We study theoretically the ultracold two-component fermionic gases when a gradient magnetic field is used to tune scattering length between atoms. For $^{6}\mathrm{Li}$ at narrow resonance ${B}_{0}=543.25\text{ }\text{ }\mathrm{G}$, it shown that would be in coexistence of regimes BCS, Bose-Einstein condensation (BEC), and unitarity limit with present experimental technique. In case thermal chemical equilibrium, we investigate density distribution show double peak can give us clear evidence...

The exchange antisymmetry of identical fermions leads to an exponential computational bottleneck in ab initio simulations, known as the fermion sign problem. thermodynamic approach fictitious particles (Y. Xiong and H. Xiong, J. Chem. Phys. 157, 094112 (2022)) provides efficient accurate means simulate some fermionic systems by overcoming This method has been significantly promoted used National Ignition Facilities for simulations is believed have wide application prospects warm dense...

The mean ground-state occupation number and condensate fluctuations of interacting noninteracting Bose gases confined in a harmonic trap are considered by using canonical ensemble approach. To obtain the fluctuations, an analytical description for probability distribution function is provided directly starting from analysis partition system. For ideal gas, found to be Gaussian one case trap. unified approach calculated based on lowest-order perturbation method Bogoliubov theory. It that...

Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and been used in path integral Monte Carlo accurately simulate warm dense matter with up 1000 electrons [T. Dornheim et al., J. Phys. Chem. Lett. 15, 1305 (2024)1948-718510.1021/acs.jpclett.3c03193]. The inclusion of molecular dynamics (PIMD) can provide another systems. In recent paper [Y. M. Y. Feldman 159, 154107 (2023)0021-960610.1063/5.0173749], Hirshberg improved recursive...

For the Bose-condensed gas confined in a magnetic trap and two-dimensional optical lattice, non-uniform distribution of atoms different lattice sites is considered based on Gross-Pitaevskii equation. A propagator method used to investigate time evolution 2D interference patterns after (i)only swithed off, (ii)both are off. An analytical description motion side peaks presented by using density momentum space.

Most recently, the path integral molecular dynamics has been successfully used to consider thermodynamics of single-component identical bosons and fermions. In this work, is developed simulate thermodynamics, Green's function, momentum distribution two-component in three dimensions. As an example our general method, we up 16 a three-dimensional harmonic trap. For noninteracting spinor bosons, simulation shows bump heat capacity. repulsive interaction strength increases, however, find gradual...

We investigate the interference pattern evolution process for a coherent array of Bose–Einstein condensates in magnetic trap after optical lattices are switched off. It is shown that there decay and revival density oscillation confined trap. find that, due to confinement trap, effect much stronger than found experiment performed by Pedri et al (Pedri P 2001 Phys. Rev. Lett. 87 220401), where also The interaction correction discussed distribution central peak.

The critical temperature and condensate fraction of a trapped interacting Bose gas are investigated when both atom-atom interaction finite-size effects taken into account. A canonical ensemble is used to obtain the equations on for near below temperature. In our approaches corrections due obtained simultaneously system. An analytical high-order correction given.

The analytical probability distribution of the quasi-2D (and purely 2D) ideal and interacting Bose gas are investigated by using a canonical ensemble approach. Using condensate, statistical properties such as mean occupation number particle fluctuations condensate calculated. Researches show that there is continuous crossover from to 2D or gases. Different case 3D gas, interaction between atoms changes in deep way nature fluctuations.

For two-component Fermi gases at zero temperature, through a general derivation based on the BCS wave function, our research shows that nonuniform molecular Bose-Einstein condensate has off-diagonal long-range order and can be described well by an parameter when size of molecules is much smaller than whole system. We also give equation state nonlinear evolution for condensates, which similar to Gross-Pitaevskii atomic Bose condensate. The applied consider Josephson effect two weakly linked...

We consider the Josephson effect when two independent Bose superfluids are weakly connected. In presence of interparticle interaction and based on calculations one-particle density matrix whole system, we find that can be factorized which satisfies general criterion superfluid proposed by Penrose Onsager. By introducing an effective order parameter for our research shows there is superfluids.

After removing the double-well potential trapping two initially independent Bose condensates, density expectation value is calculated when both exchange symmetry of identical bosons and interatomic interaction are considered. The evolution equations obtained based on first-quantization second-quantization methods. When considered carefully, after overlapping it shown that there a nonzero interference term in value. It found with this model agrees pattern observed experiment by Andrews...

We investigate the particle-number fluctuations due to collective excitations created in a two-dimensional (2D) and quasi-2D Bose-Einstein condensates (BECs) at low temperature. find that display an anomalous behavior, i.e., for 2D BEC they are proportional ${N}^{2},$ where N is total number of particles. For BEC, not only ${N}^{2}$ but also square root trapping frequency strongly confined direction.

We investigate the fluctuations of condensate in ideal and weakly interacting Bose gases confined a box volume V within canonical ensemble. Canonical ensemble is developed to describe behavior when different methods approximation are used. Research shows that exhibit anomalous for gas box.

We have studied the interference effect of a Bose—Einstein condensate expanding in ring-shaped trap. The dynamic process is analyzed based on Gross—Pitaevskii equation. Our numerical results show that petal-like pattern formed during expansion within petal number depends evolution time, which can be well explained by two flows condensate.

The thermodynamical properties of the trapped interacting Bose gas are investigated when both atom-atom interactions and finite size taken into account. Using ordinary sum method for grand canonical ensemble mean-field theory, effects due to system given simultaneously.

In an exciting experiment by MIT's group (Science 275, 637 (1997)), clear interference fringes were observed for two initially independent Bose condensates in dilute gas. Presently, there are different theories (measurement-induced theory and interaction-induced theory) which can both explain experimental results. Based on our theory, we consider the evolution of density-density correlation after releasing a double-well potential trapping condensates. find that exhibit behavior emergence...

We investigate the phase diffusion of a Bose–Einstein condensate (BEC) confined in combined potential magnetic trap and one-dimensional optical lattice. show that whole lattice is evident can be measured from interference pattern expanding subcondensates after switched off. The maximum density decreases significantly due to mixing appears different subcondensates. This suggests way detect experimentally notable BECs.

For a series of incoherent and ultracold atoms with an orbital angular momentum (or vortices) released from optical lattice, we consider the density-density correlation this freely expanding gases. Because unique phase structure originating quantized momentum, it is shown that plays important role in distribution through appearance crescent-shaped peaks accompanying ordinary round-shaped peaks. In particular, found orientation corresponds rotation direction prepared lattices.

We investigate the collapses and revivals of interacting Bose–Einstein condensate based on coherent state description condensate. Our research shows that revival time is larger than previous predication [Phys. Rev. Lett. 77 (1996) 2158] when high-order expansion chemical potential considered. In particular, we predict an obvious damping effect in process

Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and been used in path integral Monte Carlo (PIMC) accurately simulate warm dense matter with up 1000 electrons (T. Dornheim et al., arXiv:2311.08098 (2023)). The inclusion of molecular dynamics (PIMD) can provide another systems. In recent paper (J. Chem. Phys. 159, 154107 (2023)), Feldman Hirshberg improved recursive formula for PIMD N bosons, significantly reducing computational...