We propose a time crystal based on a quantum black-hole laser, where the genuinely spontaneous character of the symmetry breaking stems from the self-amplification of spontaneous Hawking radiation. The resulting Hawking time crystal (HTC) is characterized by the periodic dependence of the out-of-time density-density correlation function, while equal-time observables are time independent because they embody averages over different realizations with a random oscillation phase. The HTC provides a nonlinear periodic analog of the Andreev-Hawking effect, exhibiting anticorrelation bands resulting from the spontaneous, quantum emission of pairs of dispersive waves and solitons into the upstream and downstream regions. Remarkably, we prove that any parametric amplifier has associated a time operator, which leads to a unique characterization of the time-crystal formation in terms of two time operators: one associated with the initial black-hole laser and another associated with the final spontaneous Floquet state.
We propose a time crystal based on a quantum black-hole laser, where the genuinely spontaneous character of the symmetry breaking stems from the self-amplification of spontaneous Hawking radiation. The resulting Hawking time crystal (HTC) is characterized by the periodic dependence of the out-of-time density-density correlation function, while equal-time observables are time independent because they embody averages over different realizations with a random oscillation phase. The HTC provides a nonlinear periodic analog of the Andreev-Hawking effect, exhibiting anticorrelation bands resulting from the spontaneous, quantum emission of pairs of dispersive waves and solitons into the upstream and downstream regions. Remarkably, we prove that any parametric amplifier has associated a time operator, which leads to a unique characterization of the time-crystal formation in terms of two time operators: one associated with the initial black-hole laser and another associated with the final spontaneous Floquet state.
The black-hole laser (BHL) effect is the self-amplification of Hawking radiation in the presence of a pair of horizons which act as a resonant cavity. In a flowing atomic condensate, the BHL effect arises in a finite supersonic region, where Bogoliubov-Cherenkov-Landau (BCL) radiation is coherently excited by any static perturbation. Thus, experimental attempts to produce a black-hole laser unavoidably deal with the presence of a strong BCL background, making the observation of the BHL effect still a major challenge in the analog gravity field. Here, we perform a theoretical study of the BHL-BCL crossover using an idealized model where both phenomena can be unambiguously isolated. By drawing an analogy with an unstable pendulum, we distinguish three main regimes according to the interplay between quantum fluctuations and classical stimulation: quantum BHL, classical BHL, and BCL. Based on quite general scaling arguments, the nonlinear amplification of the initial amplitude of the quantum fluctuations up to saturation is identified as the most robust trait of a quantum BHL. A classical BHL behaves instead as a linear quantum amplifier, where the output is proportional to the input. The BCL regime also acts as a linear quantum amplifier, but its gain is exponentially smaller as compared to a classical BHL. In addition, we find that the decrease in the amplification for increasing BCL amplitude or the nonmonotonic dependence of the growth rate with respect to the background parameters are complementary signatures of black-hole lasing. We also identify interesting analog phenomena such as Hawking-stimulated white-hole radiation or quantum BCL-stimulated Hawking radiation. The results of this work not only are of interest for analog gravity, where they help to distinguish each phenomenon and to design experimental setups leading to a clear observation of the BHL effect, but they also open the prospect of finding applications of analog concepts in quantum technologies.
We numerically study an analog black hole with two horizons with parameters similar to a recent experiment. We find that the Hawking radiation exists on a background which contains a density oscillation, a zero-frequency ripple. The Hawking radiation evolves from spontaneous to self-amplifying, while the background ripple grows steadily with no qualitative change. It is seen that the self-amplifying Hawking radiation has a nonzero frequency. This frequency is independent of the reference frame since it is the magnitude of the wave which oscillates, as in a standing wave. The background ripple appears even before the inner horizon is created, in contrast to predictions. Furthermore, we find that technical noise and shot-to-shot variations in the number of atoms are not sufficient to cause the observed correlation function. This work is in agreement with the recent observation of self-amplifying Hawking radiation, and explains some of the features seen. In contrast to some recent works, our study differentiates between the Hawking radiation observed, and the evolution of the background.
A black hole laser in analogues of gravity amplifies Hawking radiation, which is unlikely to be measured in real black holes, and makes it observable. There have been proposals to realize such black hole lasers in various systems. However, no progress has been made in electric circuits for a long time, despite their many advantages such as high-precision electromagnetic wave detection. Here we propose a black hole laser in Josephson transmission lines incorporating metamaterial elements capable of producing Hawking-pair propagation modes and a Kerr nonlinearity due to the Josephson nonlinear inductance. A single dark soliton obeying the nonlinear Schrödinger equation produces a black hole-white hole horizon pair that acts as a laser cavity through a change in the refractive index due to the Kerr effect. We show that the resulting laser is a squeezed-state laser characterized by squeezing parameters. We also evaluate the degree of quantum correlation between Hawking and its partner radiations using entanglement entropy which does not require simultaneous measurements between them. As a result, the obtained entanglement entropy depending on the soliton velocity provides strong evidence that the resulting laser is derived from Hawking radiation with quantum correlation generated by pair production from the vacuum.
We propose the concept of a spontaneous many-body Floquet state. This is a state that, in the absence of external periodic driving, self-oscillates like in the presence of a periodic Hamiltonian, this behavior being spontaneously induced by many-body interactions. In addition, its quantum fluctuations are described by regular Floquet theory. Furthermore, it is also a time crystal, presenting long-range time-periodic order. However, this crystalline behavior is very different to that of conventional Floquet discrete time crystals: here, there is no external periodic driving, energy is conserved, and the nature of the spontaneous symmetry breaking is continuous instead of discrete. We demonstrate that spontaneous many-body Floquet states can emerge in a variety of canonical many-body problems, ranging from interacting fermions to Bose-Hubbard models. We specifically show that a spontaneous many-body Floquet state is a universal intrinsic state of a one-dimensional flowing atom condensate, both subsonic and supersonic, resulting from a dynamical phase transition and robust against external perturbations and quantum fluctuations, proposing also realistic experimental scenarios for its observation. A spontaneous many-body Floquet state not only represents a realization of a continuous time crystal, but also another paradigm in Floquet physics.
We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes that induce a laser effect. This effect constitutes a dynamical instability and is due to the fact that the supersonic region acts as a resonant cavity. We numerically compute the complex frequencies and density–density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.
Abstract We present a theoretical study on the origin of some findings of recent experiments on sonic analogs of gravitational black holes (BHs). We focus on the realization of a BH lasing configuration, where the conclusive identification of stimulated Hawking radiation (HR) requires dealing with the implications of the nonstationary character of the setup. To isolate the basic mechanisms responsible for the observed behavior, we use a toy model where nonstationarity can be described in terms of departures from adiabaticity. Our approach allows one to study which aspects of the characterization of BH lasing in static models are still present in a dynamical scenario. In particular, variations in the role of the dynamical instabilities can be traced. Arguments to conjecture the twofold origin of the detected amplification of sound are given: the differential effect of the instabilities on the mean field and on the quantum fluctuations gives some clues to separate a deterministic component from self-amplified HR. The role of classical noise, present in the experimental setup, is also tackled: we discuss the emergence of differences with the effect of quantum fluctuations when various unstable modes are relevant to the dynamics.