This work introduces a synergistic combination of analytical methods and numerical simulations to study the propagation of weak wave-packet modes in an optical medium containing the analog of a pair white-black hole. We apply our tools to analyze several aspects of the evolution, such as (i) the region of the parameter space where the analogy with the Hawking effect is on firm ground and (ii) the influence that ambient thermal noise and detector inefficiencies have on the observability of the Hawking effect. We find that aspects of the Hawking effect that are of quantum origin, such as quantum entanglement, are extremely fragile to the influence of inefficiencies and noise. We propose a protocol to amplify and observe these quantum aspects, based on seeding the process with a single-mode squeezed input.
This work introduces a synergistic combination of analytical methods and numerical simulations to study the propagation of weak wave-packet modes in an optical medium containing the analog of a pair white-black hole. We apply our tools to analyze several aspects of the evolution, such as (i) the region of the parameter space where the analogy with the Hawking effect is on firm ground and (ii) the influence that ambient thermal noise and detector inefficiencies have on the observability of the Hawking effect. We find that aspects of the Hawking effect that are of quantum origin, such as quantum entanglement, are extremely fragile to the influence of inefficiencies and noise. We propose a protocol to amplify and observe these quantum aspects, based on seeding the process with a single-mode squeezed input.
This Letter introduces a synergistic combination of analytical and numerical methods to study the Hawking effect in optical systems containing the analog of a white-black hole pair. Our analytical treatment, based on techniques from Gaussian quantum information, provides a simple and efficient model to describe all aspects of the out-state, including the entanglement between any bipartition. We complement the study with a numerical analysis and apply our tools to investigate the influence that ambient thermal noise and detector inefficiencies have on the out-state. We find that aspects of the Hawking effect that are of quantum origin, i.e., quantum entanglement, are extremely fragile to the influence of inefficiencies and noise. We propose a protocol to amplify and observe these quantum aspects, based on seeding the process with a single-mode squeezed input, opening the door to new possibilities for experimental verification of the Hawking effect.
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.
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)].
The aim of this thesis is to highlight applications of quantum optics in two very distinct fields: space-based quantum communication and the Hawking effect in analogue gravity. Regarding the former: We simulate and analyze a constellation of satellites, equipped with entangled photon-pair sources, which provide on-demand entanglement distribution ser- vices to terrestrial receiver stations. Satellite services are especially relevant for long-distance quantum-communication scenarios, as the loss in satellite-based schemes scales more favor- ably with distance than in optical fibers or in atmospheric links, though establishing quantum resources in the space-domain is expensive. We thus develop an optimization technique which balances both the number of satellites in the constellation and the entanglement-distribution rates that they provide. Comparisons to ground-based quantum-repeater rates are also made. Overall, our results suggest that satellite-based quantum networks are a viable option for establishing the backbone of future quantum internet. Regarding the latter: The Hawking effect was discussed in the astrophysical context of the spontaneous decay of black holes into blackbody radiation, i.e. Hawking radiation. However, this effect seems to be universal, appearing anywhere that an event horizon (a region which restricts the flow of information to one direction) forms. Here, we analyze the Hawking effect in an optical-analogue gravity system, building on prior theoretical results regarding this effect in dielectric media. We provide a simplification of the process via the Bloch- Messiah decomposition, which allows us to decompose the Hawking effect into a discrete set of elementary processes. With this simplification and utilizing a popular entanglement measure (the logarithmic negativity), we examine the quantum correlations of the stimulated Hawking effect, explicitly showing that an environmental background temperature, along with backscattering, can lead to entanglement “sudden-death", even when the number of entangled Hawking-pairs is comparatively large. We also discuss the prospect of enhancing and “reviving" entanglement using single-mode, non-classical resources at the input. Though much of the discussion is phrased in terms of an optical-analogue model, the methods used and results obtained apply just as well to a variety of other systems supporting this effect. Finally, we provide decompositions of more exotic scenarios consisting of e.g. a white-hole– black-hole pair which share an interior region.
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.
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.