Two-Body and Three-Body Contacts for Identical Bosons near Unitarity

Smith, D. Hudson; Braaten, Eric; Kang, Daekyoung; Platter, Lucas

doi:10.1103/physrevlett.112.110402

Cited by 58 publications

(98 citation statements)

References 39 publications

(102 reference statements)

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“…These are obtained via a Jastrow ansatz and hypernetted-chain approximation [30], a quantum Monte Carlo calculations based on a Jastrow-Feenberg ansatz [31], and a time-dependent variational ansatz for the many-body state [32]. The value c 2 ρ −4/3 22, extracted from an analysis of the experimental data [27], appears significantly larger than our theoretical predictions.…”

Section: Supplementary Item 2: Contact Density At Low Temperaturementioning

confidence: 65%

“…The slow decrease of c 2 for increasing R 0 ρ 1/3 (absent at high temperature, λ th ρ 1/3 → 0) corresponds to a small suppression of g (2) (r) at short distance, indirectly caused by the hyperradial cutoff. At high temperature, our first-principles results for the contact density rapidly fall below the predictions of the virial expansion [27][28][29] (Fig. 3(d)), leveling off at intermediate temperature, and finally decreasing at lower temperature.…”

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confidence: 92%

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Momentum Distribution in the Unitary Bose Gas from First Principles

Comparin

Krauth

2016

Phys. Rev. Lett.

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We consider a realistic bosonic N -particle model with unitary interactions relevant for Efimov physics. Using quantum Monte Carlo methods, we find that the critical temperature for BoseEinstein condensation is decreased with respect to the ideal Bose gas. We also determine the full momentum distribution of the gas, including its universal asymptotic behavior, and compare this crucial observable to recent experimental data. Similar to the experiments with different atomic species, differentiated solely by a three-body length scale, our model only depends on a single parameter. We establish a weak influence of this parameter on physical observables. In current experiments, the thermodynamic instability of our model from the atomic gas towards an Efimov liquid could be masked by the dynamical instability due to three-body losses.First predicted in 1970[1], the Efimov effect describes the behavior of three strongly interacting bosons when any two of them cannot bind. At unitarity, when the scattering length diverges, the three-body bound states are scale invariant and they form a sequence up to vanishing binding energy and infinite spatial extension. Efimov trimers had been intensely discussed in nuclear physics, but it was in an ultracold gas of caesium atoms that they were finally discovered [2]. To observe Efimov trimers, experiments in atomic physics rely on Feshbach resonances [3], which permits to instantly switch a gas between weak interactions and the unitary limit. Such a control of interactions lacks in nuclear physics or condensed matter experiments, and singular interactions can be probed there only in the presence of accidental fine tuning [4]. Beyond the original system[2], Efimov trimers have now been observed for several multi-component systems, including bosonic, fermionic and Bose-Fermi mixtures [5][6][7]. These experimental findings are interpreted in terms of the theory of few-body strongly interacting quantum systems. For three identical bosons in three dimensions, a complete universal theory is available, on and off unitarity [4]. Further theoretical work is aimed at understanding bound states for more than three bosons, mixtures, and the effects of dimensionality.Near-unitary interparticle interactions also impact the thermodynamics of the atomic gas, the description of which presents a challenge beyond the traditional theory of the Efimov effect. In addition, mean-field theory does not apply to infinite interactions [8], and the virial expansion [9] fails to describe the low-temperature state. Moreover, in atomic-physics experiments, strong interactions enhance the three-body loss rate, making the gas of bosons unstable. A characterization of the universal dynamics of these losses has been recently achieved [10][11][12]. On the other hand, a single breakthrough experiment [13] has addressed the low-temperature thermodynamics for a unitary bosonic gas, coming to the conclusion that equilibrium was approached faster than the system life-time. The importance of this system stems from its univer...

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Section: Supplementary Item 2: Contact Density At Low Temperaturementioning

confidence: 65%

mentioning

confidence: 92%

Momentum Distribution in the Unitary Bose Gas from First Principles

Comparin

Krauth

2016

Phys. Rev. Lett.

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“…It was unclear which dominates until recently when a JILA experiment on 85 Rb by Makotyn et al [2] firmly established that the three-body loss rate is much slower than the equilibration rate. This pleasant surprise opens the door to the possibility of exploring the rich physics underlying strongly interacting Bose gases [29][30][31][32][33][34][35][36][37] and has motivated, together with experimental works such as [43], a flurry of theoretical studies concerning quenched nonequilibrium dynamics [1,[44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium states of a quenched Bose gas

Kain

Ling

2014

Phys. Rev. A

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Yin and Radzihovsky [1] recently developed a self-consistent extension of a Bogoliubov theory, in which the condensate number density nc is treated as a mean field that changes with time, in order to analyze a JILA experiment by Makotyn et al.[2] on a 85 Rb Bose gas following a deep quench to a large scattering length. We apply this theory to construct a closed set of equations that highlight the role ofṅc, which is to induce an effective interaction between quasiparticles. We show analytically that such a system supports a steady state characterized by a constant condensate density and a steady but periodically changing momentum distribution, whose time average is described exactly by the generalized Gibbs ensemble. We discuss how theṅc-induced effective interaction, which cannot be ignored on the grounds of the adiabatic approximation for modes near the gapless Goldstone mode, can significantly affect condensate populations and Tan's contact for a Bose gas that has undergone a deep quench.

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“…We now demonstrate that the outlined sampling scheme provides a reliable description of Bose systems at unitarity, which have attracted a great deal of attention recently experimentally and theoretically [43][44][45][46][47][48][49][50]. While the properties of unitary Fermi systems with zero-range interactions are fully determined by the s-wave scattering length [12,14,[51][52][53][54] those of Bose systems additionally depend on a three-body parameter [15,17].…”

Section: Three Dimensional Testsmentioning

confidence: 99%

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

Yan¹,

Blume²

2015

Phys. Rev. A

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Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that N -body systems with two-body zero-range interactions can be treated reliably and efficiently by the finite temperature and ground state path integral Monte Carlo approaches, using the exact two-body propagator for zero-range interactions in the pair product approximation. Harmonically trapped one-and three-dimensional systems are considered. A new propagator for the harmonically trapped two-body system with infinitely strong zero-range interaction, which may also have applications in real time evolution schemes, is presented.

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Two-Body and Three-Body Contacts for Identical Bosons near Unitarity

Cited by 58 publications

References 39 publications

Momentum Distribution in the Unitary Bose Gas from First Principles

Momentum Distribution in the Unitary Bose Gas from First Principles

Nonequilibrium states of a quenched Bose gas

Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

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