Observation of Entanglement in a Cold Atom Analog of Cosmological Preheating
Victor Gondret, Clothilde Lamirault, Rui Dias, Léa Camier, Amaury Micheli, Charlie Leprince, Quentin Marolleau, Jean-René Rullier, Scott Robertson, Denis Boiron, Christoph Ira Westbrook
We observe entanglement between collective excitations of a Bose-Einstein condensate in a configuration analogous to particle production during the preheating phase of the early Universe. In our setup, the oscillation of the inflaton field is mimicked by the transverse breathing mode of a cigar-shaped condensate, which parametrically excites longitudinal quasiparticles with opposite momenta. After a short modulation period, we observe entanglement of these pairs that reveals the role played by vacuum fluctuations in seeding the parametric growth, confirming the quantum origin of the excitations. As the system continues to evolve, we observe a decrease in correlations and a disappearance of nonclassical features. These point toward future experimental probes of the late-time nonlinear regime where further analogies can be drawn with reheating, i.e., the thermalization of the postinflationary Universe.
We observe entanglement between collective excitations of a Bose-Einstein condensate in a configuration analogous to particle production during the preheating phase of the early Universe. In our setup, the oscillation of the inflaton field is mimicked by the transverse breathing mode of a cigar-shaped condensate, which parametrically excites longitudinal quasiparticles with opposite momenta. After a short modulation period, we observe entanglement of these pairs that reveals the role played by vacuum fluctuations in seeding the parametric growth, confirming the quantum origin of the excitations. As the system continues to evolve, we observe a decrease in correlations and a disappearance of nonclassical features. These point toward future experimental probes of the late-time nonlinear regime where further analogies can be drawn with reheating, i.e., the thermalization of the postinflationary Universe.
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.
In the leading paradigm of cosmology, most particles are created during a reheating period following inflation. Part of this creation proceeds via parametric resonance [1], a process referred to as preheating. Since inflation essentially dilutes any pre-existing particles, particle production proceeds from fields in their vacuum state, a phenomenon of purely quantum origin similar to a dynamical Casimir effect (DCE). While the predicted quantum origin seems hard to test in the cosmological context, experiments involving genuine quantum fields evolving under the same dynamics have been realised. Ref. [2] reports on such an experiment in an elongated cigar-shaped Bose-Einstein condensate (BEC). The BEC is periodically modulated and acts as a classical field exciting its own quantum perturbations (phonons), created in pairs of opposite momenta ±k, with occupation number n_k and correlation amplitude c_k. Entanglement of the generated pairs is known to be a signature of pair production seeded by vacuum fluctuations [3] but is also fragile. Indeed, in [2] the observed pair correlation c_k was much weaker than expected and far from the regime c_k > n_k indicating entanglement. In a series of publications, the theoretical description behind the experiment was re-analysed in increasing detail to account for the absence of entanglement.First, in [3] weak dissipation of the excitations was phenomenologically introduced and shown to be able to prevent the generation of entanglement. A fully nonlinear numerical study of the modulated gas based on the Truncated Wigner Approximation (TWA) was then conducted in [4]. It confirmed that phonon-phonon interactions can induce an effective dissipation acting against the parametric resonance.In [5], we identified the dominant interaction channel for small occupation numbers in 1D quasi-BEC as Beliaev-Landau scatterings between the resonant mode and the thermal population. We analytically derived its rate and checked it against TWA simulations.Finally, in [6], whose results I will present in the talk, we demonstrate that the phenomenological model of [3], when supplemented by the rate derived in [5], accurately reproduces the particle and correlation generation seen in TWA simulations akin to that of [4].In this talk, I will first emphasise the subtle interplay between growth and dissipation, leading to distinct particle generation regimes. Then, informed by these findings, I will briefly discuss different optimal experimental strategies to achieve observation of entanglement.[1] D. Figueroa and F. Torrentí, JCAP02(2017)001 (2016)[2] J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)[3] X. Busch, R. Parentani and S. Robertson, Phys. Rev. A 89, 063606 (2014)[4] S. Robertson, F. Michel and R. Parentani, Phys. Rev. D 98, 056003 (2018)[5] A. Micheli and S. Robertson, Phys. Rev. B 106, 214528 (2022)[6] A. Micheli and S. Robertson, Comptes Rendus Physique, Online first (2024), pp. 1-34. doi: 10.5802/crphys.250
Cosmic reheating describes the transition of the post-inflationary universe to a hot and thermal state. In order to shed light on the nature of this process, we propose a quantum simulation of cosmic reheating in an ultracold Bose gas. In our model, the inflaton field dynamics is mapped onto that of an atomic Bose-Einstein condensate whose excitations are identified with the particles produced by the decaying inflaton field. The expansion of the universe as well as the oscillations of the inflaton field are encoded in the 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 non-thermal 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 only capture the earlier stages of the dynamics for weak couplings, the \nproposed experimental implementation provides a protocol for the quantum simulation of the entire evolution even beyond the weak coupling regime.
We theoretically propose an atomic Bose-Einstein condensate as an analog model of backreaction effects during the preheating stage of the early Universe. In particular, we address the out-of-equilibrium dynamics where the initially excited inflaton field decays by parametrically exciting the matter fields. We consider a two-dimensional, ring-shaped BEC under a tight transverse confinement whose transverse breathing mode and the Goldstone and dipole excitation branches simulate the inflaton and quantum matter fields, respectively. A strong excitation of the breathing mode leads to an exponentially growing emission of dipole and Goldstone excitations via parametric pair creation: Our numerical simulations of the BEC dynamics show how the associated backreaction effect results not only in an effective friction of the breathing mode, but also in a quick loss of longitudinal spatial coherence of the initially in-phase excitations. Implications of this result on the validity of the usual semiclassical description of backreaction are finally discussed.
By exciting the transverse breathing mode of an elongated Bose–Einstein condensate, we parametrically produce longitudinal collective excitations in a pairwise manner. This process, also referred to as Faraday wave generation, can be seen as an analog to cosmological particle production. Building upon single particle detection, we investigate the early time dynamics of the exponential growth and compare our observations with a Bogoliubov description. The growth rate we observe experimentally is in very good agreement with theoretical predictions, demonstrating the validity of the Bogoliubov description and thereby confirming the smallness of quasiparticle interactions in such an elongated gas. We also discuss the presence of oscillations in the atom number, which are due to pair correlations and to the rate at which interactions are switched off.
In standard cosmological models, inflation is driven by a quantum field, the inflaton, whos constant energy density drove the superluminal expansion of the universe [1]. When inflation stops, the universe has an extremely low density btu the inflaton field starts to oscillate arround its minimum of energy and decays into entengled pairs of particles [2], known as the pre-heating phase. Created pairs of particles then start to interact leading to decoherence and thermalization : the re-heating stage. If in situ observation of inflaton particle creation process is impossible, this pair production through parametric amplification is analogous to the creation of phonon pairs in a Bose-Einstein (BEC) condensate whose interaction strenght is time modulated. Modulating the stiffness of a dipole trap of a cigar-shape BEC being equivalent to modulate the effective one-dimensionnal interaction strenght in a BEC, we are able to probe the correlation of entengled metastable helium atoms by the use of a micro-channel plate detector (MCP). Our experimental procedure is the following [3] : we modulate in time the trap stiffness of the dipole trap laser and then release the trap (see figure 1). During expansion, the phonon kinetic energy is adiabatically transferred to one atom that is detected by the MCP after a 300 ms time of flight. The amount of created phonon pairs is expected to depend on the duration of the excitation, its amplitude and the excitation frequency. However, the region in which the entenglement of the phonon pairs can be observed is expected to be quite narrow [4]. We propose to investigate the entenglement and correlations of those pairs of particles. [1] L. Kofman, A. Linde, and A. Starobinsky, Phys. Rev. D 56, 3258 (1997). [2] D. Campo and R. Parentani, Phys. Rev. D 74, 025001 (2006). [3] S. Robertson, F. Michel, and R. Parentani, Phys. Rev. D 95, 065020 (2017). [4] J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012).