Pair creation is a fundamental prediction of quantum field theory in curved spacetimes. While classical aspects of this phenomenon have been observed, the experimental confirmation of its quantum origin remains elusive. In this article, we quantify the entanglement produced by pair creation in two dimensional Bose-Einstein condensate (BEC) analogs of expanding universes and examine the impact of various experimental factors, including decoherence from thermal noise and losses. Our analysis evaluates the feasibility of detecting entanglement in these systems and identifies optimal experimental configurations for achieving this goal. Focusing on the experimental setup detailed in Viermann et al. [Quantum field simulator for dynamics in curved spacetime, Nature (London) 611, 260 (2022)], we demonstrate that entanglement can be observed in these BEC analogs at a significance level of $\ensuremath{\sim}2\ensuremath{\sigma}$ with current capabilities, and at $\ensuremath{\gtrsim}3.3\ensuremath{\sigma}$ with modest improvements. Achieving this would provide unequivocal evidence of the quantum nature of pair creation and validate one of the most iconic predictions of quantum field theory in curved spacetimes.
Pair creation is a fundamental prediction of quantum field theory in curved spacetimes. While classical aspects of this phenomenon have been observed, the experimental confirmation of its quantum origin remains elusive. In this article, we quantify the entanglement produced by pair creation in two dimensional Bose-Einstein condensate (BEC) analogs of expanding universes and examine the impact of various experimental factors, including decoherence from thermal noise and losses. Our analysis evaluates the feasibility of detecting entanglement in these systems and identifies optimal experimental configurations for achieving this goal. Focusing on the experimental setup detailed in Viermann et al. [Quantum field simulator for dynamics in curved spacetime, Nature (London) 611, 260 (2022)], we demonstrate that entanglement can be observed in these BEC analogs at a significance level of \ensuremath∼2\ensuremathσ with current capabilities, and at \ensuremath≳3.3\ensuremathσ with modest improvements. Achieving this would provide unequivocal evidence of the quantum nature of pair creation and validate one of the most iconic predictions of quantum field theory in curved spacetimes.
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 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, 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.
Recent experiments have employed rapidly expanding toroidal Bose-Einstein condensates (BECs) to mimic the inflationary expansion in the early universe. One expected signature of the expansion in such experiments is spontaneous particle creation (of phonons) which is observable in density-density correlations. We study entanglement of these particles, which are known to result in a two-mode squeezed state. Using techniques for Gaussian states of continuous variable systems, we quantify the entanglement generated in this system, including effects such as decoherence and the use of an initially squeezed state, which can suppress and enhance entanglement, respectively. We also describe a protocol to experimentally measure the correlations entering the covariance matrix, allowing an experimental quantification of the entanglement properties of the inflationary BEC.
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.
This thesis investigates thermalisation, correlations and entanglement in Bose-Einstein condensates. Bose-Einstein condensates are ultra-cold collections of identical bosonic atoms which accumulate in a single quantum state, forming a mesoscopic quantum object. They are clean and controllable quantum many-body systems that permit an unprecedented degree of experimental flexibility compared to other physical systems. Further, a tractable microscopic theory exists which allows a direct and powerful comparison between theory and experiment, propelling the field of quantum atom optics forward at an incredible pace. Here we explore some of the fundamental frontiers of the field, examining how non-classical correlations and entanglement can be created and measured, as well as how non-classical effects can lead to the rapid heating of atom clouds. We first investigate correlations between two weakly coupled condensates, a system analogous to a superconducting Josephson junction. The ground state of this system contains non-classical number correlation arising from the repulsion between the atoms. Such states are of interest because they may lead to more precise measurement devices such as atomic gyroscopes. Unfortunately thermal fluctuations can destroy these correlations, and great care is needed to experimentally observe non-classical effects. We show that adiabatic evolution can drive the isolated quantum system out of thermal equilibrium and decrease thermal noise, in agreement with a recent experiment [Esteve et al. Nature 455, 1216 (2008)]. This technique may be valuable for observing and using quantum correlated states in the future. Next, we analyse the rapid heating that occurs when a condensate is placed in a moving periodic potential. The dynamical instability responsible for the heating was the subject of much uncertainty, which we suggest was due to the inability of the mean-field approximation to account for important spontaneous scattering processes. We show that a model including non-classical spontaneous scattering can describe dynamical instabilities correctly in each of the regimes where they have been observed, and in particular we compare our simulations to an experiment performed at the University of Otago deep inside the spontaneous scattering regime. Finally, we proposed a method to create and detect entangled atomic wave-packets. Entangled atoms are interesting from a fundamental perspective, and may prove useful in future quantum information and precision measurement technologies. Entanglement is generated by interactions, such as atomic collisions in Bose-Einstein condensates. We analyse the type of entanglement generated via atomic collisions and introduce an abstract scheme for detecting entanglement and demonstrating the Einstein-Podolsky-Rosen paradox with ultra-cold atoms. We further this result by proposing an experiment where entangled wave-packets are created and detected. The entanglement is generated by the pairwise scattering that causes the instabilities in moving periodic potentials mentioned above. By careful arrangement, the instability process can be controlled to to produce two well-defined atomic wave-packets. The presence of entanglement can be proven by applying a series of laser pulses to interfere the wave-packets and then measuring the output populations. Realising this experiment is feasible with current technology.
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