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 setups, specially, for (i) 3-D harmonically trapped interacting Bose-Einstein condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical lattice.
Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators. Here we present a framework to systematically include quantum effects arising from the mass-energy equivalence in harmonically trapped systems. We find that the mass-energy equivalence leads to squeezing, displacement and frequency changes of harmonic modes associated with different internal energies. The framework predicts new phenomena, notably, the existence of a lower bound to the fractional frequency shift in atomic clocks arising from the…
System of a two-flavor mixture of ultra-cold fermions confined in a one-dimensional harmonic trap is studied in the frame of the center of mass. We present a numerical method of obtaining energetic spectra in this frame for an arbitrary mass ratio of fermionic species. We identify a specific invariant encoded in many-body correlations which enable one to determine an eigenstate of the Hamiltonian and to label excitations of the center of mass. The tool presented may be particularly useful in experimental analysis of the interparticle interactions which do not affect the center of mass excitati…
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolu…
We study the non-equilibrium dynamics of a one-dimensional Bose gas trapped by a harmonic potential for a quench from zero to infinite interaction. The different thermodynamic limits required for the equilibrium pre- and post-quench Hamiltonians are the origin of a few unexpected phenomena that have no counterparts in the translational invariant setting. We find that the dynamics is perfectly periodic with breathing time related to the strength of the trapping potential. For very short times, we observe a sudden expansion leading to an extreme dilution of the gas and to the emergence of slowly…
We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated \textit{ab~initio} studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can accou…
We unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analyzed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity.…
We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the non-interacting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial a…
We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimens…
We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two and the one dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsi…
Progress towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons
本文研究了具有附加谐波囚禁的准一维波导中超冷玻色子原子的吸引相互作用动力学。首先，我们准备系统在其基态，然后移动零的谐波陷阱和开关附近的陷阱中心的额外的窄散射势。在与势垒碰撞两次后，我们建议测量与初始条件相反的原子数。量子增强干涉测量与量子亮孤子使我们能够预测检测的散射电位的偏移与单粒子实验相比，精度大大提高。在未来的实验实现中，这可能导致测量由重力势中的小水平梯度引起的弱力-分辨率为几微米，主要由孤子的大小决定。我们的数值模拟的基础上严格证明有效的潜在的方法[物理评论快报。102，010403（2009）和Phys. Rev. Lett. 103，210402（2009）]。我们选择我们的参数，使证明的先决条件（孤子不能分裂，能量的原因）总是满足，从而探索一个参数制度无法通过Gross-Pitaevskii方程的平均场描述由于薛定谔猫态发生在多粒子量子动力学。
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。
This study investigates the quantumness of gravity under the setup of the atomic interferometry from the viewpoint of mass-energy equivalence. We evaluated interference visibility considering a particle with internal energy levels in a harmonic trapping potential. As per the result, for a spatially superposed gravitational source mass, interference visibility exhibits collapse and revival behavior, which implies that an initial separable internal state evolves to the entangled state with respect to the degrees of freedom of the center of mass, the internal energy levels, and the external sourc…
