Number-conserving solution for dynamical quantum backreaction in a Bose-Einstein condensate

Abstract

We provide a number-conserving approach to the backreaction problem of small quantum fluctuations onto a classical background for the exactly soluble dynamical evolution of a Bose-Einstein condensate, experimentally realizable in the ultracold gas laboratory. A force density exerted on the gas particles which is of quantum origin is uniquely identified as the deviation from the classical Eulerian force density. The backreaction equations are then explored for the specific example of a finite size uniform density condensate initially at rest. By assuming that the condensate starts from a non-interacting regime, and in its ground state, we fix a well-defined initial vacuum condition, which is driven out-of-equilibrium by instantaneously turning on the interactions. The assumption of this initial vacuum accounts for the ambiguity in choosing a vacuum state for interacting condensates, which is due to phase diffusion and the ensuing condensate collapse. As a major finding, we reveal that the time evolution of the condensate cloud leads to condensate density corrections that cannot in general be disentangled from the quantum depletion in measurements probing the power spectrum of the total density. Furthermore, while the condensate is initially at rest, quantum fluctuations give rise to a nontrivial condensate flux, from which we demonstrate that the quantum force density attenuates the classical Eulerian force. Finally, the knowledge of the particle density as a function of time for a condensate at rest determines, to order $N^0$, where $N$ is the total number of particles, the quantum force density, thus offering a viable route for obtaining experimentally accessible quantum backreaction effects.

arXiv comment15 pages, 6 figures

References in corpus (32)

• Dynamics of collapsing and exploding Bose-Einstein condensates
• Bose-Einstein condensation of atoms in a uniform potential
• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Observation of thermal Hawking radiation at the Hawking temperature in an analogue black hole
• The truncated Wigner method for Bose condensed gases: limits of validity and applications
• Numerical observation of Hawking radiation from acoustic black holes in atomic Bose-Einstein condensates
• A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
• Observations of density fluctuations in an elongated Bose gas: ideal gas and quasi-condensate regimes
• Quantum Gases in Optical Boxes
• A classical field method for time dependent Bose condensed gases
• Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole
• Quantum depletion of a homogeneous Bose-Einstein condensate
• Hawking radiation without black hole entropy
• Mean-field expansion in Bose-Einstein condensates with finite-range interactions
• A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas
• Comment on ``Phase and Phase Diffusion of a Split Bose-Einstein Condensate''
• Super-resolution microscopy of cold atoms in an optical lattice
• Backreaction in an analogue black hole experiment
• Homodyne Measurements on a Bose-Einstein Condensate
• A Wavefunction Microscope for Ultracold Atoms
• Quantum backreaction in dilute Bose-Einstein condensates
• Quantum effects in Acoustic Black Holes: the Backreaction
• Induced density correlations in a sonic black hole condensate
• On the existence of steady-state black hole analogues in finite quasi-one-dimensional Bose-Einstein condensates
• Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws
• Back-reaction in canonical analogue black holes
• Coherence and Instability in a Driven Bose-Einstein Condensate: A Fully Dynamical Number-Conserving Approach
• Measurement-induced Squeezing of a Bose-Einstein Condensate
• Evanescent Modes and Step-like Acoustic Black Holes
• Renormalized scalar propagator around a dispiration
• Particle creation in Bose--Einstein condensates: Theoretical formulation based on conserving gapless mean field theory