Dark stationary matter waves via parity-selective filtering in a Tonks-Girardeau gas

Abstract

We propose a scheme for observing dark stationary waves in a Tonks-Girardeau (TG) gas. The scheme is based on parity-selective dynamical "evaporation" of the gas via a time-dependent potential, which excites the gas from its ground state towards a desired specially-tailored many-body state. These excitations of the TG gas are analogous to linear partially coherent nondiffracting beams in optics, as evident from the mapping between the quantum dynamics of the TG gas and the propagation of incoherent light in one-dimensional linear photonic structures. Trapped bose gases confined to one-dimensional (1D) geometry are highly attractive for studying quantum many-body dynamics because pertinent models yield exact solutions [1,2,3,4], these regimes are experimentally accessible [5,6,7,8], and quantum effects are enhanced [9,10,11]. Tonks-Girardeau (TG) gas is a system of 1D bosons with "impenetrable core" repulsive interactions [1]. In the fashion of the Pauli exclusion principle, "impenetrable cores" prevent bosons to occupy the same position in space, which causes TG gas to exhibit fermionic properties. This similarity is manifested in the mapping between 1D noninteracting fermions and TG bosons [1,4]. From the properties of atomic interactions in tight atomic waveguides [9] it follows that the TG regime can be reached at low temperatures, low linear densities or stronger effective interactions [9,10,11]. The experimental realizations of the TG gas in 2004 [6,7] boosted the physical relevance of the model. A recent experiment has demonstrated that such gas does not relax to the thermodynamic equilibrium even after numerous collisions [8], due to the integrability of the underlying model. This work inspired a theoretical study of 1D "impenetrable core" bosons on a lattice, which suggested that the system can undergo irreversible relaxation to a steady state carrying more memory of the initial conditions than the usual thermodynamic equilibrium [12]. Some aspects of the TG quantum dynamics have been studied theoretically within the context of so-called "dark solitons" [4,13], matter-wave interference [14], 1D expansion [15,16], irregular dynamics [17], and coherent states [18]. In this work, we study the dynamical tailoring of the TG gas via a time-dependent potential to produce dark stationary states, as well as point out the relation between TG dynamics and the propagation of incoherent light in linear photonic structures.The Fermi-Bose mapping [1,4], applicable both in the static [1] and time-dependent case [4], prescribes the construction of the exact many-body wavefunction of the TG gas from single-particle (SP) wavefunctions, which obey a set of uncoupled linear SP Schrödinger equations. In Ref.[4] Girardeau and Wright discuss the dynamics of the TG gas within the context of dark solitons [19,20,21,22]. Dark solitons are fundamental nonlinear excitations, which have been studied theoretically within the nonlinear mean-field theories applicable for weakly interacting gases [19,21,22], and observed experimentally i...

Momentum Distribution Dynamics of a Tonks-Girardeau Gas: Bragg Reflections of a Quantum Many-Body Wave Packet

“…Before closing, we note that dynamics of interacting Bose gases (including TG regime) may be related to incoherent light behavior in nonlinear and linear photonic structures [28,29], which motivate studies of the recently observed phenomena in optics [30] with Bose gases.…”

Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas

“…This work complements the studies of nonequilibrium dynamics of interacting Bose gases which have been addressed by use of the LL model away from [18,19,20,32] and in the TG limit [35,36,43,44,45,46,47,48,49]. The phenomenological relevance of these studies is underlined by the fact that nonequilibrium dynamics is accessible experimentally [7,8].…”

Momentum-space interferometry with trapped ultracold atoms

“…It is hence clear that the observation of such effect in any of these dual systems would be difficult, and we turn our attention to a closely related alternative approach. Recently, a parity-selective evaporation (PSE) method has been proposed which allows to prepare in principle excited states composed exclusively of odd-parity single-particle eigenstates [21]. This is achieved by shinning a blue-detuned laser at y ∼ 0 which removes the even-parity eigenstates.…”