Time-domain modulation based single-photon switch implementation method and system, and storage medium

Abstract

The application discloses a single-photon switch implementation method and system based on time-domain modulation, and a storage medium, and the method comprises the steps of: establishing a waveguide QED system model of an atom-cavity-waveguide; constructing a dynamic expression of an atomic frequency; calculating a related Hamiltonian of the waveguide QED system; calculating a differential equation set of photon motion; calculating photon transmittance and reflectance by using the differential equation set of photon motion; and realizing a dynamic single-photon switch according to a dynamic change relationship between the atomic frequency and the photon transmittance. The application solves the problems of limited controllability and low switching efficiency of the single-photon switch in the related art.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication technology, and in particular relates to a method, system and storage medium for implementing single-photon switches based on time-domain modulation. Background Technology

[0002] Waveguide-based quantum optical emission (QED) systems have become one of the main models for studying single-photon scattering. Extensive research into the transmission and reflection of single photons in waveguide-based QED systems has led to the rapid development of related quantum optical devices, such as photonic switches, quantum routers, and quantum frequency combs.

[0003] Current single-photon switch implementation schemes have two shortcomings: (1) The efficiency of a single-photon switch is related to physical parameters such as the atom-cavity and cavity-waveguide coupling strength. However, in solid-state physical systems, these parameters are all related to their relative positions. Once the sample is prepared, their relative positions are also determined, which limits the controllability of the switch. (2) Current switching schemes are often only applicable to certain selected frequencies. Once the input photon frequency changes, the switching efficiency of the photon will decrease rapidly or even disappear, which will greatly limit its application in quantum information processing processes such as quantum communication networks.

[0004] To realize a wide-range single-photon switch and improve the controllability and switching efficiency of the photon switch, a method, system and storage medium for realizing a single-photon switch based on time-domain modulation are proposed. Summary of the Invention

[0005] This invention proposes a method, system, and storage medium for implementing a single-photon switch based on time-domain modulation, in order to at least solve the problems of limited controllability and low switching efficiency of single-photon switches in related technologies.

[0006] According to an embodiment of the present invention, a method for implementing a single-photon switch based on time-domain modulation is proposed, comprising:

[0007] Establish a waveguide QED system model of atom-cavity-waveguide;

[0008] Construct dynamic expressions for atomic frequencies;

[0009] Calculate the relevant Hamiltonian of the waveguide QED system;

[0010] Calculate the system of differential equations for the motion of photons;

[0011] The transmittance and reflectance of photons are calculated using a set of differential equations governing the motion of photons.

[0012] Dynamic single-photon switching is achieved based on the dynamic relationship between atomic frequency and photon transmittance.

[0013] In an exemplary embodiment, the waveguide QED system model consists of a one-dimensional waveguide, a single-mode optical cavity, and two-level atoms; the two-level atoms are placed in the single-mode optical cavity and interact with each other, and the one-dimensional waveguide is coupled to the atom-cavity system through the single-mode optical cavity side.

[0014] In one exemplary embodiment, the dynamic expression for constructing the atomic frequency is a cosine wave expression ω for the atomic frequency as a function of time. a =w0+ηcosvt, where w0 represents the fixed part of the atomic frequency, η represents the amplitude of the part of the atomic frequency that varies, and v represents the frequency of the part of the atomic frequency that varies.

[0015] In one exemplary embodiment, calculating the relevant Hamiltonian of the waveguide QED system includes the following steps:

[0016] The free Hamiltonian of an atom is calculated based on its atomic frequency and its dissipation rate.

[0017] The free Hamiltonian of the optical cavity is calculated based on the cavity's frequency and dissipation rate.

[0018] The Hamiltonian of the interaction between the atom and the cavity is calculated based on the Bessel function of the amplitude and frequency of the part of the atomic frequency variation.

[0019] The free Hamiltonian of waveguide photons is calculated based on the group velocity of photons propagating within the waveguide.

[0020] The Hamiltonian of the waveguide-cavity interaction is calculated based on the coupling strength between the waveguide and the cavity.

[0021] In one exemplary embodiment, the calculation of the set of differential equations for photon motion includes the steps of:

[0022] Calculate the eigenstates of the system in a single excitation subcavity-waveguide space;

[0023] The Schrödinger equation is constructed based on the relevant Hamiltonian, photon frequency, and eigenstate of the waveguide QED system.

[0024] The system of differential equations for the motion of photons is obtained by solving the conventional Schrödinger equation.

[0025] In one exemplary embodiment, calculating the transmittance and reflectance of photons using a set of differential equations governing photon motion includes the following steps:

[0026] A single photon is incident from one side of the waveguide with a wave vector, and the amplitude probability expression of the photon is obtained;

[0027] When a photon reaches the coupling point between the cavity and the waveguide, the incident photon is either reflected or transmitted. The transmittance and reflectance of the photon are calculated based on the differential equations of the photon's motion and the amplitude probability expression of the photon.

[0028] In an exemplary embodiment, the step of realizing a dynamic single-photon switch based on the dynamic relationship between atomic frequency and photon transmittance includes the following steps:

[0029] The relationship between atomic frequency and photon transmittance was calculated based on the relationship between atomic frequency and photon transmittance.

[0030] Dynamic single-photon switching is achieved by modulating the atomic frequency to switch the transmittance of waveguide photons of different frequencies between 0 and 1.

[0031] In an exemplary embodiment, the step of calculating the relationship between atomic frequency and photon transmittance based on the relationship between atomic frequency and photon transmittance includes the following steps:

[0032] The correlation between the amplitude-frequency ratio of the atomic frequency variation portion and the group velocity of photons propagating in the waveguide was obtained by dynamic modulation.

[0033] Substitute the relevant relationships into the expression for photon transmittance and reflectance to solve for photon transmittance;

[0034] The relationship between atomic frequency and photon transmittance is calculated based on the photon transmittance corresponding to different atomic amplitude frequency ratios.

[0035] A computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform the methods described above.

[0036] According to another embodiment of the present invention, a single-photon switch implementation system based on time-domain modulation is provided, comprising:

[0037] Waveguide QED system;

[0038] processor;

[0039] Memory;

[0040] as well as

[0041] One or more programs, wherein the one or more programs are stored in memory and configured to be executed by the processor, the programs causing the computer to perform the methods described above.

[0042] The advantages of the time-domain modulation-based single-photon switch implementation method, system, and storage medium of the present invention are:

[0043] (1) Construct a dynamic expression for the atomic frequency and use the relevant Hamiltonian and Schrödinger equation of the waveguide QED system to solve the expression for the transmittance and reflectance of the photon. Compared with the traditional single-photon switching implementation method, it can accurately analyze the single-photon dynamic characteristics of the time-domain modulated waveguide QED system.

[0044] (2) Calculate the expressions for single-photon transmittance and reflectance including influencing factors. Compared with the traditional single-photon switch technology, it can effectively analyze the influence of atomic frequency time-domain modulation on single-photon transmittance and reflectance.

[0045] (3) Adjusting the amplitude and frequency ratio of the atomic frequency in the cavity can switch the transmittance and reflectance of waveguide photons of different frequencies between 0 and 1. Compared with the traditional single-photon switch implementation method, it can effectively realize a wide-range dynamically adjustable photon switch, expanding the application of single-photon switches in quantum information. Attached Figure Description

[0046] Figure 1 This is a flowchart of a method for implementing a single-photon switch based on time-domain modulation according to an embodiment of the present invention;

[0047] Figure 2 This is a flowchart of sub-step S03 in an embodiment of the present invention;

[0048] Figure 3 This is a flowchart of sub-step S04 in an embodiment of the present invention;

[0049] Figure 4 This is a flowchart of step S05 in an embodiment of the present invention;

[0050] Figure 5 This is a flowchart of sub-step S06 in an embodiment of the present invention;

[0051] Figure 6 This is a flowchart of sub-step S061 in an embodiment of the present invention;

[0052] Figure 7 (a) is a transmittance curve of the input resonant photon under time-domain modulation according to an embodiment of the present invention;

[0053] Figure 7 (b) is a transmittance curve of input detuned photons under time-domain modulation according to an embodiment of the present invention;

[0054] Figure 8 This is a schematic diagram of a time-domain modulated single-photon switch according to an embodiment of the present invention;

[0055] Figure 9 This is a schematic diagram of a single-photon switch implementation system based on time-domain modulation according to an embodiment of the present invention. Detailed Implementation

[0056] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0057] A method for implementing a single-photon switch based on time-domain modulation according to an embodiment of the present invention is shown in the flowchart below. Figure 1 As shown, the steps include:

[0058] Step S01: Establish a waveguide QED system model of atom-cavity-waveguide;

[0059] Step S02: Construct the dynamic expression for atomic frequencies;

[0060] Step S03: Calculate the relevant Hamiltonian of the waveguide QED system;

[0061] Step S04: Calculate the system of differential equations for the motion of photons;

[0062] Step S05: Calculate the transmittance and reflectance of photons using the differential equations of photon motion;

[0063] Step S06: Implement dynamic single-photon switching based on the dynamic relationship between atomic frequency and photon transmittance.

[0064] In an exemplary embodiment, the waveguide QED system model consists of a one-dimensional waveguide, a single-mode optical cavity, and two-level atoms; the two-level atoms interact within the single-mode optical cavity, and the one-dimensional waveguide is coupled to the atom-cavity system via the single-mode optical cavity. In this embodiment, the frequency of the optical cavity is denoted as ω. c The coupling strength between the waveguide and the cavity is denoted as V, and the coupling strength between the atom and the cavity is denoted as g.

[0065] In one exemplary embodiment, the dynamic expression for constructing the atomic frequency is a cosine wave expression ω for the atomic frequency as a function of time. a =w0+ηcosvt, where w0 represents the fixed part of the atomic frequency, η represents the amplitude of the part of the atomic frequency that varies, and v represents the frequency of the part of the atomic frequency that varies.

[0066] In this embodiment, the single-mode optical cavity interacting with the two-level atoms is coupled to a one-dimensional waveguide. The atomic frequency changes over time, and its expression is as follows:

[0067] ω a =w0+ηcosvt (1)

[0068] The expression (1) includes a fixed atomic frequency part w0 and a variable atomic frequency part ηcosvt, where η is the amplitude of the variable part and v is the frequency of the variable part.

[0069] In an exemplary embodiment, step S03, calculating the relevant Hamiltonian of the waveguide QED system, is illustrated in the flowchart below. Figure 2 As shown, it includes:

[0070] Step S031: Calculate the free Hamiltonian of the atom based on the atomic frequency and the atom's dissipation rate.

[0071] Step S032: Calculate the free Hamiltonian of the optical cavity based on the frequency and dissipation rate of the optical cavity;

[0072] Step S033: Calculate the Hamiltonian of the interaction between the atom and the cavity based on the Bessel functions of the amplitude and frequency of the atomic frequency variation portion;

[0073] Step S034: Calculate the free Hamiltonian of the waveguide photon based on the group velocity of the photon propagating in the waveguide;

[0074] Step S035: Calculate the Hamiltonian of the waveguide-cavity interaction based on the coupling strength between the waveguide and the cavity.

[0075] In this embodiment, the frequency of the atoms in this system changes periodically. The relevant Hamiltonians of the waveguide QED system are calculated using real-space methods, and are as follows:

[0076] Calculate the free Hamiltonian of an atom based on its atomic frequency and dissipation rate.

[0077]

[0078] Among them, H a The free Hamiltonian of an atom is represented by w0, which is the fixed part of the atomic frequency, and γ. a / 2 represents the dissipation rate of the atom, σ ee =σ eg σ g , σ eg The ascending operator for atoms, σ ge The descent operator for atoms.

[0079] Calculate the free Hamiltonian of the optical cavity based on its frequency and dissipation rate:

[0080]

[0081] Among them, H c ω represents the free Hamiltonian of the optical cavity. c It is the frequency of the optical cavity, γ c / 2 represents the dissipation rate of the optical cavity. C represents the photon generation operator in the optical cavity, and C represents the photon annihilation operator in the optical cavity.

[0082] Calculate the Hamiltonian of the interaction between the atom and the cavity based on the Bessel functions of the amplitude and frequency of the atomic frequency variation portion:

[0083]

[0084] Among them, H ac The Hamiltonian represents the interaction between the atom and the cavity, g is the coupling strength between the cavity and the atom, f = η / v represents the ratio of the amplitude η to the frequency v of the atom's frequency variation, and J0(f) is the Bessel function related to the ratio f of the amplitude to the frequency of the atom's frequency variation.

[0085] Calculate the free Hamiltonian of waveguide photons based on the group velocity of photons propagating within the waveguide:

[0086]

[0087] Among them, H w The free Hamiltonian of the waveguide photon, v g It is the group velocity of photons propagating within the waveguide. C represents the production operator of a right-traveling light beam at position x. R (x) represents the annihilation operator of a right-traveling light beam at position x. C represents the production operator of a left-traveling beam of light at position x. L (x) represents the annihilation operator of a left-moving beam of light at position x.

[0088] Calculate the Hamiltonian of the waveguide-cavity interaction based on the coupling strength between the waveguide and the cavity:

[0089]

[0090] Among them, H wc The Hamiltonian represents the interaction between the waveguide and the cavity, V is the coupling strength between the waveguide and the cavity, and the function δ(x) represents the coupling between the cavity and the atom and the waveguide at x = 0.

[0091] In an exemplary embodiment, step S04, calculating the differential equations of photon motion, is illustrated in the flowchart below. Figure 3 As shown, it includes:

[0092] Step S041: Calculate the eigenstates of the system in the single excitation sub-cavity-waveguide space;

[0093] Step S042: Construct the Schrödinger equation based on the relevant Hamiltonian, photon frequency, and eigenstates of the waveguide QED system;

[0094] Step S043: Obtain the set of differential equations for the motion of photons by solving the conventional Schrödinger equation.

[0095] In this embodiment, the research object is a single photon. In the single exciter cavity-waveguide space, the excitation number of the system is conserved, and the eigenstate of the system is represented as:

[0096]

[0097] The Schrödinger equation is constructed based on the relevant Hamiltonian, photon frequency, and eigenstates of the waveguide QED system:

[0098]

[0099] Where H represents the correlated Hamiltonian of the system, and ω represents the photon frequency.

[0100] By solving the conventional Schrödinger equation, we obtain a set of differential equations for the motion of photons:

[0101]

[0102]

[0103]

[0104]

[0105] Where, φ R (x) is the probability amplitude of the photon moving to the right, φ L (x) is the probability amplitude of the photon moving to the left, μ c μ represents the probability amplitude of a photon being in the optical cavity. e This represents the probability amplitude of a photon being in an excited state.

[0106] In an exemplary embodiment, step S05, calculating the transmittance and reflectance of photons using a set of differential equations governing photon motion, is illustrated in the flowchart below. Figure 4 As shown, it includes:

[0107] Step S051: A single photon is incident from one side of the waveguide with a wave vector, and the amplitude probability expression of the photon is obtained;

[0108] Step S052: When a photon reaches the coupling point between the cavity and the waveguide, the incident photon is either reflected or transmitted. The transmittance and reflectance of the photon are calculated based on the differential equations of the photon's motion and the amplitude probability expression of the photon.

[0109] In this embodiment, studying the scattering behavior of a single photon requires solving for parameters such as the photon's transmittance and reflectance. Assuming the single photon is incident from the left side of the waveguide with wave vector k, the probability amplitude expression φ of the photon scattering to the right can be obtained. R(x) and the amplitude probability expression φ of the photon pointing to the left. L (x):

[0110] φ R (x)=e ikx [s(-x)+ts(x)],

[0111] φ L (x)=e -ikx rs(-x), (13)

[0112] The step function s(x) is expressed as:

[0113]

[0114] A photon is incident from the left side of the waveguide at a position x < 0 and propagates freely within the waveguide. When it reaches the point where the cavity couples with the waveguide (x = 0), due to the interaction between the waveguide and the cavity-atom, the incident photon may be reflected or transmitted. The transmittance t and reflectance r can be solved:

[0115]

[0116]

[0117] In an exemplary embodiment, step S06, which involves realizing a dynamic single-photon switch based on the dynamic relationship between atomic frequency and photon transmittance, is illustrated in the flowchart below. Figure 5 As shown, it includes:

[0118] Step S061: Calculate the relationship between atomic frequency and photon transmittance based on the relationship between atomic frequency and photon transmittance;

[0119] Step S062: By modulating the atomic frequency, the transmittance of waveguide photons of different frequencies is switched between 0 and 1, thereby realizing dynamic single-photon switching.

[0120] In an exemplary embodiment, step S061, calculating the relationship between atomic frequency and photon transmittance based on the relationship between atomic frequency and photon transmittance, is illustrated in the flowchart below. Figure 6 As shown, it includes:

[0121] Step S0611: Obtain the correlation between the amplitude-frequency ratio of the atomic frequency variation portion and the group velocity of photons propagating in the waveguide through dynamic modulation;

[0122] Step S0612: Substitute the relevant relationships into the photon transmittance and reflectance expression to solve for the photon transmittance;

[0123] Step S0613: Calculate the relationship between atomic frequency and photon transmittance based on the photon transmittance corresponding to different atomic amplitude frequency ratios.

[0124] In this embodiment, when the atom-cavity coupling strength is fixed, the amplitude of transmittance is affected by the photon frequency and the J0(f) value, while the J0(f) value is determined by ω. a =w0+ηcosvt, where f=ηIv is determined. Through dynamic modulation, it was found that when (1)f=0, J0(f)=1, gJ0(f)=30v g (2) When f = 1.8, J0(f) = 0.34, gJ0(f) = 10.2v g (3) When f = 2.405, J0(f) = 0.0009, gJ0(f) = 0.027v g ;

[0125] Substituting the above parameters into formula (15), we find that when w = ω c When w = ω, we will get (1) t = 1, (2) t = 1, (3) t = 0; c ±10.2v g When, we will get (1)t≈1, (2)t=0.

[0126] Regardless of the input resonant photon (w = ω) c ) or detuned photon (w=ω c ±10.2v g Its transmittance is significantly related to η / ν. Figure 7 (a) represents the transmittance curve of the input resonant photon under time-domain modulation. Figure 7 (b) represents the transmittance curve of the input detuned photon under time-domain modulation.

[0127] The above results demonstrate that by dynamically modulating the atomic frequency, the transmittance of waveguide photons of different frequencies can be switched between 0 and 1. A schematic diagram of the time-domain modulated dynamic single-photon switch is shown below. Figure 8 As shown.

[0128] Therefore, in this embodiment of the invention, by controlling the amplitude-frequency ratio of atoms, photons at a frequency of w = w c Dynamic switching of single photons can be achieved over a wide frequency range at ±g.

[0129] An embodiment of the present invention provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform the above-described method.

[0130] A single-photon switch implementation system based on time-domain modulation according to an embodiment of the present invention is shown in the schematic diagram below. Figure 9 As shown, it includes:

[0131] Waveguide QED system;

[0132] processor;

[0133] Memory;

[0134] as well as

[0135] One or more programs, wherein the one or more programs are stored in memory and configured to be executed by the processor, the programs causing the computer to perform the methods described above.

[0136] Of course, those skilled in the art should recognize that the above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Any changes or modifications to the above embodiments that are within the scope of the present invention will fall within the protection scope of the present invention.

Claims

1. A method for implementing a single-photon switch based on time-domain modulation, characterized in that, include: Establish a waveguide QED system model of atom-cavity-waveguide; Construct dynamic expressions for atomic frequencies; Calculate the relevant Hamiltonian of the waveguide QED system; the Hamiltonian includes the free Hamiltonian of atoms, the free Hamiltonian of optical cavities, the Hamiltonian of the interaction between atoms and cavities, the free Hamiltonian of waveguide photons, and the Hamiltonian of the interaction between waveguide and cavities. Calculate the system of differential equations for the motion of photons; The transmittance and reflectance of photons are calculated using a set of differential equations governing the motion of photons. Dynamic single-photon switching is achieved based on the dynamic relationship between atomic frequency and photon transmittance, including: obtaining the correlation between the amplitude-frequency ratio of the atomic frequency variation and the group velocity of photons propagating in the waveguide through dynamic modulation; The photon transmittance is solved by substituting the relevant relationships into the photon transmittance expression; the relationship between atomic frequency and photon transmittance is calculated based on the photon transmittance corresponding to different atomic amplitude-frequency ratios; and the transmittance of waveguide photons of different frequencies is switched between 0 and 1 by modulating the atomic frequency, thereby realizing dynamic single-photon switching.

2. The method for implementing a single-photon switch based on time-domain modulation according to claim 1, characterized in that, The waveguide QED system model consists of a one-dimensional waveguide, a single-mode optical cavity, and two-level atoms; the two-level atoms are placed in the single-mode optical cavity and interact with each other, and the one-dimensional waveguide is coupled to the atom-cavity system through the single-mode optical cavity side.

3. The method for implementing a single-photon switch based on time-domain modulation according to claim 2, characterized in that, The dynamic expression for constructing the atomic frequency is a cosine wave expression for the atomic frequency as a function of time. , where w0 represents the fixed atomic frequency, η represents the amplitude of the variable atomic frequency, and v represents the frequency of the variable atomic frequency.

4. The method for implementing a single-photon switch based on time-domain modulation according to claim 3, characterized in that, The calculation of the relevant Hamiltonian of the waveguide QED system includes the following steps: The free Hamiltonian of an atom is calculated based on its atomic frequency and its dissipation rate. The free Hamiltonian of the optical cavity is calculated based on the cavity's frequency and dissipation rate. The Hamiltonian of the interaction between the atom and the cavity is calculated based on the Bessel function of the amplitude and frequency of the part of the atomic frequency variation. The free Hamiltonian of waveguide photons is calculated based on the group velocity of photons propagating within the waveguide. The Hamiltonian of the waveguide-cavity interaction is calculated based on the coupling strength between the waveguide and the cavity.

5. The method for implementing a single-photon switch based on time-domain modulation according to claim 4, characterized in that, The set of differential equations for calculating photon motion includes the following steps: Calculate the eigenstates of the system in a single excitation subcavity-waveguide space; The Schrödinger equation is constructed based on the relevant Hamiltonian, photon frequency, and eigenstate of the waveguide QED system. The system of differential equations for the motion of photons is obtained by solving the conventional Schrödinger equation.

6. The method for implementing a single-photon switch based on time-domain modulation according to claim 5, characterized in that, The calculation of photon transmittance and reflectance using a set of differential equations governing photon motion includes the following steps: A single photon is incident from one side of the waveguide with a wave vector, and the amplitude probability expression of the photon is obtained; When a photon reaches the coupling point between the cavity and the waveguide, the incident photon is either reflected or transmitted. The transmittance and reflectance of the photon are calculated based on the differential equations of the photon's motion and the amplitude probability expression of the photon.

7. A computer-readable storage medium storing a computer program for electronic data interchange, wherein, The computer program causes the computer to perform the method as described in any one of claims 1-6.

8. A single-photon switch implementation system based on time-domain modulation, characterized in that... include: Waveguide QED system; processor; Memory; as well as One or more programs, wherein the one or more programs are stored in memory and configured to be executed by the processor, the programs causing the computer to perform the method as described in any one of claims 1-6.

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