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

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

S. Banik, M. Gutierrez Galan, H. Sosa-Martinez, M. J. Anderson, S. Eckel, I. B. Spielman, and G. K. Campbell

Phys. Rev. Lett. 128, 090401 – Published 28 February 2022

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) and Eckel et al., SciPost Phys. 10, 64 (2021)].

Received 19 July 2021
Revised 16 November 2021
Accepted 7 February 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.090401

Physics Subject Headings (PhySH)

Bose-Einstein condensates Laboratory studies of gravity

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalGravitation, Cosmology & Astrophysics

Authors & Affiliations

S. Banik ¹, M. Gutierrez Galan¹, H. Sosa-Martinez¹, M. J. Anderson¹, S. Eckel², I. B. Spielman ¹, and G. K. Campbell ¹

¹Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, College Park, Maryland 20742, USA
²Sensor Sciences Division, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, Maryland 20899, USA

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Vol. 128, Iss. 9 — 4 March 2022

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Images

Figure 1
Ring-trapping potential and resulting atomic density. The green surface schematically depicts the trapping potential; the orange lines mark the typical chemical potential $μ$ . The blue-dashed curve shows a power law fit to the potential (up to $μ$ ) around $ρ = | r - R | = 0$ giving exponent 2.02(3) for this example. The measured 2D density $n_{2 D} (ρ, θ)$ is shown in the $e_{x} − e_{y}$ plane (with peak density $165 μ m^{- 2}$ ) and the white dashed arc marks the mean radius $R$ . Because of the short $500 μ s$ TOF, the observed width of the ring is slightly in excess of that anticipated from the in situ TF approximation.
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Figure 2
Phonon evolution in a contracting toroidally shaped BEC, averaged over three measurements. (a) Density perturbations for a ring with $R_{i} = 38.4 (6) μ m$ at 10 ms and 35 ms, and $R_{f} = 11.9 (2) μ m$ at 45 ms and 53 ms. The density scale of images before contraction is multiplied by 2. The horizontal bar corresponds to $80 μ m$ . (b) Experimental measurements and (c) fit to Eq. (1) of angular density perturbation $δ n_{1 D}$ as a function of azimuthal angle $θ$ and time $t$ , where the ring contraction occurs at $t_{i}$ . (d) Phonon amplitude $δ n$ as a function of time. The circles plot the phonon amplitude obtained from fitting each time slice of (b) to a sinusoid [26]. The red curve is the instantaneous amplitude from the fit in (c). The diamonds are the measured BEC mean radius and the blue line is the programmed radius. The grayscale bar encodes the value of $| \dot{R} / R |$ , with a maximum of $328 (11) s^{- 1}$ at $t_{peak} = 41 ms$ . The arrow indicates $t_{i} = 38.2 ms$ .
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Figure 3
Phonon amplitude $δ n$ as a function of time $t$ for (a) expanding and (b) contracting tori. The symbols, curves, and grayscale bars are all as notated in Fig. 2. The expansion data (a) used $R_{i} = 11.9 (2) μ m$ and $R_{f} = 38.4 (6) μ m$ , and vice versa for contraction (b). The red curves show simultaneous fits to a complete dataset, which includes all expansions or contractions.
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Figure 4
Phonon amplitude vs phase. (a) Data (black circles), fit (red curve), and oscillation envelope (blue curve) used to extract the amplitude $A_{f}$ at $t_{peak}$ . The grayscale bar is as notated in Fig. 2. (b) Ratio of amplitudes $A_{f} / A_{i}$ versus $φ_{peak}$ , the oscillation’s phase at $t_{peak}$ . The black circles plot the data, and the error bars correspond to the fit uncertainty in the determination of $A_{f}$ . The gray dashed, blue solid, and gray dashed-dot curves show the prediction of Eq. (1) for $γ_{H} = 0$ , 0.36, and 1, respectively, with $α = 0.52$ . The red line indicates the prediction for an adiabatic contraction.
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