Regimes of Quantum Degeneracy in Trapped 1D Gases

Petrov, D. S.; Shlyapnikov, G. V.; Walraven, J.T.M.

doi:10.1103/physrevlett.85.3745

Cited by 687 publications

(1,056 citation statements)

References 40 publications

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“…Theoretically no lower sharp second transition to a true BEC, in which only the ground state is occupied is expected, but rather a "quasicondensate" is formed. The formation of the quasicondensate is driven by interactions, which surpress density fluctuations while the phase still fluctuates [59]. The observations conform to this description.…”

Section: The 3d Transition To 1dsupporting

confidence: 71%

Generalized Bose–Einstein Condensation

Mullin

Sakhel

2011

J Low Temp Phys

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Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or "normal" BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the "channel" potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the "cigar trap" (anisotropic harmonic potential), and the "Casimir prism" (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature Tc and another "one-dimensional" transition at a lower temperature T1 into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, T1 merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, T1 becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.

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Section: The 3d Transition To 1dsupporting

confidence: 71%

Generalized Bose–Einstein Condensation

Mullin

Sakhel

2011

J Low Temp Phys

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“…by considering a thermodynamic equilibrium situation, where ρ ∼ e −H/kBT → |G G| for temperature T → 0. In particular, in the context of ultracold atomic quantum gases, much of the interest of the last few years has focused on engineering specific Hamiltonians based on control of microscopic system parameters via external fields [1,2,3,4,5,6], opening the door to a quantum simulation of strongly correlated ground states [7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Quantum states and phases in driven open quantum systems with cold atoms

et al. 2008

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An open quantum system, whose time evolution is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the system-reservoir coupling. This points out a route towards preparing many body states and non-equilibrium quantum phases by quantum reservoir engineering. Here we discuss in detail the example of a driven dissipative Bose Einstein Condensate of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via the atomic current representing local dissipation. In the absence of interactions the lattice gas is driven into a pure state with long range order. Weak interactions lead to a weakly mixed state, which in 3D can be understood as a depletion of the condensate, and in 1D and 2D exhibits properties reminiscent of a Luttinger liquid or a KosterlitzThouless critical phase at finite temperature, with the role of the "finite temperature" played by the interactions.

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“…This occurs in a regime of low temperatures and densities * Electronic address: girardeau@optics.arizona.edu † Electronic address: olshanii@phys4adm.usc.edu where both the chemical potential µ and the thermal energy k B T are less than the transverse oscillator level spacing ω ⊥ , so transverse oscillator modes are frozen and the dynamics is described by a one-dimensional (1D) Hamiltonian with zero-range interactions [16,17]. This 1D regime has already been reached experimentally [8,18,19], as has a regime with µ < ω ⊥ but k B T > ω ⊥ [6,10].…”

Section: Introductionmentioning

confidence: 99%

“…II B the derivation of effective 1D pseudopotentials will be presented, for application not only to the spinless Bose gas but also to the case of spinor Fermi and Bose gases, for which the definition of pseudopotentials is much more delicate due to wave function discontinuities induced in the zero-range limit by 1D odd-wave interactions derived from 3D p-wave scattering. In the spatially uniform case (no longitudinal trapping potential) the zero-temperature properties of an N -atom spinless Bose gas are determined by a dimensionless coupling constant γ B = mg B 1D /n 2 [16,17,23] where m is the atomic mass and n = N/L is the 1D number density, L being the length of the periodic box. The exact N -boson ground state was found in the spatially uniform case by the Bethe Ansatz method in a famous paper of Lieb and Liniger (LL) [23], and spawned later development of a powerful and more general approach [24].…”

Section: Introductionmentioning

confidence: 99%

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Girardeau

Nguyen

Olshanii

2004

Optics Communications

141

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Derivation of effective zero-range one-dimensional (1D) interactions between atoms in tight waveguides is reviewed, as is the Fermi-Bose mapping method for determination of exact and stronglycorrelated many-body ground states of ultracold bosonic and fermionic atomic vapors in such waveguides, including spin degrees of freedom. Odd-wave 1D interactions derived from 3D p-wave scattering are included as well as the usual even-wave interactions derived from 3D s-wave scattering, with emphasis on the role of 3D Feshbach resonances for selectively enhancing s-wave or p-wave scattering so as to reach 1D confinement-induced resonances of the even and odd-wave interactions. A duality between 1D fermions and bosons with zero-range interactions suggested by Cheon and Shigehara is shown to hold for the effective 1D dynamics of a spinor Fermi gas with both even and odd-wave interactions and that of a spinor Bose gas with even and odd-wave interactions, with even(odd)-wave Bose coupling constants inversely related to odd(even)-wave Fermi coupling constants. Some recent applications of Fermi-Bose mapping to determination of many-body ground states of Bose gases and of both magnetically trapped, spin-aligned and optically trapped, spin-free Fermi gases are described, and a new generalized Fermi-Bose mapping is used to determine the phase diagram of ground-state total spin of the spinor Fermi gas as a function of its even and odd-wave coupling constants.

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Regimes of Quantum Degeneracy in Trapped 1D Gases

Cited by 687 publications

References 40 publications

Generalized Bose–Einstein Condensation

Generalized Bose–Einstein Condensation

Quantum states and phases in driven open quantum systems with cold atoms

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

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