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arXiv:2307.02141 · New Journal of Physics

Anisotropic inflation in dipolar Bose–Einstein condensates

Arun Rana, Abhijit Pendse, Sebastian Wüster, S Panda

Published Nov 1, 2023• 1 citation
arXivHTMLPDF

Abstract

Abstract Early during the era of cosmic inflation, rotational invariance may have been broken, only later emerging as a feature of low-energy physics. This motivates ongoing searches for residual signatures of anisotropic space-time, for example in the power spectrum of the cosmic microwave background. We propose that dipolar Bose–Einstein condensates (BECs) furnish a laboratory quantum simulation platform for the anisotropy evolution of fluctuation spectra during inflation, exploiting the fact that the speed of dipolar condensate sound waves depends on direction. We construct the anisotropic analogue space-time metric governing sound, by linking the time-varying strength of dipolar and contact interactions in the BEC to the scale factors in different coordinate directions. Based on these, we calculate the dynamics of phonon power spectra during an inflation that renders the initially anisotropic Universe isotropic. We find that the expansion speed provides an experimental handle to control and study the degree of final residual anisotropy. Gravity analogues using dipolar condensates can thus provide tuneable experiments for a field of cosmology that was until now confined to a single experiment, our Universe.

DOI
10.1088/1367-2630/ad091f

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Abstract Early during the era of cosmic inflation, rotational invariance may have been broken, only later emerging as a feature of low-energy physics. This motivates ongoing searches for residual signatures of anisotropic space-time, for example in the power spectrum of the cosmic microwave background. We propose that dipolar Bose–Einstein condensates (BECs) furnish a laboratory quantum simulation platform for the anisotropy evolution of fluctuation spectra during inflation, exploiting the fact that the speed of dipolar condensate sound waves depends on direction. We construct the anisotropic analogue space-time metric governing sound, by linking the time-varying strength of dipolar and contact interactions in the BEC to the scale factors in different coordinate directions. Based on these, we calculate the dynamics of phonon power spectra during an inflation that renders the initially anisotropic Universe isotropic. We find that the expansion speed provides an experimental handle to control and study the degree of final residual anisotropy. Gravity analogues using dipolar condensates can thus provide tuneable experiments for a field of cosmology that was until now confined to a single experiment, our Universe.
Cosmic inflation is the theory that the universe underwent a violent, rapid expansion at the beginning of time, giving rise to much of the observed structure in the universe 1. This theory is supported by indirect observational evidence from many different sources (e.g. see 2). However, direct experimental investigation of inflation is of course impossible. For this reason there has been considerable interest in analog models for astrophysics (e.g. see 3), in which analogous behavior is studied in systems that are experimentally convenient. Due to their cleanness and great flexibility, dilute ultra-cold atomic gases (particularly Bose-Einstein condensates) form an attractive system for realizing such analog models. Indeed, a number of such table-top-astrophysics experiments have been conducted with Bose-Einstein condensates. For example, supernova-like collapse and explosion dynamics 4, controlled by modifying inter-atomic interactions using Feshbach resonances, and later interpreted as cosmological particle creation 5; Faster-than-sound flow of a condensate has been used to produce a sonic black hole analog 6; The in situ measurements of density fluctuations in a quenched quasi-two-dimensional condensate have demonstrated Sakharov like oscillations, analogous to the process thought to give rise to the anisotropy in the cosmic microwave background radiation 7. In Quantum simulations of the early universe Opanchuk and collaborators 8 propose using a two component condensate to simulate the inflationary phase of the early universe (see Fig. 1). In appropriate limits the relative phase between the two fields describing the condensate components is known to obey the sine-Gordon equation 9. The sine-Gordon model (SGM) is one of many scalar models for inflation that have been investigated in cosmology. It is thought to provide an acceptable model of the beginning of inflation where, starting from an unstable vacuum state, quantum fluctuations seed the cosmological inhomogeneities that lead to structure formation. However, the SGM likely fails to describe the end of inflation as its scalar potential does not generate efficient parametric resonances needed to ensure reheating of the universe 10, 11. The SGM also has applications in cosmology beyond inflation, and is a model for the “axion” matter field considered as a promising candidate for dark matter12. An important innovation in the scheme proposed by Opanchuk et al. is the introduction of a microwave (linear) coupling between the components that provides a practical way to initialize the system into an unstable vacuum state and controllably explore the subsequent evolution. Approximate numerical simulations, performed using the truncated Wigner approach, verify dynamical clustering can occur within experimentally realistic parameter regimes. The main challenge to realizing the proposed scenario will be finding an atom, and a pair of internal states, with suitable interaction parameters. It is likely that such an atom will be available given the increasing diversity of atomic species that have been Bose-condensed, and the great control over interactions afforded by Feshbach resonances. Aided by the rich toolbox of techniques available to ultra-cold atomic physics an array of opportunities present themselves for developing this line of research, such as: Engineering gravitational-like effects through including long range interactions, e.g. through electromagnetically induced gravity 13; Enhancing quantum fluctuations through stronger interactions or by confining the system in an optical lattice; Engineering richer models by including more spin states and other species of atoms.
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.
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.
Generalizing the one-component case, we demonstrate that the propagation of sound waves in two-component Bose-Einstein condensates can also be described in terms of effective sonic geometries under appropriate conditions. In comparison with the one-component case, the two-component setup offers more flexibility and several advantages. In view of these advantages, we propose an experiment in which the evolution of the inflaton field, and thereby the generation of density fluctuations in the very early stages of our universe during inflation, can be simulated, realizing a quantum simulation via analogue gravity models.
Recent interest and realization of ultracold bosons confined in shell-shaped, or bubble, traps have opened up several directions in the study of Bose-Einstein condensates (BECs) in intrinsically curved geometries. Here, we explore the prospect of using thin spherical shell-shaped BECs as analog gravity simulators of an expanding or contracting curved universe. We study an interacting BEC bubble subject to a temporal quench of the interaction strength. Our theoretical approach, which uses a Bogoliubov treatment following a dimensional reduction of a spherical BEC to the low-energy excitations of a shell-shaped structure, demonstrates how this system serves as a laboratory analog for a positively curved universe having a time-varying scale factor. We investigate spontaneous pair production triggered by quenches associated with exponentially decaying or growing interaction strengths, focusing on the emergence of oscillations in the structure factor---analogous to Sakharov oscillations in the Cosmic Microwave Background angular power spectrum. We quantify the entanglement of the produced pairs via logarithmic negativity, and show how this measure may be extracted from the power spectrum. These findings establish a bridge between quantum information science and early-universe cosmology in a laboratory setting.
We measure the excitation spectrum of a dipolar chromium Bose-Einstein condensate with Raman-Bragg spectroscopy. The energy spectrum depends on the orientation of the dipoles with respect to the excitation momentum, demonstrating an anisotropy that originates from the dipole-dipole interactions between the atoms. We compare our results with the Bogoliubov theory based on the local density approximation and, at large excitation wavelengths, with the numerical simulations of the time-dependent Gross-Pitaevskii equation. Our results show an anisotropy of the speed of sound.