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.
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.
Hawking radiation is a fundamental spontaneous phenomenon in which the event horizon of a black hole transforms the vacuum state into a pair of correlated particles: the Hawking radiation and its partner. This emission can also be stimulated by a state other than the vacuum. A similar phenomenon, known as analogue Hawking radiation, has been observed across various physical systems, but experimental realizations have largely remained in the classical regime. This work presents an experimental verification of analogue Hawking radiation stimulated by a single-particle state, producing a verifiably single-photon Hawking output. Using heralded single photons generated via spontaneous four-wave mixing, we stimulate the analogue Hawking effect in an optical fiber. We characterize the resulting Hawking signal by measuring its spectral dependence, intensity scaling, and heralded second-order correlation. Our results establish a platform for exploring quantum correlations and entanglement in analogue gravity. Researchers experimentally demonstrate analogue Hawking radiation stimulated by a single photon in an optical fiber. This work enables new studies of quantum effects in nonlinear optics and analogue gravity.
The Hawking effect is an exciting physical prediction lying at the intersection of the two most successful theories of the past century, namely, Einstein’s theory of relativity and quantum mechanics. In this dissertation, we put special emphasis on the quantum aspects of the Hawking process encoded in the entanglement shared by the emitted fluxes of created quanta. In particular, we employ sharp tools from quantum information theory to quantify the entanglement produced by the Hawking effect throughout the black hole evaporation process. Our framework allows us to extend previous calculations of entanglement to a larger set of cases, for instance, the situation where a black hole is immersed in a thermal bath, such as the cosmic microwave background (CMB), and the quantum state of infalling radiation is, therefore, mixed. Motivated by recent intense experimental efforts, we extend our framework to the case of an optical white-black hole pair analog gravity system created by a strong electromagnetic pulse propagating in a non-linear dielectric medium. One of the main results presented in this dissertation is the development of a numerical code that recreates the Hawking process in such an optical analog. Utilizing this code together with our quantum information tools, we study how different input quantum states of light alter the amount of the entanglement produced in the Hawking pairs. We find that although ambient thermal noise and detector inefficiencies, unsurprisingly, tend to reduce quantum correlations in the Hawking process, when horizons are illuminated with single-mode squeezed states of light, the entanglement generated increases in a tunable manner. As a last application in optical analogs, we investigate the laser configuration in which two strong electromagnetic pulses propagate in a non-linear dielectric medium exchanging Hawking quanta, thus, stimulating each other. In such a setup, we observe that not only the number of Hawking quanta created is exponentially increased but also the entanglement shared between the mode of the electromagnetic field inside the laser cavity with the modes of the field outside the cavity grows with time. We conclude that these novel results open a promising window for the observability of the quantum origin of the Hawking effect in the lab.
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.
In this work, we describe optically inspired models for unitary black hole (BH) evaporation. The goal of these models are (i) to be operationally simple, (ii) approximately preserve the thermal nature of the emitted Hawking Radiation (HR), and (iii) attempt to reproduce the Page Curve that purports that information flows forth from the BH when it has evaporated to approximately half its initial mass. We concentrate on modeling the BH as a single mode squeezed state successively interacting, by means of beam splitters and squeezers, with vacuum modes near the horizon, giving rise to entangled pairs representing the external Hawking radiation and its partner particle inside the horizon. Since all states and operations are Gaussian throughout, we use a symplectic formalism to track the evolution of the composite system through the evolving means and variances of their quadrature operators. This allows us to easily compute correlations and entanglement between the BH and the HR, as well as calculate correlations between the BH at early and late times.
We introduce a convenient set of analytical tools (the Gaussian formalism) and diagrams (symplectic circuits) to analyze multimode scattering events in analogue gravity, such as pair creation \`a la Hawking by black hole and white hole analogue event horizons. The diagrams prove to be valuable Ans\"atze for the scattering dynamics, especially in settings where direct analytic results are not straightforward and one must instead rely on numerical simulations. We use these tools to investigate entanglement generation in single- and multihorizon scenarios, in particular when the Hawking process is stimulated with classical (e.g., thermal noise) and nonclassical (e.g., single-mode squeezed vacuum) input states---demonstrating, for instance, that initial squeezing can enhance the production of entanglement and overcome the deleterious effects that initial thermal fluctuations have on the output entanglement. To make further contact with practical matters, we examine how attenuation degrades quantum correlations between Hawking pairs. The techniques that we employ are generally applicable to analogue gravity setups of (Gaussian) bosonic quantum systems, such as analogue horizons produced in optical analogues and in Bose-Einstein condensates, and should be of great utility in these domains. We show the applicability of these techniques by putting them in action for an optical system containing a pair white-black hole analogue, extending our previous analysis of [Phys. Rev. Lett. 128, 091301 (2022)].
Hawking radiation is a fundamental result of quantum field theory in curved spacetime, yet its direct observation remains beyond current experimental capabilities. Circuit quantum electrodynamics provides a practical platform for realizing analogue systems where Hawking-like radiation may be studied under controlled laboratory conditions. In this work, we analyze two superconducting-circuit analogues of Schwarzschild black holes: a tunable dc-SQUID transmission line and a SNAIL-based transmission line supporting solitonic solutions of the KdV equation. We investigate the conditions under which these architectures can generate an observable Hawking temperature and study the impact of dissipation and thermal noise using an open quantum systems approach. To assess the observability of the Hawking signal, we propose complementing particle number measurements with estimates of the Hilbert-Schmidt distance to the thermal bath. Our analysis establishes practical detectability thresholds and shows that Hawking temperatures above approximately 73 mK remain distinguishable under realistic experimental conditions. While the tunable transmission line architecture can reach temperatures of about 113 mK and therefore appears more viable, the solitonic model requires further optimization and more demanding experimental conditions.