state with higher quality is generated.
Description
Technical Field
The invention relates to a nonlinear photonic crystal design technology in the technical field of quantum entanglement generation, in particular to a two-dimensional nonlinear photonic crystal and a two-photon frequency and multi-pair discrete path super-entanglement generation method thereof, which are a two-dimensional nonlinear photonic crystal and a design scheme for directly generating two-photon frequency and multi-pair discrete path super-entanglement thereof.
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 necessarily requiresSatisfy the condition of energy conservation (omega)P＝ωS+ωI) It is not necessary to satisfy the conservation of momentum condition
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. At present, the optical spontaneous parametric down-conversion process is a main method for preparing a photon entanglement source, mainly because the process is stable, the intensity of a generated optical signal is high, and the generated photon pair has 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
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 a two-photon frequency and multi-pair discrete path super-entanglement source by utilizing a two-dimensional nonlinear photonic crystal.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a two-dimensional nonlinear photonic crystal and a two-photon frequency and multi-pair discrete 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 multi-pair discrete path super-entanglement is provided, and the nonlinear photonic crystal selects LiNbO with MgO doping under the conditions of two-dimensional structure, room temperature and I-type phase matching3And (4) crystals.
Preferably, the room temperature refers to the working temperature of the nonlinear photonic crystal design and 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: second-order nonlinear polarization coefficient chi of nonlinear photonic crystal in set coordinate system(2)Reversing at a specific position in the xoy plane to realize second-order nonlinear polarization coefficient chi(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)A domain of-1 appears with a set law in both x and y dimensions.
According to another aspect of the present invention, there is provided a two-photon frequency and discrete 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
And a unit vector parallel to the y-axis constituting a pumping light plane, pumping light wave vector
Amount of phase mismatch in xoy plane perpendicular to nonlinear photonic crystal compensation
Generating signal light and idle light after interaction, wherein the signal light and the idle light are respectively positioned above and below a pumping light plane; signal light and idle lightN pairs of discrete paths are selectable, where n is a positive integer greater than or equal to 2, with respect to
The straight lines are symmetrically distributed; the signal light and the idle light meet the frequency and multi-pair discrete path super-entanglement relation.
Preferably, the frequency and the quantum state | ψ > of the multi-pair discrete path super-entanglement relationship are expressed as:
in the formula, n is a positive integer greater than or equal to 2, subscript S represents signal light, namely, the photon 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; in the spatial distribution cross section of the signal light and the idle light, (theta)j)SThe connecting line of the signal light position and the pump light position forms an angle theta with the y-axisj(θ)j+π)IThe line connecting the idle light position and the pump light position forms an angle theta with the y-axisjCase of + π, 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 condition is n pairs, and n is a positive integer greater than or equal to 2; wherein, the quasi-phase matching condition of the path j and the path n + j point-symmetric by O' is recorded as the jth aligned phase matching condition, and respectively:
(1)
(2)
in the formula,
is a frequency of omegaPThe wave vector of the pump light is on the space distribution cross section of the signal light and the idle light,
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega1The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega2The wave vector of the idle light of (1),
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega2The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega1The wave vector of the idle light of (1),
is a radial vector
A phase mismatch amount in a direction;
accordingly, all 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。
Preferably, the z-axis phase mismatch amount in the matched spontaneous parameter down-conversion process is zero, so that the efficiency of the conversion process under all the spontaneous parameters is the same, 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 method for generating the super-entanglement of the two-photon frequency and the multiple pairs of discrete paths, provided by the invention, are designed to be capable of simultaneously matching n pairs (n is a positive integer greater than or equal to 2) of spontaneous parameters in a down-conversion process at room temperature (20-25 ℃), so that the super-entangled photon pairs of the frequency and the multiple pairs of discrete paths can be directly generated when only one beam of pump light is injected without a heating furnace.
2. The nonlinear photonic crystal and the method for generating the super-entanglement of the two-photon frequency and the multiple pairs of discrete paths can independently design the quasiperiodic lattice structure of the two-dimensional nonlinear photonic crystal, so that the quasiperiodic lattice structure can simultaneously meet the down-conversion process of multiple spontaneous parameters, and the method has stronger flexibility, which is needed for designing a quantum super-entanglement source.
3. The nonlinear photonic crystal, the two-photon frequency and multi-pair discrete path super-entanglement generation method provided by the invention are simulated, and the design scheme can be verified to generate the maximum entanglement state and effectively inhibit other parameter processes, so that the super-entanglement state with higher quality can be generated.
4. The nonlinear photonic crystal and the two-photon frequency and multi-pair discrete path super-entanglement generation method provided by the invention combine multiple disciplines such as quantum optics, nonlinear optics, crystal optics and the like, and solve the design problem of the two-dimensional nonlinear photonic crystal in the super-entanglement process of preparing the two-photon frequency and multi-pair discrete paths.
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 multiple pairs of discrete path based super-entanglement source design for a two-dimensional nonlinear photonic crystal in a preferred embodiment of the present invention.
FIG. 2 is a diagram illustrating quasi-phase matching conditions satisfied by a super-entangled two-dimensional nonlinear photonic crystal capable of generating two-photon frequencies and multiple pairs of discrete paths according to a preferred embodiment of the present invention.
FIG. 3 is a schematic diagram of the design of the quasiperiodic lattice structure of a super-entangled two-dimensional nonlinear photonic crystal that can produce two-photon frequencies and three pairs of discrete paths according to a preferred embodiment of the present invention.
FIG. 4 is a graph of the spatial Fourier transform spectrum of a quasiperiodic lattice of a super-entangled two-dimensional nonlinear photonic crystal producing two-photon frequencies and three pairs of discrete paths in a preferred 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.
An embodiment of the present invention provides a super-entangled nonlinear photonic crystal capable of directly generating two-photon frequencies and multiple pairs of discrete paths, wherein the nonlinear photonic crystal is MgO-doped LiNbO with a two-dimensional structure under room temperature and I-type phase matching conditions3And (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,the method specifically comprises the following steps: second-order nonlinear polarization coefficient chi of nonlinear photonic crystal according to coordinate system defined in figure 1(2)Reversing at a specific position in the xoy plane to realize second-order nonlinear polarization coefficient chi(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)The-1 domain appears with a defined patterning law in both x and y dimensions.
Further, the pattern was set as shown in fig. 3, the dimensions in the x and y directions of the crystal were 5mm, the dimension in the z direction was not particularly limited, and a partial enlarged view of the quasi-periodic lattice of the crystal was shown in a dotted frame.
Further, in this partial enlarged view, the crystal is in a portion χ of a dark (gray) circle having a radius R of 56.67 μm(2)X +1 in the rest(2)-1; points A, B and C are circle centers and have the coordinates: a (233.17,250.70), B (374.86,322.50) and C (233.17,87.10) μm; tiling vector for expressing law of crystal pattern
Given the coordinates of any center of a circle (e.g., point A) in the graph, the radius R of the circle, and the tiling vector
And
the quasiperiodic lattice structure of a two-dimensional nonlinear photonic crystal can be uniquely determined.
In another embodiment of the present invention, a two-photon frequency and multi-pair discrete path super-entanglement generation method based on the nonlinear photonic crystal provided in the previous embodiment is provided, including:
as shown in fig. 1, the super-entanglement generation method of two-photon frequency and multiple pairs of discrete paths 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, pumping light wave vector
And a unit vector parallel to the y-axis constituting a pumping light plane, pumping light wave vector
Amount of phase mismatch in xoy plane perpendicular to nonlinear photonic crystal compensation
Generate signal light (with frequency of omega) after interactionSO light) and idle light (frequency ωIO light). The signal light and the idle light are provided with n pairs of discrete paths (n is a positive integer greater than or equal to 2) in total, and the discrete paths are selectable
The straight lines are symmetrically distributed. The signal light and the idle light satisfy a frequency and path super-entanglement relationship.
As a preferred embodiment, the pump light wavelength is preferably 775 nm.
In a preferred embodiment, the signal light wavelength is preferably 1530nm, and the idle light wavelength is preferably 1570.5 nm; accordingly, the number of the first and second electrodes,
representing the signal light (or idler light) wave vector of FIG. 1
(or
) And pumping light wave vector
The angle of,
shows the radial vectors in FIG. 2
Amount of phase mismatch in direction
The modulus value of (a).
As a preferred embodiment, as shown in fig. 2, the nonlinear photonic crystal adopts n pairs (n is a positive integer greater than or equal to 2) of quasi-phase matching to generate n pairs of spontaneous parametric down-conversion processes; wherein,
taking the jth pair (path j and path n + j point-symmetric with O') as an example, the quasi-phase matching conditions are respectively:
(1)
(2)
in the formula,
is a frequency of omegaPThe wave vector of the pump light is on the space distribution cross section of the signal light and the idle light,
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega1The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega2The wave vector of the idle light of (1),
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega2The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega1The wave vector of the idle light of (1),
is a radial vector
A phase mismatch amount in a direction;
accordingly, all 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。
As a preferred embodiment of the method according to the invention,
shows the radial vectors in FIG. 2
Amount of phase mismatch in direction
The modulus value of (a).
The two-dimensional nonlinear photonic crystal can simultaneously match the n pairs of spontaneous parametric 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 xoy plane, while the mismatch in the z-direction only affects its conversion efficiency. In the case of fig. 2, all processes satisfy momentum matching in the z-direction, and therefore the efficiency of the non-linear process will be highest and the same, which means that this is the most super-entanglement.
As a preferred embodiment, the frequency and quantum state | ψ > of a multi-pair discrete path super-entanglement relationship is expressed as:
in the formula, n is a positive integer greater than or equal to 2, subscript S represents signal light, namely, the photon 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; in the spatial distribution cross section of the signal light and the idle light, (theta)j)SThe connecting line of the signal light position and the pump light position forms an angle theta with the y-axisj(θ)j+π)IThe line connecting the idle light position and the pump light position forms an angle theta with the y-axisjCase of + π, 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).
The technical solution provided by the above embodiment of the present invention is further described in detail with reference to the drawings and three pairs of discrete paths as specific application examples.
In the specific application example, the nonlinear photonic crystal capable of directly generating the super-entanglement of the two-photon frequency and the three pairs of discrete paths selects the 5 percent MgO-doped LiNbO with a two-dimensional structure under the conditions of room temperature (preferably 25 ℃) and I-type phase matching (e → o + o)3And (4) crystals.
Based on the nonlinear photonic crystal, the method for generating super-entanglement of two-photon frequency and three pairs of discrete paths of the nonlinear photonic crystal provided by the specific application example comprises the following steps:
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
And is parallel to the y-axisThe unit vectors of the rows constitute the pump light plane,
amount of phase mismatch in xoy plane perpendicular to nonlinear photonic crystal compensation
And generating signal light and idle light after interaction, wherein the signal light and the idle light are respectively positioned above and below the plane of the pump light. The signal light and the idle light have three pairs of discrete paths for selection,
the six discrete paths relate to
The straight lines are uniformly and symmetrically distributed. The signal light and the idle light meet the frequency and three pairs of discrete path super-entanglement relations.
Further, the quantum state | ψ > of the frequency and three pairs of discrete path super-entanglement relationships is expressed as:
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; in the spatial distribution cross section of the signal light and the idle light, let j equal 1,2,3, (θ)j)SThe connecting line of the signal light position and the pump light position forms an angle theta with the y-axisj(θ)j+π)IThe line connecting the idle light position and the pump light position forms an angle theta with the y-axisjCase of + π, 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).
Further, θj＝(j-1)*π/3，θn+j＝θj+ pi, where j ═1,2,3. So that path 1 to path 6 relate to
The straight lines are uniformly and symmetrically distributed.
Further, three pairs (paths 1 and 4, paths 2 and 5, and paths 3 and 6, which are point symmetric with O') of quasi-phase matching conditions are:
(1)
(2)
(1)
(2)
(1)
(2)
in the formula,
is a frequency of omegaPWave vector of the pump light. On the spatial distribution cross section of the signal light and the idle light, let n be 3, j be 1,2,3,
is the line connecting the position of the path j and the position of the pump light and yAxis angle thetajOf frequency omega1The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega2The wave vector of the idle light of (1),
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega2The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega1The wave vector of the idle light of (1),
is a radial vector
A phase mismatch amount in a direction;
modulus of
Accordingly, all 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。
Furthermore, the z-axis phase mismatch amount in the conversion process under the matched spontaneous parameters is zero, so that the conversion process under all the spontaneous parameters has the same efficiency, and the maximum degree of super-entanglement is generated.
As shown in fig. 3, the quasi-periodic lattice structure of the super-entangled two-dimensional nonlinear photonic crystal capable of generating two-photon frequencies and three pairs of discrete paths is specifically: the dimensions of the crystal in the x and y directions are 5mm according to the coordinate system defined in fig. 1, the dimensions in the z direction are not particularly limited, and a partial enlargement of the quasiperiodic lattice of the crystal is shown in the dashed box. In this partial magnification, the crystal has a second order nonlinear polarization coefficient χ in the portion of a dark (gray) circle having a radius R of 56.67 μm(2)X +1 in the rest(2)-1; points A, B and C are circle centers and have the coordinates: a (233.17,250.70), B (374.86,322.50) and C (233.17,87.10) μm; tiling vector for expressing law of crystal pattern
Given the coordinates of any center of a circle (e.g., point A) in the graph, the radius R of the circle, and the tiling vector
And
the quasiperiodic lattice structure of a two-dimensional nonlinear photonic crystal can be uniquely determined.
As shown in fig. 4, it is a spatial fourier transform spectrum diagram of a quasiperiodic lattice of a super-entangled two-dimensional nonlinear photonic crystal that can generate two-photon frequencies and three pairs of discrete paths, and it can be seen that the spatial fourier transform spectrum of the quasiperiodic lattice is relatively pure, and the fourier coefficients of the dominant frequencies are consistent. Therefore, the frequency bandwidth of the signal light and the idle light generated by the nonlinear photonic crystal designed in the way is narrow, other parameter processes are effectively inhibited, and the maximum entangled state can be realized.
The above embodiments of the present invention provide a two-photon frequency sum capable of being directly generatedThe nonlinear photonic crystal adopts 5% magnesium oxide (MgO) doped lithium niobate (LiNbO) with a two-dimensional structure under the conditions of room temperature and I-type phase matching (e → o + o)3) And (4) crystals. According to the method for generating the super-entanglement of the two-photon frequency and the multiple pairs of discrete paths based on the nonlinear photonic crystal, the pumping 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 super-entanglement relation of the frequency and the multiple pairs of discrete paths. The nonlinear photonic crystal, the two-photon frequency and multi-pair discrete path super-entanglement generation method thereof are simulated, and the verification proves that the embodiment of the invention can 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 (10)
1. The nonlinear photonic crystal capable of directly generating double-photon frequency and multi-pair discrete path super-entanglement is characterized in that the nonlinear photonic crystal adopts MgO-doped LiNbO with a two-dimensional structure under the conditions of room temperature and I-type phase matching3And (4) crystals.
2. The nonlinear photonic crystal of claim 1, wherein the room temperature is 20-25 ℃ which is the working temperature of the nonlinear photonic crystal design.
3. The nonlinear photonic crystal of claim 1, wherein 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.
4. The nonlinear photonic crystal according to claim 1, wherein the amount of MgO doped is 5%.
5. The nonlinear photonic crystal of claim 1, wherein the quasi-periodic lattice structure of the nonlinear photonic crystal is: second-order nonlinear polarization coefficient chi of nonlinear photonic crystal in set coordinate system(2)Reversing at a specific position in the xoy plane to realize second-order nonlinear polarization coefficient chi(2)Crystal domain of +1 and second-order nonlinear polarization coefficient χ(2)The-1 domain appears with a defined patterning law in both x and y dimensions.
6. A two-photon frequency and discrete path super-entanglement generation method of the nonlinear photonic crystal according to any one of claims 1 to 5, 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
And a unit vector parallel to the y-axis constituting a pumping light plane, pumping light wave vector
Amount of phase mismatch in xoy plane perpendicular to nonlinear photonic crystal compensation
Generating signal light and idle light after interaction, wherein the signal light and the idle light are respectively positioned above and below a pumping light plane; the signal light and the idle light have n pairs of discrete paths which are selectable, wherein n is a positive integer greater than or equal to 2, and the discrete paths are related to
The straight lines are symmetrically distributed; the signal light and the idle light meet the frequency and multi-pair discrete path super-entanglement relation.
7. A two-photon frequency and discrete path super-entanglement generation method according to claim 6, wherein the quantum state | ψ > of the frequency and multiple pairs of discrete path super-entanglement relationships is expressed as:
in the formula, n is a positive integer greater than or equal to 2, subscript S represents signal light, namely, the photon 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; in the spatial distribution cross section of the signal light and the idle light, (theta)j)SThe connecting line of the signal light position and the pump light position forms an angle theta with the y-axisj(θ)j+π)IThe line connecting the idle light position and the pump light position forms an angle theta with the y-axisjCase of + π, 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).
8. The two-photon frequency and discrete path super-entanglement generation method of claim 6, 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.
9. A two-photon frequency and discrete path super-entanglement generation method according to claim 8, wherein said quasi-phase matching condition is n pairs, n being a positive integer equal to or greater than 2; wherein, the quasi-phase matching condition of the path j and the path n + j point-symmetric by O' is recorded as the jth aligned phase matching condition, and respectively:
(1)
(2)
in the formula,
is a frequency of omegaPThe wave vector of the pump light is on the space distribution cross section of the signal light and the idle light,
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega1The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega2The wave vector of the idle light of (1),
is an angle theta between the line connecting the path j and the position of the pump light and the y-axisjOf frequency omega2The wave vector of the signal light of (1),
the angle theta between the connection line of the path n + j and the position of the pump light and the y-axisj+ pi, frequency omega1The wave vector of the idle light of (1),
is a radial vector
A phase mismatch amount in a direction;
accordingly, all matched spontaneous parameter down-conversion processes are: one frequency of omegaPThe pumping light photon is converted into one by the nonlinear photonic crystalFrequency of omegaSAnd a signal light photon of frequency omegaISaid conversion process satisfies the energy conservation ωP＝ωS+ωI。
10. A two-photon frequency and discrete path super-entanglement generation method according to claim 9, wherein the z-axis phase mismatch amount in the matched spontaneous parameter down-conversion process is zero, so that the efficiency of the down-conversion process is the same for all spontaneous parameters, thereby generating the maximum degree of super-entanglement.
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