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arXiv:2107.08097 · Physical Review Letters

Accurate Determination of Hubble Attenuation and Amplification in Expanding and Contracting Cold-Atom Universes

S. Banik, Monica Gutierrez Galan, H. Sosa-Martinez, Madison J. Anderson, Stephen Eckel, Ian B. Spielman, Gretchen K. Campbell

Published Feb 28, 2022• 40 citations
arXivHTMLPDF

Abstract

In the expanding universe, relativistic scalar fields are thought to be attenuated by "Hubble friction," which results from the dilation of the underlying spacetime metric. By contrast, in a contracting universe this pseudofriction would lead to amplification. Here, we experimentally measure, with fivefold better accuracy, both Hubble attenuation and amplification in expanding and contracting toroidally shaped Bose-Einstein condensates, in which phonons are analogous to cosmological scalar fields. We find that the observed attenuation or amplification depends on the temporal phase of the phonon field, which is only possible for nonadiabatic dynamics. The measured strength of the Hubble friction disagrees with recent theory [Gomez Llorente et al., Phys. Rev. A 100, 043613 (2019)PLRAAN2469-992610.1103/PhysRevA.100.043613 and Eckel et al., SciPost Phys. 10, 64 (2021)SPCHCW2542-465310.21468/SciPostPhys.10.3.064].

DOI
10.1103/physrevlett.128.090401

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In the expanding universe, relativistic scalar fields are thought to be attenuated by "Hubble friction," which results from the dilation of the underlying spacetime metric. By contrast, in a contracting universe this pseudofriction would lead to amplification. Here, we experimentally measure, with fivefold better accuracy, both Hubble attenuation and amplification in expanding and contracting toroidally shaped Bose-Einstein condensates, in which phonons are analogous to cosmological scalar fields. We find that the observed attenuation or amplification depends on the temporal phase of the phonon field, which is only possible for nonadiabatic dynamics. The measured strength of the Hubble friction disagrees with recent theory [Gomez Llorente et al., Phys. Rev. A 100, 043613 (2019)PLRAAN2469-992610.1103/PhysRevA.100.043613 and Eckel et al., SciPost Phys. 10, 64 (2021)SPCHCW2542-465310.21468/SciPostPhys.10.3.064].
In the expanding universe, relativistic scalar fields are thought to be attenuated by friction, which results from the dilation of the underlying spacetime metric. By contrast, in a contracting universe this pseudo-friction would lead to amplification. Here, we experimentally measure both Hubble attenuation and amplification in expanding and contracting toroidally-shaped Bose-Einstein condensates, in which phonons are analogous to cosmological scalar fields. We find that the observed attenuation or amplification depends on the temporal phase of the phonon field, which is only possible for non-adiabatic dynamics, in contrast to the expanding universe in its current epoch, which is adiabatic. The measured strength of the Hubble friction disagrees with recent theory [J. M. Gomez Llorente and J. Plata, Phys. Rev. A 100 043613 (2019) and S. Eckel and T. Jacobson, SciPost Phys. 10 64 (2021)], suggesting that our model does not yet capture all relevant physics. While our current work focuses on coherent-state phonons, it can be extended to regimes where quantum fluctuations in causally disconnected regions of space become important, leading to spontaneous pair-production.
We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon’s direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by \dot{\mathcal{V}}/{\mathcal{V}} 𝒱 ̇ / 𝒱 , where \mathcal{V} 𝒱 is the volume of the background condensate. This behavior is analogous to the redshifting and ``Hubble friction’’ for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.
This thesis presents the construction and characterization of an experimental apparatus to produce sodium Bose-Einstein condensates (BECs) in arbitrary potentials. Particular attention is devoted to the study of toroidal BECs as platforms for analogue cosmology models. We also report the first results from this apparatus in which we studied the red-shifting and attenuation of azimuthal phonons in expanding toroidal BECs as well as blue-shifting and amplification of azimuthal phonons in contracting toroidal BECs. The amplification and attenuation of the azimuthal phonons is the result of a non-dissipative friction term that arises from the changing geometry of the background BEC, this non-dissipative friction is analogous to the Hubble friction present in cosmology models.
Phonons have the characteristic linear dispersion relation of massless relativistic particles. They arise as low-energy excitations of Bose-Einstein condensates and, in nonhomogeneous situations, are governed by a space- and time-dependent acoustic metric. We discuss how this metric can be experimentally designed to realize curved spacetime geometries, in particular, expanding Friedmann-Lema\^{\i}tre-Robertson-Walker cosmologies, with negative, vanishing, or positive spatial curvature. A nonvanishing Hubble rate can be obtained through a time-dependent scattering length of the background condensate. For relativistic quantum fields, this leads to the phenomenon of particle production, which we describe in detail. We explain how particle production and other interesting features of quantum field theory in curved spacetime can be tested in terms of experimentally accessible correlation functions.
We analytically study the expansion of a Bose-Einstein condensate in a ring-shaped trap with an increasing central radius. The evolution of the ground state is described using a scaling transform. Additionally, the dynamics of excited azimuthal modes over the varying ground state is analyzed through a generalization of the Bogoliubov--de Gennes approach. Our results explain some of the features observed in recent experiments focused on testing the applicability of the system as a parallel of cosmological inflationary models. The radial dynamics, which corresponds to the inflaton field of the cosmological counterpart, is analytically characterized: The expansion is found to induce the oscillatory displacement of the condensate as well as the coupled variation of the radial and vertical widths. Our findings account also for the observed redshift and emergence of the Hubble friction in the evolution of initially prepared azimuthal modes. Our description, which traces the role of the different components of the setup in the expansion, enhances the controllability and therefore the potential of the system as a ground for emulating the inflationary dynamics of cosmological models.
We show the possibility of simulating a dual universe in a pseudospin-1/2 Bose-Einstein condensate (BEC), wherein two phononic modes experience distinct curved spacetime metrics. Through ramping the interspecies interaction of the BEC, we observe that one universe expands, and in the mean time, the other contracts. These findings can be directly verified in existing cold-atom experimental setups by detecting the correlators of the scaled density contrast (SDC): The sizes of the expanded/contracted universes can be deduced from the SDC's oscillating frequencies, while the expanding/contracting histories are reflected in the SDC's amplitude. Our study demonstrates the great potential of spinor BECs for exploring multiverse-related physics in laboratory settings.