Observation of Reduced Three-Body Recombination in a Correlated 1D Degenerate Bose Gas

Tolra, B. Laburthe; O’Hara, K. M.; Huckans, John; Phillips, William D.; Rolston, S. L.; Porto, J. V.

doi:10.1103/physrevlett.92.190401

Cited by 390 publications

(369 citation statements)

References 29 publications

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“…This parameter quantifies the ratio of the average interaction energy to the kinetic energy calculated with mean-field theory. Notice that γ varies smoothly as the interatomic coupling is increased from values γ ≪ 1 for a weakly interacting 1D Bose gas, to γ ≫ 1 for the strongly-interacting Tonks-Girardeau gas, with an approximate "crossover regime" being around γ ∼ O(1), attained experimentally as well [144,145].…”

Section: Weakly-and Strongly-interacting 1d Bose Gases the Tonks-girmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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Section: Weakly-and Strongly-interacting 1d Bose Gases the Tonks-girmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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“…All that is required is that the energy gap in the transverse direction be much greater than the gap in the longitudinal direction [22]. Also, one dimensional geometries have been observed to display higher critical transition temperatures to BEC [23], and substantially reduced three-body recombination rates [24]. These developments underscore the importance of the three-body problem with short-range interactions in one dimension.…”

Section: Introductionmentioning

confidence: 99%

Three bosons in one dimension with short-range interactions: Zero-range potentials

Mehta

Shepard

2005

Phys. Rev. A

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We consider the three-boson problem with δ-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle off of a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the 1+2 scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pair-wise interactions are short-range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling. *

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“…The 1D Bose gas, with its well-understood conservation laws [6] and exact solutions [7,8] is an excellent testing ground for these ideas. Second-order correlations in thermal equilibrium with repulsive interactions have been predicted [9][10][11][12] and verified experimentally [13,14]. In these systems, there is evidence of steady-states that do not have a Gibbs structure [15,16].…”

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One-dimensional Bose gas dynamics: Breather relaxation

Opanchuk

Drummond

2017

Phys. Rev. A

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One-dimensional Bose gases are a useful testing-ground for quantum dynamics in many-body theory. They allow experimental tests of many-body theory predictions in an exponentially complex quantum system. Here we calculate the dynamics of a higher-order soliton in the mesoscopic case of N = 10 3 − 10 4 particles, giving predictions for quantum soliton breather relaxation. These quantum predictions use a truncated Wigner approximation, which is a 1/N expansion, in a regime where other exactly known predictions are recovered to high accuracy. Such dynamical calculations are testable in forthcoming BEC experiments.Techniques for observing near lossless quantum dynamics have led to quantitative tests of quantum field dynamics in photonic systems [1][2][3][4]. Improvements in ultra-cold quantum gas experiments mean that these experiments can now also compare first principles calculations of many-body quantum dynamics with observations [5]. The 1D Bose gas, with its well-understood conservation laws [6] and exact solutions [7,8] is an excellent testing ground for these ideas. Second-order correlations in thermal equilibrium with repulsive interactions have been predicted [9][10][11][12] and verified experimentally [13,14]. In these systems, there is evidence of steady-states that do not have a Gibbs structure [15,16]. Attractive matter-wave solitons have also been experimentally observed [17][18][19][20][21][22].Here we show that the dynamical stability of higherorder matter-wave solitons prepared by quenching is experimentally testable. Fragmentation and damping of breathing oscillations [23,24] are predicted to persist even up to a mean particle number of N = 1000. These calculations use the truncated Wigner approximation, which is a 1/N expansion [25][26][27]. Known conserved quantities are replicated with high accuracy. This is a regime accessible to current BEC experiments [22,24,28]. We show that direct experimental tests of predictions for soliton fragmentation and centerof-mass dynamics are possible in an exponentially complex regime where exact calculation is extremely difficult.Fragmentation causes a decay in oscillation that is predicted to happen gradually, without the abrupt changes after a short evolution time found by variational methods [29]. Such methods are known to disagree with exact COM spreading results [30], which means that they violate Galilean invariance [31]. We show that this is because the number of dissociation channels is much larger than the number of variational modes used in such calculations. The oscillation decay found here is slower than predicted at very small particle number [23], and also less pronounced than the predicted fragmentation at small N obtained from exact analysis [24]. However, this difference is qualitatively consistent with the scaling we find with N : where fragmentation and breather relaxation are reduced as N increases.Here we investigate the dynamics of a higher-order soliton or breather. In this case, even more dramatic effects can occur due to quantum fragment...

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Observation of Reduced Three-Body Recombination in a Correlated 1D Degenerate Bose Gas

Cited by 390 publications

References 29 publications

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Three bosons in one dimension with short-range interactions: Zero-range potentials

One-dimensional Bose gas dynamics: Breather relaxation

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