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arXiv:cond-mat/0310330 · Journal de Physique IV (Proceedings)

Using magnetic chip traps to study Tonks-Girardeau quantum gases

Jakob Reichel, Joseph H. Thywissen

Published Oct 1, 2004• 24 citations
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Abstract

We discuss the use of microfabricated magnetic traps, or "chip traps," to study quasi-one-dimensional quantum gases. In particular, we discuss the feasibility of studying the Tonks-Girardeau limit, in which the gas is strongly interacting. We review the scaling of the oscillation frequencies of a chip trap, and show that it seems feasible to attain a Tonks-Girardeau parameter as large as 200. The primary difficulty of this approach is detection, since the strongly interacting limit occurs for low densities. We propose a way to "freeze" the distribution, and then measure it with a single-atom detector. This method can also be applied to optical dipole traps.

DOI
10.1051/jp4:2004116016

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We discuss the use of microfabricated magnetic traps, or "chip traps," to study quasi-one-dimensional quantum gases. In particular, we discuss the feasibility of studying the Tonks-Girardeau limit, in which the gas is strongly interacting. We review the scaling of the oscillation frequencies of a chip trap, and show that it seems feasible to attain a Tonks-Girardeau parameter as large as 200. The primary difficulty of this approach is detection, since the strongly interacting limit occurs for low densities. We propose a way to "freeze" the distribution, and then measure it with a single-atom detector. This method can also be applied to optical dipole traps.
Cold atoms on chips constitute a fascinating and non-trivial physical system. A gas of atoms can be cooled and trapped in a configuration in which one or more of the dimensions is so tightly confined, that they are "frozen out" leaving a one or two dimensional gas. Such a gas exhibits a rich variety of behavior depending on the interplay between the thermal energy of the atoms and their mutual interactions [1]. At very low temperature, a very dilute gas becomes strongly correlated entering the so-called Tonks-Girardeau regime, while at high density the gas behaves as a quasi-condensate whose density resembles that of a true condensate but whose phase fluctuates. At higher temperatures the gas can behave like an ideal bose gas, or enter a "quantum decoherent" regime in which the gas is strongly degenerate, but in which density fluctuations are large. I will discuss experiments investigating some of these regimes using direct measurements of density fluctuations in a gas on an atom chip. The measurement techniques are closely related to several other correlation techniques introduced recently in the field of cold atoms. These techniques are developing rapidly and I will comment on some of them. [1] K. Kheruntsyan, D. Gangardt, P. Drummond, G. Shlyapnikov, Phys. Rev. A 71, 053615 (2005).
Several experimental groups are currently working towards realizing quasi-one-dimensional (1D) atom waveguides and loading them with ultracold atoms. The dynamics becomes truly 1D in a regime (Tonks gas) of low temperatures and densities and large positive scattering lengths for which the transverse mode becomes frozen, in which case the many-body Schrodinger dynamics becomes exactly soluble via a Fermi-Bose mapping theorem. In this paper we review our recent work on the exact ground state and quantum dynamics of 1D Tonks gases and assess the possibility of approaching the Tonks regime using Bessel beam optical dipole traps.
We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.
We present results from quantum Monte Carlo simulations of trapped bosons in optical lattices, focusing on the crossover from a gas of softcore bosons to a Tonks-Girardeau gas in a one-dimensional optical lattice.We find that depending on the quantity being measured, the behavior found in the Tonks-Girardeau regime is observed already at relatively small values of the interaction strength.A finite critical value for entering the Tonks-Girardeau regime does not exist.Furthermore, we discuss the computational efficiency of two quantum Monte Carlo methods to simulate large scale trapped bosonic systems: directed loops in stochastic series expansions and the worm algorithm.
Possible signatures are discussed of a super-Tonks-Girardeau gas in bosonic systems of trapped quasi-one-dimensional dipoles at zero temperature. We provide an estimation of the frequency of the lowest compressional mode and compare it to analytical results derived using the harmonic approach in the high-density regime. We construct an exact mapping of the ground-state wave function of a one-dimensional dipolar system of bosons, fermions, and a Bose-Fermi mixture and conclude that the local properties and energy are the same at zero temperature. The question as to what extent the dipolar potential can be treated as long or short range is discussed.