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arXiv:2101.03691 · Classical and Quantum Gravity

Detection of gravitational waves using parametric resonance in Bose–Einstein condensates

Matthew P. G. Robbins, Niayesh Afshordi, Alan O. Jamison, Robert B. Mann

Published Jun 21, 2022• 10 citations
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Abstract

Abstract An interesting proposal for detecting gravitational waves involves quantum metrology of Bose–Einstein condensates (BECs). We consider a forced modulation of the speed of sound of a BEC, whose modulation frequency matches that of an incoming continuous gravitational wave. The speed of sound modulation induces parametric resonance in the BEC, which in turn enhances sensitivity of the BEC to gravitational waves. We find that such a BEC detector could potentially be used to detect gravitational waves across several orders of magnitude in frequency, with the sensitivity depending on the speed of sound, size of the condensate, and frequency of the phonons. We discuss the sensitivity of a possible BEC experiment and comment on the current technological limitations. We also comment on the noise sources as well as what is necessary for such a detector to become feasible.

DOI
10.1088/1361-6382/ac7b05

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Abstract An interesting proposal for detecting gravitational waves involves quantum metrology of Bose–Einstein condensates (BECs). We consider a forced modulation of the speed of sound of a BEC, whose modulation frequency matches that of an incoming continuous gravitational wave. The speed of sound modulation induces parametric resonance in the BEC, which in turn enhances sensitivity of the BEC to gravitational waves. We find that such a BEC detector could potentially be used to detect gravitational waves across several orders of magnitude in frequency, with the sensitivity depending on the speed of sound, size of the condensate, and frequency of the phonons. We discuss the sensitivity of a possible BEC experiment and comment on the current technological limitations. We also comment on the noise sources as well as what is necessary for such a detector to become feasible.
We investigate a Bose-Einstein condensate (BEC) as a gravitational wave detector, and study its sensitivity by optimizing the properties of the condensate and the measurement duration. We show that detecting kilohertz gravitational waves is limited by current experimental techniques in squeezing BEC phonons. Without focussing on a specific detector setup, our study shows that substantive future improvements in technology (e.g., increasing the squeezing of BEC states or their physical size) will be necessary for such a detector to be competitive in measuring gravitational waves of astrophysical and/or cosmological origin.
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.
Quasiparticles in a Bose-Einstein condensate are sensitive to space-time distortions. Gravitational waves can induce transformations on the state of phonons that can be observed through quantum state discrimination techniques. We show that this method is highly robust to thermal noise and depletion. We derive a bound on the strain sensitivity that shows that the detection of waves in the kHz regime is not significantly affected by temperature in a wide range of parameters that are well within current experimental reach.
Squeezed, nonclassical states are an integral tool of quantum metrology due to their ability to push the sensitivity of a measurement apparatus beyond the limits of classical states. While their creation in light has become a standard technique, the production of squeezed states of the collective excitations in gases of ultracold atoms, the phonons of a Bose-Einstein condensate (BEC), is a comparably recent problem. This task is continuously gaining relevance with a growing number of proposals for BEC-based quantum metrological devices and the possibility to apply them in the detection of gravitational waves. The objective of this thesis is to find whether the recently described effect of an oscillating external potential on a uniform BEC can be exploited to generate two-mode squeezed phonon states, given present day technology. This question brings together elements of a range of fields beyond cold atoms, such as general relativity and Efimov physics. To answer it, the full transformation caused by the oscillating potential on an initially thermal phononic state is considered, allowing to find an upper bound for the magnitude of this perturbation as well as to quantify the quality of the final state with respect to its use in metrology. These findings are then applied to existing experiments to judge the feasibility of the squeezing scheme and while the results indicate that they are not well suited for it, a setup is proposed that allows for its efficient implementation and seems within experimental reach. In view of the vast parameter space leaving room for optimization, the considered mechanism could find applications not only in the gravitational wave detector that originally motivated this work, but more generally in the field of quantum metrology based on ultracold atoms.
A gravitational-wave (GW) detector that utilizes the phononic excitations of a Bose-Einstein condensate (BEC) has recently been proposed [NJP 16, 085003 (2014)]. A subsequent and independent study, [arXiv:1807.07046v1], has suggested an alternative GW detection scheme that also uses phonons of a BEC but which was found to be many orders of magnitude away from being feasible. Here we make clear that the two proposed schemes are very different and that the conclusions of [arXiv:1807.07046v1] do not apply to the original proposal [NJP 16, 085003 (2014)].
We show how to vary the physical properties of a Bose-Einstein condensate (BEC) in order to mimic an effective gravitational-wave spacetime. In particular, we focus in the simulation of the recently discovered creation of particles by a real spacetime distortion in box-type traps. We show that, by modulating the speed of sound in the BEC, the phonons experience the effects of a simulated spacetime ripple with experimentally amenable parameters. These results will inform the experimental programme of gravitational wave astronomy with cold atoms.