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.
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.
A bstract Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.
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.
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.
In this paper, we formulate quantum field theory on an analogue curved spacetime in a Bose-Einstein condensate where quantum particles on curved spacetime are equated with Bogoliubov quasi-particle excitations on the Bose-Einstein condensate. By using our formulation, we numerically investigate a particle creation in analogue expanding Universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate and obtain its spectrum which shows the thermal Maxwell-Boltzmann distribution, the temperature of which can be experimentally accessible. This is the first direct numerical simulation for the particle creation and its spectrum on analogue curved spacetime by using the system of Bose-Einstein condensates.
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.
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