Hartree-Fock Theory for Double Condensates

Esry, B. D.; Greene, Chris H.; Burke, J. P.; Bohn, John L.

doi:10.1103/physrevlett.78.3594

Cited by 548 publications

(433 citation statements)

References 12 publications

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“…The coupled mean-field equations are equivalent to those for a two-component condensate [18] if one replaces one of the two components by a single impurity. In writ-ing Eqs.…”

Section: Self-consistent Mean-field Treatmentmentioning

confidence: 99%

Interaction-induced localization of an impurity in a trapped Bose-Einstein condensate

2006

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We study the ground state properties of a trapped Bose condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This "collapse" can possibly be investigated in bosenova-type experiments.

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“…The coupled mean-field equations are equivalent to those for a two-component condensate [18] if one replaces one of the two components by a single impurity. In writ-ing Eqs.…”

Section: Self-consistent Mean-field Treatmentmentioning

confidence: 99%

Interaction-induced localization of an impurity in a trapped Bose-Einstein condensate

2006

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“…Depending on the various nonlinear coefficients, a vast array of solutions can be supported by a binary condensate. These include, ground-state solutions [302][303][304], small-amplitude excitations [305][306][307][308], bound states of dark-bright [309] and dark-dark [310], dark-gray, brightgray, bright-antidark and dark-antidark [311] complexes of solitary waves, vector solitons with embedded domain-walls (DWs) [312], spatially periodic states [313], and modulated amplitude waves [314]. Extensions of some of these patterns in two dimensions, namely DWs, have been investigated in Refs.…”

Section: Spinor/multicomponent Condensatesmentioning

confidence: 99%

“…Extensions of some of these patterns in two dimensions, namely DWs, have been investigated in Refs. [303,304,[315][316][317][318][319][320][321].…”

Section: Spinor/multicomponent Condensatesmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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“…Static and dynamical properties of Bose-Einstein condensates have been extensively and successfully explored in the community by employing the mean-field Gross-Pitaevskii theory [11,12], for reviews see [8][9][10] and for individual applications to condensates and mixtures [13][14][15][16][17][18][19] and [20][21][22][23][24][25], respectively. Gross-Pitaevskii theory is an excellent theory for weaklyinteracting bosons whenever a single macroscopic one-particle wavefunction is sufficient to describe the reality.…”

Section: Introductionmentioning

confidence: 99%

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

2008

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The evolution of Bose-Einstein condensates is amply described by the time-dependent GrossPitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent oneparticle state throughout the propagation process. In this work, we go beyond mean-field and develop an essentially-exact many-body theory for the propagation of the time-dependent Schrödinger equation of N interacting identical bosons. In our theory, the time-dependent many-boson wavefunction is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where both the expansion coefficients and the permanents (orbitals) themselves are timedependent and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations-of-motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and non-linear integro-differential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multi-configurational timedependent Hartree for bosons, or MCTDHB(M ), where M specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed.

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Hartree-Fock Theory for Double Condensates

Cited by 548 publications

References 12 publications

Interaction-induced localization of an impurity in a trapped Bose-Einstein condensate

Interaction-induced localization of an impurity in a trapped Bose-Einstein condensate

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

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