Entanglement entropy of cosmological perturbations

Brahma, Suddhasattwa; Alaryani, Omar; Brandenberger, Robert H.

doi:10.1103/physrevd.102.043529

Cited by 64 publications

(85 citation statements)

References 80 publications

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“…This squeezing parameter is responsible for the quantum correlation with unobservable partner particles trapped in the cavity. The entanglement entropy for the two-mode squeezed states is given in the well-known form 33 , 34 as Note that the entanglement entropy depends on the relative soliton velocity u as shown in Fig. 8 since the squeezing parameter involves the Hawking temperature depending on the soliton velocity.…”

Section: Resultsmentioning

confidence: 99%

Quantum-circuit black hole lasers

Katayama

2021

Sci Rep

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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.

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Section: Resultsmentioning

confidence: 99%

Quantum-circuit black hole lasers

Katayama

2021

Sci Rep

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“…This area of research begun in earnest in the early 1990s [12,[67][68][69][70][71][72] is still being pursued vibrantly today. For a sample of recent work, see, for example, [21,22], where other earlier references can be found. We shall discuss this topic with a detailed background summary in a companion paper under preparation [73];…”

Section: Related Issues: Decoherence and Entanglementmentioning

confidence: 99%

“…This is referred to as entanglement entropy in cosmology. Recent work includes [22,[98][99][100][101], where earlier references can be found.…”

Section: Coarse-graining By Partitioningmentioning

confidence: 99%

“…Entropy of quantum cosmological perturbations is an important topic which has by now clocked almost three decades of investigations [1][2][3]. In terms of its theoretical foundation, it is built upon the bigger issue of (I) the entropy of quantum fields, where investigation started in the mid-1980s [4][5][6][7] continuing on into the 1990s [8][9][10][11][12], 2000s [13][14][15][16][17] and has been rekindled in recent years [18][19][20][21][22]. There are two aspects in this theme: (1) the quantum field theory component depicting particle creation from the vacuum and quantum cosmological perturbations; (2) the nonequilibrium statistical mechanics aspect describing the evolutionary dynamics of a quantum many-body system-the fluctuations in, and the dissipation of, a quantum field.…”

Section: Introductionmentioning

confidence: 99%

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Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

Hsiang

2021

Entropy

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Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.

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Section: Entanglement Entropymentioning

confidence: 99%

Quantum-Circuit Black Hole Lasers

Katayama

2021

Preprint

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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. However, no progress has been made in electric circuits. Here we propose an optical analogue 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 Schrodinger 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 derived from Hawking radiation and then characterized by squeezing parameters related to Hawking temperatures depending on the soliton velocity. We also evaluate the degree of quantum correlation using entanglement entropy.

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Entanglement entropy of cosmological perturbations

Cited by 64 publications

References 80 publications

Quantum-circuit black hole lasers

Quantum-circuit black hole lasers

Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

Quantum-Circuit Black Hole Lasers

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