Molecular sub-doppler cooling magneto-optical trap design method based on artificial intelligence algorithm

Abstract

The application discloses a kind of molecular sub-Doppler cooling magneto-optical trap design method based on artificial intelligence algorithm, belong to molecular laser cooling technical field.First, construct three-dimensional molecular magneto-optical trap scheme model, then solve the optical Bloch equation of three-dimensional molecular magneto-optical trap scheme model, obtain trapping and cooling acceleration from this;Further optimize trapping and cooling acceleration calculated by optical Bloch equation, to obtain the best parameter point that can simultaneously have trapping and cooling in preset speed and preset spatial range.The present application first introduces Bayesian optimization algorithm into molecular magneto-optical trap design, solves the big problem that has plagued molecular laser cooling, i.e.sub-Doppler heating effect in type II magneto-optical trap.Three-dimensional Monte Carlo simulation shows that the scheme can reduce the temperature of molecular magneto-optical trap to 40 μK, and its phase space density increases by two orders of magnitude, which is a key step to realize molecular Bose-Einstein condensation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of molecular laser cooling, in particular to a design method of a molecular sub-Doppler cooling magneto-optical trap based on an artificial intelligence algorithm. BACKGROUND

[0002] Ultracold polar molecules have very broad application prospects in the fields of high-resolution spectroscopy and precision measurement, quantum computing and simulation, dark matter detection, etc. Since Hansch et al. proposed the idea of laser cooling atoms in 1975, a series of major progress and fruitful results have been achieved in the theoretical and experimental research of atomic magneto-optical traps, which has brought about a historic change in laser science, quantum optics and cold atom physics, promoted the rapid development of atomic optics, and won the Nobel Prize in Physics in 1997. We seize this opportunity for the development of this discipline and carry out theoretical and experimental research on laser cooling of neutral molecules and molecular magneto-optical traps. The main difference between molecules and atoms is the complex internal degrees of freedom of molecules, such as vibration and rotation energy levels, which brings many difficulties to molecular cooling, so the molecular magneto-optical trap is an experiment full of opportunities and challenges.

[0003] In the process of molecular laser cooling, the complex internal energy level structure brings many new problems, for example, in the molecular magneto-optical trap, due to the existence of type II transition, its speed-dependent force mainly includes two forms, namely, sub-Doppler heating effect in a small speed range (≤5m / s) and Doppler cooling effect in a large speed range (>5m / s). This results in a higher temperature of the molecules that can be finally cooled in the magneto-optical trap. The temperature of the molecular magneto-optical trap that has been achieved internationally is about 1mk. In contrast, the atomic magneto-optical trap has a cooling effect in the whole speed range, and the temperature of the magneto-optical trap is about 100μK. The complex hyperfine energy level splitting of molecules corresponds to a large number of adjustable parameters, and each variable will affect the final form of the trapping and cooling force. Therefore, an optimization algorithm is needed to help find the best parameter values of the molecular magneto-optical trap. SUMMARY

[0004] The present application discloses a design method of a molecular sub-Doppler cooling magneto-optical trap based on an artificial intelligence algorithm, which is characterized by using a Bayesian optimization algorithm plus an optical Bloch equation to predict the probability distribution of the trapping and cooling acceleration at any parameter point in the molecular magneto-optical trap, so as to find a set of optimal parameters that can provide trapping and cooling for the molecular magneto-optical trap in a small speed (≤5m / s) and a small space (≤3mm) range.

[0005] The technical scheme adopted by the present application is as follows:

[0006] A design method of a molecular sub-Doppler cooling magneto-optical trap based on an artificial intelligence algorithm, which utilizes a Bayesian optimization algorithm and an optical Bloch equation to optimize the design of sub-Doppler cooling in a molecular magneto-optical trap, comprising the following steps:

[0007] Step A: constructing a three-dimensional molecular magneto-optical trap scheme model;

[0008] Step B: solving the optical Bloch equation of the three-dimensional molecular magneto-optical trap scheme model by Julia language, thereby obtaining the trapping and cooling acceleration;

[0009] Step C: using the Scikit-Optimize tool of python to optimize the trapping and cooling acceleration calculated by the optical Bloch equation, thereby obtaining the optimal parameter point that can simultaneously have trapping and cooling within the preset speed and preset spatial range.

[0010] Further, step A comprises:

[0011] Step A1: setting the coordinate axis system of laser-molecule interaction;

[0012] Step A2: setting the parameter range of model optimization, mainly including laser polarization: left / right circularly polarized light + / - , laser detuning: -10≤δ≤10Γ;

[0013] Step A3: setting the three-dimensional space magnetic field of the magneto-optical trap: wherein A represents the magnetic field gradient, represents the coordinate axis vector, and B represents the magnetic field;

[0014] Setting the total intensity value of the laser and the laser beam waist radius, and uniformly distributing them in four laser frequency components;

[0015] Step A4: setting the velocity calculation range of the magneto-optical trap cooling force as 0-5m / s, and the displacement calculation range of the magneto-optical trap trapping force as 0-3mm in the z-axis direction.

[0016] Further, step B comprises:

[0017] Using the DifferentialEquations.j1 toolkit of Julia language to calculate the multi-frequency optical Bloch equation corresponding to the three-dimensional molecular magneto-optical trap scheme model described in step A, and respectively calculating the average cooling acceleration of the velocity and the trapping acceleration along the z-axis direction;

[0018] In the cooling acceleration calculation process, in order to obtain the real three-dimensional magneto-optical trap cooling acceleration, for a certain velocity intensity v, a plurality of different spatial positions r x , r y , rz and velocity direction v x , v y , v z , satisfy:

[0019] 0≤r x , r y , r z ≤λ

[0020]

[0021] where λ is wavelength, v x , v y , v z have a common factor ω m ;

[0022] When solving the optical Bloch equation of the three-dimensional molecular magneto-optical trap scheme model, each parameter (such as energy level spacing, solving time, etc.) is taken as a common parameter factor ω m , in order to make the optical Bloch equation obtain a periodic oscillation metastable state solution. Considering that there is a phase difference between the laser fields in different coordinate axis directions, a random phase θ1, θ2 needs to be added; then the accelerations a x , a y , a z along the three velocity directions are solved respectively, and the acceleration a along the random velocity direction is solved by using the formula a = (a x ·v x +a y ·v y +a z ·v z ) / v, and the average is taken as the cooling acceleration at the velocity;

[0023] In the calculation process of the trapping acceleration, generally, in order to make the equation converge faster, a smaller velocity v = (0.02-0.2)f / k is given, and a plurality of different groups of spatial positions r x , r y , r z and velocity directions v x , v y , v z are randomly selected, only the acceleration a z along the z-axis direction needs to be solved, and the average is taken as the trapping force acceleration at the given velocity, and enough velocity average (200-500 groups) can eliminate the influence on the trapping force.

[0024] Further, the common factor takes a value satisfying:

[0025]

[0026] where ω m is a common factor, Γ is the decay rate from the excited state to the ground state, and k is the wave vector.

[0027] Further, step C can use the PyCall package in Julia software to call the Scikit-Optimize package in Python to optimize the calculated magnetic optical trap trapping and cooling acceleration in the set range, including:

[0028] Step C1: separately calculate and obtain the optimal trapping acceleration a tm and the cooling acceleration a cm of the magnetic optical trap.

[0029] Step C2: define the final optimization target f:

[0030] f=a t / a tm +a c / a cm

[0031] wherein a t and a c represent the trapping force acceleration and the cooling acceleration calculated in each iteration, respectively, and a tm and a cm represent the optimal trapping acceleration and the cooling acceleration of the magnetic optical trap when optimized separately.

[0032] Step C3: use the Bayesian optimization algorithm to optimize and find the maximum f value and the corresponding parameter point.

[0033] Step C4: calculate the trapping and cooling accelerations at the parameter point after optimization in step C3, and check whether they meet the expectations, and if not, return to step C3 to start a new round of optimization.

[0034] Compared with the prior art, the Bayesian optimization algorithm is first introduced into the molecular magnetic optical trap and successfully finds a new scheme that can provide both trapping force and sub-Doppler cooling force. Compared with other mature optimization algorithms, the Bayesian optimization algorithm has the advantages of fewer iteration times, global search, high upper limit of optimized parameters, consideration of prior parameters, etc., and solves the difficult problem in molecular laser cooling, i.e., the sub-Doppler heating effect in type II magnetic optical traps. Monte Carlo simulation shows that this scheme can reduce the temperature of the molecular magnetic optical trap to 40 muK, and the phase space density is increased by two orders of magnitude, which is a key step to realize molecular Bose-Einstein condensation. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a model diagram of the molecular magnetic optical trap constructed by the present application.

[0036] Figure 2 The hyperfine level structure of calcium fluoride (CaF) molecule and the parameter adjustment range of Bayesian optimization algorithm studied in the present application;

[0037] Figure 3 The optimal parameter position map for the sub-Doppler cooling magneto-optical trap of CaF molecule found by Bayesian optimization algorithm;

[0038] Figure 4 The CaF molecule trapping and cooling acceleration curve for the optimal parameter point position calculated by optical Bloch equation;

[0039] Figure 5 The block diagram of Bayesian optimization principle. DETAILED DESCRIPTION

[0040] The present application is further described below in conjunction with the accompanying drawings.

[0041] Referring to the accompanying drawings Figure 1 The magneto-optical trap model used in the present application specifically includes: a three-dimensional retro-reflective laser field, a molecular cloud cluster at the center of the magneto-optical trap, and a spatially distributed magnetic field generated by a reversed Helmholtz coil (the magnetic field is not shown in the figure, and can be specifically referred to the formula:

[0042]

[0043] wherein A represents the magnetic field gradient, in the present embodiment, A = 15 (G / cm), represents the coordinate axis vector, and B represents the magnetic field.

[0044] Each direction of incident laser includes four laser frequency components to ensure that the four hyperfine levels of CaF molecule can be simultaneously covered. Each laser component includes three different variables of polarization, detuning, and laser intensity. Here, in order to simplify the model, the intensity of the four laser components is set to be equal in the present embodiment. In the magneto-optical trap, a pair of counter-incident laser components always have a pair of polarizations, i.e. if the polarization of the laser incident from the positive direction of the x-axis is σ + , then the polarization of the counter-incident laser is σ - . This means that as long as the polarization and detuning of all four lasers in one direction are determined, the polarization and detuning of the four laser components counter-incident thereto are also determined, and the laser fields in the y and z-axis directions are the same as those in the x-axis direction. Specifically, a pair of counter-incident σ + σ - laser fields are as follows:

[0045]

[0046] And the three-dimensional laser field formula is:

[0047]

[0048] wherein, represents a coordinate axis vector, E is an electric field intensity, k is a wave vector 2pi / lambda, lambda is a wavelength, and theta1, theta2 are phase differences of the laser in three-dimensional directions.

[0049] In one specific implementation of the present application, the total intensity of the laser in the magneto-optical trap is set to 200mW, and is uniformly distributed on the four laser groups, and the laser beam waist radius is 10mm.

[0050] On the basis of the above-mentioned magneto-optical trap model, the optical Bloch equation of the three-dimensional molecular magneto-optical trap scheme model is solved, so as to obtain the trapping and cooling acceleration; and based on the Bayesian optimization algorithm, the trapping and cooling acceleration calculated by the optical Bloch equation is optimized, so as to obtain the optimal parameter point capable of simultaneously having trapping and cooling within a preset speed and a preset spatial range.

[0051] The Bayesian optimization algorithm adopted in the present application is specifically described as follows:

[0052] The probability distribution of the real black box function (target function) to be found is replaced by a surrogate function, and the next most possible parameter point is found by using an acquisition function. The construction of the surrogate function is based on Gaussian process, that is, the data set {x t+1 , f t+1} of any parameter point and the previously observed data {x 1：t , f 1：t} are subject to joint Gaussian distribution, so that the value of the unknown function at any position can be predicted according to the posterior distribution of Gaussian process. The acquisition function needs to consider two aspects, one is to use the current developed area (exploitation), and the other is to explore the area that has not been developed (exploration), so as to consider the local and global maximum value search, and find the optimal solution in the whole parameter range. The commonly used acquisition function is the maximum expected improvement. The specific workflow of Bayesian optimization is shown as follows Figure 5 :

[0053] 1. Initial random sampling to obtain parameter point x init , substitute into the target function f(x) to obtain the initial data set {x, f}, train and generate the prior surrogate function by using Gaussian process;

[0054] 2. Determine whether to continue searching, if so, use the acquisition function to obtain the next parameter point x with the largest possible increase in the current maximum value new , otherwise terminate the loop;

[0055] 3. Substitute the new parameter point x new into the objective function f(x) to calculate and obtain the corresponding f new value;

[0056] 4. Add the new data point (x new , f new ) to the existing data set, train and update the surrogate function, obtain a posterior distribution, and use it as the prior distribution for the next loop;

[0057] 5. Repeat steps 2-4 until the maximum number of iterations is reached.

[0058] Referring to the accompanying drawings Figure 2 , the hyperfine level splitting diagram of CaF molecule is shown, and the meanings of the letters in the figure are as follows: F represents the hyperfine levels of the molecular ground state X 2 ∑ + , and F' represents the hyperfine levels of the molecular excited state A 2 Π 1 / 2 . From bottom to top, the hyperfine levels of the four ground states F=1, 0, 1, 2 are represented by black solid lines, and the excited state mainly includes two energy levels F'=0, 1. The energy level interval is marked in the figure and is in MHz. The laser frequency component covering the four hyperfine levels is represented by a black dashed line, and the adjustable range of laser polarization and detuning is marked thereon. The polarization mainly includes left / right circularly polarized light, σ + / - , and the detuning represents the frequency difference of the laser frequency relative to the energy level interval, δ=ω L -ω0, where ω0 represents the energy level interval of the molecular ground state and the excited state, and ω L represents the laser frequency. The adjustable range of δ is -10~10Γ, and Γ represents the rate of decay of the excited state to the ground state, and for CaF molecule, Γ=8.3MHz. The vertical arrow represents the relative excited state energy level F'=1 of each laser transition.

[0059] Referring to the accompanying drawings Figure 3 , a set of optimal optimization results of the molecular sub-Doppler cooling magneto-optical trap is given, and it can be seen that the detuning of the laser covering the four hyperfine levels F=1, 0, 1, 2 from bottom to top is: δ1=1.7Γ, δ2=1.9Γ, δ3=-2Γ, δ4=1.6Γ, and the corresponding polarization is: σ - , σ - , σ + , σ - .

[0060] See appendix Figure 4 This shows the appendix of the optical Bloch equation calculation. Figure 3 The graph shows the cooling and trapping accelerations under the corresponding parameter conditions. The upper part represents the velocity-dependent cooling acceleration, and the lower part represents the position-dependent trapping acceleration. The shaded area in the graph represents the 68% confidence interval, and the solid black line represents the average result. As can be seen from the graph, within the set calculation range, both cooling and trapping accelerations are negative, meaning that this scheme simultaneously possesses cooling and trapping effects.

[0061] This scheme is a two-stage magneto-optical trap (MET) approach. After loading molecules into a conventional molecular MET to obtain a high-temperature, low-density CaF molecular cloud, the scheme parameters can be quickly switched to a second step of cooling confinement, resulting in even lower temperatures and higher densities. Using the calculated confinement cooling force, three-dimensional Monte Carlo simulations show that the final temperature can reach 40 μK, and the phase space density can be increased by two orders of magnitude compared to current molecular METs.

[0062] This invention is applicable to all molecules currently being studied using molecular laser cooling, including magnesium fluoride (MgF), strontium fluoride (SrF), calcium hydride (CaH), ytterbium fluoride (YbF), yttrium oxide (YO), etc. The method is also applicable to the optimization of complex multi-parameter systems.

[0063] The above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for designing a molecular subDoppler cooled magneto-optical trap based on artificial intelligence algorithms, characterized in that, Includes the following steps: Step A: Construct a three-dimensional molecular magneto-optical trap model; Step B: Solve the optical Bloch equations for the three-dimensional molecular magneto-optical trap model to obtain the confinement and cooling accelerations; Step C: Optimize the confinement and cooling accelerations calculated by the optical Bloch equations to obtain the optimal parameter points that can simultaneously achieve confinement and cooling within a preset velocity and space range; Step C includes: Step C1: Calculate and obtain the optimal trapping acceleration for the magneto-optical trap separately. and cooling acceleration ; Step C2: Define the final optimization objective : ； in, , These represent the confinement force acceleration and cooling acceleration calculated in each iteration, respectively. , These represent the optimal trapping acceleration and cooling acceleration of the magneto-optical trap when optimized individually; Step C3: Use the Bayesian optimization algorithm to optimize and find the maximum value. Values ​​and their corresponding parameter points; Step C4: Calculate the trapping and cooling acceleration at the parameter points after optimization in step C3, and check whether they meet expectations. If they do not meet expectations, return to step C3 to start a new round of optimization.

2. The molecular subdoppler cooled magneto-optical trap design method based on artificial intelligence algorithm according to claim 1, characterized in that, Step A includes: Step A1: Set up the coordinate axis system for the laser-molecule interaction; Step A2: Set the parameter ranges for model optimization, mainly including laser polarization: left / right circularly polarized light. Laser detuning: ; Step A3: Set the three-dimensional spatial magnetic field of the magneto-optical trap: Where A represents the magnetic field gradient, Represents the coordinate axis vector. Indicates a magnetic field; Set the total intensity value and laser beam waist radius of the laser, and distribute them evenly across the four laser frequency components; Step A4: Set the velocity calculation range of the magneto-optical trap cooling force to 0 – 5 m / s, and the displacement calculation range of the magneto-optical trap confinement force to 0 – 3 mm in the z-axis direction.

3. The molecular subdoppler cooled magneto-optical trap design method based on artificial intelligence algorithm according to claim 1, characterized in that, Step B includes: The multi-frequency optical Bloch equation corresponding to the three-dimensional molecular magneto-optical trap scheme model described in step A is calculated to obtain the velocity-averaged cooling acceleration and the trapping acceleration along the z-axis. In the aforementioned cooling acceleration calculation process, for a certain velocity intensity Randomly select several different spatial locations and velocity direction ,satisfy: ； ； in, For wavelength, Having a common common denominator ; When solving the optical Bloch equations for the three-dimensional molecular magneto-optical trap model, all parameters are expressed in terms of... As a common parameter factor, considering the phase difference of the laser field in different coordinate axis directions, a random phase needs to be added. Then, calculate the acceleration along the three velocity directions respectively. Using the formula Find the acceleration along the random velocity direction. The average value is taken as the cooling acceleration at that speed; In the aforementioned calculation of imprisonment acceleration, a given velocity Randomly select several different spatial locations and velocity direction We only need to find the acceleration along the z-axis. The average value is taken as the confinement force acceleration at that given velocity.

4. The molecular subdoppler cooled magneto-optical trap design method based on artificial intelligence algorithm according to claim 3, characterized in that, The common common divisor values ​​satisfy: ； in, For the common divisor, The decay rate from the excited state to the ground state. It is a wave vector.

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