| Rydberg atoms are becoming an important cornerstone for emerging quantum technologies due to their unique properties such as long-lived and strong interactions,and extremely sensitive to the environment.These unique features make Rydberg atoms have a broad application prospect in quantum sensors,quantum optics and quantum simulators.Recent advances in controllable Rydberg atoms with long-range interactions have significantly enhanced prospects in quantum sensing and metrology.The measurement precision is limited by the standard quantum limit Δθ=1/N1/2,but the spin squeezed state can overcome the limit and increase the sensitivity of optical lattice clocks and atomic interferometers.This thesis adopts a scheme that generates spin squeezed states through direct spinspin interactions,which are realized by the strong van der Waals interactions between Rydberg atoms.We consider an array of N Rydberg atoms.However,current techniques are not applicable for the dynamic study of such a large spin system.For example,the exponential growth of the Hilbert space with the number of atoms hinders the exact diagonalization of the system Hamiltonian,density matrix renormalization group method is widely used for one-dimensional systems,and the truncated Wigner approximation method is only effective for short times.When dissipation is considered,numerical simulation becomes more challenging.The truncated Wigner approximation with discretization is a simple and effective numerical simulation method commonly used for the dynamics of large spin systems with long-range interactions.By considering additional fluctuations,this method allows for the numerical simulation of the dynamics of manybody systems in the presence of dephasing and decay.Here,this method will be used to numerically simulate the spin squeezing generated by a spin echo scheme in arrays of strontium and rubidium atoms.Firstly,we introduce Discrete truncated Wigner approximation（DTWA）and Dissipative discrete truncated Wigner approximation（DDTWA）in detail.DDTWA combines mean-field dynamics with Monte Carlo sampling of a spin ensemble.Repeat random sampling and evolve for many times.The expectation values of observables can be approximated by the statistical average of the trajectory.The method is suitable for closed quantum systems.Similarity to DTWA,DDTWA takes into account the effects of dephasing and decay on system by replacing the deterministic mean-field evolution with a stochastic process.The method is suitable for open quantum system.Then,we used the method of DTWA to simulate the dynamics of two-dimensional strontium atomic array for N=5 × 5,16 × 16 and 32 × 32.The optimal squeezing parameters calculated with DTWA were consistent with the analytical solutions.In addition,we use DDTWA to simulate the optimal squeezing of rubidium atomic array.The Rabi frequency and the two-photon detuning may fluctuate in experiment.We discuss the influence of the variation of these parameters via the Monte Carlo sampling. |
