Quantum switch based on PT symmetric spin orbit coupling and Rydberg system support

Abstract

The invention provides a quantum switch based on PT symmetric spin orbit coupling and Rydberg system support, and belongs to the technical field of optical information processing. The control light and the auxiliary light are irradiated in the Rydberg atomic gas to modulate and generate PT symmetric lattice potential, so that the regulation and control range of the optical lattice potential can be expanded from a real number form to a complex number form, and the application range of the experimental device is greatly expanded. By adjusting the imaginary part of PT symmetric lattice potential, the change of a system eigenvalue from a real number to a complex number is realized, so that the change of a vortex soliton from a stable state to an unstable state is controlled, and finally the change from PT symmetry to PT symmetric breaking is realized, namely, the realization of the quantum switch is realized. And a new possibility is provided for the development of the fields of quantum calculation, quantum communication and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of optical information processing and relates to a quantum switch based on PT symmetric spin-orbit coupling and Rydberg system support. Background Art

[0002] The formation of multidimensional nonlinear localized waves is of fundamental interest in various fields of physics, including nonlinear optics, Bose-Einstein condensates (BECs), superconductors, semiconductors, ferromagnetic media, and field theory in general. Compared with their two-dimensional (2D) and one-dimensional (1D) bright solitons (matter waves), the generation of three-dimensional (3D) bright solitons presents a more severe challenge. A key prerequisite for the formation of matter waves is the existence of attractive (or self-focusing) nonlinearities. However, this cubic Kerr nonlinearity can also lead to wave collapse, especially in high-dimensional geometries such as the 3D case. In addition, it also induces pronounced azimuthal modulation instabilities in states with intrinsic vorticity. Therefore, it is a serious challenge to identify robust 3D elementary matter waves and vortex matter waves in materials that exhibit cubic nonlinearities. Several potential stabilization scenarios have been proposed by scholars at home and abroad. For example, robust 3D matter waves may appear in materials with saturable or competing nonlinearities, nonlocalized nonlinearities, or through special nonlinear interactions. Furthermore, stable matter waves can occur in systems of Rydberg atoms and in binary Bose-Einstein condensates (BECs) affected by spin-orbit coupling (SOC).

[0003] The experimentally realized spin-orbit coupled Bose-Einstein condensates (BECs) have received extensive attention in recent years. Many interesting phenomena have been discovered in this system, including vortices, monopoles, multi-domain modes, and matter waves. Studies have shown that the change in dispersion of 3D condensates caused by SOC may offset the attractive nonlinearity, leading to the formation of metastable matter waves; the introduction of spatial periodic potential can be used to stabilize high-dimensional matter waves; the stability of matter waves can be promoted by fine-tuning the amplitude of nonlinearity and external potential; PT symmetric lattice potential can stabilize basic soliton states and states with vorticity.

[0004] Rydberg cold atoms constitute a paradigmatic platform for the generation of stable multidimensional matter waves covering both fundamental and vortex species. Rydberg-Rydberg long-range interactions (RRI) can be transformed into nonlocal nonlinearities via electromagnetically induced transparency (EIT). The relatively long lifetime of Rydberg atomic states, on the order of tens of microseconds, ensures the stability of the generated nonlinearities. These properties allow Rydberg systems to be used to design quantum devices such as single-photon switches and transistors, quantum memory cells and phase gates.

[0005] Despite recent progress, 3D vortex matter waves in binary condensates supported by SOC and RRI in PT-symmetric lattice potentials are not fully understood. The goal of this work is to systematically construct 3D stable matter waves in binary atomic BECs with SOC by combining transcendental mean-field interactions and PT-symmetric potentials through comprehensive numerical analysis. We show that there exist 3D stable matter waves characterized by semi-vortex (SV) and mixed-mode (MM) configurations satisfying the condition (|S|≤4). Moreover, our findings reveal that the imaginary part of the PT-symmetric potential, the SOC coefficient, as well as the Rydberg interaction parameter, all have a significant impact on the distribution and stability range of these two higher-order matter waves.

[0006] Similar to the corresponding products of classical electronic devices, quantum switches are a new type of electrical switch that uses the principles of quantum mechanics to achieve fast electronic control. Based on the principle of quantum uncertainty, quantum switches enable electronic control to achieve unprecedented speed and efficiency. It can ensure the super security of critical data transmission in wireless access environments, and realize the security reinforcement of distribution equipment commands through quantum encryption technology. Quantum switches have a wide range of applications in high-speed data transmission, computer memory, power grid distribution equipment and other fields. Especially in the field of 5G quantum encryption smart switches, it can use existing public network wireless communication resources to achieve flexible and ubiquitous access to power grid distribution equipment, and improve the intelligence and security of the power grid. With the continuous development and application of quantum computing technology, quantum switches are expected to play an important role in smart homes, the Internet of Things and other fields, and promote the intelligence and security of these fields. Summary of the invention

[0007] The purpose of the present invention is to provide a quantum switch based on PT symmetric spin-orbit coupling and Rydberg system support in view of the above-mentioned problems existing in the prior art. The technical problem to be solved by the present invention is to provide a quantum switch.

[0008] The present invention designs a device capable of stably generating semi-vortex (SVs) and mixed mode (MMs) matter waves:

[0009] It is a Bose-Einstein condensate (BECs) based on spin-orbit coupling (SOC) and Rydberg-Rydberg interaction (RRI) in a PT-symmetric lattice potential, as follows:

[0010] Realization of Bose-Einstein condensates (BECs) through laser cooling and evaporative cooling;

[0011] To realize BECs, you first need to lower the temperature of the atomic gas to near absolute zero. In this process, laser cooling technology plays a key role. The atoms are cooled in two steps: laser cooling and evaporative cooling.

[0012] Laser cooling can control the interaction between laser and atoms by adjusting laser parameters (such as laser power, pulse width, repetition frequency, wavelength and polarization, etc.), thereby effectively reducing the thermal motion speed of atoms and achieving cooling. Specifically, the basic principle of laser cooling is to use the light pressure effect of laser beam on matter. When the laser beam is irradiated on atoms, photons will interact with atoms, thereby changing the momentum of atoms and generating light pressure. Due to the Doppler effect, the wavelength felt by atoms moving toward the laser will appear shorter, so the effect is strong; while the wavelength felt by atoms moving away from the laser will be longer, so the effect is very weak. In this way, if there is a laser beam in six directions: front, back, left, right, up and down, the speed of atoms can be reduced to achieve cooling.

[0013] After reaching a certain low temperature, in order to further realize BECs, it is necessary to further reduce the temperature through technologies such as evaporative cooling. Evaporative cooling is a method of reducing the temperature of a system by removing high-energy atoms from the system. Through evaporative cooling, the temperature of the atomic gas can be reduced to a level close to absolute zero, at which point the atoms will gather into the lowest energy quantum state to form BECs.

[0014] pass 88 Sr atoms generate Rydberg atoms and place the Rydberg atoms in a cylindrical (not limited to cylindrical) container.

[0015] First, there needs to be a 88 A sample of Sr atoms will 88 Sr atoms are placed at low density (10 10 cm -3 order of magnitude) in a gas environment to reduce the interaction with other atoms and select a 88 A laser with a wavelength that matches the specific energy level transition of the Sr atom is used to adjust the laser parameters: intensity, frequency and pulse time to match 88 The transition energy of the Sr atom from the ground state to the Rydberg state; secondly, the adjusted laser beam is focused on 88 Sr atomic samples are placed on the surface of the atoms to make them absorb laser energy and complete the transition from the ground state to the Rydberg state. Secondly, the material and size of the container are selected. The material of the container should be non-conductive or insulating to avoid unnecessary electromagnetic interference to the Rydberg atoms. The size of the container should be large enough to avoid the influence of boundary effects on the Rydberg atoms. The inside of the container should maintain a high vacuum to reduce the collision of other gas molecules or atoms with the Rydberg atoms. Finally, the temperature and magnetic field inside the container are precisely controlled according to actual needs, which helps to eliminate the influence of thermal noise and magnetic field noise on the Rydberg atoms. In quantum switches, Rydberg-Rydberg interactions can be used to realize nonlinear coupling and interaction between quantum states, thereby enhancing the functionality and complexity of quantum switches.

[0016] The PT-symmetric lattice potential is modulated in a Rydberg cold atomic gas by controlling light and auxiliary light irradiation.

[0017] In the three-level atomic energy level structure, consider an atom with a ground state, an intermediate excited state, and a highly excited Rydberg state. Control light and auxiliary light are usually used to couple these energy levels to achieve the transition of atoms between different energy levels. Use control light and auxiliary light to couple the ground state to the intermediate excited state and the intermediate excited state to the Rydberg state, respectively. By adjusting the frequency, phase, polarization, intensity, etc. of the control light and the auxiliary light, an interference pattern with PT symmetry can be formed in space, thereby generating a PT symmetric lattice potential. For example Figure 1 In the design of quantum switches, the special properties of the PT symmetric lattice potential are used to achieve effective control over the transmission and evolution of quantum states. By adjusting the parameters of the lattice potential, precise control over the speed and direction of quantum state transmission can be achieved.

[0018] The model is in 88 In this case, the relevant value of the physical parameter is C6 = 2π × 81.6 GHz·μm 6 , Rydberg blocking radius R b =10 μm, and the time normalized unit τ = 0.14 s.

[0019] principle:

[0020] 1. By adjusting laser parameters and controlling the interaction between laser and atoms, and further reducing the temperature through technologies such as evaporative cooling, Bose-Einstein condensate can be achieved.

[0021] 2. Through incentives 88 Sr enters the Rydberg excited state, presenting a three-level structure with a ladder-like structure. This excited state has the characteristics of long-range interaction and long lifetime, which helps to maintain the nonlocal nonlinearity in the light field, thereby enhancing the functionality and complexity of the quantum switch.

[0022] 3. By controlling the light and auxiliary light irradiated in the Rydberg atomic gas, the PT symmetric lattice potential is modulated, so that the control range of the optical lattice potential can be expanded from real to complex form, greatly increasing the application range of the experimental device. By adjusting the imaginary part of the PT symmetric lattice potential, the system eigenvalue changes from real to complex, thereby controlling the transition of the vortex soliton from stable to unstable, and finally realizing the change from PT symmetry to PT symmetry breaking, that is, the realization of quantum switch.

[0023] 4. By introducing angular momentum through topological charges, vortex matter waves are modulated to allow matter waves to carry more information. In quantum switches, the introduction of spin-orbit coupling enables more precise control of quantum states, including the transmission speed and direction of quantum states, and thus realizes quantum switches through the form of vortex matter waves.

[0024] Application scenarios include but are not limited to the following three:

[0025] 1. The device can be used for quantum switching.

[0026] 2. The device can be used for topology protection and calculation.

[0027] 3. The device can be used for quantum information processing, transmission and measurement.

[0028] Recent studies have shown that excited states of half-vortex and mixed-mode matter waves are intrinsically unstable in high-dimensional spin-orbit coupled Bose-Einstein condensates (BECs) characterized by contact interactions. Here, we explore a stabilization strategy for these states using a framework that combines spin-orbit coupling and Rydberg-Rydberg interactions in a PT-symmetric lattice potential. Our results show that excited states of half-vortex matter waves have topological charges of S and S+1 between their two components, each of which acts as an eigenstate of angular momentum. These states are robust up to the topological charge magnitude of |S|=4. The introduction of angular momentum via topological charges modulates the generation of vortex matter waves, allowing the matter waves to carry more information. In quantum switches, the introduction of spin-orbit coupling enables more refined control over quantum states, including the speed and direction of quantum state transmission, and thus enables quantum switching via the morphology of vortex matter waves. In addition, mixed-mode matter waves exhibit a unique interwoven necklace-like structure with opposite fractional angular momentum values ​​for each component. The energy and orbital angular momentum of these states depend on their respective topological charges. In addition, the imaginary part of the PT-symmetric lattice potential, as well as the spin-orbit coupling coefficient and the Rydberg interaction parameter, all show an influence on the distribution and stability range of these higher-order matter waves. By adjusting the imaginary part of the PT-symmetric lattice potential, the change of the system eigenvalue from real to complex is achieved, thereby controlling the transition of the vortex soliton from stable to unstable, and finally achieving the change from PT symmetry to PT symmetry breaking, that is, the realization of quantum switching. This invention can not only achieve effective control over the transmission and evolution of quantum states, but also enhance the control ability and complexity of quantum states, providing new possibilities for the development of quantum computing, quantum communication and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Figure (a) is a schematic diagram of a device for modulating Rydberg atoms to generate matter waves; Figure 1 Figure (b) is an atomic energy level structure diagram; Figure 1 Figure (c) is the real part of the PT symmetric potential; Figure 1 Figure (d) is the imaginary part of the PT symmetric potential

[0030] Figure 2 is the density distribution of SV-type matter waves (the first to third rows are SV+matter waves, SV-matter waves, and mixed modes, respectively; the topological charge S from the first to the fifth column is + 0~4, S - =S + +1; the inset is the corresponding phase and intensity distribution in the (x,y) plane).

[0031] Figure 3 are MM matter waves of MM+ and MM- types (from the first to the fourth column, the topological charges are S1=0, 1, 2, 3, 4, and S2=S1+1; the first to the fifth rows are MM+ components, MM- components and the total mode, respectively; the fixed parameters are shown in Table 1).

[0032] Figure 4 is the number of particles of SV-type matter waves as a function of (a) the SOC coefficient λ, the (b) real and (c) imaginary parts of the PT symmetry potential, the (d) internal and (e) intercomponent components of the RRI intensity, and (f) the chemical potential μ. The inset is a zoomed-in detail of the region λ∈(2.0,4.2) in panel (a), where points A, B, C, and D correspond to Figure 1 Medium S + = 1, 2, 3, 4. The solid line and dotted line represent stable SV and unstable SV respectively.

[0033] Figure 5 The evolution of SV matter waves of type SV+ in (a) and SV- in (b). The time is t=100, 500, 700, 900. The other parameters are: S + =2,λ=3,p r =-0.1, p i =0.02, and α 11 =α 12 =α 21 =α 22 =0.1. DETAILED DESCRIPTION

[0034] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solution of the present invention, but the present invention is not limited to these embodiments.

[0035] 1. Rydberg cold atom energy level

[0036] In this work, a three-level Rydberg-decorated electromagnetically induced transparent (EIT) atomic system with a ladder configuration was used. By irradiating the Rydberg atomic gas with control light and auxiliary light, the PT-symmetric lattice potential was modulated, thereby expanding the control range of the optical lattice potential from real to complex form. Figure 1 shown.

[0037] 2. Spin-orbit coupled BECs with Rydberg cold atoms

[0038] In this study, we strive to predict stable states within a (3+1)-dimensional spin-orbit (SO) coupled BEC system consisting of SV and MM matter waves under the influence of the PT symmetric structure in the SO coupled BEC system. Our study focuses on matter waves in a Rydberg atomic gas, where the interplay of PT symmetry and long-range Rydberg interactions is expected to give rise to novel matter wave dynamics. By employing a systematic numerical approach, we explore the stability and characteristics of these matter waves, which may pave the way for a deeper understanding and manipulation of high-dimensional nonlinear wave phenomena. In the mean field, the dynamical features of the spinor wave function are described by the Gross-Pitaevskii equation (GPE).

[0039]

[0040] Where ψ=(ψ + ,ψ - ) are the two components of the spinor wave function, is the Laplace operator, r = (x, y, z), M is the mass of the atom, and g ij (i,j=1,2) is the interaction strength of the local contact within the component and between components. For simplicity in this work, let where a is the s-wave scattering intensity. Here, V SO is a Rashba-type spin-orbit coupling (SOC) operator, and the system is considered to be controlled by a PT-symmetric lattice potential V PT (r) is tightly confined. The nonlocal Rydberg interaction lattice potential in the last term of Equation 1 can be written as where C6 is the effective coefficient of the van der Waals interaction and the Rydberg blocking radius is R b , and U 12 =U 21 .

[0041] N is the number of atoms in the system, defined as N = N + +N - , where N + =∫|ψ + (r)| 2 d 3 r and N- =∫|ψ - (r)| 2 d 3 r is the number of particles of the two components of the wave function. The Rashba type SOC is expressed as as well as where λ is the strength of SOC. In addition, it is assumed that the PT symmetric lattice potential has the following form:

[0042] V PT =p r [cos 2 (ωx)+cos 2 (ωy)+cos 2 (ωz)]+ip i [sin(ωx)+sin(ωy)+sin(ωz)](2)

[0043] Here, p r and p i are the real and imaginary parts of the PT symmetric lattice potential. Therefore, this external lattice potential satisfies the following criteria: its real and imaginary parts are both even and odd functions of the coordinates, i.e., Re(V PT (r))=Re(V PT (-r)), Im(V PT (r))=-Im(V PT (-r)).

[0044] Assume that the solution of formula (1) has ψ ± =φ ± e -iμt The form of , where μ is the chemical lattice potential, φ ± is a stable solution that is independent of time. The polar coordinates (r,θ) of this system are ± The assumption is adopted as the semi-vortex (SV) mode:

[0045] φ ± =A ± r S± exp(-a ± r 2 +iS ± θ) (3)

[0046] And Mixed Mode (MM):

[0047]

[0048] Here, S - =S + +1 and S2 = S1 + 1 are the corresponding topological charges, A ± , A1 and A2 are the amplitudes of each mode, a ±, a1 and a2 are positive parameters, and θ is the azimuthal angle. Therefore, the ground state of SVs is given by (S + ,S - )=(-1,0) and (S + ,S - )=(0,1), and the excited state corresponds to S + and S - For the MM type hypothesis, the ground state corresponds to (S1, S2) = (-1, 0) and (S1, S2) = (0, 1).

[0049] Then, SVs and MMs can be obtained through imaginary time evolution. Both SVs and MMs have been found to have ground states with various integer topological charges (S +,1 =0) and excited state (S +,1 >0).

[0050] 3. Density modulation and stability of SVs and MMs

[0051] Each SV has two components, SV + and SV - , respectively with topological charge S + and S - For the combination (S + ,S - )=(0,1),SV + The components have a basic steady state, characterized by density distribution and phase structure, while the SV part has a vortex type, such as Figure 2 The total SVs have a fundamental state, because the total phase in the (x,y) plane is 0, and the density distribution is concentrated at the center, as shown in the first column of (a1) and (b1). Figure 2 (c1) shows the topological charge of the excited state (S + ,S - )=(1,2),(2,3),(3,4),(4,5), such as Figure 2 As shown in the second to fifth columns of . For the excited state of SVs, both components of SVs are vortex type. It is noted that the two components ψ + and ψ - The phases of are complementary. Therefore, the total phase of SVs is still 0, as Figure 2 As shown in the illustration. Numerical simulations have shown that the SO-coupled BEC system can support a topological charge S + ≤4 represents a robust vortex matter wave. However, when the topological charge exceeds this threshold, i.e., S + When >4, SVs are no longer robust. Figure 2The parameters of the robust SVs (vortex matter waves) are shown in Table 1, where the control parameters include the SOC intensity λ, the real part of the PT symmetric potential p r and the imaginary part p i , and the nonlocal nonlinear coefficient α ij .

[0052] For the MM hypothesis, the system is also able to support fundamental and excited matter waves. The density distribution of these mixed-mode matter waves is Figure 3 The fundamental state is shown in the first column, corresponding to the topological charge (S1, S2) = (0, 1). From the second to the fifth column, the excited states with topological charges ((S1, S2) = (0, 1), (1, 2), (2, 3), (3, 4)) are shown. In contrast to SVs, MMs are distributed as discrete necklaces around the central ring. The number of these discrete cores is given by the relation N c =2S1+1 control, where S1 represents the topological charge associated with the MM+ component. At the same time, the discrete densities of the MM+ and MM- components are arranged in an alternating pattern along the ring. Therefore, the collective density distribution of the MM matter wave exhibits a ring-like configuration.

[0053] By adjusting the system parameters (such as SO coupling strength λ, V PT The real and imaginary strengths of RRI, the intra- and inter-group strengths, and the chemical potential μ) can modulate SVs (stable vortex matter waves), such as Figure 4 By varying λ and adjusting different topological charges, the relationship described by N(λ) depicts the robust domain of SVs, as Figure 4 (a). The robust state and the unrobust state are represented by solid and dashed lines, respectively. Therefore, the robust domain of SVs with respect to λ can be characterized. It is found that the robust domain is divided into two different regions. The robust domains are located above and below λ = 0, respectively, indicating that the system cannot support robust SVs with small SOC strength. However, when the SOC strength is too large, that is, |λ|>4.2, the SVs cannot remain robust. For different topological charges, the number of SVs has different behaviors with the change of λ. When S + = 1.4, the number of particles changes smoothly with λ, and when S + = 2.3, it fluctuates violently. + =3, N increases by about 10 times from λ=3.2 to λ=4.2. When |λ>4.2, SVs are no longer robust. Further simulation results show that SVs cannot be topologically charged S + ≥5 supports. The increase of topological charge leads to population fluctuations and eventually to instability of SVs. The modulation of MMs (modal nodes) is similar to that of SVs. Therefore, in this work, we only show the results of SVs. i ,α12 When , there is also a λ gap that divides the robust domain into two parts, such as Figure 5 Here, the S of SVs + =3, S1 of MMs = 3, other parameters p r =-0.1,α 11 =α 22 =1.

[0054] In the PT symmetric structure, the real and imaginary parts are the key factors controlling the generation of robust SVs. Figure 4 (b) and (c) describe the r and p i The number of particles of the function. It is found that only negative values ​​of p r can support robust SVs, while p i can take negative and positive values. Here, p i = ±0.1 are the PT symmetry breaking points, beyond which the eigenvalues ​​become complex and no robust SVs can be obtained. i = 0, the number of particles reaches its maximum value and increases with |p i | decreases with the increase of |. r =-0.1, p i The robust domain is -0.1 to 0.1 or satisfies the ratio -1 ≤ p i / p r ≤1.

[0055] Particle number as a function of the intra- and inter-group RRI intensity, i.e., α 11 and α 12 , respectively shown in Figure 4 (d) and (e). We find that in α ij = 0, these curves have a roughly symmetrical structure. First, attract (α ij <0) and rejection (α ij >0) had the same effect on the modulation of SVs. Second, the intra- and inter-group values ​​of RRI intensity were almost equal. Third, there was no RRI (α ij =0) has the maximum SV particle number. Therefore, in order to control the matter wave particle number, adjusting the RRI intensity is a suitable method. Fourth, with a strong RRI intensity (α ij >10) will be very close to zero. In addition, Figure 4 (f) shows different S + The μ-N relation of the values ​​satisfies the anti-Vakhitov-Koroklov criterion, i.e., dμ / dN>0, which is a necessary condition for the stability of bright matter waves supported by self-repulsive nonlinearity.

[0056] To further test the stability of SVs and MMs, we performed matter wave evolution by the step-by-step Fourier method for a period of time up to t = 900. A typical example is Figure 5 As shown, the topological charge is taken as S + = 2 (for SVs) and S1 = 2 (for MMs). It is found that both components of SVs and MMs remain robust over time.

[0057] Table 1 Parameters of robust SVs and MMs

[0058]

[0059] In the mean field, the dynamic characteristics of the spinor wave function are described by the Gross-Pitaevskii equation (GPE), as shown in formula (1). The matter wave evolution is performed using the split-step Fourier method. This paper considers the density modulation and stability of SVs and MMs: (1) the density distribution and stability of SV-type matter waves; (2) the density distribution and stability of MM-type matter waves; (3) the modulation of SVs and their stability by adjusting system parameters.

[0060] (1) Density distribution and stability of SV-type matter waves. Each SV has two components: SV + and SV - , respectively with topological charge S + and S - For the combination (S + ,S - )=(0,1),SV + The component has a basic stable state, characterized by density distribution and phase structure, while the SV - Some are of vortex type, e.g. Figure 2 The total SVs have a fundamental state, because the total phase in the (x,y) plane is 0, and the density distribution is concentrated at the center, as shown in the first column of (a1) and (b1). Figure 2 (c1) shows the topological charge of the excited state (S + ,S - ) is (1,2), (2,3), (3,4) and (4,5), such as Figure 2 As shown in the second to fifth columns of + and ψ - The phases of are complementary, so the total phase of SVs is still 0, such as Figure 2 As shown in the illustration. Numerical simulations have shown that the SO-coupled BEC system can support a topological charge S + ≤4 represents a robust vortex matter wave. However, when the topological charge exceeds this threshold, i.e., S + When >4, SVs are no longer robust.

[0061] (2) Density distribution and stability of MM-type matter waves. For the MM hypothesis, the system can also support fundamental and excited matter waves. The density distribution of these mixed-mode matter waves is Figure 3 The fundamental state is shown in the first column, corresponding to the topological charge (S1, S2) = (0, 1). From the second to the fifth column, the excited states with topological charges ((S1, S2) = (0, 1), (1, 2), (2, 3), (3, 4)) are shown. In contrast to SVs, MMs are distributed as discrete necklaces around the central ring. The number of these discrete cores is given by the relation N c =2S1+1 control, where S1 represents the topological charge associated with the MM+ component. At the same time, the discrete densities of the MM+ and MM- components are arranged in an alternating pattern along the ring. Therefore, the collective density distribution of the MM matter wave exhibits a ring-like configuration.

[0062] (3) Modulate SVs and their stability by adjusting system parameters. PT The real and imaginary strengths of RRI, the intra- and inter-group strengths, and the chemical potential μ) can modulate SVs (stable vortex matter waves), such as Figure 4 By varying λ and adjusting different topological charges, the relationship described by N(λ) depicts the robust domain of SVs, as Figure 4 (a). The robust domains are located above and below λ = 0, respectively. It is found that SOC can promote the stability of SVs. However, when the SOC strength is too large, i.e., |λ|>4.2, SVs cannot remain robust. For different topological charges, the number of SVs has different behaviors with the change of λ. Further simulation results show that SVs cannot be stabilized by topological charge S + ≥ 5 supports. The increase of topological charge will lead to the fluctuation of particle population and eventually cause the instability of SVs.

[0063] In the PT symmetric structure, the real part p r and the imaginary part p i It is the key factor controlling the generation of robust SVs. Figure 4 (b) and (c) describe the r and p i The number of particles of the function. It is found that only negative values ​​of p r can support robust SVs, while p i can take negative and positive values. Here, p i = ±0.1 are the PT symmetry breaking points, beyond which the eigenvalues ​​become complex and no robust SVs can be obtained. i = 0, the number of particles reaches its maximum value and increases with |p i| decreases with the increase of |. r =-0.1, p i The robust domain is Or satisfy the ratio -1≤p i / p r ≤1.

[0064] Particle number as a function of the intra- and inter-group RRI intensity, i.e., α 11 and α 12 , respectively shown in Figure 4 (d) and (e). We find that in α ij = 0, these curves have a roughly symmetrical structure. First, attract (α ij <0) and rejection (α ij >0) had the same effect on the modulation of SVs. Second, the intra- and inter-group values ​​of RRI intensity were almost equal. Third, there was no RRI (α ij =0) has the maximum SV particle number. Therefore, in order to control the matter wave particle number, adjusting the RRI intensity is a suitable method. Fourth, with a strong RRI intensity (α ij >10) will be very close to zero. In addition, Figure 4 (f) shows different S + The μ-N relation of the values ​​satisfies the anti-Vakhitov-Koroklov criterion, i.e., dμ / dN>0, which is a necessary condition for the stability of bright matter waves supported by self-repulsive nonlinearity.

[0065] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. Quantum switch based on PT symmetric spin-orbit coupling and Rydberg system support, characterized by: It includes a device capable of stably generating semi-vortex (SVs) and mixed-mode (MMs) matter waves, by 88 Sr atoms generate Rydberg atoms and place the Rydberg atoms in a cylindrical container, inject auxiliary laser and control laser into the cylindrical container along the axis of the cylindrical container, and realize Bose-Einstein condensate at a temperature close to absolute zero by adjusting laser parameters and controlling the interaction between laser and atoms. Through incentives 88 Sr enters the Rydberg excited state, which presents a three-level structure with a ladder structure. This excited state has the characteristics of long-range interaction and long lifetime, which helps to maintain the non-local nonlinearity in the light field, thereby enhancing the functionality and complexity of the quantum switch; By controlling the light and auxiliary light irradiated in the Rydberg atomic gas, the PT symmetric lattice potential is modulated, so that the control range of the optical lattice potential can be expanded from real to complex form, greatly increasing the application range of the experimental device. By adjusting the imaginary part of the PT symmetric lattice potential, the system eigenvalue changes from real to complex, thereby controlling the transition of the vortex soliton from stable to unstable, and finally realizing the change from PT symmetry to PT symmetry breaking, that is, the realization of quantum switch.

2. A quantum switch based on PT symmetric spin-orbit coupling and Rydberg system support according to claim 1, characterized in that: The device realizes Bose-Einstein condensates (BECs) through laser cooling and evaporative cooling.

3. A quantum switch based on PT symmetric spin-orbit coupling and Rydberg system support according to claim 1, characterized in that: By introducing angular momentum through topological charges, vortex matter waves are modulated to allow the matter waves to carry more information. In quantum switches, the introduction of spin-orbit coupling can achieve more precise control over quantum states, including the transmission speed and direction of quantum states, and thus realize quantum switches through the morphology of vortex matter waves.

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