Low-density, one-dimensional quantum gases in a split trap

We investigate degenerate quantum gases in one dimension trapped in a harmonic potential that is split in the centre by a pointlike potential. Since the single particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi-Bose mapping theorem. We calculate the exact many-particle ground-state wave-functions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well-known physics of Bose gases described by the Gross-Pitaevskii equation. We also address the experimentally important questions of creation and detection of such states.Comment: 7 pages, 5 figure

Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap

The exact N-particle ground state wave function for a one-dimensional condensate of hard core bosons in a harmonic trap is employed to obtain accurate numerical results for the one-particle density matrix, occupation number distribution of the natural orbitals, and momentum distribution. Our results show that the occupation of the lowest orbital varies as N^{0.59}, in contrast to N^{0.5} for a spatially uniform system, and N for a true BEC.Comment: 10 pages, 6 figures, submitted to Phys. Rev.

Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short range correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio

Measurement of one-particle correlations and momentum distributions for trapped 1D gases

van Hove's theory of scattering of probe particles by a macroscopic target is generalized so as to relate the differential cross section for atomic ejection via stimulated Raman transitions to one-particle momentum-time correlations and momentum distributions of 1D trapped gases. This method is well suited to probing the longitudinal momentum distributions of 1D gases in situ, and examples are given for bosonic and fermionic atoms.Comment: 4 pages, 2 .eps figure

Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons

We show that the time-dependent nonlinear Schrodinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference between split condensates that are recombined, whereas an exact many-body treatment shows minimal interference.Comment: 4 pages, 2 EPS figure

Quasi-one-dimensional Bose gases with large scattering length

Bose gases confined in highly-elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1d model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1d Bose gas become independent of the actual value of the 3d scattering length. In this unitary regime, the energy of the system is well described by a hard rod equation of state. We investigate the stability of quasi-1d Bose gases with positive and negative 3d scattering length.Comment: 5 pages, 3 figure

Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200

Density distributions for trapped one-dimensional spinor gases

We numerically evaluate the density distribution of a spin-1 bosonic condensate in its ground state within a modifed Gross-Pitaevskii theory, which is obtained by the combination of the exact solution of the corresponding integrable model with the local density approximation. Our study reveals that atoms in the m_F = 0 state are almost completely suppressed for the anti-ferromagnetic interactions in both weakly and strongly interacting regimes, whereas all three components remain non-vanishing for ferromagnetic interactions. Specially, when the system is in the Tonks-Girardeau (TG) regime, obvious Fermi-like distribution emerges for each component. We also discuss the possible deviation of the spatial distribution from the Fermi-like distribution when the spin-spin interaction is strong enough.Comment: 6 pages, 3 figures, version to be published in Phys. Rev.

An exactly solvable model of the BCS-BEC crossover

We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.Comment: corrected typos, minor modifications, submitted versio

Optical dipole traps and atomic waveguides based on Bessel light beams

We theoretically investigate the use of Bessel light beams generated using axicons for creating optical dipole traps for cold atoms and atomic waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated dipole traps allowing for the study of one-dimensional trapped gases and realization of a Tonks gas of impentrable bosons. First-order Bessel beams are shown to be able to produce tight confined atomic waveguides over centimeter distances.Comment: 20 pages, 5 figures, to appear in Phys. Rev.