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arXiv:2503.20267

Dual Phonon Universe in a Spinor Bose Gas

Jiabin Wang, Yunfei Xue, Chen Li, Ren Zhang

Published Mar 26, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2503.20267

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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.
Abstract We study the low energy phonon dynamics of a Bose–Einstein condensate (BEC) with a density profile that is equivalent, via a coordinate transformation, to phonons traveling in a “spherical” curved spacetime that realizes the Friedman–Lemaître–Robertson–Walker (FLRW) metric. The metric of this BEC is characterized by its curvature κ\kappa κ κ and a time-dependent scale factor a ( t ), with an increase in the latter corresponding to an expansion of the analog FLRW universe. We study the propagation of classical phonons in such BECs, finding that a sudden change in the scale factor induces ripples in the wave motion. In addition, we study quantum phonon creation (or vacuum amplification) due to the scale-factor modification and quantify their entanglement.
The analogy between the propagation of a massless scalar field in curved spacetime and the propagation of sound waves in a Bose-Einstein Condensate (BEC) gives rise to the possibility of observing the analogues of black hole radiance effects, such as Hawking Radiation and superradiance, in the laboratory. In order to provide a solid foundation for realising such analogue gravity models in an experimental setting, we have conducted a numerical investigation of phonon scattering from a BEC vortex by solving the time-dependent Gross-Pitaevskii (GP) equation, describing the dynamics of dilute gas BECs. The consideration of phonon superradiance in BECs in advance of Hawking Radiation is motivated by the fact superradiance may be easier to detect. ¶ We first present the results of one-dimensional simulations of sound waves propagating in a BEC and reflecting from a vortex-like density profile. Using these results as a guide, two-dimensional simulations of sound propagation in a BEC, and reflection from a BEC vortex, are performed. The technique of propagating the wavefunction in imaginary time was employed to find the vortex ground state. The accuracy of the simulations and the convergence of the solution to the vortex ground state was verified using a range of numerical diagnostics. Finally, preliminary simulations were performed within the superradiant frequency regime for the purposes of determining whether the amplification of incoming waves occurs given an appropriate choice of parameters. Overall, the two-dimensional modelling of reflection of cylindrical waves from a BEC vortex provides a basis for a systematic study of phonon superradiance in BECs.
Abstract We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.
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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.
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.