Abstract In this article, we analytically explore the quantum phenomena of scattering by harmonically trapped 2D quantum gases. We show the temperature’s dependence on the differential scattering cross-section (DSC) near and around the critical transition regime for both particle and light scattering cases separately. For the particle scattering case, we consider scatterers with quantized bound motion in a harmonic trap. Our findings on the structure factor for light scattering give phase transition phenomena for 2D bosonic atoms and the thermal behavior of the system. This result has practical significance for recent experimental setups such as in situ image analysis and bosonic simulations. Finally, we show the temperature-dependent refractive index for a 2D harmonically trapped bosonic medium. This parameter is important in neutron scattering experiments.
Abstract In this article, we analytically explore the quantum phenomena of scattering by harmonically trapped 2D quantum gases. We show the temperature’s dependence on the differential scattering cross-section (DSC) near and around the critical transition regime for both particle and light scattering cases separately. For the particle scattering case, we consider scatterers with quantized bound motion in a harmonic trap. Our findings on the structure factor for light scattering give phase transition phenomena for 2D bosonic atoms and the thermal behavior of the system. This result has practical significance for recent experimental setups such as in situ image analysis and bosonic simulations. Finally, we show the temperature-dependent refractive index for a 2D harmonically trapped bosonic medium. This parameter is important in neutron scattering experiments.
Abstract We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged Fermi–Huang δ p 3 interactions (Fermi 1936 Ric. Sci. 7 13; Huang and Yang 1957 Phys. Rev. 105 767) 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 setups, specially, for (i) 3D harmonically trapped interacting Bose–Einstein condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical lattice.
Abstract We have analytically explored the quantum phenomena of particle scattering by rotating trapped quantum gases of electrically neutral bosons and fermions for the short-ranged Fermi-Huang interactions between the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature and angular velocity dependencies in this regard, in particular, for an ideal Bose gas in a rotating harmonic trap, an ideal Fermi gas in a rotating harmonic trap, and a weakly interacting Bose gas in a slow rotating harmonic trap. We have theoretically probed the lattice-pattern of the vortices in a rapidly rotating strongly interacting Bose–Einstein condensate by the particle scattering method. We also have obtained de Haas-van Alphen-like oscillations in the differential scattering cross-section for an ideal ultracold Fermi gas in a rotating harmonic trap. Our predictions on the differential scattering cross-sections can be tested within the present-day experimental setups.
We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size L, and not as powers of 1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and we verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.
While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path-integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wavelength is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal-to-noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a noninteracting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase-transition-like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.
We have analytically explored the phenomenon of quantum scattering for unfixed quantum scatterers. We have considered short ranged (Fermi-Huang δp3 [1]) interaction between the incident `particle' and the scatterer with no interactions among the scatterers, and the scatterers as (i) particle(s) in a 1-D box, (ii) particle(s) in a 1-D double box, (iii) particle(s) in a 1-D grating, (iv) particle(s) in a 2-D rectangular box, (v) particle(s) in a 3-D harmonic trap, (vi) Bose-Einstein condensates in a double well, (vii) Bose-Einstein condensates in an optical lattice, etc. Coherent scattering from all possible positions of the quantum scatterers in the finite geometry gives rise to rich physics. We have predicted differential scattering cross-section for `particle' scattering, not only for the above cases, but also for 3-D harmonically trapped Bose and Fermi gases in thermodynamic equilibrium. Our predictions can be tested within the present day experimental setups.
Quantum criticality emerges when the collective fluctuations of matter undergo a continuous phase transition at zero temperature and has been a research focus in conventional condensed-matter physics over the past several decades. In the quantum critical regime, the exotic and universal properties are expected. These properties are independent of the microscopic details of the system, but depend only on a few general properties of the system, such as its dimensionality and the symmetry of the order parameter. The research of quantum criticality can not only help us to understand quantum phase transitions, but also provide a novel route to new material design and discovery.Ultracold bosonic gases have provided a clean system for studying the quantum critical phenomena. The critical behavior of a weakly interacting three-dimensional (3D) Bose gas should be identical to that of 4He at the superfluid transition, which belongs to the 3D XY universality class. From the normal fluid to the superfluid, the system undergoes a phase transition from completely disorder to long-range order, while in the vicinity of the phase transition point, the system parameters will show some singularity characteristics. In this paper, we observe the critical behavior of 87Rb Bose gas in a quadrupole-Ioffe configuration (QUIC) trap near the phase transition temperature Tc. A novel singularity behavior of the full width at half maximum of momentum distribution (FWHMMD) of atomic gas is discovered in the experiment. Prior to our experiment, we prepare a sample with 7.8105 87Rb atoms in the 5S1/2 |F=2, mF=2 state. Then the sample is held in a QUIC trap for a presetting period of time to control the temperature of atom sample precisely. During the holding time, the sample is heated up due to background gas collisions or fluctuations of the trap potential. In our experiment, the heating rate is deduced to be 0.3480.078 nK/ms from the absorption image. For a bosonic gas in a harmonic trap, critical gas can only cover a finite-size region due to a spatially varying density. We define the finite-size region as a critical region determined by the Ginzburg criterion. Then the FWHMMDs of atomic gas in the critical region are measured for different temperatures near the critical point. To this aim, we first extract the momentum distribution of atomic gas from the absorption image of the atomic clouds released from the QIUC trap after free expansion. Thus momentum distribution of atomic gas in the critical region can be extracted from the absorption image by subtracting the momentum distribution of thermal gas outside the critical region. According to the statistical results of the FWHMMD at different temperatures, we find that the FWHMMD suddenly reduces, thus revealing a very notable singularity behavior when the temperature is very close to the phase transition temperature Tc.