Atom Chips and One‐Dimensional Bose Gases

Bouchoule, Isabelle; Druten, N. J. van; Westbrook, Christoph I

doi:10.1002/9783527633357.ch11

Cited by 22 publications

(33 citation statements)

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“…1. These results reveal that E kin /N varies considerably as the degeneracy and interaction strength are changed; thus it is a useful observable for discriminating between different regimes of the 1D Bose gas [6][7][8]. We identify three broad regimes of behavior.…”

Section: Gρgmentioning

confidence: 83%

“…Finally, we compare the kinetic energy and temperature predictions of the YY thermometry with those of the SPGPE and also find excellent agreement between the two approaches. While the SPGPE technique is limited to the degenerate yet high-temperature weakly interacting regime, the YY thermodynamic formalism applies to all repulsive interaction strengths and temperatures and therefore its usefulness extends beyond the regimes studied here.A uniform 1D Bose gas in the thermodynamic limit is completely characterized by two parameters [4][5][6][7][8][9]: the dimensionless interaction strength γ = mg/h 2 ρ and the reduced temperature t ≡ 2k B Th 2 /mg 2 , where ρ is the linear (1D) density, g 2hω ⊥ a is the effective 1D coupling strength [20], a is the 3D s-wave scattering length, and ω ⊥ the transverse radial harmonic trapping frequency [21]. The 1D regime is realized when the transverse excitation energyhω ⊥ is much larger than the thermal energy k B T and chemical potential μ.…”

mentioning

confidence: 99%

“…A uniform 1D Bose gas in the thermodynamic limit is completely characterized by two parameters [4][5][6][7][8][9]: the dimensionless interaction strength γ = mg/h 2 ρ and the reduced temperature t ≡ 2k B Th 2 /mg 2 , where ρ is the linear (1D) density, g 2hω ⊥ a is the effective 1D coupling strength [20], a is the 3D s-wave scattering length, and ω ⊥ the transverse radial harmonic trapping frequency [21]. The 1D regime is realized when the transverse excitation energyhω ⊥ is much larger than the thermal energy k B T and chemical potential μ.…”

mentioning

confidence: 99%

“…The one-dimensional (1D) Bose gas with repulsive interactions has emerged as a paradigm system because exact solutions are available for both eigenstates [4] and thermodynamic quantities [5] (see Ref. [6] and references therein). Furthermore, this system exhibits a surprisingly rich variety of regimes [7,8] connected by broad crossovers.…”

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confidence: 99%

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Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

et al. 2012

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We describe the use of the exact Yang-Yang solutions for the one-dimensional Bose gas to enable accurate kinetic-energy thermometry based on the root-mean-square width of an experimentally measured momentum distribution. Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide a quantitative description of the full momentum distribution measurements of Van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)]. We find the fitted temperatures from the stochastic projected Gross-Pitaevskii approach are in excellent agreement with those determined by Yang-Yang kinetic-energy thermometry. Ultracold gases offer a unique opportunity to study fundamental problems in quantum many-body physics, allowing experimental observations to be compared directly with microscopic theories. An area of significant recent interest has been the measurement of thermodynamic relations [1][2][3]. The one-dimensional (1D) Bose gas with repulsive interactions has emerged as a paradigm system because exact solutions are available for both eigenstates [4] and thermodynamic quantities [5] (see Ref.[6] and references therein). Furthermore, this system exhibits a surprisingly rich variety of regimes [7,8] connected by broad crossovers. Most studies of the 1D Bose gas have focused on the position-space distributions [3,[8][9][10] and local correlations [7,8,[11][12][13][14], which can be directly obtained from the exact theories.A recent experiment by Van Amerongen et al.[10] measured the position and momentum distributions of a trapped 1D Bose gas throughout the crossover from an ideal gas to the quasicondensate regime. The position-space measurements were compared with the Yang-Yang (YY) thermodynamic solutions [5] within the local density approximation (LDA), and showed smooth behavior throughout the crossover. In contrast, the momentum distributions showed a pronounced temperature dependence, and, to the best of our knowledge, have been unexplained by theory to date. Previous work on the momentum properties of the 1D Bose gas has focused on limiting cases [12,13,15].Here we investigate the momentum properties of the 1D Bose gas and their application to thermometry through measurements of the system kinetic energy. Our methods provide a reliable foundation for accurate thermometry in all regimes of a 1D Bose gas with repulsive interactions, including the strongly correlated regime. This approach is reminiscent of molecular dynamics calculations, where the average kinetic energy per particle is a direct measure of the temperature [16].First, we use the exact YY thermodynamic formalism [5] to calculate the root-mean-square (rms) width of the momentum distribution, which is equivalent to determining the average kinetic energy per particle. In combination with * Current address: SRON, Netherlands Institute for Space Research, Utrecht, The Netherlands.the LDA for trapped (nonuniform) quasi-1D systems, we show how the YY kinetic energy results can be applied to accurate thermometry for a broad range of conditions that are re...

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Section: Gρgmentioning

confidence: 83%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

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“…The literature on bosons in cigar traps is much too large to summarize here and no definitive GBEC has yet been seen experimentally. A good review is the paper of Bouchoule et al [54] and a recent relevant experiment is described by Armijo et al [55]. Actual experiments here are on finite systems, of course, and sharp transitions are not observed.…”

Section: The 3d Transition To 1dmentioning

confidence: 99%

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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Introduction and Theoretical Basics

Rauer

2019

Springer Theses

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Atom Chips and One‐Dimensional Bose Gases

Cited by 22 publications

References 63 publications

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas

Generalized Bose–Einstein Condensation

Introduction and Theoretical Basics

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