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Chinese Physics B

Excitation spectrum and structure factor of a two-component Bose—Einstein condensate in different hyperfine states

Yufeng Han, Liang Chen, Houtong Liu, Xianshan Huang

Published Aug 1, 2013• 0 citations
Publisher

Abstract

The elementary excitation spectrum of a two-component Bose—Einstein condensate in different hyperfine states is obtained by Green's function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green's functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.

DOI
10.1088/1674-1056/22/8/080308

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We report a measurement of the excitation spectrum omega(k) and the static structure factor S(k) of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the superfluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spectrum in the local density approximation, even close to the long-wavelength limit of the region of applicability. Feynman's relation between omega(k) and S(k) is verified, within an overall constant.
The excitation spectrum for symmetric two-component Bose-Einstein condensate (BECs) in optical lattices is obtained, with emphasis on its quantitative dependence on intercomponent interaction parameter. The resulting two branches of the excitation spectrum have a linear spectrum asymptotically in the low momentum limit, which is expected as a behavior of superfluid. The critical superfluid velocity, depending on the intercomponent interaction parameter, is then obtained, which is quite different from the result obtained in other reference. A requirement of real excitation spectrum also results in a condition on the interaction parameters, which coincides with the phase separation condition. Hence in real spectrum excitation, it is proposed that there should be two branches of superfluid with different critical superfluid velocities, while in the complex spectrum it is predicted that there should be phase separation in the two-branch superfluid system. The excitation spectrum for an asymmetric two-component BEC system is also presented and analyzed.
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Abstract While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.