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arXiv:2603.16095

Efimovian Phonon Production for an Analog Coasting Universe in Bose-Einstein Condensates

Yunfei Xue, Jiabin Wang, Li Chen, Chenwei Lv, Ren Zhang

cond-mat.quant-gasquant-phSubmitted Mar 17, 2026• Announced Mar 18, 2026• 0 citations
arXivHTMLPDF

Abstract

Efimov effects arise from scale invariance, a fundamental symmetry with universal implications. While spatial Efimov physics has been extensively studied, realizing its temporal counterpart remains challenging, as it requires a dynamical system that breaks time-translation symmetry yet preserves the essential time-scaling symmetry. Analog cosmology offers a powerful platform to address this challenge, bridging the domains of Efimov physics and cosmology. Here, we predict a temporal Efimov effect in an analog linearly expanding universe realized with a quasi-two-dimensional Bose-Einstein condensate. The invariance of phonon mode equations under time rescaling leads to particle production with two distinct dynamics: power-law growth and log-periodic oscillations, with the latter being the hallmark signature of the Efimov effect. Furthermore, these dynamics map directly onto sub- and super-horizon cosmological modes. Our predictions can be directly verified through time-averaged measurements of the density-fluctuation spectrum $S_{k}(t)$ in current experiments.

Comments
9+10 pages, 5+2 figures

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Efimov effects arise from scale invariance, a fundamental symmetry with universal implications. While spatial Efimov physics has been extensively studied, realizing its temporal counterpart remains challenging, as it requires a dynamical system that breaks time-translation symmetry yet preserves the essential time-scaling symmetry. Analog cosmology offers a powerful platform to address this challenge, bridging the domains of Efimov physics and cosmology. Here, we predict a temporal Efimov effect in an analog linearly expanding universe realized with a quasi-two-dimensional Bose-Einstein condensate. The invariance of phonon mode equations under time rescaling leads to particle production with two distinct dynamics: power-law growth and log-periodic oscillations, with the latter being the hallmark signature of the Efimov effect. Furthermore, these dynamics map directly onto sub- and super-horizon cosmological modes. Our predictions can be directly verified through time-averaged measurements of the density-fluctuation spectrum Sk(t)S_{k}(t)Sk​(t) in current experiments.
We experimentally study cosmological particle production in a two-dimensional Bose-Einstein condensate, whose density excitations map to an analog cosmology. The expansion of spacetime is realized with tunable interactions. The particle spectrum can be understood through an analogy to quantum mechanical scattering, in which the dynamics of the spacetime metric determine the shape of the scattering potential. Hallmark scattering phenomena such as resonant forward scattering and Bragg reflection are connected to their cosmological counterparts, namely linearly expanding space and bouncing universes. We compare our findings to a theoretical description that extends beyond the acoustic approximation, which enables us to apply the model to high-momentum excitations.
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.
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We present a theoretical study of the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analog inflationary universe. As the system expands, we find that phonons in the BEC undergo redshift and damping due to quantum pressure effects, owing to the thinness of the ring. We predict that rapidly expanding toroidal BEC's can exhibit spontaneous particle creation, and study this phenomenon in the context of an initial coherent state wave function. We show how particle creation would be revealed in the atom density and density correlations, and discuss connections to the cosmological theory of inflation.
We present a study of analog cosmological models in Bose-Einstein condensates (BEC) and in graphene, and superfluidity in a box-shaped traps. We start by examining the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analog inflationary universe. The expanding condensate forces phonons to undergo redshift and damping due to quantum pressure, owing to the thinness of the ring. We predict that such expanding BECs can exhibit spontaneous phonon creation from the vacuum state and show how it would manifest in the atom density and density correlations and discuss connections with the inflationary theory. We then extend this work to study entanglement of the spontaneously generated phonon pairs, for which we use the techniques of quantum continuous variables. We then develop a protocol to experimentally measure the correlations entering the covariance matrix, allowing an experimental quantification of the entanglement properties of the inflationary BEC. We then present a of how a spatially-varying quasiparticle velocity in honeycomb lattices, achievable using strained graphene or in engineered cold-atom optical lattices that have a spatial dependent tunneling amplitude, can yield the Rindler Hamiltonian embodying an observer accelerating in Minkowski spacetime. Within this setup, a sudden switch-on of the spatially-varying strain yields a spontaneous production of electron-hole pairs, an analog version of the Unruh effect characterized by the Unruh temperature. We discuss how this thermal behavior, along with Takagi's statistics inversion, can manifest themselves in photo-emission and scanning tunneling microscopy experiments. We show that the electronic conductivity grows linearly with frequency ω\omegaω, vanishing in the DC limit. Finally, we find that the total electronic energy at zero environment temperature looks like Planck's blackbody result for photons due to the aforementioned statistics inversion, whereas for an initial thermally excited state of fermions, the total internal energy undergoes stimulated particle reduction. Finally, we study ultracold Fermi gases trapped inside a three-dimensional box with vanishing boundary conditions, with interactions modeled using the Fermi-Huang pseudopotential. Taylor expanding the pairing to linear order in position, solves the gap equation yielding the transition temperature and local pairing amplitude that vanishes at the edges.
We consider an analogue de Sitter cosmos in an expanding quasi-two-dimensional Bose-Einstein condensate with dominant dipole-dipole interactions between the atoms or molecules in the ultracold gas. It is demonstrated that a hallmark signature of inflationary cosmology, the scale invariance of the power spectrum of inflaton field correlations, experiences strong modifications when, at the initial stage of expansion, the excitation spectrum displays a roton minimum. Dipolar quantum gases thus furnish a viable laboratory tool to experimentally investigate, with well-defined and controllable initial conditions, whether primordial oscillation spectra deviating from Lorentz invariance at trans-Planckian momenta violate standard predictions of inflationary cosmology.