We have studied the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of the Bose-Einstein transition temperature. We show that, for a non-interacting gas and near this temperature, the ground-state density has the same order of magnitude as the excited states density at the centre of the trap. This holds in a range of temperatures where the ground-state population is negligible compared to the total atom number. We compare the exact calculations, available in a harmonic trap, to semi-classical approximations. We show that these latter should include the ground-state contribution to be accurate..
We introduce a method for the coherent acceleration of atoms trapped in an optical lattice, using the well-known model for stimulated Raman adiabatic passage (STIRAP). Specifically, we show that small harmonic modulations of the optical lattice amplitude, with frequencies tuned to the eigenvalue spacings of three "unperturbed" eigenstates, reveals a three-state STIRAP subsystem. We use this model to realize an experimentally achievable method for transferring trapped atoms from stationary to motional eigenstates.
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 …
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…
We examine the stability and dynamics of a family of crossed dark solitons in a harmonically confined Bose-Einstein condensate in two dimensions. Working in a regime where the fundamental snake instability is suppressed, we show the existence of an instability which leads to an interesting collapse and revival of the initial state for the fundamental case of two crossed solitons. The instability originates from the singular point where the solitons cross, and we characterise it by examining the Bogoliubov spectrum. Finally, we extend the treatment to systems of higher symmetry.
We present a family of generalized unitary transformations that simplifies the Hamiltonian for a harmonically trapped two level atom (or ion) interacting with a plane wave laser field. Novel near resonant single as well as double vibrational phonon dynamical regimes are found. The validity condition of the often used motional rotating wave approximation (MRWA) is examined both numerically and analytically. Large errors are found within typical regimes of MRWA with respect to the motional degrees of freedom. The effects of MRWA in trapped ion systems are shown to be opposite to that of the rota…
We present a density-functional theory for the one dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the Local Density Approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for strong enough interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in t…
We study harmonically trapped one-dimensional atoms subjected to an equal combination of Rashba and Dresselhaus spin-orbit coupling induced by Raman transition. We first examine the wave function and the degeneracy of the single-particle ground state, followed by a study of two weakly interacting bosons or fermions. For the two-particle ground state, we focus on the effects of the interaction on the degeneracy, the spin density profiles, and the density-density correlation functions. Finally we show how these studies help us to understand the many-body properties of the system.
The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity, and can therefore be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour …
Employing a short-range two-channel description we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a new parameterization of the energy-dependent scattering length which differs from the one previously employed. We validate the model by comparison to full numerical calculations for Li-Rb and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.
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…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle subjected to a sudden transition to a harmonic potential can be described by a simple coordinate transformation applied at the transition time. This procedure is computationally more efficient than either state-projection or propagator techniques. A concatenation of the map and its inverse allows us to map from one harmonic oscillator to another with a different …
We present a method for solving trapped few-body problems and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical coordinates, i.e. the two-dimensional version of three-body hyperspherical coordinates, we discover an underlying ${\rm C}_{6v}$ symmetry. This symmetry simplifies the calculation of energy eigenstates of the full Hamiltonian in a truncated Hilbert space constructed from the trap Hamiltonian eigenstates. Particle superselection rules are implemented by choosing t…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of identical particles, parity inversion, and the separability of the center-of-mass. The exact solutions for the non-interacting and infinitely repulsive cases are reduced with respect to these symmetries. This reduction explains how states of single-component and multi-component fermions and bosons transform under adiabatic evolution from non-interacting to s…
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 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 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 study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other…
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 study the splitting of a harmonically trapped atomic Bose-Einstein condensate when we continuously turn up an optical lattice (or a double-well) potential. As the lattice height is increased, quantum fluctuations of atoms are enhanced. The resulting nonequilibrium dynamics of the fragmentation process of the condensate, the loss of the phase coherence of atoms along the lattice, and the reduced atom number fluctuations in individual lattice sites are stochastically studied within the truncated Wigner approximation. We perform a detailed study of the effects of temperature and lattice height…
We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the est…
The resonant heating of a harmonically trapped ion by a standing-wave light field is described as a quantum stochastic process combining a coherent Schroedinger evolution with Bohr-Einstein quantum jumps. Quantum and semi-quantum treatments are compared.
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…
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…
We compute single-particle energy spectra for a one-body hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner dis…
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…
We model the dynamics of attractively interacting ultracold bosonic atoms in a quasi-one-dimensional wave-guide with additional harmonic trapping. Initially, we prepare the system in its ground state and then shift the zero of the harmonic trap and switch on an additional narrow scattering potential near the center of the trap. After colliding with the barrier twice, we propose to measure the number of atoms opposite to the initial condition. Quantum-enhanced interferometry with quantum bright solitons allows us to predict detection of an offset of the scattering potential with considerably in…
Non-adiabatic interaction ramps are considered for trapped Bose-Einstein condensates. The deviation from adiabaticity is characterized through the heating or residual energy produced during the ramp. We find that the dependence of the heat on the ramp time is very sensitive to the ramp protocol. We explain features of this dependence through a single-parameter effective description based on the dynamics of the condensate size.
We show theoretically that elongated vortex-antivortex dipoles can be created controllably in trapped Bose-Einstein condensates, using known experimental techniques. Vortex dipoles of sufficient length are unstable and cascade into slow vortex rings which ultimately decay via sound emission. This instability of antiparallel vortex line elements, which self-generates Kelvin waves on vortex loops and in trapped atomic gases, may play a role in bridging the Kelvin-wave and Kolmogorov-Richardson cascades of quantum turbulence.
In this letter, atom optic techniques are proposed to control the excitation of a Bose-Einstein condensate in an atomic trap. We show that by employing the dipole potential induced by four highly detuned travelling-wave laser beams with appropriate phases and frequencies, one can coherently excite a trapped Bose-Einstein condensate composed of ultracold alkali atoms into a state rotating around the trap center. The connection to vortex states is discussed.
The problem of particle fluctuations in arbitrary nonuniform systems with Bose-Einstein condensate is considered. This includes the case of trapped Bose atoms. It is shown that the correct description of particle fluctuations for any nonuniform system of interacting atoms always results in thermodynamically normal fluctuations.
A geometry-based mechanism for generating steady-state internal circulation of local thermal currents is demonstrated by harmonically coupled quantum oscillators formulated by the Redfield quantum master equation (RQME) and the Bose Hubbard model (BHM) of phonons formulated by the Lindblad quantum master equation (LQME) using the simple multi-path geometry of a triangle. Driven by two reservoirs at different temperatures, both systems can exhibit an atypical local thermal current flowing against the total current. However, the total thermal current behaves normally. While the RQME of harmonica…
We show that a multiply-quantized vortex line core can be energetically stable in a harmonically trapped two-component atomic Bose-Einstein condensate. The structure, in which the condensate component with the vortex line is surrounded by the second component forming a vortex ring, can be identified as a particlelike Skyrmion with a multiply-quantized winding number, and closely resembles cosmic vortons.
