Ultra-cold atomic wave function density measurement method, device and system and storage medium

Abstract

The invention relates to the technical field of quantum precision measurement, in particular to a super-cold atomic wave function density measurement method, device and system and a storage medium. According to the method, a dark-state selective transfer mechanism of three-energy-level atoms is utilized, two groups of spatial modulation lattice light with the same frequency and adjustable phases are precisely designed, sub-wavelength detection of super-cold atomic wave function density distribution is achieved, and compared with a super-cold atomic wave function density imaging technology in the prior art, the method has the advantages that the sub-wavelength detection efficiency is improved. The requirements of spatial resolution and high signal-to-noise ratio are considered at the same time, and the wave function density measurement and imaging precision is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of quantum precision measurement technology, and in particular to a method, apparatus, system and storage medium for measuring the wave function density of ultracold atoms. Background Technology

[0002] In exploring quantum many-body physics phenomena (such as phase transitions, quantum correlations, tunneling, and transport), high-speed and high-resolution imaging of the wave function density distribution of ultracold atoms is required. However, traditional optical microscopy is limited by the diffraction limit, and its spatial resolution and sensitivity are significantly insufficient when the imaging scale is reduced to the micrometer or even nanometer scale.

[0003] Quantum microscopy has become an effective means to overcome the optical diffraction limit, but its complex system structure and high equipment cost pose challenges for its widespread application in many-body physics experiments. In addition, two types of super-resolution imaging methods have been proposed both domestically and internationally: one is based on random super-resolution technology, which is mainly for point source imaging but struggles to obtain continuous density distribution information within a single lattice site; the other is subwavelength imaging based on nonlinear optical responses, which utilizes the nonlinear response of atoms to spatial changes in the light field to achieve subwavelength resolution. However, in practical applications, as resolution increases, the signal-to-noise ratio decreases rapidly, often requiring multiple measurements to be superimposed to obtain a usable signal, thus limiting measurement efficiency and atomic retention. Summary of the Invention

[0004] Therefore, it is necessary to provide a method and device for measuring the wave function density of ultracold atoms to address the above problems. By utilizing the dark-state selective transfer mechanism of three-level atoms and through the precise design of two sets of spatially modulated lattice lights with the same frequency and adjustable phase, subwavelength detection of the wave function density distribution of ultracold atoms is achieved. Compared with the existing technology for imaging the wave function density of ultracold atoms, it simultaneously meets the requirements of spatial resolution and high signal-to-noise ratio, effectively improving the accuracy of wave function density measurement and imaging.

[0005] In one embodiment, the present invention provides a method for measuring the wavefunction density of ultracold atoms, comprising: S10, obtain ultracold atomic groups in the ground state; among them, ultracold atomic groups are three-level atomic groups; S20, apply a phase-tunable dual-lattice light field to the ultracold atomic cluster and determine the probability of the ultracold atomic cluster in the ground state transitioning to the target state under the action of the Hamiltonian of the dual-lattice light; wherein, the dual-lattice light field includes a probe light and a coupling light of the same frequency, the probe light and the coupling light have a phase difference and their Rabi frequency peak ratio is... ; S30, the phase modulation device controlling the probe light and coupling light scans the phase of the two lattice lights from 0° to 360° with a fixed phase difference, and obtains a set of transition probabilities corresponding to the ultracold atomic group transitioning from the ground state to the target state for each phase; S40, turn off the coupling light and the probe light, and reconstruct the wave function density distribution map of the ultracold atomic group according to a set of transition probabilities corresponding to the transition from the ground state to the target state of the ultracold atomic group in each phase.

[0006] Furthermore, S20 includes, S201, constructing a system that meets the requirements of "adjustable phase, identical frequency, existence of phase difference, and Rabi peak frequency ratio". The light field of the two lattice beams is represented as follows: in, To detect the spatial distribution of the light field, The spatial distribution of the optical field of the coupled light. To detect the Rabi frequency peak of light, The peak value of the Rabi frequency of the coupled light. This provides the spatial coordinates of the light field. The phase difference between the two beams of lattice light. For wave number, , The wavelength of the laser; S202, simultaneously activating the probe light and coupling light, under the influence of the Hamiltonian of the probe light and coupling light, the ultracold atomic group in the ground state transitions to the target state or forms a space-dependent dark state; wherein, the Hamiltonian is expressed as follows: H= Among them, the diagonal element represents the three energy levels of the ultracold atom (the ground state and target state energy levels are 0, and the intermediate resonance state energy level is 2Δ). To detect the spatial distribution of the light field, The spatial distribution of the optical field of the coupled light; The dark state The normalized expression is as follows: ; S203, based on the spatial positions of the probe light and the coupling light and the phase difference, determine the transition probability of the ultracold atomic cluster from the ground state to the target state; wherein, the probability of the ultracold atomic cluster in the ground state transitioning to the target state is expressed as follows: .

[0007] Furthermore, in S202, two beams of lattice light, under the influence of Hamiltonian, couple with the intermediate resonance state of ultracold atoms through two-photon resonance, transferring the ultracold atom cluster in the ground state to the target state; wherein, the resonance condition of the two beams of lattice light is as follows: in, It is Planck's constant. To detect the frequency of the light and the coupled light, This represents the energy of the intermediate resonance state.

[0008] Furthermore, in S202, when the adiabatic condition is met, the ultracold atom transitions from the ground state to the target state; where the adiabatic condition is that the switching time of the light field is much longer than the transition period of the ultracold atom.

[0009] Furthermore, the Rabi frequency peak ratio of the probe light and the coupling light .

[0010] Furthermore, in S30, the fixed phase difference is 1°.

[0011] Furthermore, S10 includes, S101, obtain three-level atoms, and cool the three-level atoms to obtain high-density atomic clusters; S102, perform ultracold state optimization on the obtained high-density atomic clusters to obtain optimized ultracold atomic clusters; S103, the ultracold atomic group is prepared in its ground state to obtain an ultracold atomic group in its ground state.

[0012] In one embodiment, the present invention also provides an ultracold atom wavefunction density measurement device, comprising: The acquisition module is used to acquire ultracold atomic groups in their ground state; wherein, the ultracold atomic groups are three-level atomic groups; A determination module is used to apply a phase-tunable dual-lattice light field to the ultracold atomic cluster and determine the probability that the ultracold atomic cluster in the ground state will transition to the target state under the action of the Hamiltonian of the dual-lattice light; wherein, the dual-lattice light field includes a probe light and a coupling light of the same frequency, the probe light and the coupling light have a phase difference and their Rabi frequency peak ratio is... ; The control module is used to control the phase modulation device of the probe light and the coupling light to scan the phase of the two lattice lights from 0° to 360° with a fixed phase difference, and obtain a set of transition probabilities corresponding to the ultracold atomic group transitioning from the ground state to the target state for each phase; The reconstruction module is used to turn off the coupling light and the probe light, and reconstruct the wave function density distribution map of the ultracold atomic group based on a set of transition probabilities corresponding to the transition from the ground state to the target state of the ultracold atomic group in each phase.

[0013] In one embodiment, the present invention also provides an ultracold atom wave function density measurement system, including a control device, a coupling laser, a probe laser, and a phase modulation device. The phase modulation device is connected to the coupling laser and the probe laser respectively. The control device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps of the measurement method described above.

[0014] In one embodiment, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the measurement method described in any of the preceding claims.

[0015] Compared with the prior art, the present invention has the following advantages: 1. Significantly improved resolution This invention achieves subwavelength detection of the wave function density distribution of ultracold atoms by precisely designing the phase and Rabi frequency peak ratio of the dual-lattice light field, with a spatial resolution of up to 10 nm, breaking through the limitations of the traditional diffraction limit and outperforming existing super-resolution technologies.

[0016] 2. Enhanced signal-to-noise ratio This invention utilizes the dark-state selective transfer mechanism of three-level atoms to maintain an extremely high signal-to-noise ratio under high-resolution imaging conditions. Example results show that the signal-to-noise ratio is improved from 0.86 in a single-lattice configuration to 1 in a dual-lattice configuration, a relative improvement of approximately 16.3%, significantly enhancing the resolvability and edge sharpness of the image signal.

[0017] 3. Simplified system configuration and controllable cost Compared with dedicated super-resolution instruments such as quantum microscopes, this invention only requires two sets of phase-controllable optical lattices for the core optical path. The hardware structure is simple, the control is stable and reliable, and its design is easy to integrate with existing ultracold atom experimental platforms. This effectively avoids the development and use costs of dedicated equipment and reduces the complexity of equipment purchase and maintenance. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Furthermore, the accompanying drawings are not drawn to a 1:1 scale, and the relative dimensions of the various components are shown in the drawings only as examples and not necessarily to actual scale.

[0021] Figure 1 This is a schematic flowchart of the ultracold atom wave function density measurement method provided in an embodiment of the present invention; Figure 2 This is an energy level structure diagram of a three-level atom involved in an embodiment of the present invention; Figure 3 This is a schematic diagram of the spatial distribution of the light field of a dual-lattice light provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the change of spatial resolution with phase difference in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the change of transfer probability with spatial location under existing single-lattice light and weakly homogeneous light configurations. Figure 6 This is a schematic diagram illustrating the variation of the transfer probability with spatial position under a dual-lattice optical configuration provided in an embodiment of the present invention. Figure 7 This is a schematic diagram of the structure of the ultracold atom wave function density measurement device provided in an embodiment of the present invention. Detailed Implementation

[0022] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0023] See Figure 1 , Figure 1 A flowchart illustrating an embodiment of the ultracold atom wavefunction density measurement method of the present invention is shown, including: S10, obtain ultracold atomic groups in the ground state; among them, ultracold atomic groups are three-level atomic groups; Specifically, alkali metal atoms with N ≥ 3 energy levels can be selected to prepare ultracold atomic clusters. Alkali metal atoms have a clear energy level structure, making it easier to achieve coupling between the ultracold state and three energy levels. In this embodiment, three-level 87Rb atoms are selected to prepare ultracold atomic clusters. Further details can be found in the following sections. Figure 2 The energy level structure of a three-level atom is as follows: ground state : The initial state of the initial population of atoms (energy E1=0); target state The final target state (energy E2=0) used to measure the population. intermediate resonance state The coupling energy level of the two-photon resonance (energy E3 = 2Δ) enables indirect coupling between the ground state and the intermediate resonance state, and between the target state and the intermediate resonance state. Understandably, the target state is a low-energy target state used for population measurement and light detection. Coupled from ground state to intermediate resonant state, coupled light Couple the target state to the intermediate resonant state.

[0024] Furthermore, S10 includes, S101, obtain three-level atoms, and cool the three-level atoms to obtain high-density atomic clusters; Specifically, after obtaining the three-level 87Rb atoms, the three-level 87Rb atoms can be cooled using magneto-optical trap (MOT) technology to reduce the atomic temperature to the μK level, forming a high-density atomic cluster (number of atoms ≈ 10). 6 ~10 8 ).

[0025] S102, perform ultracold state optimization on the obtained high-density atomic clusters to obtain optimized ultracold atomic clusters; Specifically, after obtaining a high-density atomic cluster through cooling, the cooling laser of the magneto-optical trap is turned off, and the optical dipole trap (ODT) is turned on to confine the high-density atomic cluster. The temperature of the high-density atomic cluster is further reduced to the nK level (ultra-cold state) through evaporative cooling, thereby avoiding wave function broadening caused by the thermal motion of atoms.

[0026] S103, the ultracold atomic group is prepared in its ground state to obtain an ultracold atomic group in its ground state.

[0027] Specifically, after obtaining the ultracold atomic clusters, laser spectroscopy technology can be used to precisely arrange the ultracold atomic clusters to the ground state; in this embodiment, non-ground state ultracold atomic clusters can be further removed by radio frequency field or laser pulse, thereby ensuring that the purity of the obtained ultracold atomic clusters in the ground state is ≥99%.

[0028] S20, apply a phase-tunable dual-lattice light field to the ultracold atomic cluster and determine the probability of the ultracold atomic cluster in the ground state transitioning to the target state under the action of the Hamiltonian of the dual-lattice light; wherein, the dual-lattice light field includes a probe light and a coupling light of the same frequency, the probe light and the coupling light have a phase difference and their Rabi frequency peak ratio is... ; Understandably, lattice light is a periodic optical field formed by the interference of laser beams. Lattice light is formed by the interference of laser beams propagating in opposite directions, producing a spatially periodic intensity distribution, thus forming a periodic potential field. Ultracold atoms are trapped in this potential field through Stark shift. Depending on the detuning between the laser frequency and the atomic resonance frequency, the ultracold atoms are concentrated at potential extrema. For example, in a blue-detuned lattice, atoms are concentrated at the maximum potential value (the valley of light intensity), and in a red-detuned lattice, atoms are concentrated at the minimum potential value (the peak of light intensity). Red detuning occurs when the laser frequency is less than the atomic resonance frequency (detuning Δ < 0), and blue detuning occurs when the laser frequency is greater than the atomic resonance frequency (detuning Δ > 0).

[0029] Furthermore, S20 includes, S201, constructing a system that meets the requirements of "adjustable phase, identical frequency, existence of phase difference, and Rabi peak frequency ratio". "The double lattice light field; Specifically, two narrow-linewidth semiconductor lasers can be selected to form a dual-lattice optical field by outputting probe and coupling beams with the same frequency. In this embodiment, the wavelengths of the probe and coupling beams can be 788 nm to match the selected 87Rb atoms and achieve two-photon resonance. By using an optical fiber beam splitter or beam combiner, the frequencies of the probe and coupling beams are made the same to ensure coherence. Figure 3 The spatial distribution of the dual-lattice light field of the coupled and probe beams with a phase difference in space is given. , The manifestation of this. Understandably, phase difference... The phase difference determines the interference contrast between the two beams; the smaller the phase difference, the finer the spatial modulation and the higher the spatial resolution. Therefore, in this embodiment, a phase difference is pre-set between the probe beam and the coupling beam to improve the spatial modulation fineness of the two lattice beams. The spatial distribution of the light field of the two lattice beams is shown below: in, To detect the spatial distribution of the light field, The spatial distribution of the optical field of the coupled light. To detect the Rabi frequency peak of light, The peak value of the Rabi frequency of the coupled light. For the spatial position information of ultracold atoms in the light field, The phase difference between the two beams of lattice light. For wave number, , is the laser wavelength.

[0030] Specifically, the periodic spatial distribution of the two lattice beams forms an alternating "node-antinode" structure, thus providing a spatial scale for subwavelength detection. In this embodiment, the power of the coupling beam is set higher than that of the probe beam, such that the peak Rabi frequency ratio of the probe beam and the coupling beam is higher than that of the probe beam. This ensures that spatial modulation is dominated by the coupled light, further refining the spatial resolution. Simultaneously, the stability of the Rabi frequency peak ratio of the probe and coupled light can be ensured by measuring the resonant transition rates of ultracold atoms in the dual-lattice light field.

[0031] Furthermore, phase modulation devices are installed on the radiation paths of the two beams of lattice light that excite ultracold atoms to adjust the phase difference between the probe light and the coupling light. These phase modulation devices can be high-precision electro-optic modulators (EOMs) or acousto-optic modulators (AOMs). By setting and calibrating the two phase modulation devices on the optical path, a phase difference is established between the probe light and the coupling light. And the phase difference The system stabilizes at the initial set value, thus preventing phase jitter. Understandably, the smaller the phase difference, the finer the spatial modulation. Figure 4 A graph showing the variation of spatial resolution with phase difference is provided.

[0032] S202, controlling the simultaneous activation of the probe light and coupling light, under the influence of the Hamiltonian of the probe light and coupling light, the ultracold atomic group in the ground state transitions to the target state or forms a space-dependent dark state; wherein, the Hamiltonian is expressed as follows: H= Among them, the diagonal element represents the three energy levels of the ultracold atom (the ground state and target state energy levels are 0, and the intermediate resonance state energy level is 2Δ). To detect the spatial distribution of the light field, The spatial distribution of the optical field of the coupled light; The dark state The normalized expression is as follows: Specifically, there are phase differences and Rabi frequency peak ratios. Two beams of lattice light (coupled beam and probe beam), under the influence of the Hamiltonian, couple with the intermediate resonance state of ultracold atoms through two-photon resonance. This can transfer ultracold atomic clusters in the ground state to the target state, avoiding the decoherence of atomic spontaneous emission caused by single-photon resonance and ensuring the stability of the quantum state. The two-photon resonance condition can be understood as follows: in, To detect the photon energy of light, The photon energy of the coupled light. This represents the energy level difference between the intermediate resonance state and the ground state. It is Planck's constant. To detect the frequency of light, The frequency of the coupled light; To ensure that the sum of the energies of the two lattice beams exactly matches the energy difference between the ground state and the intermediate state, enabling two-photon resonance to couple from the ground state to the target state and guaranteeing optical field coherence to form stable interference fringes, this embodiment sets the frequencies of the two lattice beams of the probe beam and the coupling beam to be the same, i.e., the photon energies are the same. The resonance condition for the two photons is then: ;in, To detect the frequency of the light and the coupled light.

[0033] Understandably, two beams of lattice light cannot directly achieve cross-level coupling between the ground state and the target state; therefore, "indirect coupling" is achieved through the intermediate resonance state of ultracold atoms. (Probe light) With the formation of a "virtual coupling" between the ground state and the intermediate resonance state, ultracold atoms will briefly be in a superposition state of the ground state and the intermediate resonance state, coupled with light. By forming a "virtual coupling" with the target state and the intermediate resonance state, the ultracold atom briefly exists in a superposition state of the ground state |2>+ and the intermediate resonance state. When two beams of lattice light of the same frequency excite the ultracold atom, the atom absorbs a probe photon and a coupling photon, with a total energy of Just equal to (Two-photon resonance) At this point, "virtual coupling" is transformed into "effective coupling," and ultracold atoms can transmit interactions between the ground state and the target state through an intermediate resonance state. Understandably, the intermediate resonance state has no atomic population.

[0034] When two beams of lattice light with the same frequency excite ultracold atoms, they satisfy the two-photon resonance condition, allowing the energy of the two beams to synergistically fill the energy level differences between the ground state and the intermediate resonance state, as well as between the target state and the intermediate resonance state. This enables the ground state and the target state to form an "energy level connection" through the intermediate resonance state, achieving effective coupling between the ground state and the target state. Understandably, the coupling strength of the two beams is determined by their respective Rabi frequencies and is related to the spatial distribution of the light field. , Strong correlation.

[0035] Furthermore, in step S202, under the influence of the Hamiltonian of the probe light and the coupling light, the ultracold atoms cannot transfer all the ultracold atom groups in the ground state to the target state. When the adiabatic condition is met, the ultracold atoms transfer from the ground state to the target state. Therefore, the ultracold atoms adiabatically transfer from the ground state to the target state or form a space-dependent dark state. The bright and dark states formed by the transfer to the target state can directly map the spatial density distribution of the wave function. Specifically, the energy level lifetime of the intermediate resonance state matches the light field interaction time. Therefore, the adiabatic condition is that the switching time of the light field is much greater than the transition period of the ultracold atoms, that is, the change rate of the Rabi frequency of the light field is much smaller than the equivalent Rabi frequency. When the adiabatic transfer time of the light field is much greater than the lifetime of the intermediate resonance state, the ultracold atoms transfer from the ground state to the target state to ensure the coupling strength.

[0036] Furthermore, the two beams of lattice light are coupled to the intermediate resonance state through two-photon resonance, achieving effective coupling between the ground state and the target state. Then, a dark state is formed through quantum destructive interference between the ground state and the target state. Therefore, it can be understood that the dark state is a quantum superposition state formed by the coherent superposition of the ground state and the target state. It has no independent energy levels; its energy is determined by the energies of the ground state and the target state, E1 = E2 = 0, therefore the energy of the dark state is 0. Because of the quantum destructive interference between the ground state and the target state in the quantum superposition state, i.e., "the transition amplitudes are completely canceled out," atoms in the dark state do not couple with the light field, and the coupling strength with the light field is 0. Ultracold atomic clusters in the dark state will not be excited to the intermediate resonance state by the light field; only ultracold atomic clusters in the non-dark state will transfer to the target state.

[0037] Under the coupling effect of two beams of lattice light, the dark state (quantum superposition state) of the ultracold atomic cluster is represented as follows: in, , This is the superposition coefficient; Understandably, the coupling strength between an atom and the light field is determined by the "transition amplitude." The larger the transition amplitude, the higher the probability that the atom is excited to the target state. The essence of the transition amplitude is the "sum of contributions" of the ground state and the target state to the light field in the quantum superposition. Specifically, the transition amplitude of the ground state coupling with the intermediate resonance state through probe light can be expressed as: ( (This refers to the coupling strength of the probe light at spatial position x); the transition amplitude of the target state coupled with the intermediate state through the coupling light can be expressed as: ( (This refers to the coupling intensity of the coupled light at spatial position x); the dark state requires that "the total transition amplitude is 0" (i.e., atoms are not coupled with the light field), so the transition amplitude of the dark state can be expressed as... (Because of the opposite phase, it exhibits destructive interference), from which we can conclude: =0 The normalized expression for the dark state is further obtained as follows: S203, based on the spatial positions of the probe light and the coupling light and the phase difference, determine the transition probability of the ultracold atomic cluster from the ground state to the target state; wherein, the probability of the ultracold atomic cluster in the ground state transitioning to the target state is expressed as follows: Understandably, the transfer probability of ultracold atomic groups Indicates spatial location The probability of an atom at a given location transitioning from its ground state to its target state varies with its spatial location. Changes, different spatial locations Corresponding to different transition probabilities ,because ,therefore It will exhibit a periodic distribution of "narrow peaks and wide valleys". The peak value corresponds to a high atomic density (atoms can transition from the ground state to the target state). In regions where the valley value corresponds to a low atomic density (dark state), the valley value represents the region where the valley value corresponds to ... This creates a spatially dependent "high-resolution population distribution" within a specific region. Understandably, this involves the transition probability... The full width at half maximum (FWHM) is the spatial resolution, and its expression is as follows: It can be seen that the phase difference The smaller the detection light and coupled light The more intense the interference, the higher the transition probability. The narrower the peak value, the higher the spatial resolution (FWHM). Therefore, the phase difference between the two lattice beams can be controlled. And the Rabi peak frequency ratio compresses the spatial resolution to the subwavelength scale.

[0038] The spatial distribution of the dark states formed by ultracold atoms and the bright states transferred to the target state can be mapped to the wave function density of the ultracold atom cluster, and its spatial distribution is spatially modulated by two beams of lattice light. and phase difference To determine, in certain spatial locations (For example, at the nodes of the lattice light). At this time, the dark state The probability of an atom transitioning from its ground state to its target state. At this time, there is no fluorescent signal; in other spatial locations (e.g., at the antinode of a strong light field). When quantum destructive interference is broken, the atom is no longer in a dark state and will transition from the ground state to the target state through an intermediate resonance state. The probability of transitioning to the target state... .

[0039] The following example illustrates this: With a wavelength of 788nm, For example, Figure 5 The graph shows the variation of the transfer probability with spatial location (in wavelength) in the prior art. The light fields of single-lattice light and homogeneous light configurations, although transferred to... The transition probability P of the state can reach 1; however, the minimum transition probability point is located at the antinode of the single-lattice light. =1, because there is weak uniform light at this time ( Its transition probability P is approximately 0.14, and it is calculated as follows: Signal-to-noise ratio (SNR) can be understood as the contrast or modulation depth of the transition probability, and its calculation formula is as follows: According to the above formula, the signal-to-noise ratio at this time is: Also using a wavelength of 788nm, , For example, Figure 6 The diagram showing the transition probability as a function of spatial location (in wavelength) in the scheme provided by this invention is presented. For a dual-lattice configuration consisting of a coupling light and a probe light with the same frequency and a phase difference, the light located in the strong lattice (coupled light)... hour , transferred to The transition probability at the highest point P=1 occurs when the light is in the weak lattice (probe) state. =0, transition to The transition probability at the state is at its minimum point P=0; According to the above formula, the signal-to-noise ratio at this time is: Therefore, in this embodiment, by precisely designing two sets of spatially modulated lattice lights with the same frequency and adjustable phase, subwavelength detection of the wave function density distribution of ultracold atoms is achieved. Compared with the existing technology for imaging ultracold atom wave function density, it simultaneously meets the requirements of spatial resolution and high signal-to-noise ratio.

[0040] S30, by controlling the phase modulation devices connected to the probe light and the coupling light respectively, the phase of the two lattice lights is scanned from 0° to 360° with a fixed phase difference, and a set of transition probabilities corresponding to the ultracold atomic group transitioning from the ground state to the target state in each phase is obtained; Specifically, the phase change of the two beams is controlled by a fixed phase difference, which moves the interference fringes of the double-lattice light field to perform point-by-point detection of the ultracold atomic cluster at a subwavelength scale. Each phase corresponds to a set of spatial position transition probabilities. Preferably, the fixed phase difference is 1°. During the scanning process, the laser power and frequency of the coupling light and the probe light, as well as the temperature of the ultracold atomic cluster, are kept stable to avoid signal distortion caused by external factors (such as vibration and temperature changes).

[0041] S40, turn off the coupling light and the probe light, and reconstruct the wave function density distribution map of the ultracold atomic group according to a set of transition probabilities corresponding to the transition from the ground state to the target state of the ultracold atomic group in each phase.

[0042] Understandably, the probability density of an atomic wavefunction is proportional to the transition probability of the atom to the target state, as expressed below: In this embodiment, The spatial distribution directly reflects the wave density distribution of atoms. After obtaining a set of transition probabilities corresponding to the transition of the ultracold atomic group from the ground state to the target state in each phase, a plot is drawn. Depending on spatial location The wave function density distribution map of the ultracold atomic group can be obtained by observing the change curve.

[0043] The ultracold atom wave function density measurement method provided by this invention, through precise design of two sets of spatially modulated double-lattice light with tunable phases, identical frequencies, and a phase difference, utilizes the dark-state coupling between the three-level structure of the ultracold atom cluster and the double-lattice light field to transform the wave function density distribution into a measurable value. By analyzing the population distribution and then breaking the diffraction limit through phase scanning, the full width at half maximum (FWHM) of the population can be compressed to the subwavelength scale, thereby achieving subwavelength, high signal-to-noise ratio imaging. Only two sets of phase-tunable dual-lattice light are required, eliminating the need for the complex interference optical paths or dedicated detectors of quantum microscopes, resulting in a simpler and lower-cost system.

[0044] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but may be executed at different times. The execution order of these steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the steps or stages in other steps.

[0045] In one embodiment, such as Figure 7 As shown, a method and apparatus for measuring the wave function density of ultracold atoms are provided, including, The acquisition module M1 is used to acquire ultracold atomic groups in the ground state; wherein, the ultracold atomic groups are three-level atomic groups; Module M2 is configured to apply a phase-tunable dual-lattice optical field to the ultracold atomic cluster and determine the probability of the ultracold atomic cluster in the ground state transitioning to the target state under the influence of the Hamiltonian of the dual-lattice light; wherein the dual-lattice optical field includes a probe light and a coupling light of the same frequency, the probe light and the coupling light having a phase difference and their Rabi frequency peak ratio being... ; The control module M3 is used to scan the phase of the two lattice beams from 0° to 360° with a fixed phase difference by controlling the phase modulation devices connected to the probe beam and the coupling beam respectively, so as to obtain a set of transition probabilities corresponding to the ultracold atomic group transitioning from the ground state to the target state in each phase; The reconstruction module M4 is used to turn off the coupling light and the probe light, and reconstructs the wave function density distribution map of the ultracold atomic group based on a set of transition probabilities corresponding to the transition from the ground state to the target state of the ultracold atomic group in each phase.

[0046] Specific limitations regarding the ultracold atom wavefunction density measurement device can be found in the limitations of the ultracold atom wavefunction density measurement method described above, and will not be repeated here. Each module in the aforementioned ultracold atom wavefunction density measurement device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0047] In one embodiment, the present invention also provides an ultracold atom wave function density measurement system, including a control device, a coupling laser, a probe laser, and a phase modulation device. The phase modulation device is connected to the coupling laser and the probe laser respectively. The control device includes a memory and a processor. The memory stores a computer program, including the steps of implementing any of the measurement methods provided in the above embodiments when the processor executes the computer program.

[0048] In one embodiment, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the measurement methods provided in the above embodiments.

[0049] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0050] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0051] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for measuring the wave function density of ultracold atoms, characterized in that, include: S10, obtain ultracold atomic groups in the ground state; among them, ultracold atomic groups are three-level atomic groups; S20, apply a phase-tunable dual-lattice light field to the ultracold atomic cluster and determine the probability of the ultracold atomic cluster in the ground state transitioning to the target state under the action of the Hamiltonian of the dual-lattice light; wherein, the dual-lattice light field includes a probe light and a coupling light of the same frequency, the probe light and the coupling light have a phase difference and their Rabi frequency peak ratio is... ; S30, control and probe light and coupling light connected to phase modulation devices respectively scan the phase of the two lattice light beams from 0° to 360° with a fixed phase difference, and obtain a set of transition probabilities corresponding to the ultracold atomic group transitioning from the ground state to the target state in each phase; S40, turn off the coupling light and the probe light, and reconstruct the probability density distribution map of the ultracold atomic group based on a set of transition probabilities corresponding to the transition from the ground state to the target state of the ultracold atomic group in each phase.

2. The method for measuring the wave function density of ultracold atoms according to claim 1, characterized in that, S20 includes, S201, construct a system that meets the requirements of "adjustable phase, identical frequency, phase difference, and Rabi peak frequency ratio". The light field of the two lattice beams is represented as follows: in, To detect the spatial distribution of the light field, The spatial distribution of the optical field of the coupled light. To detect the Rabi frequency peak of light, The peak value of the Rabi frequency of the coupled light. This provides the spatial coordinates of the light field. The phase difference between the two beams of lattice light. For wave number, , The wavelength of the laser; S202, controlling the simultaneous activation of the probe light and coupling light, under the influence of the Hamiltonian of the probe light and coupling light, the ultracold atomic group in the ground state transitions to the target state or forms a space-dependent dark state; wherein, the Hamiltonian is expressed as follows: H= Among them, the diagonal element represents the three energy levels of the ultracold atom (the ground state and target state energy levels are 0, and the intermediate resonance state energy level is 2Δ). To detect the spatial distribution of the light field, The spatial distribution of the optical field of the coupled light; The dark state The normalized expression is as follows: ； S203, based on the spatial positions of the probe light and the coupling light and the phase difference, determine the transition probability of the ultracold atomic cluster from the ground state to the target state; wherein, the probability of the ultracold atomic cluster in the ground state transitioning to the target state is expressed as follows: 。 3. The method for measuring the wave function density of ultracold atoms according to claim 2, characterized in that, In S202, two beams of lattice light, under the influence of Hamiltonian, couple with the intermediate resonance state of ultracold atoms through two-photon resonance, transferring the ultracold atom cluster in the ground state to the target state; the resonance conditions of the two beams of lattice light are as follows: in, It is Planck's constant. To detect the frequency of the light and the coupled light, This represents the energy of the intermediate resonance state.

4. The method for measuring the wave function density of ultracold atoms according to claim 2, characterized in that, In S202, when the adiabatic condition is met, the ultracold atom transitions from the ground state to the target state; where the adiabatic condition is that the switching time of the light field is much longer than the transition period of the ultracold atom.

5. The method for measuring the wave function density of ultracold atoms according to claim 1, characterized in that, The peak Rabi frequency ratio of the probe light and the coupling light .

6. The method for measuring the wave function density of ultracold atoms according to claim 1, characterized in that, In S30, the fixed phase difference is 1°.

7. The method for measuring the wave function density of ultracold atoms according to claim 1, characterized in that, S10 includes, S101, obtain three-level atoms, and cool the three-level atoms to obtain high-density atomic clusters; S102, perform ultracold state optimization on the obtained high-density atomic clusters to obtain optimized ultracold atomic clusters; S103, the ultracold atomic group is prepared in its ground state to obtain an ultracold atomic group in its ground state.

8. A device for measuring the wave function density of ultracold atoms, characterized in that, include: The acquisition module is used to acquire ultracold atomic groups in their ground state; wherein, the ultracold atomic groups are three-level atomic groups; A determination module is used to apply a phase-tunable dual-lattice light field to the ultracold atomic cluster and determine the probability that the ultracold atomic cluster in the ground state will transition to the target state under the action of the Hamiltonian of the dual-lattice light; wherein, the dual-lattice light field includes a probe light and a coupling light of the same frequency, the probe light and the coupling light have a phase difference and their Rabi frequency peak ratio is... ; The control module is used to scan the phase of the two lattice beams from 0° to 360° with a fixed phase difference by controlling the phase modulation devices connected to the probe beam and the coupling beam respectively, so as to obtain a set of transition probabilities corresponding to the ultracold atomic group transitioning from the ground state to the target state in each phase; The control module is used to turn off the coupling light and the probe light, and reconstruct the wave function density distribution map of the ultracold atomic group based on a set of transition probabilities corresponding to the transition from the ground state to the target state of the ultracold atomic group in each phase.

9. A system for measuring the wave function density of ultracold atoms, comprising a control device, a coupling laser, a probe laser, and a phase modulation device, wherein the phase modulation device is connected to the coupling laser and the probe laser respectively, and the control device comprises a memory and a processor, wherein the memory stores a computer program, characterized in that, The step includes implementing the measurement method according to any one of claims 1 to 7 when the processor executes the computer program.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the measurement method according to any one of claims 1 to 7.

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