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arXiv:1304.7036 · Physical Review A

Excitations of a trapped two-component Bose-Einstein condensate

Christopher Ticknor

Published Jul 15, 2013• 29 citations
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Abstract

We present an analysis of the excitation spectrum for a two-component quasi-two-dimensional Bose-Einstein condensate (BEC). We study how excitations change character across the miscible to immiscible phase transition. We find that the bulk excitations are typical of a single-component BEC with the addition of interface bending excitations. We study how these excitations change as a function of the interaction strength.

DOI
10.1103/physreva.88.013623

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We present an analysis of the excitation spectrum for a two-component quasi-two-dimensional Bose-Einstein condensate (BEC). We study how excitations change character across the miscible to immiscible phase transition. We find that the bulk excitations are typical of a single-component BEC with the addition of interface bending excitations. We study how these excitations change as a function of the interaction strength.
We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two-dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a rotonlike IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single-component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled nonlocal Gross-Pitaevskii equations.
We study the normal modes and the stability of two component condensates in a phase separated regime. In such a regime, the system can undergo a quantum phase-transition upon the change of interaction strength between bosons of the same species or the variation of the trap frequencies. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of the interface tension, and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. We found new branches of normal modes which are specific for trapped multicomponent condensates and are analogous to the waves at the interface between two layers of immiscible fluids under gravity. At the point of the phase transition, the frequencies of those modes go to 0 and become imaginary which causes an instability. The interface tension shifts the normal-mode frequencies and changes the stability region of the system.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.
Abstract We compute the Bogoliubov–de Gennes excitation spectrum in a trapped two-component spin-orbit-coupled (SOC) Bose–Einstein condensate (BEC) in quasi-two-dimensions as a function of linear and angular momentum and analyze them. The excitation spectrum exhibits a minima-like feature at finite momentum for the immiscible SOC-BEC configuration, which implies dynamical instability. We augment these results by computing the dynamic structure factor in the density and pseudo-spin sector, and discuss its interesting features that can be experimentally measured through Bragg spectroscopy of such ultracold condensates.
Abstract We numerically investigate the collision dynamics of a dark soliton with a domain wall in an immiscible, two-component Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. The role of the inter-species interaction strength δ=g12/g11\delta = g_{12}/g_{11}δ=g12​/g11​ and the soliton's initial displacement Δx\Delta_xΔx​ is investigated thoroughly. Our results reveal a clear bifurcation into two distinct dynamical regimes: a penetrationregimepenetration regimepenetrationregime, where the soliton decays into vortex pairs that cross the interface, and a non−penetrationregimenon-penetration regimenon−penetrationregime, where the soliton's energy is dissipated at the interface through sound emission and vortex annihilation. We present a phase diagram that maps these outcomes across the (δ,Δx)(\delta, \Delta_x)(δ,Δx​) parameter space. Furthermore, within the non-penetration regime, we identify a complex excited state characterized by the combination of component breakup in one component and vortex formation in the other. This work provides the systematic study of dark soliton-domain wall interactions in a 2D phase-separated binary BEC, offering new insights into interfacial dynamics and non-equilibrium transport in multi-component quantum fluids.