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Hubble Attenuation and Amplification in Expanding and Contracting Cold-Atom Universes

Sarmistha Banik, Monica Gutierrez Galan, H. Sosa-Martinez, M. Anderson, Stephen Eckel, Ian B. Spielman, Gretchen K. Campbell

Published Jul 16, 2021• 2 citations
OpenAlex

Abstract

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.

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In standard cosmological models, inflation is driven by a quantum field, the inflaton, whos constant energy density drove the superluminal expansion of the universe [1]. When inflation stops, the universe has an extremely low density btu the inflaton field starts to oscillate arround its minimum of energy and decays into entengled pairs of particles [2], known as the pre-heating phase. Created pairs of particles then start to interact leading to decoherence and thermalization : the re-heating stage. If in situ observation of inflaton particle creation process is impossible, this pair production through parametric amplification is analogous to the creation of phonon pairs in a Bose-Einstein (BEC) condensate whose interaction strenght is time modulated. Modulating the stiffness of a dipole trap of a cigar-shape BEC being equivalent to modulate the effective one-dimensionnal interaction strenght in a BEC, we are able to probe the correlation of entengled metastable helium atoms by the use of a micro-channel plate detector (MCP). Our experimental procedure is the following [3] : we modulate in time the trap stiffness of the dipole trap laser and then release the trap (see figure 1). During expansion, the phonon kinetic energy is adiabatically transferred to one atom that is detected by the MCP after a 300 ms time of flight. The amount of created phonon pairs is expected to depend on the duration of the excitation, its amplitude and the excitation frequency. However, the region in which the entenglement of the phonon pairs can be observed is expected to be quite narrow [4]. We propose to investigate the entenglement and correlations of those pairs of particles. [1] L. Kofman, A. Linde, and A. Starobinsky, Phys. Rev. D 56, 3258 (1997). [2] D. Campo and R. Parentani, Phys. Rev. D 74, 025001 (2006). [3] S. Robertson, F. Michel, and R. Parentani, Phys. Rev. D 95, 065020 (2017). [4] J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012).

•May 27, 2023•0 citations
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.
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].
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.
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.
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.
Phonons in expanding Bose–Einstein condensates with wavelengths much larger than the healing length behave in the same way as quantum fields within a universe undergoing an accelerated expansion. This analogy facilitates the application of many tools and concepts known from general relativity (such as horizons) and the prediction of the corresponding effects such as the freezing of modes after horizon crossing and the associated amplification of quantum fluctuations. Basically the same amplification mechanism is (according to our standard model of cosmology) supposed to be responsible for the generation of the initial inhomogeneities—and hence the seeds for the formation of structures such as our galaxy—during cosmic inflation (i.e., a very early epoch in the evolution of our universe). After a general discussion of the analogy ( analogue cosmology ), we calculate the frozen and amplified density–density fluctuations for quasi-two-dimensional (Q2D) and three-dimensional (3D) condensates which undergo a free expansion after switching off the (longitudinal) trap.
In standard cosmological models, inflation is driven by a quantum field, the inflaton, whos constant energy density drove the superluminal expansion of the universe [1]. When inflation stops, the universe has an extremely low density btu the inflaton field starts to oscillate arround its minimum of energy and decays into entengled pairs of particles [2], known as the pre-heating phase. Created pairs of particles then start to interact leading to decoherence and thermalization : the re-heating stage. If in situ observation of inflaton particle creation process is impossible, this pair production through parametric amplification is analogous to the creation of phonon pairs in a Bose-Einstein (BEC) condensate whose interaction strenght is time modulated. Modulating the stiffness of a dipole trap of a cigar-shape BEC being equivalent to modulate the effective one-dimensionnal interaction strenght in a BEC, we are able to probe the correlation of entengled metastable helium atoms by the use of a micro-channel plate detector (MCP). Our experimental procedure is the following [3] : we modulate in time the trap stiffness of the dipole trap laser and then release the trap (see figure 1). During expansion, the phonon kinetic energy is adiabatically transferred to one atom that is detected by the MCP after a 300 ms time of flight. The amount of created phonon pairs is expected to depend on the duration of the excitation, its amplitude and the excitation frequency. However, the region in which the entenglement of the phonon pairs can be observed is expected to be quite narrow [4]. We propose to investigate the entenglement and correlations of those pairs of particles. [1] L. Kofman, A. Linde, and A. Starobinsky, Phys. Rev. D 56, 3258 (1997). [2] D. Campo and R. Parentani, Phys. Rev. D 74, 025001 (2006). [3] S. Robertson, F. Michel, and R. Parentani, Phys. Rev. D 95, 065020 (2017). [4] J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012).