Analogue simulation of gravitational waves in a 3+1 -dimensional Bose-Einstein condensate

Abstract

The recent detections of gravitational waves (GWs) by the LIGO and Virgo collaborations have opened the field of GW astronomy, intensifying interest in GWs and other possible detectors sensitive in different frequency ranges. Although strong GW producing events are rare and currently unpredictable, GWs can in principle be simulated in analogue systems at will in the lab. Simulation of GWs in a manifestly quantum system would allow for the study of the interaction of quantum phenomena with GWs. Such predicted interaction is exploited in a recently proposed Bose-Einstein condensate (BEC) based GW detector. In this paper, we show how to manipulate a BEC to mimic the effect of a passing GW. By simultaneously varying the external potential applied to the BEC, and an external magnetic field near a Feshbach resonance, we show that the resulting change in speed of sound can directly reproduce a GW metric. We also show how to simulate a metric used in the recently proposed BEC based GW detector, to provide an environment for testing the proposed metrology scheme of the detector. Explicit expressions for simulations of various GW sources are given. This result is also useful to generally test the interaction of quantum phenomena with GWs in a curved spacetime analogue experiment.

Gravitational wave background from Standard Model physics: complete leading order

“…Most of the energy density carried by thermally produced gravitational radiation peaks in the microwave frequency range today. Conceivably, this physics can be probed by tabletop experiments in the future [45][46][47][48][49][50][51][52][53], even if the sensitivity goal is quite formidable.…”

Evolution of confined quantum scalar fields in curved spacetime. Part II

“…The phonon field can be described by a real scalar massless quantum field. In the case that the condensate remains stationary, the quantum field obeys a Klein–Gordon equation in an effective metric (with minimal coupling) which corresponds to the gravitational wave metric with the speed of sound in the condensate replacing the speed of light in the component [ 35 – 38 ]. We work in the TT-gauge and normalise the speed of sound .…”

Quantum simulation of dark energy candidates

“…Eq. (16) has been derived in [35,48] and includes the effect of a (in general) curved background space-time metric in a natural way through a covariant formalism. This allows us to include any effects of the background metric arising at low (non-relativistic) energies when taking the non-relativistic limit to model real experiments.…”

“…Excerpts from this catalogue of analogue models include conformal Schwarzschild black holes [26,27], rotating black holes [28], Bañados-Teitelboim-Zanelli (BTZ) black holes [29], Friedmann-Robertson-Walker geometries [30,31], inflation [32,33] and extensions to general relativity such as aether fields [26]. Three of us have extended this catalogue to include gravitational wave space-times [34,35]. As an example, there has recently been an experimental implementation of a waterfall horizon leading to observation of density correlations across the horizon [36,37], and controversy over their interpretation as entangled acoustic…”