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arXiv:1403.3262 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum entanglement in analogue Hawking radiation: When is the final state nonseparable?

Xavier Busch, Renaud Parentani

Published May 23, 2014• 67 citations
arXivHTMLPDF

Abstract

We study the quantum entanglement of the quasiparticle pairs emitted by analog black holes. We use a phenomenological description of the spectra in dispersive media to study the domains in parameter space where the final state is nonseparable. In stationary flows, three modes are involved in each sector of fixed frequency, and not two as in homogeneous situations. The third spectator mode acts as an environment for the pairs, and the strength of the coupling significantly reduces the quantum coherence. The nonseparability of the pairs emitted by white holes is also considered and compared with that of black holes.

DOI
10.1103/physrevd.89.105024

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We study the quantum entanglement of the quasiparticle pairs emitted by analog black holes. We use a phenomenological description of the spectra in dispersive media to study the domains in parameter space where the final state is nonseparable. In stationary flows, three modes are involved in each sector of fixed frequency, and not two as in homogeneous situations. The third spectator mode acts as an environment for the pairs, and the strength of the coupling significantly reduces the quantum coherence. The nonseparability of the pairs emitted by white holes is also considered and compared with that of black holes.
We theoretically study the entanglement of Hawking radiation pairs emitted by an analogue black hole. We find that this entanglement can be measured by the experimentally accessible density-density correlation function, vastly simplifying the measurement. We find that while the Hawking radiation exiting the black hole might be Planck-distributed, the correlations between the Hawking radiation and the partner particles has a distribution which is weaker but broader than Planckian. Thus, the high-energy tail of the distribution of Hawking radiation should be entangled, whereas the low-energy part should not be. This confirms previous studies. The full Peres-Horodecki criterion is considered, as well as a simpler criterion in the stationary, homogeneous case. Our method applies to systems which are sufficiently cold that the thermal phonons can be neglected.
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.
Abstract We consider a quantum circuit model describing the evaporation process of black holes. We specifically examine the behavior of the multipartite entanglement represented by this model, and find that the entanglement structure depends on the black hole mass M and the frequency of the Hawking radiation ω . For sufficiently small values of , the black hole and the radiation system becomes a separable state after the Page time and a firewall-like structure appears. On the contrary, for larger values of , the entanglement between the black hole and the radiation is not lost. These behaviors imply that owing to the monogamy property of the multipartite entanglement, low frequency modes of the Hawking radiation destroy the quantum correlation between the black hole and the emitted Hawking radiation.
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.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the black hole mass is 0, the radiation state is pure and one-to-one with the initial state forming the black hole. Thus there is no information loss upon full evaporation. The original Hawking's pair entanglement between infalling and outgoing particles gets transferred to outgoing particles via entanglement swapping, without violation of no-signalling or the entanglement's monogamy. The final state after the full black hole evaporation is pure, without loss of information, violation of monogamy, or the equivalence principle.