Atomic properties

Pethick, C. J.; Smith, H. Grayson

doi:10.1017/cbo9780511755583.004

Cited by 1 publication

(3 citation statements)

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“…For convenience of notation, we split this Hamiltonian into a sum of terms in orders of the powers of the number eigenvalues (again, we denote the set of number eigenvalues N c ). So we writeĤ 3 …”

Section: Reduction To a Third-order Hamiltonianmentioning

confidence: 99%

“…To the next order of approximation, a first-order approximation onĤ 3 . Working with this Hamiltonian and Eq.…”

Section: First Ordermentioning

confidence: 99%

“…Thermal effects are then frequently considered negligible, to the extent that a Hartree-Fock mean-field approach is often utilized [2,3]. In this zero-temperature limit, the resultant dynamical description of the condensate is provided by the Gross-Pitaevskii (GP) equation (a cubic nonlinear Schrödinger equation), which propagates a classical field with a form reminiscent of a Schrödinger wave function [2].…”

Section: Introductionmentioning

confidence: 99%

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Number-conserving approaches ton-component Bose-Einstein condensates

Mason

Gardiner

2014

Phys. Rev. A

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We develop the number-conserving approach that has previously been used in a single component Bose-Einstein condensed dilute atomic gas, to describe consistent coupled condensate and noncondensate number dynamics, to an n-component condensate. The resulting system of equations comprises, for each component, of a generalised Gross-Pitaevskii equation coupled to modified Bogoliubov-de Gennes equations. Lower-order approximations yield general formulations for multi-component Gross-Pitaevskii equations, and systems of multicomponent Gross-Pitaevskii equations coupled to multi-component modified number-conserving Bogoliubovde Gennes equations. The analysis is left general, such that, in the n-component condensate, there may or may not be mutually coherent components. An expansion in powers of the ratio of noncondensate to condensate particle numbers for each coherent set is used to derive the self-consistent, second-order, dynamical equations of motion. The advantage of the analysis developed in this article is in its applications to dynamical instabilities that appear when two (or more) components are in conflict and where a significant noncondensed fraction of atoms is expected to appear.

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Section: Reduction To a Third-order Hamiltonianmentioning

confidence: 99%

“…To the next order of approximation, a first-order approximation onĤ 3 . Working with this Hamiltonian and Eq.…”

Section: First Ordermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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