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Register a new userInteraction-induced Bloch Oscillation in a Harmonically Trapped and Fermionized Quantum Gas in One Dimension
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Motivated by a recent experiment by F. Meinert et al, arxiv:1608.08200, we study the dynamics of an impurity moving in the background of a harmonically trapped one-dimensional Bose gas in the hard-core limit. We show that due to the hidden lattice structure of background bosons, the impurity effectively feels a quasi-periodic potential via impurity-boson interactions that can drive the Bloch oscillation under an external force, even in the absence of real lattice potentials. Meanwhile, the inhomogeneous density of trapped bosons imposes an additional harmonic potential to the impurity, resulting in a similar oscillation dynamics but with different periods and amplitudes. We show that the sign and the strength of impurity-boson coupling can significantly affect above two potentials so as to determine the impurity dynamics.
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We study a system of two bosons of one species and a third boson of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter- and intra-species interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical ansatzs gaining physical insight over the numerically obtained wavefunctions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wavefunction when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the inter-species and/or the intra-species interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systemss ground state resembles that of three indistinguishable bosons. Contrarily, the systemss ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit to built up different correlations in the system and lead to different spatial distributions of the three atoms.
We experimentally study the energy-temperature relationship of a harmonically trapped Bose-Einstein condensate by transferring a known quantity of energy to the condensate and measuring the resulting temperature change. We consider two methods of heat transfer, the first using a free expansion under gravity and the second using an optical standing wave to diffract the atoms in the potential. We investigate the effect of interactions on the thermodynamics and compare our results to various finite temperature theories.
We predict the existence of a dip below unity in the second-order coherence function of a partially condensed ideal Bose gas in harmonic confinement, signaling the anticorrelation of density fluctuations in the sample. The dip in the second-order coherence function is revealed in a canonical-ensemble calculation, corresponding to a system with fixed total number of particles. In a grand-canonical ensemble description, this dip is obscured by the occupation-number fluctuation catastrophe of the ideal Bose gas. The anticorrelation is most pronounced in highly anisotropic trap geometries containing small particle numbers. We explain the fundamental physical mechanism which underlies this phenomenon, and its relevance to experiments on interacting Bose gases.
We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.
Motivated by previous suggestions that three-body hard-core interactions in lower-dimensional ultracold Bose gases might provide a way for creation of non-Abelian anyons, the exact ground state of a harmonically trapped 1D Bose gas with three-body hard-core interactions is constructed by duality mapping, starting from an $N$-particle ideal gas of mixed symmetry with three-body nodes, which has double occupation of the lowest harmonic oscillator orbital and single occupation of the next $N-2$ orbitals. It has some similarity to the ground state of a Tonks-Girardeau gas, but is more complicated. It is proved that in 1D any system of $Nge 3$ bosons with three-body hard-core interactions also has two-body soft-core interactions of generalized Lieb-Liniger delta function form, as a consequence of the topology of the configuration space of $N$ particles in 1D, i.e., wave functions with emph{only} three-body hard core zeroes are topologically impossible. This is in contrast with the case of 2D, where pure three-body hard-core interactions do exist, and are closely related to the fractional quantized Hall effect. The exact ground state is compared with a previously-proposed Pfaffian-like approximate ground state, which satisfies the three-body hard-core constraint but is not an exact energy eigenstate. Both the exact ground state and the Pfaffian-like approximation imply two-body soft-core interactions as well as three-body hard-core interactions, in accord with the general topological proof.
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