Phase Separation of Bose-Einstein Condensates

Timmermans, Eddy

doi:10.1103/physrevlett.81.5718

Cited by 528 publications

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“…[3], but it revealed only the fact that such a homogeneous system is dynamically unstable against long-wavelength perturbations and, hence, tends to become phase-separated. One can think that dynamics of a phase separated system with an interface between the components 1 and 2 in the long-wavelength regime is adequately described by a concept of a surface tension with the surface tension constant inferred from the ground state properties [9]. However, a rigorous proof of this result was still lacking.…”

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“…In the latter case, a new physics related to the intercomponent boundary arises. The steady-state energetics of such an interface was estimated by Timmermans [9]. Ao and Chui [10] performed more detailed analysis, in particular, they found that there are two different regimes called, correspondingly, weakly and strongly segregated phase.…”

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“…In the present paper, we consider a case of absence of any external potential, so the coupled set of the GrossPitaevskii equations [5,9] is reduced to…”

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Waves on an interface between two phase-separated Bose-Einstein condensates

Mazets

2002

Phys. Rev. A

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We examine waves localized near a boundary between two weakly segregated Bose-Einstein condensates. In the case of a wavelength of order of or larger than the thickness of the overlap region the variational method is used. The dispersion laws for the two oscillation branches are found in analytic form. The opposite case of a wavelength much shorter than the healing length in the bulk condensate is also discussed.PACS numbers: 03.75. Fi, 05.30.Jp, The studies of mixtures of two superfluid Bose liquids ascend to the early work by Khalatnikov [1] who determined the possible sound modes in such a system within a macroscopic (hydrodynamical) approach. Later a microscopic theory was developed: Bassichis [2] considered a neutral mixture of two charged Bose gases with Coulomb interactions, and Nepomnyashchii [3] considered a system composed of bosons of two kinds interacting via shortrange potentials. In Ref.[3], most closely related to the case of a two-component degenerate dilute atomic vapor, the two-branch spectrum of elementary excitations and following from it criterion for stability of the ground state were found.The advances in experiments on Bose-Einstein condensation of trapped alkali atoms gave rise to an interest to this subject. The ground state configuration of a two-component atomic Bose-Einstein condensate (BEC) in the presence of a harmonic confining potential at zero temperature was calculated by Ho and Shenoy [4] in the Thomas-Fermi limit. The collective oscillation frequencies for trapped binary BECs were also determined [5][6][7]. Interesting numerical results are obtained by Pu and Bigelow [8]. These studies reveal that if the number of trapped atoms of each kind is large enough, the ground state physics can be qualitatively understood from the arguments valid for a case of absence of a trap [3]. In the latter case, the ground state properties are determined by a certain relation between the coupling constants. Namely, if the intercomponent repulsion (we do not consider attractive potentials in the present paper) is small enough, i.e., if g 12 < √ g 11 g 22 , where g ij = 2πh[m i m j /(m i + m j )] −1 a ij , a ij is the corresponding s-wave scattering length of a pair of ultracold atoms when one of them is of the jth kind and another is of the ith kind, m j is the mass of an atom for the jth component of the mixed BEC, i j = 1, 2, then the two degenerate Bose gases are miscible, i.e. they co-exist in all the volume. In the opposite case, g 12 > √ g 11 g 22 , the two components are immiscible and separated in space. In the latter case, a new physics related to the intercomponent boundary arises. The steady-state energetics of such an interface was estimated by Timmermans [9]. Ao and Chui [10] performed more detailed analysis, in particular, they found that there are two different regimes called, correspondingly, weakly and strongly segregated phase. The former one takes place if g 12 exceeds √ g 11 g 22 only slightly. In such a case the component interpenetration depth is quite large and proportiona...

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Waves on an interface between two phase-separated Bose-Einstein condensates

Mazets

2002

Phys. Rev. A

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“…Applying results from the two-component case, this phase separation is dominated by an instability with a characteristic exponential timescale τ F M = / 2|c 2 |n with n being the total gas density. The wavevector of the dominant instability k F M = 2m|c 2 |n/ , defines the typical size l = πk −1 F M of single-component domains in the phase-separated fluid, and also the width b ≃ k −1 F M of domain walls in which the two components still overlap [20,21].…”

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Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

Sadler

Higbie²,

Leslie³

et al. 2006

Nature

948

1,084

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A central goal in condensed matter and modern atomic physics is the exploration of manybody quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensedmatter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor BoseEinstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. 87 Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.Most ultracold atomic gases consist of atoms with nonzero total angular momentum denoted by the quantum number F , which is the sum of the total electronic angular momentum and nuclear spin. In spinor atomic gases, such as F = 1 and F = 2 gases of 23 Na [1, 2] and 87 Rb [3,4], all magnetic sublevels representing all orientations of the atomic spin may be realized [5]. The phase coherent portion of a Bose-Einsein condensed spinor gas is described by a vector order parameter and therefore exhibits spontaneous magnetic ordering. Nevertheless, considerable freedom remains for the type of ordering that can occur. For 87 Rb F = 1 spinor gases, the spindependent energy per particle in the condensate is the sum of two terms, c 2 n F 2 + q F 2 z , where F denotes the dimensionless spin vector operator. The first term describes spin-dependent interatomic interactions, with n being the number density and c 2 = (4π 2 /3m)(a 2 − a 0 ) depending on the atomic mass m and the s-wave scattering lengths a f for collisions between pairs of particles with total spin f [6,7]. Given c 2 < 0 for our system [3,4,8,9], the interaction term alone favors a ferromagnetic phase with broken rotational symmetry. The second term describes a quadratic Zeeman shift in our experiment, with q = (h × 70 Hz/G 2 )B 2 at a magnetic field of magnitude B [10]. This term favors instead a scalar phase with no net magnetization, i.e. a condensate in the |m z = 0 magnetic sublevel. These phases are divided by a second-order quantum phase transition at q = 2|c 2 |n.This article describes our observation of spontaneous symmetry breaking in a 87 Rb spinor BEC that is rapidly quenched across this quantum phase transition. Nearlypure spinor Bose-Einstein condensates were prepared in the scalar |m z = 0 phase at a high quadratic Zeeman shift (q ≫ 2|c 2 |n). By rapidly reducing the magnitude of the applied magneti...

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“…One of the significant properties characterizing multicomponent fluid systems is their miscibility; different fluids are either mutually miscible or phase separation occurs. In multicomponent BECs, the miscibility is determined by inter-and intra-species atomic interaction strengths [1] and, importantly, they can be experimentally controlled using Feshbach resonances [2,3] and Rabi coupling [4,5]. Multicomponent BECs with various degrees of miscibility are also available by choosing the internal states [6] or atomic species [7].…”

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Bouncing motion and penetration dynamics in multicomponent Bose-Einstein condensates

et al. 2016

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We investigate dynamic properties of bouncing and penetration in colliding binary and ternary Bose-Einstein condensates comprised of different Zeeman or hyperfine states of 87 Rb. Through the application of magnetic field gradient pulses, two-or three-component condensates in an optical trap are spatially separated and then made to collide. The subsequent evolutions are classified into two categories: repeated bouncing motion and mutual penetration after damped bounces. We experimentally observed mutual penetration for immiscible condensates, bouncing between miscible condensates, and domain formation for miscible condensates. From numerical simulations of the Gross-Pitaevskii equation, we find that the penetration time can be tuned by slightly changing the atomic interaction strengths. Multicomponent Bose-Einstein condensates (BECs) in dilute atomic gases are an attractive system for studying hydrodynamics of multicomponent quantum fluids owing to their unprecedented controllability. One of the significant properties characterizing multicomponent fluid systems is their miscibility; different fluids are either mutually miscible or phase separation occurs. In multicomponent BECs, the miscibility is determined by inter-and intra-species atomic interaction strengths [1] and, importantly, they can be experimentally controlled using Feshbach resonances [2,3] and Rabi coupling [4,5]. Multicomponent BECs with various degrees of miscibility are also available by choosing the internal states [6] or atomic species [7]. Employing such adjustability and selectability, intriguing phenomena that depend on the degree of miscibility have been experimentally observed, e.g., soliton generation in a counterflow of miscible fluids [8,9] The condition for miscibility in multicomponent BECs is determined by linear stability analysis of a static or steady state, and is not naively applicable to dynamical situations. Let us consider a situation in which two wave packets of different BECs collide with each other. One may think that the two wave packets pass through each other without much reflection for miscible BECs, while for immiscible BECs they do not. However, we will show that these simple predictions from the miscibility do not apply to a highly dynamic situation.In this Rapid Communication, we generate multicomponent BECs with various degrees of miscibility by utilizing the rich spin degrees of freedom of the 87 Rb atom, and investigate the dynamical properties of bouncing and penetration in colliding binary and ternary BECs in an optical trap. We observed various dynamics, including bouncing between miscible BECs and mutual penetration of immiscible BECs, which seems counterintuitive at first glance. In miscible and weakly immiscible binary and ternary systems, after a few bounces, BECs mutually penetrate and create the domain structure. In contrast, in the case of a relatively strongly immiscible system, binary BECs continue to bounce. Such repetitive bouncing motion between atoms has been observed only in a Tonks-Girardeau ga...

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Phase Separation of Bose-Einstein Condensates

Cited by 528 publications

References 17 publications

Waves on an interface between two phase-separated Bose-Einstein condensates

Waves on an interface between two phase-separated Bose-Einstein condensates

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

Bouncing motion and penetration dynamics in multicomponent Bose-Einstein condensates

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