Beyond the Tonks-Girardeau Gas: Strongly Correlated Regime in Quasi-One-Dimensional Bose Gases

Abstract

We consider a homogeneous 1D Bose gas with contact interactions and 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 a variational ansatz for the many-body wavefunction, we show that for small densities the gas-like state is stable and the corresponding equation of state is well described by a gas of hard rods. By calculating the compressibility of the system, we provide an estimate of the critical density at which the gas-like state becomes unstable against cluster formation. Within the hard-rod model we calculate the one-body density matrix and the static structure factor of the gas. The results show that in this regime the system is more strongly correlated than a Tonks-Girardeau gas. The frequency of the lowest breathing mode for harmonically trapped systems is also discussed as a function of the interaction strength. PACS numbers:The study of quasi-1D Bose gases in the quantumdegenerate regime has become a very active area of research. The role of correlations and of quantum fluctuations is greatly enhanced by the reduced dimensionality and 1D quantum gases constitute well suited systems to study beyond mean-field effects [1]. Among these, particularly intriguing is the fermionization of a 1D Bose gas in the strongly repulsive Tonks-Girardeau (TG) regime, where the system behaves as if it consisted of noninteracting spinless fermions [2]. The Bose-Fermi mapping of the TG gas is a peculiar aspect of the universal low-energy properties which are exhibited by bosonic and fermionic gapless 1D quantum systems and are described by the Luttinger liquid model [3]. The concept of Luttinger liquid plays a central role in condensed matter physics and the prospect of a clean testing for its physical implications using ultracold gases confined in highly elongated traps is fascinating [4,5].Bosonic gases in 1D configurations have been realized experimentally. Complete freezing of the transverse degrees of freedom and fully 1D kinematics has been reached for systems prepared in a deep 2D optical lattice [6,7]. The strongly interacting regime has been achieved by adding a longitudinal periodic potential and the transition from a 1D superfluid to a Mott insulator has been observed [8]. A different technique to increase the strength of the interactions, which is largely employed in both bosonic and fermionic 3D systems [9] but has not yet been applied to 1D configurations, consists in the use of a Feshbach resonance. With this method one can tune the effective 1D coupling constant g 1D to essentially any value, including ±∞, by exploiting a confinement induced resonance [10]. For large and positive values of g 1D the system is a TG gas of point-like impenetrable bosons. On the contrary, if g 1D is large and negative, we will show that a new gas-like regime is entered (super-Tonks) where the hard-core repulsion between particles becomes of finite range and correlations are stronger than in the TG...

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

“…This "simple" structure for the spectrum of the attractive model allows for an explicit calculation of the basic response functions [42]. Also, the regime of infinite attraction has intriguing properties which can be experimentally studied through a sudden quench of the interaction from the Tonks-Girardeau regime c → ∞ to this so called "Super-TG" regime c → −∞ [43]. In this way, the system is prepared in an excited state that can remain stable for suitably small density of particles.…”

“…All other permutations necessarily have components that explode as the distance between flipped sites increases, and thus have to vanish (an equivalent way to say this is to require that the scattering phase of all other permutations vanishes). These considerations yield the string structure for bound states 43) where η = ±1 is called the "parity" of the strings, and classifies the two types of complexes, with the center of mass lying either on the real axis or on the iπ axis. The energy and momentum of these M -complexes are…”

“…c → ∞ of the Lieb-Liniger model). Bosonic systems with K < 1 can be reached in the super-Tonks-Girardeau regime [43]. One of the fundamental advantages of having mapped an interacting system to a Gaussian theory like (C.25) is that the correlation functions are easily obtainable.…”

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

“…Apart from the phase transition lines we also indicate the line (dashed line) above which, in the V-SF phase, the intraspecies interaction enters into the so-called super-Tonks regime [105][106][107] with a > 0, meaning that intraspecies repulsion (i.e., repulsion between the particles with almost the same momenta) is effectively stronger than the hard-core contact repulsion. There, instead of relating the scattering length a to the Lieb-Liniger coupling constant g through Eq.…”

Adiabatic cycles in quantum systems with contact interactions

“…The adiabatic cycle described above has a immediate relevance to the population inversion in Bose gas system [9], particularly in the super-Tonks-Girardeau gas, which has attracted considerable recent attention in both experimental and theoretical studies [4,[10][11][12]. In the super-Tonks-Girardeau gas, which may be described by the Lieb-Liniger model [13] with strongly attractive interaction, the population inversion is created through an "adiabatic" process, where the interaction strength is suddenly flipped from infinitely repulsive to infinitely attractive [4,14].…”