Images of a Bose-Einstein condensate: diagonal dynamical Bogoliubov vacuum

Abstract

Evolution of a Bose-Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent Bogoliubov theory: a condensate initially in its ground state Bogoliubov vacuum evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is tailored for simulations of quantum measurements on an excited condensate. As an example we work out phase imprinting of a dark soliton followed by a density measurement.

4 pages, 2 .eps figures

References in corpus (5)

• Atom interferometry with Bose-Einstein condensates in a double-well potential
• Fully three dimensional breather solitons can be created using Feshbach resonance
• Images of the Dark Soliton in a Depleted Condensate
• The Bogoliubov Theory of a BEC in Particle Representation
• Macroscopic quantum state reduction: uniting Bose-Einstein condensates by interference measurements

Cited by in corpus (22)

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• N-conserving Bogoliubov vacuum of a two component Bose-Einstein condensate: Density fluctuations close to a phase separation condition
• Single-shot simulations of dynamics of quantum dark solitons
• Bogoliubov theory for atom scattering into separate regions
• Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
• Quantum dark solitons in Bose gas confined in a hard wall box
• Comment on "Quantum entangled dark solitons formed by ultracold atoms in optical lattices"
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• Second order quantum phase transition of a homogeneous Bose gas with attractive interactions
• Particle-Number-Conserving Bogoliubov Approximation for Bose-Einstein Condensates Using Extended Catalytic States
• Bosonic Particle-Correlated States: A Nonperturbative Treatment Beyond Mean Field
• Interference of Fock states in a single measurement
• Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring
• Phase-space stochastic quantum hydrodynamics for interacting Bose gases
• Stochastic longevity of a dark soliton in a finite-temperature Bose-Einstein condensate
• Images of a Bose-Einstein condensate in position and momentum space
• Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case