Effect of Spatial Dimension and External Potential on Joule-Thomson Coefficients of Ideal Bose Gases

Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.

Signature of Critical Point in Momentum Profile of Trapped Ultracold Bose Gases

We present a new method to identify the critical point for the Bose-Einstein condensation （BEC） of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature, and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point. More importantly, the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point, which can be used to determine the critical temperature. These predictions are also confirmed by our BEC experiment for magnetically trapped ST Rb gases.

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green＇s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analyt- ically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green＇s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose-Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose-Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lat- tices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the exDerimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 （2011）]. In square optical lattice, the emergence of peaks at（±π/a,±π/a） in the time-of-flight absorption pictures, which is believed to bea sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.

Power-law scalings in weakly-interacting Bose gases at quantum criticality

Weakly interacting quantum systems in low dimensions have been investigated for a long time,but there still remain a number of open questions and a lack of explicit expressions of physical properties of such systems.In this work,we find power-law scalings of thermodynamic observables in low-dimensional interacting Bose gases at quantum criticality.We present a physical picture for these systems with the repulsive interaction strength approaching zero;namely,the competition between the kinetic and interaction energy scales gives rise to power-law scalings with respect to the interaction strength in characteristic thermodynamic observables.This prediction is supported by exact Bethe ansatz solutions in one dimension,demonstrating a simple 1/3-power-law scaling of the critical entropy per particle.Our method also yields results in agreement with a non-perturbative renormalization-group computation in two dimensions.These results provide a new perspective for understanding many-body phenomena induced by weak interactions in quantum gases.

Cluster mean-field study of spinor Bose-Hubbard ladder:Ground-state phase diagram and many-body population dynamics

We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose-Hubbard ladder(BHL).For unbiased BHL,we find superfluid(SF)phase and integer filling Mott insulator(Int MI)phase.For biased BHL,in addition to the SF and Int MI phases,there appears half-integer filling Mott insulator(HInt MI)phase.The phase transition between the SF and Int MI phases can be first order at a part of phase boundaries,while the phase transition between the SF and HInt MI phases is always second order.By tuning the bias energy,we report on the change of the nature of SF-MI phase transitions.Furthermore,we study the effect of the spin-dependent interaction on the many-body population dynamics.The spin-dependent interaction can lead to rich dynamical behaviors,but does not influence the particle transfer efficiency.Our results indicate a way to tune the nature of the SF-MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.

Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices

We clarify some technical issues in the present generalized effective-potential Landau theory （GEPLT） to make the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero temper- ature. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo （QMC） simulations.