A method for preparing multi-magnon dark solitons based on vector optical displacement

Abstract

This invention discloses a method for preparing multi-magnetic-state dark solitons based on vector optical displacement, belonging to the field of ultracold atom and quantum control technology. The method involves preparing a quasi-one-dimensional Bose-Einstein condensate in a vacuum cavity and applying a stable bias magnetic field to define the quantization axis. Atoms are then prepared from a single magnetic state into a multi-component Bose-Einstein condensate containing at least two magnetic levels using radio frequency or microwave pulses. A far-detuned circularly polarized light field with a spatial step or smooth step intensity distribution is constructed, creating a spatially dependent vector optical displacement potential within the condensate. Different magnetic states acquire vector optical displacements of different signs at the same spatial position, thereby generating state-dependent phase steps. After removing the vector optical displacement, multi-magnetic-state dark solitons are synchronously generated on the same density background during the nonlinear dynamic evolution of the condensate.

Description

Technical Field

[0001] This invention relates to the field of ultracold atom and quantum control technology, specifically to a method for preparing multi-magneton state dark solitons based on vector optical displacement. Background Technology

[0002] Dark solitons are a class of nonlinear excited states existing in Bose-Einstein condensates with repulsive interactions. In quasi-one-dimensional systems, dark solitons can be considered as quasiparticles with effective mass and effective interactions. When multiple dark solitons exist simultaneously, their interactions, collision-induced phase shifts, and dissipative coupling with non-condensed parts make multi-dark-soliton systems an important physical platform for studying controllable nonlinear many-body dynamics.

[0003] In existing experiments, multiple dark solitons are usually prepared by laser phase imprinting: that is, a phase step is generated in different spatial regions of a condensate using a far-detuned laser, thereby forming paired or multiple dark solitons. However, this method is mainly for atomic clusters with a single magneton energy level (single spin component), and experimental studies on multiple dark soliton systems involving different magneton states are still relatively limited.

[0004] In addition, traditional multi-soliton preparation schemes usually require multiple independent laser pulses to complete phase imprinting at different spatial locations, which requires high time synchronization and spatial matching accuracy. Small inconsistencies in excitation position or time can lead to different solitons being under different background densities or initial phase conditions, thereby introducing asymmetry in soliton depth, velocity and density wave excitation.

[0005] Therefore, there is an urgent need for a new method to simultaneously prepare multi-magnetic-state dark solitons under a single gradient optical structure, in order to simplify the optical system structure and improve the reproducibility and symmetry of the experiment. Summary of the Invention

[0006] To address the problems of existing dark soliton preparation methods that mainly rely on phase imprinting with multiple independent laser beams, making it difficult to achieve simultaneous preparation of multiple magnetic soliton states, and requiring high precision in temporal synchronization and spatial matching, and easily introducing background density asymmetry and additional density wave excitation, this invention provides a method for preparing multi-magnetic solitons based on vector light displacement. Utilizing the differences in the response of different magnetic soliton states to vector light displacement, simultaneous phase imprinting of multi-magnetic solitons is achieved under a single gradient light structure; multi-magnetic solitons are prepared under the same spatial location and temporal conditions, avoiding the artificial asymmetry caused by different excitation positions or excitation sequences in traditional methods; while ensuring the contrast and stability of dark solitons, the accompanying density wave excitation is effectively suppressed, thereby obtaining a more "pure" soliton state.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for preparing multi-magnetic-state dark solitons based on vector optical displacement includes the following steps: Step 101: Initial preparation of quasi-one-dimensional condensates and multi-magnetic states: First, quasi-one-dimensional Bose-Einstein condensates are prepared; then, a stable bias magnetic field is applied. Using microwave or radio frequency coherent pulses as the quantization axis, the internal states of atoms are manipulated to prepare atoms from a single magneton state into a coherent superposition of multiple magneton states, thereby obtaining a multi-component Bose-Einstein condensate that satisfies the vector light shift state dependence condition; the target energy state structure expression is: in, This represents the magnetic quantum number of an atom in the direction of the applied bias magnetic field. The zero magneton state is represented by mF = +1 and mF = -1, which represent the positive and negative magneton states, respectively, corresponding to the two orientations of the magnetic moment along the quantization axis. Step 102: Construction of the vector optical displacement potential: (1) Introduce the far-detuned imprint light as the light source to generate AC Stark displacement; adjust the far-detuned imprint light into circularly polarized light through a polarization device, and control its propagation direction so that the propagation direction of the far-detuned imprint light is aligned with the bias magnetic field. The direction is parallel; (2) Construct a step-like or smooth step-like light intensity distribution in the lateral direction through spatial modulation. (3) The step-type or smooth step-type light intensity distribution is projected onto the quasi-one-dimensional Bose-Einstein condensate through the imaging system, so that the condensate forms an illumination structure of a single gradient light region along the specified direction, thereby constructing a space-dependent vector light displacement potential. Step 103: Synchronize phase imprinting to generate multi-magnetic-state dark solitons (1) During the phase imprinting stage, a polarization gradient vector light displacement pulse with a duration of τ is applied to the Bose-Einstein condensate so that the target magnetic state obtains a preset spatial phase distribution at the same spatial position; under the action of the vector light displacement, the atomic wave functions of different magnetic states obtain phase steps with opposite or different amplitudes; (2) After the phase imprinting is completed, the far detuned imprinting light is removed, and the condensate is allowed to evolve freely for a preset time t under the combined action of its own nonlinear interaction and kinetic energy term. Multiple dark soliton density depressions are formed synchronously on the original uniform density background, so that the phase defect is transformed into a density depression structure and a dark soliton is formed. (3) For multi-component Bose-Einstein condensate systems, corresponding multi-magnetic-state dark solitons are simultaneously formed in the two magneton state components of the m_F=+1 state and the m_F=-1 state. The multi-magnetic-state dark solitons are defect states that are coupled with density dark solitons and spin / magnetization texture.

[0008] Furthermore, the method for preparing quasi-one-dimensional Bose-Einstein condensates is as follows: (1) Select alkali metal atoms and complete the laser cooling, trapping and evaporation cooling process of the atomic cloud in sequence in a vacuum chamber to obtain an ultracold atomic cloud; (2) It is then loaded into a quasi-one-dimensional confined potential well to make the system satisfy the quasi-one-dimensional condition, thereby preparing a quasi-one-dimensional Bose-Einstein condensate.

[0009] Furthermore, alkali metal atoms adopt 87 Rb atoms.

[0010] Furthermore, the internal states of atoms can be manipulated using microwave or radio frequency π / 2 pulses.

[0011] Furthermore, in step 102, the spatial modulation means specifically refers to: using a light-shielding plate, a blade, or a semi-shielding structure to form an approximate step light intensity distribution, or forming a smooth step light intensity distribution through imaging projection or spatial light modulation technology.

[0012] Furthermore, based on the induced dipole interaction between atoms and the far-detuned imprinted light, the displacement potential energy sensed by the atoms is obtained by utilizing the constructed vector light displacement potential. It is strongly correlated with the magneton energy state of the atom; when the atom is in At that time, the perceived displacement potential is positively correlated with the light intensity; when the atom is in At that time, the perceived displacement potential is negatively correlated with the light intensity, that is: in, This represents the light field intensity distributed along the spatial coordinate x. , These represent the vector optical displacement potential experienced by the atom when it is in the magneton state of mF=+1 and mF=-1, respectively. This indicates that the displacement potentials produced by different magneton states under the same light intensity distribution have opposite signs, thus reflecting the state-dependent characteristics of vector light displacement.

[0013] Furthermore, by utilizing the spatial characteristics of the step light intensity distribution, the potential energy spatial distribution sensed by the atomic cluster exhibits a state-dependent difference, thus providing the physical premise for the differential formation of the phase step; at this time, the phase sensed by the atomic cluster is also related to the magneton state: in, To Spatial phase distribution of the component imprint, To Spatial phase distribution of the component imprint, Let be the spatial coordinates along the one-dimensional binding axis.

[0014] Furthermore, set the duration of the imprint pulse. With peak light intensity This causes the vector light displacement to produce the required phase step amplitude within the target region, and the phase step amplitude is close to π.

[0015] Furthermore, smooth switching is employed on the rising and falling edges of the imprint pulse to reduce the density wave introduced by abrupt switching.

[0016] Compared to existing technologies, the advantages of this invention are as follows: 1. It introduces a new degree of freedom for control, enabling soliton engineering dependent on magneton states. This invention utilizes the relationship between vector light displacement and the selectivity of magneton states to imprint phase onto different atomic states. This allows different magneton states to obtain phase steps with opposite signs or different amplitudes under the same light intensity distribution. Compared to traditional scalar phase imprinting methods that rely solely on light intensity distribution, this approach introduces atomic spin (magneton state) as a new degree of freedom in the dark soliton preparation process, realizing the extension of soliton states from "pure density excitation" to "density-spin coupled excitation," providing a new technical means for constructing multi-magneton-state dark solitons, spin dark solitons, and related topological defects.

[0017] 2. Simultaneous preparation of dark solitons in multiple magnetic states under a single gradient light structure. In this invention, different magnetic states naturally respond differently to the same vector light displacement field. Therefore, only a single spatial step (or smooth step) gradient light region needs to be constructed to simultaneously complete phase imprinting and generate dark solitons in multiple magnetic states. Compared with traditional methods that require multiple laser beams to imprint the phase in different spatial regions, this scheme significantly simplifies the optical system structure and reduces the experimental complexity of multi-beam alignment, power matching, and stability control.

[0018] 3. Time synchronization and spatial matching avoid artificial asymmetry. Traditional multi-soliton preparation schemes often suffer from the following problems due to solitons being excited at different locations or times: different excitation locations lead to different background densities, introducing depth and velocity deviations; different excitation times result in different initial phases and velocities, affecting the controllability of soliton interactions. This invention achieves synchronous phase imprinting of multiple magnon states at the same spatial location and time conditions through vector optical displacement, fundamentally avoiding the aforementioned artificial asymmetry factors. This ensures high consistency in initial conditions for dark solitons of different magnon states, making it particularly suitable for studying multi-soliton interactions, collisions, and dissipation behavior.

[0019] 4. The generated dark solitons are more "pure," significantly suppressing density wave excitation. This invention does not rely on abrupt scalar potential energy perturbations during phase imprinting; instead, it introduces phase changes through state-dependent vector light shifts, thus effectively reducing unnecessary excitation of the overall density distribution. This is achieved by defining a density wave index. It can quantitatively characterize the intensity of density wave (phonon) excitation. The results show that, under the same phase step condition, the vector phase imprinting scheme corresponds to... The difference is significantly smaller than that of the traditional scalar phase imprinting scheme, indicating that the generated dark soliton states have less phonon background and higher coherence purity. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0021] Figure 1 This is a flowchart of a method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to the present invention.

[0022] Figure 2 for 87 A schematic diagram of the energy levels of different magnetic states of an Rb atom. On the left, F=1 indicates the atom is in the same hyperfine state, where magnetic states are not distinguished. The bifurcated structure in the middle represents the projection of the atom's internal states into multiple magnetic level components under an applied bias magnetic field. The upper right branch corresponds to a magnetic state with a magnetic quantum number of mF=+1; the lower right branch corresponds to a magnetic state with a magnetic quantum number of mF=-1.

[0023] Figure 3 This is a schematic diagram of the potential energy sensed on an atom based on vector light displacement imprinting.

[0024] Figure 4 This diagram compares the density evolution of dark solitons under two conditions: time-synchronized and spatially matched, and time-asynchronous and spatially mismatched. The left diagram represents dark soliton states generated by imprinting at different locations, requiring precise spatial control of the imprinting positions to produce two equivalent dark solitons. The middle diagram shows imprinting at the same location but at different times, which also leads to unequal dark solitons. The right diagram shows imprinting at the same location and at the same time, resulting in the superposition of two equivalent dark solitons. By comparing these three diagrams, it can be seen that the imprinting process under time-synchronized and spatially matched conditions produces dark solitons with consistent velocity depth, simultaneously exciting multiple solitons at the same location. This addresses the need to study the generation, separation, and interaction of nonlinear many-body excitations under completely consistent conditions.

[0025] Figure 5 Numerical simulation results of purity preparation of multi-magnetic-state dark solitons based on vector optical displacement.

[0026] Figure 6 This is a schematic diagram of the optical path and apparatus layout for preparing dark solitons in a Bose-Einstein condensate (BEC). Imprinting light is directed through a light-shielding plate to form the desired light distribution. A LODT (Low-Least-Dimensional) optical dipole trap is used as the quasi-one-dimensional environment required for dark soliton preparation. Microwave pulses are generated via a microwave horn to prepare a coherent superposition of two magneton states. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0028] Example 1: Please refer to the accompanying drawings in the instruction manual. Figure 1 A method for preparing multi-magnetic-state dark solitons based on vector optical displacement includes the following steps: Step 101: Initial preparation of quasi-one-dimensional condensates and multi-magneton states (1) Select alkali metal atoms (e.g. 87 Using Rb atoms as experimental samples, the atomic cloud underwent laser cooling, trapping, and evaporation cooling processes sequentially within a vacuum chamber to obtain an ultracold atomic cloud.

[0029] (2) It is then loaded into a quasi-one-dimensional confined potential well to make the system satisfy the quasi-one-dimensional condition, thereby preparing a quasi-one-dimensional Bose-Einstein condensate.

[0030] (3) Next, apply a stable bias magnetic field. As a quantization axis, it completes the zero-point compensation and long-term stable control of the magnetic field, ensuring that the internal states of atoms are only subject to the selection rule of circularly polarized light. Based on this, by manipulating the internal states of atoms through microwave or radio frequency π / 2 pulses, atoms are prepared from a single magneton state into a coherent superposition of multiple magneton states, thereby obtaining a multi-component Bose-Einstein condensate that satisfies the vector light shift state dependence condition. The target energy state structure expression is: in, This represents the magnetic quantum number of an atom in the direction of the applied bias magnetic field. The zero magneton state is represented by mF = +1 and mF = -1, which represent the positive and negative magneton states, respectively, corresponding to the two orientations of the magnetic moment along the quantization axis. Step 102: Construction of Vector Optical Displacement Potential (1) Introducing far-detuned imprinted light, which is far detuned relative to the atomic resonance frequency, to reduce atomic scattering and system heating effects, and at the same time serves as a light source for generating AC Stark shift; the far-detuned imprinted light is adjusted to circularly polarized light by a polarization device, and its propagation direction is controlled so that the propagation direction of the far-detuned imprinted light is aligned with the bias magnetic field. The directions are parallel to ensure that the vector light displacement is different. The sign of the magneton state is opposite to its amplitude; (2) A step-like or smooth step-like light intensity distribution is constructed in the lateral direction by means of spatial modulation. The spatial modulation means are: to form an approximate step-like light intensity distribution by using a light shield, a blade or a semi-shielding structure, or to form a smooth step-like light intensity distribution by means of imaging projection or spatial light modulation technology. The smooth step-like light intensity distribution is preferably a tanh function distribution transition.

[0031] (3) The step-type or smooth step-type light intensity distribution is projected onto the quasi-one-dimensional Bose-Einstein condensate through the imaging system, so that the condensate forms an illumination structure of a single gradient light region along the specified direction, thereby constructing a space-dependent vector light displacement potential.

[0032] (4) Please refer to Figure 3 Based on the induced dipole interaction between atoms and the far-detuned imprinted light (non-resonant laser beam), the displacement potential energy sensed by the atoms is obtained by utilizing the vector light displacement potential constructed above. It is strongly correlated with the magneton energy state of the atom; when the atom is in At that time, the perceived displacement potential is positively correlated with the light intensity; when the atom is in At that time, the perceived displacement potential is negatively correlated with the light intensity. That is: in, This represents the light field intensity distributed along the spatial coordinate x. , These represent the vector optical displacement potential experienced by the atom when it is in the magneton state of mF=+1 and mF=-1, respectively. This indicates that the displacement potentials produced by different magneton states under the same light intensity distribution have opposite signs, thus reflecting the state-dependent characteristics of vector light displacement.

[0033] (5) Through the spatial characteristics of the step light intensity distribution, the potential energy spatial distribution sensed by the atomic cluster exhibits state-dependent differences, thus providing the physical premise for the differential formation of the phase step. At this time, the phase sensed by the atomic cluster is also related to the magneton state: in, To Spatial phase distribution of the component imprint, To Spatial phase distribution of the component imprint, Let be the spatial coordinates along the one-dimensional binding axis.

[0034] Step 103: Synchronize phase imprinting to generate multi-magnetic-state dark solitons (1) During the phase imprinting stage, a polarization gradient vector light displacement pulse with a duration of τ is applied to the Bose-Einstein condensate so that the target magnetic state (m_F=±1 state) obtains a preset spatial phase distribution at the same spatial position; under the action of vector light displacement, the atomic wave functions of different magnetic states obtain phase steps with opposite or different amplitudes.

[0035] (2) After the phase imprinting is completed, the far detuned imprinting light is removed, and the condensate is allowed to evolve freely for a preset time t under the combined action of its own nonlinear interaction and kinetic energy term. Multiple dark soliton density depressions are formed synchronously on the original uniform density background, so that the phase defect is transformed into a density depression structure and a dark soliton is formed. (3) For multi-component Bose-Einstein condensate systems, corresponding multi-magnetic-state dark solitons are simultaneously formed in the two magneton state components of the m_F=+1 state and the m_F=-1 state. The multi-magnetic-state dark solitons are defect states that are coupled with density dark solitons and spin / magnetization texture.

[0036] Furthermore, the specific control details of step 103 include: a) Set the imprint pulse duration With peak light intensity This allows the vector light displacement to generate the required phase step amplitude (a phase difference close to π) within the target region, while ensuring that the scattering heating is within an acceptable range.

[0037] (b) While maintaining condensate trapping conditions, a vector light displacement pulse is applied, causing the wavefunctions of different magneton states to undergo different phase evolutions at the same spatial location, forming a vector light displacement potential for a specific magneton state. Since the step light intensity results in a spatial phase step, different magneton states receive phase step amplitudes or signs that differ, thus forming state-dependent phase defects within the same density background.

[0038] c) Use soft-on / soft-off (shaping pulse) on the rising / falling edge of the imprinting pulse to reduce density waves introduced by sudden switching.

[0039] d) By fixing The polarization relationship ensures the consistency of velocity / depth between the two solitons in each preparation.

[0040] The performance of the multi-magnetic-state dark soliton prepared in this embodiment was tested and compared with that of the traditional scalar phase imprinting scheme. The results are as follows: 1. Simultaneous preparation of dark solitons in multiple magnetic states under a single gradient light structure: This invention uses vector optical displacement for imprinting. Different magnetic states naturally respond differently to the same vector optical displacement field. Therefore, only a single spatial step (or smooth step) gradient light region needs to be constructed to simultaneously complete phase imprinting and generate dark solitons in multiple magnetic states. Compared with traditional methods that require multiple laser beams to imprint the phase in different spatial regions, this scheme significantly simplifies the optical system structure and reduces the experimental complexity of multi-beam alignment, power matching, and stability control.

[0041] 2. Time synchronization and spatial matching to avoid artificial asymmetry: Traditional multi-soliton preparation schemes ( Figure 4 Because solitons are excited at different locations or at different times, the following problems often arise: different excitation locations lead to different background densities for the solitons, thus introducing depth and velocity deviations; different excitation times lead to different initial phases and initial velocities, affecting the controllability of soliton interactions. This invention achieves simultaneous phase imprinting of multiple magnon states at the same spatial location and time condition through vector optical displacement, fundamentally avoiding the aforementioned artificial asymmetry factors. This ensures high consistency in initial conditions for dark solitons of different magnon states, making it particularly suitable for studying multi-soliton interactions, collisions, and dissipation behavior. Since this invention does not rely on abrupt scalar potential energy perturbations during phase imprinting but introduces phase changes through state-dependent vector optical displacement, it effectively reduces unnecessary excitation of the overall density distribution.

[0042] 3. The generated dark solitons are more "pure," significantly suppressing density wave excitation: such as Figure 5 As shown, by defining the density wave index ,in, Let the density at a certain location be at time t. The ground-state density is represented by the D-parameter, which is then averaged over the entire space (all lattice points). This index reflects the overall density fluctuation intensity in the system except for the dark soliton central region, and therefore can serve as a global quantitative characterization of the degree of density wave (phonon) excitation. From the density wave index... The evolution curve over time shows that, under the same phase step condition, the vector phase imprinting scheme of this invention corresponds to... The density wave in the vector scheme consistently exhibits lower purity than that of the traditional scalar phase imprinting scheme. Over time, the density wave in the vector scheme grows more slowly, indicating that the phonon background is continuously suppressed. The curves corresponding to different magneton states highly overlap, further demonstrating the scheme's advantages in temporal synchronization and spatial consistency. These results demonstrate that the dark soliton states prepared by the vector optical displacement scheme maintain higher coherence purity during dynamical evolution.

[0043] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for preparing multi-magnetic-state dark solitons based on vector optical displacement, characterized in that, Includes the following steps: Step 101: Initial preparation of quasi-one-dimensional condensates and multi-magnetic states: First, quasi-one-dimensional Bose-Einstein condensates are prepared; then, a stable bias magnetic field is applied. Using microwave or radio frequency coherent pulses as a quantization axis, the internal states of atoms are manipulated to prepare atoms from a single magnetic state into a multi-component Bose-Einstein condensate containing at least two magnetic level energy levels; the target energy state structure expression of the multi-component Bose-Einstein condensate is: in, This represents the magnetic quantum number of an atom in the direction of the applied bias magnetic field. The zero magneton state is represented by mF = +1 and mF = -1, which represent positive and negative magneton states, respectively. Step 102: Construction of the vector optical displacement potential: (1) Introduce the far-detuned imprint light as the light source to generate AC Stark displacement; adjust the far-detuned imprint light into circularly polarized light through a polarization device, and control its propagation direction so that the propagation direction of the far-detuned imprint light is aligned with the bias magnetic field. The direction is parallel; (2) Construct a step-like or smooth step-like light intensity distribution in the lateral direction through spatial modulation. (3) The step-type or smooth step-type light intensity distribution is projected onto the quasi-one-dimensional Bose-Einstein condensate through the imaging system, so that the condensate forms an illumination structure of a single gradient light region along the specified direction, thereby constructing a space-dependent vector light displacement potential. Step 103: Synchronize phase imprinting to generate multi-magnetic-state dark solitons (1) During the phase imprinting stage, a polarization gradient vector light displacement pulse with a duration of τ is applied to the Bose-Einstein condensate so that the target magnetic state obtains a preset spatial phase distribution at the same spatial position; under the action of the vector light displacement, the atomic wave functions of different magnetic states obtain phase steps with opposite or different amplitudes; (2) After the phase imprinting is completed, the far detuned imprinting light is removed, and the condensate is allowed to evolve freely for a preset time t under the combined action of its own nonlinear interaction and kinetic energy term. Multiple dark soliton density depressions are formed synchronously on the original uniform density background, so that the phase defect is transformed into a density depression structure and a dark soliton is formed. (3) For multi-component Bose-Einstein condensate systems, corresponding multi-magnetic-state dark solitons are simultaneously formed in the two magneton state components of the m_F=+1 state and the m_F=-1 state. The multi-magnetic-state dark solitons are defect states that are coupled with density dark solitons and spin / magnetization texture.

2. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 1, characterized in that, The method for preparing quasi-one-dimensional Bose-Einstein condensates is as follows: (1) Select alkali metal atoms and complete the laser cooling, trapping and evaporation cooling process of the atomic cloud in sequence in a vacuum chamber to obtain an ultracold atomic cloud; (2) It is then loaded into a quasi-one-dimensional confined potential well to make the system satisfy the quasi-one-dimensional condition, thereby preparing a quasi-one-dimensional Bose-Einstein condensate.

3. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 2, characterized in that, Alkali metal atoms adopt 87 Rb atoms.

4. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 3, characterized in that, Manipulating the internal states of atoms using microwave or radio frequency π / 2 pulses.

5. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 4, characterized in that, In step 102, the spatial modulation means specifically refers to: using a light-shielding plate, a blade, or a semi-shielding structure to form an approximate step light intensity distribution, or forming a smooth step light intensity distribution through imaging projection or spatial light modulation technology.

6. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 5, characterized in that, By utilizing the constructed vector optical displacement potential, the displacement potential energy experienced by the atoms is... It is strongly correlated with the magneton energy state of the atom; when the atom is in At that time, the perceived displacement potential is positively correlated with the light intensity; when the atom is in At that time, the perceived displacement potential is negatively correlated with the light intensity, that is: in, This represents the light field intensity distributed along the spatial coordinate x. , These represent the atoms in different states. and The vector optical displacement potential experienced in the magneton state, The sign of the displacement potential produced by different magneton states under the same light intensity distribution is opposite.

7. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 6, characterized in that, The phase sensed by the atomic group is also related to the magneton state: in, To Spatial phase distribution of the component imprint, To Spatial phase distribution of the component imprint, Let be the spatial coordinates along the one-dimensional binding axis.

8. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 7, characterized in that, Set the duration of the imprint pulse. With peak light intensity This causes the vector light displacement to produce a phase step amplitude close to π within the target region.

9. The method for preparing multi-magnetic-state dark solitons based on vector optical displacement according to claim 8, characterized in that, Smooth switching is used on the rising and falling edges of the imprint pulse.

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