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Analogs to the dynamical Casimir effect in Bose-Einstein condensates (Orale)

Christoph Ira Westbrook

Published Jun 24, 2013• 0 citations
OpenAlex

Abstract

It is a remarkable prediction of quantum field theory that the vacuum can generate real particles when boundary conditions are suddenly changed. Thus the 'dynamical Casimir effect' results in the spontaneous generation of photon pairs in an empty cavity with nonuniformly accelerating boundaries. Recent advances have permitted the realization of this effect, or analogs to it in a variety of systems, some of which will be discussed at this workshop. Bose Einstein condensates are attractive candidates in which to study acoustic analogs to such phenomena because their low temperatures promise to reveal quantum effects. I will discuss a recent experiment in our group to realize an acoustic analog to the dynamical Casimir effect by modulating the confinement of a Bose-Einstein condensate. We observe correlated pairs of Bogoliubov quanta, both phonon-like and particle-like, are excited by this modulation in a process that formally resembles parametric down conversion. I will discuss our current ideas on how to observe and quantify the degree of entanglement in the excitations we observe.

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An acoustic analog to the dynamical Casimir effect in a BEC

Christoph Ira Westbrook

I discuss a modulation technique to produce correlated phonon pairs with a method inspired by the dynamical Casimir effect.

•Jul 9, 2012•0 citations
It is a remarkable prediction of quantum field theory that the vacuum can generate real particles when boundary conditions are suddenly changed. Thus the 'dynamical Casimir effect' results in the spontaneous generation of photon pairs in an empty cavity with nonuniformly accelerating boundaries. Recent advances have permitted the realization of this effect, or analogs to it in a variety of systems, some of which will be discussed at this workshop. Bose Einstein condensates are attractive candidates in which to study acoustic analogs to such phenomena because their low temperatures promise to reveal quantum effects. I will discuss a recent experiment in our group to realize an acoustic analog to the dynamical Casimir effect by modulating the confinement of a Bose-Einstein condensate. We observe correlated pairs of Bogoliubov quanta, both phonon-like and particle-like, are excited by this modulation in a process that formally resembles parametric down conversion. I will discuss our current ideas on how to observe and quantify the degree of entanglement in the excitations we observe.
In a quantum fluid such as a condensed Bose gas, elementary excitations such as phonons behave as quantized fields with dispersion relations and non-linearities that bear some resemblance to those of the electromagnetic field. The very low temperatures of these gases means that in some cases quantum fluctuations are important. Several remarkable phenomena in quantum electrodynamics have found acoustic analogs, and I will discuss two of them. The first is the dynamical Casimir effect, a prediction that the vacuum can generate real particles when boundary conditions are suddenly changed. That is, photon pairs can be spontaneously generated in an empty cavity with nonuniformly accelerating boundaries. A second is Hawking radiation. Here again photon pairs are generated at the horizon of a black hole. I will discuss how certain aspects of both these effects can be mimicked in a Bose Einstein condensate, and outline the state of the experimental art in this domain.
We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.
Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising platform for studying the dynamical Casimir effect, since they allow one to achieve relativistic, i.e., near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems, ultracold atoms allow one to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this paper, we discuss theoretically two types of experiments with interacting one-dimensional condensates with moving boundaries. Our analysis is based on the Luttinger liquid model which utilizes the emergent conformal symmetry of the low-energy sector of the Lieb-Liniger model. The first system we consider is a variable-length interferometer with two Y-shaped junctions connected back to back. We demonstrate that dynamics of the relative phase between the two arms of the interferometer can be analyzed using the formalism developed by Moore in the problem of electromagnetic vacuum squeezing in a cavity with moving mirrors. The second system we discuss is a single condensate in a box potential with periodically moving walls. This system exhibits classical excitation of the mode resonant with the drive as well as nonlinear generation of off-resonant modes. In addition, we find strong parametric multimode squeezing between modes whose energy difference matches integer multiples of the drive frequency.