Binary mixtures of dilute bose gases with repulsive interactions at low temperature

Larsen, David M.

doi:10.1016/0003-4916(63)90066-6

Cited by 77 publications

(61 citation statements)

References 8 publications

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“…where n 0 = n ↑ + n ↓ and E kin , E trap , E MF and E LHY denote the kinetic, potential, mean-field and quantum fluctuation (Lee-Huang-Yang) contributions to the energy density of the mixture, respectively. Furthermore, V trap = 1 2 mω 2 r 2 corresponds to the harmonic confinement of the optical waveguide and f (x, y) = ± 1 + y ± (1 − y) 2 + 4xy 5/2 /4 √ 2 [42]. This en-ergy functional results in the extended Gross-Pitaevskii equation given in the main text…”

Section: B Theoretical Analysismentioning

confidence: 90%

Bright Soliton to Quantum Droplet Transition in a Mixture of Bose-Einstein Condensates

et al. 2018

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Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states: bright solitons and quantum droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in an optical waveguide. We show theoretically that, depending on atom number and interaction strength, solitons and droplets can be smoothly connected or remain distinct states coexisting only in a bistable region. We measure their spin composition, extract their density for a broad range of parameters, and map out the boundary of the region separating solitons from droplets.

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Section: B Theoretical Analysismentioning

confidence: 90%

Bright Soliton to Quantum Droplet Transition in a Mixture of Bose-Einstein Condensates

et al. 2018

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“…The leading correction to the MF energy for identical bosons with hard-sphere interactions was later obtained by Lee-Huang-Yang (LHY) [2] in the homogeneous case. These results were then extended to the case of twocomponent bosons by D. Larsen [3].…”

Section: Introductionmentioning

confidence: 91%

“…After summarizing known results to set the notation, we review the analytic LHY energy known for the special case of a mixture with largely imbalanced densities, with the majority component being the lighter species, i.e. the case of heavy impurities [3]. Then, we propose our approximated formula for the LHY energy and we show its limits of applicability by comparing it with the exact numerical results of the LHY integral.…”

Section: Introductionmentioning

confidence: 99%

Effective expression of the Lee-Huang-Yang energy functional for heteronuclear mixtures

et al. 2019

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We show that the Lee-Huang-Yang (LHY) energy functional for a heteronuclear Bose mixture can be accurately approximated by an expression that has the same functional form as in the homonuclear case. It is characterized by two exponents, which can be treated as fitting parameters. We demonstrate that the values of these parameters which preserve the invariance under permutation of the two atomic species are exactly those of the homonuclear case. Deviations from the actual expression of LHY energy functional are discussed quantitatively.

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“…The validity condition for this approximation is simply na 3 ≪ 1 (here and after for qualitative estimates we omit subscripts assuming that the masses are of the same order of magnitude, m 1 ∼ m 2 ∼ m, and the same holds for the densities, n 1 ∼ n 2 ∼ n, and scattering lengths, a 11 ∼ a 22 ∼ |a 12 | ∼ a). The equations of motion δL/δΨ ′ * i = 0 and δL/δΨ ′ i = 0 give two Bogoliubov excitation branches [14,15] …”

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confidence: 99%

Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture

2015

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According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, g 2 12 > g11g22. We show that instead of collapsing such a mixture gets into a dilute liquid-like droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The droplet thus automatically evaporates itself to zero temperature, the property potentially interesting by itself and from the viewpoint of sympathetic cooling of other systems.PACS numbers: 03.75. Mn,03.75.Kk The mean-field and the first beyond mean-field contribution, the famous Lee-Huang-Yang (LHY) correction, to the ground state energy of a homogeneous weaklyrepulsive Bose gas read [1]where n is the density and a > 0 and g = 4π 2 a/m are, respectively, the scattering length and coupling constant characterizing the interparticle interaction. The LHY correction originates from the zero-point motion of the Bogoliubov excitations and is thus intrinsically quantum. It is also universal in the sense that it depends only on the two-body scattering length and not on other parameters of the two-body or higher-order interactions. Quite naturally the experimental observation of this fundamental beyond mean-field effect came from the field of ultra-cold gases [2][3][4][5][6][7], where the gas parameter na 3 and, therefore, the relative contribution of the LHY term, can be enhanced by using Feshbach resonances [8]. Note however that the effect is perturbative; for na 3 ∼ 1 higher order terms and processes, in particular, three-body decay, come into play. A different situation is predicted for spinor gases where quantum fluctuations lift the degeneracy in the ground-state manifold [9,10] or lead to quantum mass acquisition [11]. In this Letter we point out that in a Bose-Bose mixture the mean-field term and the LHY term depend on the inter-and intraspecies coupling constants in a different manner. Therefore, one can independently control them and make them comparable to each other without ever leaving the weakly-interacting regime. In particular, an interesting situation, impossible in the singlecomponent case, arises when the mean-field term, ∝ n 2 , is negative and the LHY one, ∝ n 5/2 , is positive. Because of its steeper density scaling the quantum LHY repulsion neutralizes the mean-field attraction and stabilizes the system against collapse. The mixture can then exist as a droplet in equilibrium with vacuum without any external trapping [12]. This phenomenon naturally suggests a proof-of-principle experiment for observing the LHY quantum correction. The droplet can be prepared from currently available homo-and heteronuclear atomic mixtures by tuning the inter-and intraspecies scattering lengths into the unstable (from the mean-field viewpoin...

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Binary mixtures of dilute bose gases with repulsive interactions at low temperature

Cited by 77 publications

References 8 publications

Bright Soliton to Quantum Droplet Transition in a Mixture of Bose-Einstein Condensates

Bright Soliton to Quantum Droplet Transition in a Mixture of Bose-Einstein Condensates

Effective expression of the Lee-Huang-Yang energy functional for heteronuclear mixtures

Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture

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