Optical lattice synchronous multi-parameter floquet control method and system

Abstract

The application discloses a kind of optical lattice synchronous multi-parameter floquet control method and system, it is related to quantum precision measurement and quantum control technical field, the method includes: by acoustooptic modulator to the frequency modulation of lattice light, make its frequency change with time according to preset periodic function, generate frequency modulation laser after input polarization modulation module, by electro-optic modulator introduce time-varying phase delay, phase delay is converted into the periodic rotation of linear polarization direction by polarization modulation, obtain always keep linear polarization synchronous multi-parameter modulation lattice laser;Frequency modulation and polarization modulation are uniformly generated and synchronously driven by synchronous control module, and there is stable and adjustable relative phase relationship between the two. Standing wave optical field is formed using synchronous multi-parameter modulation lattice laser, realizes that polarization direction can be high-frequency dynamic modulation and always keep linear polarization, frequency and polarization are cooperatively controlled, suitable for optical lattice clock precision measurement optical lattice synchronous multi-parameter floquet control.

Description

Technical Field

[0001] This invention belongs to the field of quantum precision measurement and quantum control technology, specifically relating to a method and system for synchronous multi-parameter Flokai control of optical lattices. Background Technology

[0002] In recent years, ultracold atom systems have become an important platform for studying quantum many-body physics, topological states of matter, and quantum simulation due to their high controllability and tunability. Optical lattices constructed using laser fields can form periodic potential wells similar to the potential fields of solid crystals, allowing neutral atoms to exhibit behavior similar to that of electrons in crystals. This enables the study of various physical phenomena in many-body quantum systems.

[0003] In optical lattice systems, artificial gauge fields and spin-orbit coupling (SOC) can be realized through precise manipulation of optical field parameters. Spin-orbit coupling describes the coupling relationship between a particle's spin degree of freedom and its momentum degree of freedom; this effect plays a crucial role in topological insulators, the spin Hall effect, and quantum computing. Ultracold atom systems, due to their highly controllable experimental conditions, are considered important experimental platforms for studying spin-orbit coupling and related topological quantum states.

[0004] In ultracold atom systems, since neutral atoms themselves do not exhibit significant spin-orbit coupling, it is necessary to artificially construct effective spin-orbit coupling. A relatively mature method currently is to construct Raman coupling using laser fields, thereby achieving momentum-related coupling between different internal states of the atom. For example, in 2011, Lin et al. achieved spin-orbit coupling in a Bose-Einstein condensate using two Raman laser beams, marking a significant experimental achievement and the first realization of artificial spin-orbit coupling in an ultracold atom system. In this experimental scheme, two laser beams with different frequencies and momentum couple two internal states of the atom through Raman transitions, thereby generating a coupling term between momentum and pseudo-spin in the atom's effective Hamiltonian.

[0005] On the other hand, to further expand the achievable effective Hamiltonian structures in ultracold atom systems, researchers have proposed a method using periodic driving of system parameters, known as Flokai engineering. By periodically modulating system parameters, such as lattice depth, lattice phase, or applied field strength, new effective Hamiltonians can be obtained in a time-averaged sense, thereby realizing new quantum states of matter and topological structures.

[0006] Therefore, developing a new Frokai control method in optical lattice systems that simultaneously possesses high stability, high modulation bandwidth, and is suitable for optical lattice clock systems has become an important direction in quantum simulation research.

[0007] Currently, the main technical approaches for achieving Flokai modulation and spin-orbit coupling in cold atom systems include Raman-based spin-orbit coupling schemes and periodically driven Flokai modulation methods. In the Raman-based spin-orbit coupling scheme, coupling between internal atomic states is achieved using two Raman laser fields with different frequencies and momentum. The basic experimental steps include: preparing an ultracold atom gas and selecting two internal states as pseudo-spin states; applying two Raman laser beams with a frequency difference; achieving momentum-dependent coupling between the two spin states using two-photon Raman transitions; and forming a pseudo-spin state in the effective Hamiltonian. The spin-orbit coupling term, where, Represents the spin-orbit coupling Hamiltonian; Indicates momentum; This represents a pseudo-spin operator. This method has been implemented in various atomic systems and has become the mainstream technique for realizing SOCs in experiments. In Raman-based spin-orbit coupling schemes, common manipulation methods include: lattice depth modulation, which changes the lattice potential depth by modulating the laser intensity; lattice position oscillation, which causes the lattice position to oscillate over time by periodically changing the phase between two lattice beams; and phase modulation, which modulates the laser phase using an electro-optic modulator, thereby changing the spatial structure of the lattice potential. These methods can change the effective Hamiltonian of the system in a time-averaged sense, thus realizing various Flokai quantum states, such as topological band structures or artificial gauge fields. Furthermore, some studies have proposed achieving artificial spin-orbit coupling through magnetic field pulse sequences or cavity optical fields. For example, a spatial phase gradient can be generated through a series of pulsed magnetic fields to construct Rashba-type spin-orbit coupling. Alternatively, cavity optical fields can assist Raman transitions, forming feedback coupling between atoms and the optical field, thereby generating dynamic spin-orbit coupling.

[0008] In cold atom optical lattice systems and quantum simulation experiments, Flokai manipulation is typically achieved through periodic modulation of optical lattice parameters, such as lattice phase modulation, lattice depth modulation, lattice position wobble, and spin-orbit coupling via Raman optical coupling. However, the aforementioned existing technical solutions still have the following shortcomings: 1) Existing technologies struggle to achieve highly stable dynamic modulation of polarization direction: In some experimental schemes, it is necessary to modulate the spin-dependent potential energy of atoms by changing the polarization direction of the light field. However, existing techniques typically achieve polarization modulation through rotating mechanical waveplates, polarization controllers, or electrically controlled liquid crystal waveplates. Since mechanical rotation relies on the movement of mechanical structures, its modulation speed is relatively low, making high-frequency modulation difficult to achieve. Furthermore, the mechanical system has poor stability, easily introducing optical path drift and affecting experimental stability. Therefore, existing techniques struggle to achieve highly stable and high-frequency dynamic modulation of the polarization direction.

[0009] 2) Existing polarization modulation methods are prone to introducing elliptic polarization: In many optical lattice experiments, the atomic response to a light field depends not only on the light intensity but also on the polarization state. Existing polarization modulation schemes typically generate elliptic polarization components during modulation, which leads to changes in vector and tensor light shifts, thereby altering the spatial structure of the optical lattice potential. Therefore, current techniques struggle to guarantee the maintenance of linear polarization throughout the modulation process.

[0010] 3) The existing Flokai has limited degrees of control: Current common Flokai modulation methods mainly focus on lattice depth modulation, lattice position wobble, and laser phase modulation. However, these modulation methods primarily affect the potential well depth and lattice position, lacking dynamic control over the polarization degree of freedom of the optical field. Therefore, existing techniques have limited control dimensions in Flokai engineering, hindering the construction of more complex effective Hamiltonians.

[0011] 4) Existing methods for achieving spin-orbit coupling are complex: In cold atom experiments, spin-orbit coupling is typically achieved through Raman-coupled optical fields. This approach usually requires multiple laser beams, precise frequency locking, and complex optical path structures. Furthermore, Raman fields are prone to introducing spontaneous scattering and heating effects, thereby reducing the system's coherence time. Therefore, existing techniques for achieving spin-orbit coupling result in high system complexity.

[0012] 5) Existing control methods are not easily applied directly to optical lattice atomic clock platforms: Optical lattice atomic clock systems have extremely high requirements for optical field stability, optical frequency stability, and system noise levels. Many existing Flokai control schemes introduce additional noise during implementation, thus affecting the measurement accuracy of the atomic clock. Therefore, the applicability of existing technologies to optical lattice atomic clock platforms is limited.

[0013] Therefore, how to provide a method for synchronous multi-parameter Flokai modulation of optical lattice with high-frequency dynamic modulation of polarization direction while maintaining linear polarization, with frequency and polarization that can be coordinated and controlled, and which is suitable for precision measurement of optical lattice clocks, has become an important issue. Summary of the Invention

[0014] To address the aforementioned problems in the prior art, this invention provides a method and system for synchronous multi-parameter Flokai modulation of optical lattices.

[0015] The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, the present invention provides a method and system for synchronous multi-parameter Flokai modulation of optical lattices, comprising: Generates lattice light; The frequency of the lattice light is modulated by an acousto-optic modulator, so that the frequency of the lattice light changes with time according to a preset periodic function, thereby generating frequency-modulated laser. The frequency-modulated laser is input into a polarization modulation module, where a time-varying phase delay is introduced by an electro-optic modulator. Combined with waveplates positioned before and after the electro-optic modulator, the phase delay is converted into a periodic rotation of the linear polarization direction through polarization modulation, resulting in a synchronously multi-parameter modulated lattice laser that maintains linear polarization throughout. The frequency modulation and polarization modulation are uniformly generated and synchronously driven by a synchronization control module, and the modulation channels of the frequency modulation and polarization modulation have a stable and adjustable relative phase relationship. The synchronous multi-parameter modulated lattice laser is used to form a standing wave optical field to construct an optical lattice for trapping atoms.

[0016] Secondly, the present invention provides an optical lattice synchronous multi-parameter Flokai control system, comprising: Lattice light generation module, used to generate lattice light; A frequency modulation module is used to frequency modulate the lattice light using an acousto-optic modulator, so that the frequency of the lattice light changes with time according to a preset periodic function to generate frequency-modulated laser. A polarization modulation module is used to receive the frequency-modulated laser, introduce a time-varying phase delay through an electro-optic modulator, and combine it with waveplates respectively set before and after the electro-optic modulator. The phase delay is converted into a periodic rotation of the linear polarization direction through polarization modulation to obtain a synchronous multi-parameter modulated lattice laser that always maintains linear polarization. A standing-wave optical field forming module is used to form a standing-wave optical field using the synchronous multi-parameter modulated lattice laser to construct an optical lattice for trapping atoms; The synchronization control module is used to control the unified generation and synchronous driving of the frequency modulation and the polarization modulation, and to maintain a stable and adjustable relative phase relationship between the modulation channel of the frequency modulation and the modulation channel of the polarization modulation.

[0017] The present invention provides a synchronous multi-parameter Flokai modulation method for optical lattices, which converts frequency-modulated laser into synchronous multi-parameter modulated lattice laser with polarization direction changing periodically over time through a polarization modulation module. The synchronous multi-parameter modulated lattice laser maintains a linear polarization state throughout the entire modulation period, avoiding the vector light shift and tensor light shift caused by the introduction of elliptic polarization components in traditional polarization modulation schemes, thereby effectively suppressing the spatial structure distortion of the optical lattice potential field.

[0018] Frequency modulation and polarization modulation are uniformly generated and synchronously driven by a synchronization control module. The two modulations possess inherent high-precision phase synchronization and long-term phase stability, avoiding relative phase drift and additional phase noise caused by using multiple independent signal sources. This ensures excellent coherence of the jointly generated Flokai driving field in the optical lattice, providing a stable foundation for constructing a finely detailed Flokai effective Hamiltonian. By synergistically applying two independent control dimensions—frequency modulation and polarization direction modulation—to the same optical lattice to jointly generate the Flokai driving field, the limitations of traditional schemes that can only modulate lattice depth, phase, or position individually are overcome. Spin-related tunneling processes can be constructed in the optical lattice, thereby achieving coupling between momentum and spin. A complex Raman-coupled optical field system is unnecessary, significantly reducing the complexity of the experimental system.

[0019] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0020] Figure 1 This is a schematic flowchart of a method for synchronous multi-parameter Flokai modulation of optical lattice provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of the optical lattice Flökai control system provided in this invention. Figure 3 This is a schematic diagram of the joint control of the synchronization control module and the dual-parameter Flokai modulation provided in this invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0022] To address the limitations of existing Flokai modulation methods, such as the inability to achieve high-frequency dynamic modulation of polarization direction, the inability to maintain linear polarization, the inability to perform coordinated frequency and polarization modulation, and their unsuitability for precision measurement environments in optical lattice clocks, this invention provides a synchronous multi-parameter Flokai modulation method for optical lattices. (See [link to relevant documentation]). Figure 1 , Figure 1 This is a flowchart illustrating a method for synchronous multi-parameter Flokai modulation of optical lattices provided in an embodiment of the present invention, which specifically includes the following steps: Step S101: Generating lattice light.

[0023] See Figure 2 , Figure 2 This is a schematic diagram of the optical lattice Flokai control system provided in this invention, which can generate lattice light using a lattice laser.

[0024] Step S102: Frequency modulation of lattice light is performed by an acousto-optic modulator, so that the frequency of lattice light changes with time according to a preset periodic function, thereby generating frequency-modulated laser.

[0025] In this embodiment of the invention, frequency modulation of lattice light is performed using an acousto-optic modulator, causing the frequency of the lattice light to change with time according to a preset periodic function, thereby generating frequency-modulated laser light, including: A frequency modulation signal is generated using a synchronization control module; The frequency modulation signal is amplified by the radio frequency driver and then applied to the acousto-optic modulator (AOM) to modulate the frequency of the lattice light and generate frequency-modulated laser.

[0026] See Figure 3 , Figure 3 This is a schematic diagram of the joint control structure of the optical lattice Flokai modulation system provided in this invention. A frequency modulation signal is generated through a synchronization control module. This frequency modulation signal is amplified by a radio frequency driver and applied to an acousto-optic modulator, thereby modulating the frequency of the unmodulated laser light (lattice light) passing through the modulator, causing a periodic change in the frequency of the lattice light and generating frequency-modulated laser light. The synchronization control module includes a reference clock source, a phase-locked loop (PLL), and a direct digital synthesizer (DDS) or arbitrary waveform generator (AWG). The reference clock source provides a unified, highly stable time / frequency reference for the entire optical lattice Flokai modulation system, ensuring long-term modulation stability and long-term coherence of the Flokai drive. Reference clocks include hydrogen clocks and rubidium clocks. The PLL is used for clock locking and distribution to lock all subsequent electronic devices to the same reference clock, ensuring clock synchronization within the DDS / AWG. The direct digital synthesizer or arbitrary waveform generator is responsible for generating the modulation waveform. It uses, for example, a 10MHz master clock as the reference clock source to generate the frequency modulation signal.

[0027] In this embodiment of the invention, frequency modulation of lattice light is achieved by an acousto-optic modulator, causing its frequency to change according to a time-periodic function, thereby generating frequency-modulated laser light, including: ; in, Indicates frequency-modulated laser in Frequency of time; This indicates the frequency of the lattice light when it is not modulated; Indicates the frequency modulation amplitude; Indicates the lattice light modulation frequency; This indicates the initial phase of the modulation channel in frequency modulation.

[0028] In step S103, the frequency-modulated laser is input into the polarization modulation module. A time-varying phase delay is introduced through the electro-optic modulator in the polarization modulation module. Combined with waveplates placed before and after the electro-optic modulator, the phase delay is converted into a periodic rotation of the linear polarization direction through polarization modulation, thereby obtaining a synchronous multi-parameter modulated lattice laser that always maintains linear polarization. The frequency modulation and polarization modulation are uniformly generated and synchronously driven by the synchronization control module. The modulation channel of the frequency modulation and the modulation channel of the polarization modulation have a stable and adjustable relative phase relationship.

[0029] In this embodiment of the invention, the phase delay is converted into a periodic rotation of the linear polarization direction by polarization modulation to obtain a synchronous multi-parameter modulated lattice laser that always maintains linear polarization, including: A voltage modulation signal is generated using a synchronization control module; The voltage modulation signal is amplified by a high-voltage driver (HV Driver) and applied to the electro-optic modulator in the polarization modulation module. The phase delay is converted into a periodic rotation of the linear polarization direction by the polarization modulation module, so as to obtain a synchronous multi-parameter modulated lattice laser that always maintains linear polarization.

[0030] Among them, the waveplates disposed before and after the electro-optic modulator include the first wave plate Second wave plate The polarization adjustment module includes, in sequence, a first... Waveplate, electro-optic modulator (EOM) and second Wave plate.

[0031] Specifically, first The optical axis of the waveplate is set to an optical axis angle of 45°; second The optical axis of the waveplate is set to an optical axis angle of -45°.

[0032] By reasonably setting the operating point of the electro-optic modulator and the first wave plate Second wave plate The angle allows the output synchronous multi-parameter modulated lattice laser to always maintain linear polarization, changing only the polarization direction. Therefore, it effectively avoids the vector light shift caused by elliptic polarization, thus maintaining the stability of the optical lattice potential structure.

[0033] The polarization direction modulation process will now be explained in detail, taking into account the specific structure of the polarization modulation module: See Figure 2First, the frequency-modulated laser passes through two mirrors and then illuminates a polarizing beam splitter (PBS). The PBS splits the linearly polarized laser into two mutually perpendicular beams, with their polarization directions also perpendicular to each other. One beam is then polarized by a polarization modulation module, while the other beam is used to reference the absolute frequency of the lattice light onto a femtosecond optical frequency comb.

[0034] In this embodiment of the invention, polarization direction modulation is specifically achieved through the following steps: causing one frequency-modulated laser to sequentially pass through the first... Waveplate, electro-optic modulator and second Waveplate. Specifically, the first A waveplate converts the incident frequency-modulated laser light into elliptically polarized light, generating two orthogonal polarization components with a fixed phase relationship. The elliptically polarized light then enters an electro-optic modulator. A periodically varying voltage modulation signal, amplified by a high-voltage driver, is applied to the modulator. Driven by this signal, the refractive index of the modulator crystal dynamically changes, introducing a time-varying additional phase difference into the two orthogonal polarization components, thus achieving an electro-optic phase delay. The elliptically polarized light carrying this additional phase difference finally passes through a second... Wave plate, second The waveplate precisely converts the accumulated dynamic phase modulation into a periodic rotation of the polarization direction of the outgoing light, thereby outputting a synchronous multi-parameter modulated lattice laser. The synchronous multi-parameter modulated lattice laser maintains a linear polarization state throughout this process, with only its polarization direction angle changing periodically with time, thus achieving polarization Flokai modulation of the lattice light.

[0035] In this embodiment of the invention, synchronous multi-parameter modulated lattice laser includes: ; in, This indicates that synchronous multi-parameter modulated lattice lasers are in The polarization direction angle at that moment; Indicates the initial polarization direction angle; Indicates the modulation amplitude in the polarization direction; Indicates the Flokai modulation angular frequency; This indicates the initial phase of the modulation channel in polarization modulation.

[0036] It is important to note that and The values ​​can be the same or different. For example, in an embodiment that implements spin-orbit coupling, they are the same.

[0037] In this embodiment of the invention, the first... Waveplate, electro-optic modulator and second The waveplate modulates the polarization direction. Adjusting the waveplate angle creates a controllable polarization rotation structure when a periodic voltage is applied by the electro-optic modulator. At that time, the polarization direction of the output synchronous multi-parameter modulated lattice laser changes periodically, but always remains linearly polarized. Among these, This indicates the amplitude of the modulation voltage.

[0038] Frequency modulation and polarization direction modulation have a fixed phase relationship, and this phase remains stable or adjustable during modulation. The relative phase relationship between the modulation channel of frequency modulation and the modulation channel of polarization modulation is as follows: ; in, This indicates the relative phase between polarization modulation and frequency modulation; Indicates the initial phase of the modulation channel in frequency modulation; This indicates the initial phase of the modulation channel in polarization modulation.

[0039] Under this condition, a momentum-spin coupling term appears in the atomic Hamiltonian: This achieves spin-orbit coupling. This method is particularly suitable for alkaline earth atoms, alkaline earth-like atoms, and optical lattice clock systems (Sr optical lattice clocks and Yb optical lattice clocks). Represents the spin-orbit coupling Hamiltonian; Indicates momentum; This represents a pseudo-spin operator.

[0040] In this embodiment of the invention, the frequency modulation signal and the polarization modulation signal are generated by the same synchronization control module and are synchronized to jointly generate a Flokai driving field in the optical lattice. Both modulation signals are generated by the synchronization control module and phase synchronization is achieved through settings, thereby constructing a stable dual-parameter Flokai modulation system.

[0041] In this embodiment of the invention, a synchronization control module is used to generate frequency modulation signals and polarization modulation signals. The synchronization control module includes an arbitrary reference clock source, a phase-locked loop, and a direct digital synthesizer or an arbitrary waveform generator or equivalent device. One signal is amplified by a high-voltage driver and drives the EOM to achieve lattice light polarization modulation; the other signal is amplified by a radio frequency driver and drives the AOM to achieve lattice light frequency modulation. The synchronization control module uses a high-stability reference clock source as a reference standard, preferably a high-stability standard frequency source, including a hydrogen clock, a rubidium clock, or a crystal oscillator, to ensure long-term phase stability between the two modulation signals. By setting and adjusting the initial phases in the synchronization control module, the relative phase between polarization modulation and frequency modulation can be precisely controlled. The relative phase remains constant during system operation, thereby constructing a stable synchronous multi-parameter Flokai modulation system.

[0042] Frequency modulation and polarization modulation are both achieved by adding an acousto-optic modulator and a polarization modulation module to the original lattice optical path. There is no need to introduce Raman lasers, multiple coherent beams or complex cavity-assisted optical paths. The overall optical path structure is compact and cost-controllable, and can be easily integrated into existing cold atom optical lattice experimental systems.

[0043] Step S104: A standing wave optical field is formed using a synchronous multi-parameter modulated lattice laser to construct an optical lattice for trapping atoms.

[0044] In this embodiment of the invention, the formation of the optical lattice is based on the principle of light interference. When two coherent laser beams meet and interfere in space, a periodically distributed light field, i.e., an optical standing wave field, is formed. The light used to form the standing wave field is a synchronously multi-parameter modulated lattice laser that has undergone periodic modulation of both frequency and polarization direction. See also... Figure 2 A multi-parameter modulated lattice laser beam, used to form the optical lattice, is focused by a lens from the left and directed towards the atomic trapping region. After passing through the atomic cloud, the focused beam continues to propagate to a concave mirror (CR), where it is reflected back along the original optical path. The reflected beam overlaps with the incident beam at the location of the atomic cloud. Since the two beams have the same frequency and propagate in opposite directions, they interfere in space to form a standing wave optical field, which constitutes the optical lattice used to trap the atoms.

[0045] In step S104, the coordinated modulation of frequency and polarization in the electrical domain is transformed into a dynamic optical lattice that can be directly perceived by atoms and is precisely programmed in both space and time. The Hamiltonian sensed by atoms loaded into this optical lattice evolves due to Flokai drive into an effective Hamiltonian containing target coupling terms such as spin-orbit coupling terms, thereby achieving precise control over the atomic quantum state and providing a platform for quantum simulation and precision measurement.

[0046] In this embodiment of the invention, a new Frokai Hamiltonian engineering is achieved by synchronizing or controlling the phase difference between polarization direction modulation and lattice light frequency modulation. The effective Hamiltonian of the system can be expressed as: ; in, Indicates the effective Hamiltonian; Represents the static lattice Hamiltonian; The Hamiltonian of the Flokai modulation is derived from the combined effect of polarization modulation and frequency modulation.

[0047] In this embodiment of the invention, the frequency-modulated laser is converted into a multi-parameter modulated lattice laser whose polarization direction changes periodically with time by a polarization modulation module. The multi-parameter modulated lattice laser maintains a linear polarization state throughout the entire modulation period, thus avoiding the vector light shift and tensor light shift caused by the introduction of elliptic polarization components in traditional polarization modulation schemes, thereby effectively suppressing the spatial structure distortion of the optical lattice potential field.

[0048] The frequency modulation signal driving the frequency modulation and the voltage modulation signal driving the polarization direction modulation originate from the synchronization control module. The two modulations have natural high-precision phase synchronization and long-term phase stability, avoiding relative phase drift and additional phase noise caused by using multiple independent signal sources. This ensures that the Flokai driving field jointly generated in the optical lattice has excellent coherence, providing a stable basis for constructing a fine Flokai effective Hamiltonian.

[0049] By coordinating two independent control dimensions—frequency modulation and polarization direction modulation—within the same optical lattice, a Flokai driving field is jointly generated. This overcomes the limitations of traditional schemes that can only modulate lattice depth, phase, or position individually. Spin-related tunneling processes can be constructed within the optical lattice, thereby achieving coupling between momentum and spin. This eliminates the need for a complex Raman-coupled optical field system, significantly reducing the complexity of the experimental system.

[0050] The modulation method employed in this invention only modulates the lattice light without introducing an additional laser frequency system. Therefore, Flokai modulation can be achieved while maintaining the stable operation of the optical lattice clock. Consequently, this invention is particularly suitable for precision measurement systems such as strontium atom optical lattice clocks and ytterbium atom optical lattice clocks.

[0051] By adjusting the frequency and phase relationship between the two modulations, various Flokai drive forms can be constructed, including but not limited to: synchronous modulation, phase-tunable modulation, multi-frequency modulation, non-sinusoidal periodic modulation, modulation at different frequencies, and spin-momentum coupling modulation, thereby expanding the types of effective Hamiltonians that can be realized in optical lattice systems, including tunneling modulation, artificial gauge field construction, spin-orbit coupling, and topological band structure manipulation.

[0052] In this embodiment of the invention, a spin-momentum coupling system is constructed through the combined effect of lattice light polarization modulation and lattice light frequency modulation. To verify the spin coupling effect generated by lattice light polarization modulation and lattice frequency modulation, the following verification experiment is conducted, specifically as follows: After primary and secondary laser cooling, approximately The atoms were cooled to On the order of magnitude of light, atoms are loaded into a deep optical lattice potential well. The depth of the lattice potential well is then adiabatically reduced and maintained for a period of time, allowing the higher-temperature atoms to escape from the optical lattice. The lattice potential well is then adiabatically restored to its initial depth. Subsequently, a 689nm clock laser is used to pump the atoms to a depth of [missing information - likely a specific depth]. or At the Zeeman sublevel, atoms within the optical lattice are spectroscopically detected by combining a two-color mirror with a synchronously multi-parameter modulated lattice laser beam. To further reduce the atomic temperature, a three-dimensional sideband cooling method is used to lower the atomic temperature to 1. In this scenario, all atoms are positioned on the Bloch baseband (with an external vibrational quantum number of 0) along the direction of the synchronous multi-parameter modulated lattice laser. When ultracold atoms are loaded into a dual-parameter Flokai-modulated optical lattice, their momentum distribution is measured using time-of-flight (TOF) imaging. Specifically, atoms are loaded into the optical lattice and dual-parameter Flokai modulation is applied. After the system reaches a steady state, all light fields are turned off, allowing the atoms to expand in free space for approximately 10–20 ms. Subsequently, an EMCCD (electron multiplier-coupled device) system is used to record the spatial distribution of the atomic cloud using absorption imaging. Since the expanded spatial distribution corresponds to the initial momentum distribution of the atoms, momentum distribution information can be obtained. When spin-orbit coupling exists in the system, the atomic momentum distribution will exhibit a significant momentum shift or a bimodal structure. By acquiring fluorescence signals using a photomultiplier tube (PMT) and analyzing the variation of momentum peak positions with Flokai modulation parameters, the effective spin-orbit coupling strength can be extracted. Furthermore, the Flokai band structure can be measured using Bloch oscillations. By tilting the lattice along the direction of gravity to form Wannier-Stark (energy ladder) states, the periodic modulation causes some gravity-induced atoms to move in momentum space, periodically traversing the first Brillouin zone of the Flokai effective Hamiltonian. These atoms will then undergo Bloch oscillations within the band structure. Experimentally, the dynamic trajectory of the atoms over time can be recorded by periodically measuring their central momentum positions. The period of the Bloch oscillation is closely related to the band structure; by fitting the oscillation trajectory, the effective dispersion relation of the Flokai band can be reconstructed.

[0053] The optical lattice synchronous multi-parameter Floquet manipulation method provided in this invention can be used to construct Floquet effective Hamiltonians, spin-orbit coupling, artificial gauge fields, Floquet band structures, or topological quantum states.

[0054] In this embodiment of the invention, after Flokai modulation, the experimental methods of "observing the bimodal structure of momentum distribution by time-of-flight imaging" and "reconstructing the band dispersion relation by Bloch oscillation" were used to quantitatively verify that the optical lattice synchronous multi-parameter Flokai modulation method and system provided in this embodiment did indeed induce the spin-orbit coupling effect and achieved effective control of the quantum band structure.

[0055] Based on the same inventive concept, embodiments of the present invention also provide an optical lattice synchronous multi-parameter Flokai control system, comprising: Lattice light generation module, used to generate lattice light; The frequency modulation module is used to modulate the frequency of lattice light through an acousto-optic modulator, so that the frequency of the lattice light changes with time according to a preset periodic function to generate frequency-modulated laser. The polarization modulation module is used to receive frequency-modulated laser light, introduce a time-varying phase delay through an electro-optic modulator, and combine it with waveplates respectively placed before and after the electro-optic modulator. The phase delay is converted into a periodic rotation of the linear polarization direction through polarization modulation to obtain a synchronous multi-parameter modulated lattice laser that always maintains linear polarization. The standing wave optical field forming module is used to form a standing wave optical field using synchronous multi-parameter modulated lattice lasers to construct an optical lattice for trapping atoms; The synchronization control module is used to control the unified generation and synchronous driving of frequency modulation and polarization modulation, and to maintain a stable and adjustable relative phase relationship between the modulation channels of frequency modulation and polarization modulation.

[0056] Among them, the polarization modulation module keeps the output light in a linear polarization state throughout the modulation process.

[0057] In this embodiment of the invention, the frequency-modulated laser is converted into a synchronous multi-parameter modulated lattice laser whose polarization direction changes periodically with time by a polarization modulation module. The synchronous multi-parameter modulated lattice laser maintains a linear polarization state throughout the entire modulation period, thus avoiding the vector light shift and tensor light shift caused by the introduction of elliptic polarization components in traditional polarization modulation schemes, thereby effectively suppressing the spatial structure distortion of the optical lattice potential field.

[0058] Frequency modulation and polarization modulation are uniformly generated and synchronously driven by a synchronization control module. The two modulations possess inherent high-precision phase synchronization and long-term phase stability, avoiding relative phase drift and additional phase noise caused by using multiple independent signal sources. This ensures excellent coherence of the jointly generated Flokai driving field in the optical lattice, providing a stable foundation for constructing a finely detailed Flokai effective Hamiltonian. By synergistically applying two independent control dimensions—frequency modulation and polarization direction modulation—to the same optical lattice to jointly generate the Flokai driving field, the limitations of traditional schemes that can only modulate lattice depth, phase, or position individually are overcome. Spin-related tunneling processes can be constructed in the optical lattice, thereby achieving coupling between momentum and spin. A complex Raman-coupled optical field system is unnecessary, significantly reducing the complexity of the experimental system.

[0059] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0060] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0061] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0062] As the system medium embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.

[0063] It should be noted that the system in this embodiment of the invention is a system that applies the above-mentioned optical lattice synchronous multi-parameter Flokai control method. Therefore, all embodiments of the above-mentioned optical lattice synchronous multi-parameter Flokai control method are applicable to this system and can achieve the same or similar beneficial effects.

[0064] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for synchronous multi-parameter Flokai modulation of optical lattices, characterized in that, include: Generates lattice light; The frequency of the lattice light is modulated by an acousto-optic modulator, so that the frequency of the lattice light changes with time according to a preset periodic function, thereby generating frequency-modulated laser. The frequency-modulated laser is input into a polarization modulation module, where a time-varying phase delay is introduced by an electro-optic modulator. Combined with waveplates positioned before and after the electro-optic modulator, the phase delay is converted into a periodic rotation of the linear polarization direction through polarization modulation, resulting in a synchronously multi-parameter modulated lattice laser that maintains linear polarization throughout. The frequency modulation and polarization modulation are uniformly generated and synchronously driven by a synchronization control module, and the modulation channels of the frequency modulation and polarization modulation have a stable and adjustable relative phase relationship. The synchronous multi-parameter modulated lattice laser is used to form a standing wave optical field to construct an optical lattice for trapping atoms.

2. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, Frequency modulation of the lattice light is achieved by using an acousto-optic modulator, causing the frequency of the lattice light to change with time according to a preset periodic function, thereby generating frequency-modulated laser light, including: The synchronization control module is used to generate a frequency modulation signal; The frequency modulation signal is amplified by the radio frequency driver and then applied to the acousto-optic modulator to frequency modulate the lattice light and generate frequency-modulated laser.

3. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, The phase delay is converted into a periodic rotation of the linear polarization direction by polarization modulation to obtain a synchronous multi-parameter modulated lattice laser that always maintains linear polarization, including: The synchronization control module is used to generate a voltage modulation signal; The voltage modulation signal is amplified by a high-voltage driver and then applied to the electro-optic modulator. The phase delay is converted into a periodic rotation of the linear polarization direction by the polarization modulation module, thereby obtaining a synchronous multi-parameter modulated lattice laser that always maintains linear polarization.

4. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, The polarization modulation module includes, in sequence, a first... Waveplate, the electro-optic modulator and the second Waveplate; among which Indicates wavelength.

5. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 4, characterized in that, The first The optical axis of the waveplate is set to an optical axis angle of 45°; the second The optical axis of the waveplate is set to an optical axis angle of -45°.

6. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, The synchronous multi-parameter modulated lattice laser includes: ； in, This indicates that the synchronous multi-parameter modulated lattice laser is in The polarization direction angle at that moment; Indicates the initial polarization direction angle; Indicates the modulation amplitude in the polarization direction; Indicates the Flokai modulation angular frequency; This indicates the initial phase of the modulation channel of the polarization modulation.

7. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, Frequency modulation of the lattice light is achieved by using an acousto-optic modulator, causing the frequency of the lattice light to change with time according to a preset periodic function, thereby generating frequency-modulated laser light, including: ； in, This indicates that the frequency-modulated laser is in Frequency of time; This indicates the frequency of the lattice light when it is not modulated; Indicates the frequency modulation amplitude; Indicates the lattice light modulation frequency; This indicates the initial phase of the modulation channel of the frequency modulation.

8. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, The relative phase relationship between the frequency modulation modulation channel and the polarization modulation modulation channel is as follows: ； in, This indicates the relative phase between the modulation channel of the frequency modulation and the modulation channel of the polarization modulation; This indicates the initial phase of the modulation channel of the frequency modulation; This indicates the initial phase of the modulation channel of the polarization modulation.

9. The optical lattice synchronous multi-parameter Flokai modulation method according to claim 1, characterized in that, The optical lattice synchronous multi-parameter Floquet manipulation method is used to construct Floquet effective Hamiltonians, spin-orbit coupling, artificial gauge fields, Floquet band structures, or topological quantum states.

10. A synchronous multi-parameter Flokai control system for optical lattices, characterized in that, include: Lattice light generation module, used to generate lattice light; A frequency modulation module is used to frequency modulate the lattice light using an acousto-optic modulator, so that the frequency of the lattice light changes with time according to a preset periodic function to generate frequency-modulated laser. A polarization modulation module is used to receive the frequency-modulated laser, introduce a time-varying phase delay through an electro-optic modulator, and combine it with waveplates respectively set before and after the electro-optic modulator. The phase delay is converted into a periodic rotation of the linear polarization direction through polarization modulation to obtain a synchronous multi-parameter modulated lattice laser that always maintains linear polarization. A standing-wave optical field forming module is used to form a standing-wave optical field using the synchronous multi-parameter modulated lattice laser to construct an optical lattice for trapping atoms; The synchronization control module is used to control the unified generation and synchronous driving of the frequency modulation and the polarization modulation, and to maintain a stable and adjustable relative phase relationship between the modulation channel of the frequency modulation and the modulation channel of the polarization modulation.

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