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arXiv:physics/0607140 · New Journal of Physics

Effective-range description of a Bose gas under strong one- or two-dimensional confinement

Pascal Naidon, Eite Tiesinga, William F. Mitchell, Paul S. Julienne

Published Jan 29, 2007• 54 citations
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Abstract

We point out that theories describing s -wave collisions of bosonic atoms confined in one-dimensional (1D) or two-dimensional (2D) geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries.

DOI
10.1088/1367-2630/9/1/019

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We point out that theories describing s -wave collisions of bosonic atoms confined in one-dimensional (1D) or two-dimensional (2D) geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries.
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A dual confinement induced resonance effect first observed numerically in a paper [J. I. Kim, V. S. Melezhik and P. Schmelcher, Phys. Rev. Letters 97 (2006), 193203] predicts the possibility of suppressing the effective two-body interaction in a quasi-one dimensional (1D) cylindrical geometry. Here this low dimensionality effect is analytically modeled by applying a previous formalism to treat low energy quantum scattering processes under tight confinement [J. I. Kim, J. Schmiedmayer and P. Schmelcher, Phys. Rev. A 72 (2005), 042711]. This analytic formalism is improved in order to account non-perturbatively for the three dimensional (3D) scattering phase shift l = 1 for a given spherically symmetric interaction potential between distinguishable colliding particles. The role of the confinement on the scattering properties can then be systematically calculated up to the p-wave.
We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.
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 a(3D). 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 a(3D).
We discuss binary atomic collisions in a Bose gas tightly confined in one (axial) direction and identify two regimes of scattering. In the quasi-two-dimensional (quasi-2D) regime, where the confinement frequency ${\ensuremath{\omega}}_{0}$ greatly exceeds the gas temperature T,T,T, the scattering rates exhibit 2D features of the particle motion. At temperatures $T\ensuremath{\sim}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}$ one has a confinement-dominated 3D regime, where the confinement can change the momentum dependence of the scattering amplitudes. We describe the collision-induced energy exchange between the axial and radial degrees of freedom and analyze recent experiments on thermalization and spin-relaxation rates in a tightly (axially) confined gas of Cs atoms.