We study fluctuations in the atom number difference between two halves of a harmonically trapped Bose gas in three dimensions. We solve the problem analytically for non interacting atoms. In the interacting case we find an analytical solution in the Thomas-Fermi and high temperature limit in good agreement with classical field simulations. In the large system size limit, fluctuations in the number difference are maximal for a temperature $T\simeq 0.7 T_c$ where $T_c$ is the critical temperature, independently of the trap anisotropy. The occurrence of this maximum is due to an interference effect between the condensate and the non-condensed field.
The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the $x$ and $y$ axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being $100\%$ condensed, and the respective energies per particle and densities per particle to coincide.
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 …
We formulate a general scheme for calculation of thermodynamic properties of ideal Bose gas with microscopic number of static impurities immersed, when the system is loaded in the harmonic trapping potential with quasi-1D and quasi-2D configurations. The binding energy of a single impurity and a detailed study of the medium-induced Casimir-like forces between two impurities in trapped Bose gas are numerically calculated in wide range of temperatures and interaction strengths.
We investigate dipole modes in a trapped Bose--Fermi mixture gas in the normal phase, composed of single-species bosons and single-species fermions with $s$-wave scattering. In the extremely low temperature regime, Bose--Einstein statistics and Fermi--Dirac statistics may give rise to an interesting temperature dependence of collective modes. Applying the moment method to the linearized Boltzmann equation, we study the transition of the dipole modes between the hydrodynamic regime and the collisionless regime.
We consider the phase transition dynamics of a trapped Bose-Einstein condensate subject to Raman-type spin-orbit coupling (SOC). By tuning the coupling strength the condensate is taken through a second order phase transition into an immiscible phase. We observe the domain wall defects produced by a finite speed quench is described by the Kibble-Zurek mechanism (KZM), and quantify a power law behavior for the scaling of domain number and formation time with the quench speed.
We study thermal properties of a trapped Bose-Bose mixture in a dilute regime using quantum Monte Carlo methods. Our main aim is to investigate the dependence of the superfluid density and the condensate fraction on temperature, for the mixed and separated phases. To this end, we use the diffusion Monte Carlo method, in the zero-temperature limit, and the path-integral Monte Carlo method for finite temperatures. The results obtained are compared with solutions of the coupled Gross-Pitaevskii equations for the mixture at zero temperature. We notice the existence of an anisotropic superfluid den…
We describe a quantum droplet of a Bose-Bose mixture squeezed by an external harmonic forces in one spatial direction. Our approach is based on the self-consistent method formulated in [1]. The true spatial droplet profile in the direction of confinement is accounted for, however local density approximation is assumed in the free directions. We define a numerical approach to find the beyond-mean-field contribution to the chemical potential (Lee-Huang-Yang chemical potential) -- the quantity that determines the droplet's profile. In addition to the numerical approach, we find the Lee-Huang-Yang…
We describe a protocol to prepare solitons in a quasi-1d box-trapped Bose-Einstein condensate using only a quench of the isotropic s-wave scattering length. A quench to exactly four times the initial 1d coupling strength creates one soliton at each boundary of the box, which then propagate in a uniform background density and collide with one another. No nonsolotonic excitations are created during the quench. The procedure is robust against imperfections in the scattering length ramp rate and a mismatch of the final scattering length.
We study a harmonically confined Bose-Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross-Pitaevskii equation in the same conditions. The phase space as a function of the interaction strengths and the relation between masses is quite rich. The miscibility criterion for the homogeneous system applies rather well to the system, with some discrepancies close to the critical line for separation. We observe significant differences between the mean-field results and the Monte Carlo ones…
We present a method to detect the presence and depth of dark solitons within repulsive one-dimensional harmonically trapped Bose-Einstein condensates. For a system with one soliton, we prove that the shift of the density in Fourier space directly maps onto the depth of the soliton. For multi-soliton systems, combining our spectral method with established imaging techniques, the character of the solitons present in the condensate can be determined. We verify that the detection of solitons by the spectral shift works in the presence of waves induced by density engineering methods. Finally we dis…
In this paper, the condensate fraction and the critical atom number and its corresponding critical temperature of condensate ultracold boson atoms trapped in optical box traps, are investigated. The semiclassical approximation is employed in this study. The boxes traps are modeled by a general power-law potential. The deviation of the boxes traps from an ideal boxes traps are discussed. The out come results furnish useful quantitative theoretical results for the future BEC experiments in such traps
Supersolid is an exotic state of matter, showing crystalline order with a superfluid background, observed recently in dipolar Bose-Einstein condensate (BEC) in a trap. Here, we present exact solutions of the desired Bloch form in the self-trapped free-floating quantum fluid. Our general solutions of the amended nonlinear Schr{ö}dinger equation, governing the mean-field and beyond mean-field dynamics, are obtained through a M{ö}bius transform, connecting a wide class of supersolid solutions to the ubiquitous cnoidal waves. The solutions yield the constant condensate, supersolid behavior and the…
The decay of multicharged vortices in trapped Bose-Einstein condensates may lead to a disordered vortex state consistent with the Vinen regime of turbulence, characterized by an absence of large-scale flow and an incompressible kinetic energy spectrum $E\propto k^{-1}$. In this work, we study numerically the dynamics of a three-dimensional harmonically trapped Bose-Einstein condensate excited to a Vinen regime of turbulence through the decay of two doubly-charged vortices. First, we study the momentum distribution and observe the emergence of a power-law behavior $n(k)\propto k^{-3}$ consisten…
Generation of different nonequilibrium states in trapped Bose-Einstein condensates is studied by numerically solving nonlinear Schrodinger equation. Inducing nonequilibrium states by shaking the trap, the following states are created: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.
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.
