Under the second-order degenerate perturbation theory, we show that the physics of $N$ particles with arbitrary spin confined in a one dimensional trap in the strongly interacting regime can be described by super-exchange interaction. An effective spin-chain Hamiltonian (non-translational-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translational-invariant Heisenberg model, where a transition between Heisenberg anti-ferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished in two different methods: the first is based on their distinct response to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distribution. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques
Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in $d$ dimension and the equivalence of trapped quantum gases
从量子气体的统一统计热力学出发，系统地导出了一般幂律势阱下理想玻色和费米气体的维里系数。从维里系数的一般结果，可以得到$d=3$和$d=2$中的已知结果。但更重要的是，我们发现在$d=1$中，当气体处于简谐势作用下时，玻色子和费米子的维里系数变得相等（除了第二维里系数的符号不同）。这一结果表明玻色气体和费米气体之间的等价性，这一等价性已经由M M Faruk（J Stat Phys，DOI 10.1007/s10955-015-1344-4）为$d=1$建立。令人惊讶的是，我们的研究还表明，二维自由量子气体的维里系数是相同的一维谐波捕获的量子气体的维里系数。
Observation of local temporal correlations in trapped quantum gases
我们测量了在玻色-爱因斯坦凝聚临界温度以上和以下玻色子被困气体的时间对关联函数$g^{(2)}(τ)$。使用局部时间分辨单原子灵敏探测技术进行{ \it in situ}测量。还提取了三阶和四阶关联函数。我们开发了一个理论模型，并将其与我们的实验数据进行比较，找到了良好的定量一致性，并强调了相互作用的作用。我们的结果促进了时间相关作为新的观测研究超冷量子气体的动力学。
We report on trapping and cooling Li-6 atoms in a monolithic ring bowtie cavity. To make the cavity insensitive to magnetic fields used to tune atomic interactions, we constructed it entirely from fused silica and Zerodur. The components were assembled using hydroxide bonding, which we show can be compatible with ultra-high vacuum. Backscattering in high-finesse ring cavities readily causes trap intensity fluctuations and heating, but with phase-controlled bi-directional pumping the trap lifetime can be made long enough for quantum gas experiments in both the crossed-beam trap (unidirectional …
We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang $δ^3_p$ [1]) interactions among the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature dependence in this regard. Coherent scattering even by a single boson or fermion in the finite geometry gives rise to new tool of determining energy eigenstate of the scatterer. Our predictions on the differential scattering cross-sections, can be tested within the present day experimental …
The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often challenging because of decoherence, the process by which environmental interactions create spurious entanglements that can destroy the desired entanglement. Considering the collisional decoherence that is relevant for quantum measurements utilizing scattering in one-dimensional trapped gases, here we derive a relationship between particle masses and wave pack…
In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult.\textbf{ }In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of\ ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum …
We report on the confinement of a Bose-Einstein condensate in an annular trap with widely tunable parameters. The trap relies on a combination of magnetic, optical and radio-frequency fields. The loading procedure is discussed. We present annular traps with radii adjusted between 20 and 150 micrometers. We demonstrate the preparation of persistent flows both with a rotating laser stirrer and with a global quadrupole deformation of the ring.Our setup is well adapted for the study of superfluid dynamics.
We present a dispersive imaging method for trapped quantum gases based on digital off-axis holography. Both phase delay and intensity of the probe field are determined from the same image. Due to the heterodyne gain inherent to the holographic method it is possible to retrieve the phase delay induced by the atoms at probe beam doses two orders of magnitude lower than phase-contrast imaging methods. Using the full field of the probe beam we numerically correct for image defocusing.
For the quantum kinetic system modelling the Bose-Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman-Enskog expansion to derive its hydrodynamic approximations, include both Euler and Navier-Stokes approximations. The hydrodynamic approximations describe not only the macroscopic behavior of the BEC but also its coupling with the non-condensates, which agrees with Landau's two fluid theory.
Advances in light shaping for optical trapping of neutral particles have led to the development of box traps for ultracold atoms and molecules. These traps have allowed the creation of homogeneous quantum gases and opened new possibilities for studies of many-body physics. They simplify the interpretation of experimental results, provide more direct connections with theory, and in some cases allow qualitatively new, hitherto impossible experiments. Here we review progress in this emerging field.
We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs measures of classical field theories with quartic Hartree-type self-interaction, and to the Gibbs states of classical gases of point particles. We discuss various open problems and conjectures concerning, e.g., Bose-Einstein condensation, polymers and $\vert \boldsymbolϕ \vert^{4}$-theory.
We investigate the particle-number dependence of some features of the out-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime. We consider protocols entailing the variation of the external potential which confines the particles within a limited spatial region, in particular sudden changes of the trap size. In order to characterize the dynamic behavior of the Fermi gas, we consider various global quantities such as the ground-state fidelity for different trap sizes, the quantum work statistics associated with the protocol considered, and the Loschmidt echo measuring the ov…
