The quantum noise in a linear amplifier is shown to be thermal noise. The theory of linear amplifiers is applied first to the simplest, single or double oscillator model of an amplifier, and then to linear model of an amplifier with continuous fields and input and outputs. Finally it is shown that the thermal noise emitted by black holes first demonstrated by Hawking, and of dumb holes (sonic and other analogs to black holes), arises from the same analysis as for linear amplifiers. The amplifier noise of black holes acting as amplifiers on the quantum fields living in the spacetime surrounding the black hole is the radiation discovered by Hawking. For any amplifier, that quantum noise is completely characterized by the attributes of the system regarded as a classical amplifier, and arises out of those classical amplification factors and the commutation relations of quantum mechanics.
The quantum noise in a linear amplifier is shown to be thermal noise. The theory of linear amplifiers is applied first to the simplest, single or double oscillator model of an amplifier, and then to linear model of an amplifier with continuous fields and input and outputs. Finally it is shown that the thermal noise emitted by black holes first demonstrated by Hawking, and of dumb holes (sonic and other analogs to black holes), arises from the same analysis as for linear amplifiers. The amplifier noise of black holes acting as amplifiers on the quantum fields living in the spacetime surrounding the black hole is the radiation discovered by Hawking. For any amplifier, that quantum noise is completely characterized by the attributes of the system regarded as a classical amplifier, and arises out of those classical amplification factors and the commutation relations of quantum mechanics.
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.
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.
Hawking radiation is the proposed thermal black-body radiation of quantum nature emitted from a black hole. One common way to give an account of Hawking radiation is to consider a detector that follows a static trajectory in the vicinity of a black hole and interacts with the quantum field of the radiation. In the present work, we study the Hawking radiation perceived by a detector that follows a quantum superposition of static trajectories in Schwarzschild spacetime, instead of a unique well-defined trajectory. We analyze the quantum state of the detector after the interaction with a massless real scalar field. We find that for certain trajectories and excitation levels, there are nonvanishing coherences in the final state of the detector. We then examine the dependence of these coherences on the trajectories followed by the detector and relate them to the distinguishability of the different possible states in which the field is left after the excitation of the detector. We interpret our results in terms of the spatial distribution and propagation of particles of the quantum field.
Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes. The paper develops the quantum theory of simple optical instruments and applies the theory to a few characteristic situations, to the splitting and interference of photons and to the manifestation of Einstein–Podolsky–Rosen correlations in parametric downconversion. How to model irreversible devices such as absorbers and amplifiers is also shown. Finally, the paper develops the theory of Hawking radiation for a simple optical black hole. The paper is intended as a primer, as a nearly self-consistent tutorial. The reader should be familiar with basic quantum mechanics and statistics, and perhaps with optics and some elementary field theory. The quantum theory of light in dielectrics serves as the starting point and, in the concluding section, as a guide to understand quantum black holes.
Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes. The article develops the quantum theory of simple optical instruments and applies the theory to a few characteristic situations, to the splitting and interference of photons and to the manifestation of Einstein-Podolsky-Rosen correlations in parametric downconversion. How to model irreversible devices such as absorbers and amplifiers is also shown. Finally, the article develops the theory of Hawking radiation for a simple optical black hole. The paper is intended as a primer, as a nearly self-consistent tutorial. The reader should be familiar with basic quantum mechanics and statistics, and perhaps with optics and some elementary field theory. The quantum theory of light in dielectrics serves as the starting point and, in the concluding section, as a guide to understand quantum black holes. 1 1
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.