In this work, we study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \\approx 2.5 N^{1/3} \\hbar \\omega$ and two-body contact $C_2/N \\approx 16 N^{1/6}\\sqrt{m\\omega/\\hbar}$ for a Bose gas on resonance, where $\\omega$ is the trap frequency. Further, by considering only two-body correlations, we note that a sudden quench from small to large scattering lengths leads to out-of-equilibrium resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between $0$ and $\\infty$ , which serves to maximize the transfer probability of $N$ bosons in a harmonic trap with frequency $\\omega$ to the resonant state. We find that the intermediate scattering length should be $a\\approx3.16N^{-2/3}\\sqrt{\\hbar/(m\\omega)}$ , and that it produces an optimum transition probability of $1.03N^{-1/6}$ .In this work, we study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \\approx 2.5 N^{1/3} \\hbar \\omega$ and two-body contact $C_2/N \\approx 16 N^{1/6}\\sqrt{m\\omega/\\hbar}$ for a Bose gas on resonance, where $\\omega$ is the trap frequency. Further, by considering only two-body correlations, we note that a sudden quench from small to large scattering lengths leads to out-of-equilibrium resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between $0$ and $\\infty$, which serves to maximize the transfer probability of $N$ bosons in a harmonic trap with frequency $\\omega$ to the resonant state. We find that the intermediate scattering length should be $a\\approx3.16N^{-2/3}\\sqrt{\\hbar/(m\\omega)}$, and that it produces an optimum transition probability of $1.03N^{-1/6}$.

Jan 1, 20190 citations

Dynamics of BECs with Two- and Three-Body Interactions

Wu-Ming Liu, Emmanuel Kengne

Springer eBooksJan 1, 20191 citation

Universal properties of Bose systems with van der Waals interaction

Bo Gao

We show that universal properties of a many-atom quantum system exist at a much higher density, or a much shorter length scale, than those implied by traditional theories for a dilute Bose gas. In particular, a universal equation of state at length scale β6 = (mC6/2)1/4 (corresponding to the van der Waals interaction) is defined and investigated by combining the concept of effective potential, the constrained variational method and the analytic solution for the van der Waals potential. In one application, we show that a many-atom Bose system with negative scattering length may form a metastable liquid Bose–Einstein condensate (BEC) state with an equilibrium density that is controlled by a scaled scattering length.We show that universal properties of a many-atom quantum system exist at a much higher density, or a much shorter length scale, than those implied by traditional theories for a dilute Bose gas. In particular, a universal equation of state at length scale β6 = (mC6/2)1/4 (corresponding to the van der Waals interaction) is defined and investigated by combining the concept of effective potential, the constrained variational method and the analytic solution for the van der Waals potential. In one application, we show that a many-atom Bose system with negative scattering length may form a metastable liquid Bose–Einstein condensate (BEC) state with an equilibrium density that is controlled by a scaled scattering length.

APSMay 1, 20040 citations

Renormalization Group Study of BECs at Finite Temperature

Akimitsu Kirikoshi, Takafumi Kita

日本物理学会講演概要集Jan 1, 20200 citations

Universal properties of Bose systems with van der Waals interaction

Bo Gao

We show that universal properties of a many-atom quantum system exist at a much higher density, or a much shorter length scale, than those implied by traditional theories for a dilute Bose gas. In particular, a universal equation of state at length scale β 6 = ( mC 6 /ℏ 2 ) 1/4 (corresponding to the van der Waals interaction) is defined and investigated by combining the concept of effective potential, the constrained variational method and the analytic solution for the van der Waals potential. In one application, we show that a many-atom Bose system with negative scattering length may form a metastable liquid Bose–Einstein condensate (BEC) state with an equilibrium density that is controlled by a scaled scattering length.We show that universal properties of a many-atom quantum system exist at a much higher density, or a much shorter length scale, than those implied by traditional theories for a dilute Bose gas. In particular, a universal equation of state at length scale β 6 = ( mC 6 /ℏ 2 ) 1/4 (corresponding to the van der Waals interaction) is defined and investigated by combining the concept of effective potential, the constrained variational method and the analytic solution for the van der Waals potential. In one application, we show that a many-atom Bose system with negative scattering length may form a metastable liquid Bose–Einstein condensate (BEC) state with an equilibrium density that is controlled by a scaled scattering length.

Journal of Physics B Atomic Molecular and Optical PhysicsMay 18, 200427 citations

In this work, we study the ground state properties of a system of

N

harmonically trapped bosons of mass

m

interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle

E_0/N \\approx 2.5 N^{1/3} \\hbar \\omega

and two-body contact

C_2/N \\approx 16 N^{1/6}\\sqrt{m\\omega/\\hbar}

for a Bose gas on resonance, where

\\omega

is the trap frequency. Further, by considering only two-body correlations, we note that a sudden quench from small to large scattering lengths leads to out-of-equilibrium resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between

0

and

\\infty

, which serves to maximize the transfer probability of

N

bosons in a harmonic trap with frequency

\\omega

to the resonant state. We find that the intermediate scattering length should be

a\\approx3.16N^{-2/3}\\sqrt{\\hbar/(m\\omega)}

, and that it produces an optimum transition probability of

1.03N^{-1/6}