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arXiv:2406.08094 · Physical review. D/Physical review. D.

Cosmological particle production in a quantum field simulator as a quantum mechanical scattering problem

Christian F. Schmidt, Álvaro Parra-López, Mireia Tolosa-Simeón, Marius Sparn, Elinor Kath, Nikolas Liebster, Jelte Duchene, Helmut Strobel, Markus K. Oberthaler, Stefan Floerchinger

Published Dec 16, 2024• 10 citations
arXivHTMLPDF

Abstract

The production of quantum field excitations or particles in cosmological spacetimes is a hallmark prediction of curved quantum field theory. The generation of cosmological perturbations from quantum fluctuations in the early Universe constitutes an important application. The problem can be quantum-simulated in terms of structure formation in an interacting Bose-Einstein condensate (BEC) with time-dependent s-wave scattering length. Here, we explore a mapping between cosmological particle production in general ($D+1$)-dimensional spacetimes and scattering problems described by the nonrelativistic stationary Schr\"odinger equation in one dimension. Through this mapping, intuitive explanations for emergent spatial structures in both the BEC and the cosmological system can be obtained for analogue cosmological scenarios that range from power-law expansions to periodic modulations. The investigated cosmologies and their scattering analogs are tuned to be implemented in a ($2+1$)-dimensional quantum field simulator.

DOI
10.1103/physrevd.110.123523

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The production of quantum field excitations or particles in cosmological spacetimes is a hallmark prediction of curved quantum field theory. The generation of cosmological perturbations from quantum fluctuations in the early Universe constitutes an important application. The problem can be quantum-simulated in terms of structure formation in an interacting Bose-Einstein condensate (BEC) with time-dependent s-wave scattering length. Here, we explore a mapping between cosmological particle production in general (D+1D+1D+1)-dimensional spacetimes and scattering problems described by the nonrelativistic stationary Schr"odinger equation in one dimension. Through this mapping, intuitive explanations for emergent spatial structures in both the BEC and the cosmological system can be obtained for analogue cosmological scenarios that range from power-law expansions to periodic modulations. The investigated cosmologies and their scattering analogs are tuned to be implemented in a (2+12+12+1)-dimensional quantum field simulator.
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.
Although particle production in curved quantum field theories (cQFTs) is key to our understanding of the early universe and black hole physics, its direct observation requires extreme conditions or unrealistic sensitivities. Recent progress in quantum simulators indicates that analogues of cosmological particle production can be observed in table-top experiments of cold atomic gases described by effective cQFTs. This promises a high degree of tunability in the synthesised curved spacetimes and, moreover, sets a clear roadmap to explore the interplay of particle production with other non-perturbative effects genuine to interacting QFTs. We hereby focus on the appearance of scalar and pseudo-scalar condensates for self-interacting Dirac fermions, and study how dynamical mass generation and spontaneous symmetry breaking affects real-time dynamics through the lens of entanglement. We use the entanglement contour (EC) to analyse the spatio-temporal structure of particle production, showing that a quasi-particle picture for the EC captures the cosmological horizon in accelerating spacetimes, while also being sensitive to the effect of different symmetry-breaking processes. In particular, we show that the combined breakdown of time-reversal symmetry due to the expanding spacetime, and parity due to a pseudo-scalar condensate, manifests through the structure of the light-cone-like propagation of entanglement.
We consider excitations of a spin-1 Bose-Einstein-condensate in the vicinity of different mean-field configurations and derive mappings to emergent relativistic quantum field theories minimally coupled to curved acoustic spacetimes. The quantum fields are typically identified with Nambu-Goldstone bosons, such that the structure of the analog quantum field theories on curved spacetimes depends on the (spontaneous) symmetry breaking pattern of the respective ground state. The emergent spacetime geometries are independent of each other and exhibit bimetricity in the polar and antiferromagnetic phase, whereas one has trimetricity in the ferromagnetic phase. Compared to scalar BECs, the spinor degrees of freedom allow us to investigate massive vector and scalar fields where the former is a spin-nematic rotation mode in the polar phase, which can be cast into a Proca field that is minimally coupled to a curved spacetime that emerges on length scales larger than the spin-healing length. Finally, we specify the Zeeman couplings and the condensate trap to be spacetime-dependent such that a cosmological Friedmann-Lemaître-Robertson-Walker metric can be achieved. This work enables a pathway towards quantum-simulating cosmological particle production of Proca quanta via quenching the quadratic Zeeman coefficient or via magnetic field ramps, which both result in the creation of spin-nematic squeezed states.
Analog models of gravity have been motivated by the possibility of investigating phenomena not readily accessible in their cosmological counterparts. In this paper, we investigate the analog of cosmological particle creation in a Friedmann-Robertson-Walker universe by numerically simulating a Bose-Einstein condensate with a time-dependent scattering length. In particular, we focus on a two-dimensional homogeneous condensate using the classical field method via the truncated Wigner approximation. We show that for various forms of the scaling function the particle production is consistent with the underlying theory in the long wavelength limit. In this context, we further discuss the implications of modified dispersion relations that arise from the microscopic theory of a weakly interacting Bose gas.
Cosmological reheating describes the transition of the postinflationary universe to a hot and thermal state. In order to shed light on the underlying dynamics of this process, we propose to quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. In our setup, the excitations on top of an atomic Bose-Einstein condensate play the role of the particles produced by the decaying inflaton field after inflation. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the nonrelativistic limit by a time dependence of the atomic interactions, which can be tuned experimentally via Feshbach resonances. As we illustrate by means of classical-statistical simulations for the case of two spatial dimensions, the dynamics of the atomic system exhibits the characteristic stages of far-from-equilibrium reheating, including the amplification of fluctuations via parametric instabilities and the subsequent turbulent transport of energy towards higher momenta. The transport is governed by a nonthermal fixed point showing universal self-similar time evolution as well as a transient regime of prescaling with time-dependent scaling exponents. While the classical-statistical simulations can capture only the earlier stages of the dynamics for weak couplings, the proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
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.