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Gravitational entanglement witness through Einstein ring image Open Access

Kaku, Y; Nambu, Y

PHYSICAL REVIEW D 111 巻 ( 4 ) 2025年2月

出版者・発行元：Physical Review D

We investigate the interplay between quantum theory and gravity by exploring gravitational lensing and Einstein ring images in a weak gravitational field induced by a mass source in spatial quantum superposition. We analyze a quantum massless scalar field propagating in two distinct models of gravity: the first quantized Newtonian gravity (QG) model, which generates quantum entanglement between the mass source and other systems, and the Schrödinger-Newton (SN) gravity model, which does not produce entanglement. Visualizing the two-point correlation function of the scalar field, we find that the QG model produces a composition of multiple Einstein rings, reflecting the spatial superposition of the mass source. By contrast, the SN model yields a single deformed ring image, representing a classical spacetime configuration. Furthermore, we introduce a specific quantity named the which-path information indicator and visualize its image. The QG model again reveals multiple Einstein rings, while the image intensity in the SN model notably vanishes. Our findings provide a visual approach to witness gravity-induced entanglement through distinct features in Einstein ring images. This study advances our understanding of quantum effects in general relativistic contexts and establishes a foundation for future studies of other relativistic phenomena.

DOI： 10.1103/PhysRevD.111.046026

Hawking radiation in quantum Hall system with an expanding edge: Application of anomaly method

Yoshimoto R., Nambu Y.

Physics Letters, Section A: General, Atomic and Solid State Physics 529 巻 2025年1月

出版者・発行元：Physics Letters, Section A: General, Atomic and Solid State Physics

The relationship between gravitational anomalies and Hawking radiation of black holes was revealed by Wilczek and Robinson. In this study, we apply their method to an analogue de Sitter spacetime in the quantum Hall system with an expanding edge. The chiral nature of the system eliminates the need for imposing the condition of ingoing modes near the horizon. Moreover, this system is structured so that the de Sitter space is sandwiched between two flat spaces, and although the effects of the anomaly would not appear in an ordinal de Sitter spacetime, they manifest themselves as boundary conditions between the de Sitter and the flat regions. By performing calculations under these boundary conditions, we obtain the flux of Hawking radiation in the outer flat region with the Gibbons-Hawking temperature of the de Sitter horizon.

DOI： 10.1016/j.physleta.2024.130100

Second-order coherence as an indicator of quantum entanglement of Hawking radiation in moving-mirror models

Tomonaga, M; Nambu, Y

PHYSICAL REVIEW D 110 巻 ( 10 ) 2024年11月

出版者・発行元：Physical Review D

The second-order coherence of light is a widely recognized physical quantity used to assess the quantum characteristics of light, and its properties have been extensively investigated in the field of quantum optics. Recently, it has been proposed that second-order coherence can be utilized as an indicator of quantum entanglement. In this study, we evaluated the second-order coherence in the context of the moving-mirror model, which serves as an analog model for Hawking radiation from a black hole. We discuss the relation between entanglement and the second-order coherence of Hawking radiation paying attention to the "noise"effect due to the thermality of Hawking radiation, which reduces the quantum correlation in the entanglement-harvesting protocol with two-qubit detectors.

DOI： 10.1103/PhysRevD.110.105004

Large violation of Leggett-Garg inequalities with coherent-state projectors for a harmonic oscillator and chiral scalar field 査読有り

Hirotani, T; Matsumura, A; Nambu, Y; Yamamoto, K

PHYSICAL REVIEW A 110 巻 ( 2 ) 2024年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review A

We investigate violations of Leggett-Garg inequalities (LGIs) for a harmonic oscillator and a (1+1)-dimensional chiral scalar field with coherent-state projectors, which is equivalent to a heterodyne-type measurement scheme. For the harmonic oscillator, we found that the vacuum and thermal states violated the LGIs by evaluating the two-time quasiprobability distribution function. In particular, we demonstrate that the value of the two-time quasiprobability reaches -0.123 for a squeezed coherent-state projector, which is equivalent to 98% of the Lüders bound corresponding to the maximal violation of the LGIs. We also find a violation of the LGIs for the local mode of a quantum chiral scalar field by constructing a coherent-state projector similar to the harmonic-oscillator case. In contrast with the harmonic oscillator, the periodicity in the time direction of the quasiprobability disappears, which is related to the existence of quantum entanglement between the local mode and its complementary degrees of freedom.

DOI： 10.1103/PhysRevA.110.022217

Final burst of the moving mirror is unrelated to the partner mode of analog Hawking radiation 査読有り国際共著

Osawa, Y; Lin, KN; Nambu, Y; Hotta, M; Chen, PS

PHYSICAL REVIEW D 110 巻 ( 2 ) 2024年7月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

Flying mirrors with appropriate trajectories have been recognized as an analog system that mimics black hole Hawking evaporation and have been widely investigated. It has recently been suggested that the partner mode of the analog Hawking radiation emitted from a moving mirror would manifest itself through a final burst when the mirror executes a sudden stop. Here we argue the opposite via the partner formula for the moving mirror model. By expanding the theoretical foundation of the partner formula and augmenting it with numerical analysis, we demonstrate that the supposed final burst is induced by a shock that requires the input of external energy, whereas the Hawking radiation partner mode, which is associated with the zero-point vacuum fluctuations, is not responsible for the burst.

DOI： 10.1103/PhysRevD.110.025023

量子系が作る重力とその検証への歩み招待有り査読有り

松村央，南部保貞，山本一博

日本物理学会誌 5 巻頁： 224 - 229 2024年5月

Entanglement partners and monogamy in de Sitter universes 査読有り

Nambu, Y; Yamaguchi, K

PHYSICAL REVIEW D 108 巻 ( 4 ) 2023年8月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

We investigate entanglement of local spatial modes defined by a quantum field in a de Sitter universe. The introduced modes show disentanglement behavior when the separation between two regions where local modes are assigned becomes larger than the cosmological horizon. To understand the emergence of separability between these local modes, we apply the monogamy inequality proposed by S. Camalet. We embed the focusing bipartite mode defined by the quantum field in a pure four-mode Gaussian state, and identify its partner modes. Then applying a Gaussian version of the monogamy relation, we show that the external entanglement between the bipartite mode and its partner modes constrains the entanglement of the bipartite mode. Thus the emergence of separability of local modes in the de Sitter universe can be understood from the perspective of entanglement monogamy.

DOI： 10.1103/PhysRevD.108.045002

Particle creation and entanglement in a dispersive model with step velocity profile 査読有り

Osawa, Y; Nambu, Y

PHYSICAL REVIEW D 107 巻 ( 10 ) 2023年5月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

We investigate particle creation and entanglement structure in a dispersive model with subluminal dispersion relation. Assuming the step function spatial velocity profile of the background flow, mode functions for a massless scalar field are exactly obtained by the matching method. Power spectrums of created particles are calculated for the subsonic and the trans-sonic flow cases. For the trans-sonic case, the sonic horizon exists, and created particles show the Planckian distribution for the low frequency region, but the thermal property disappears for the high frequency region near the cutoff frequency introduced by the nonlinear dispersion. For the subsonic case, although the sonic horizon does not exist, the effective group velocity horizon appears due to the nonlinear dispersion for the high frequency region, and an approximate thermal property of the power spectrum arises. The relation between particle creation and entanglement between each mode is also discussed.

DOI： 10.1103/PhysRevD.107.105005

Analog de Sitter universe in quantum Hall systems with an expanding edge 査読有り

南部保貞

Physical Review D 107 巻 2023年

Quantumness of gravity in harmonically trapped particles 査読有り

Kaku Youka, Maeda Shin' ya, Nambu Yasusada, Osawa Yuki

PHYSICAL REVIEW D 106 巻 ( 12 ) 2022年12月

担当区分：責任著者記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

This study investigates the quantumness of gravity under the setup of the atomic interferometry from the viewpoint of mass-energy equivalence. We evaluated interference visibility considering a particle with internal energy levels in a harmonic trapping potential. As per the result, for a spatially superposed gravitational source mass, interference visibility exhibits collapse and revival behavior, which implies that an initial separable internal state evolves to the entangled state with respect to the degrees of freedom of the center of mass, the internal energy levels, and the external source state. In particular, it does not exhibit revival behavior when gravity is treated as a quantum interaction, while it revives with a finite period for a semiclassical treatment of gravity. We also examined the temporal behavior of entanglement negativity and found that the nonrevival behavior of visibility reflects the creation of the entanglement between the internal energy state and the external source state which is uniquely induced by the quantum interaction of gravity in accordance with the weak equivalence principle.

DOI： 10.1103/PhysRevD.106.126005

Entanglement Renyi Entropy of Two Disjoint Intervals for Large c Liouville Field Theory 査読有り

Tsujimura Jun, Nambu Yasusada

ENTROPY 24 巻 ( 12 ) 2022年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Entropy

Entanglement entropy (EE) is a quantitative measure of the effective degrees of freedom and the correlation between the sub-systems of a physical system. Using the replica trick, we can obtain the EE by evaluating the entanglement Renyi entropy (ERE). The ERE is a q-analogue of the EE and expressed by the q replicated partition function. In the semi-classical approximation, it is apparently easy to calculate the EE because the classical action represents the partition function by the saddle point approximation and we do not need to perform the path integral for the evaluation of the partition function. In previous studies, it has been assumed that only the minimal-valued saddle point contributes to the EE. In this paper, we propose that all the saddle points contribute comparably but not necessarily equally to the EE by dealing carefully with the semi-classical limit and then the (Formula presented.) limit. For example, we numerically evaluate the ERE of two disjoint intervals for the large c Liouville field theory with (Formula presented.). We exploit the BPZ equation with the four twist operators, whose solution is given by the Heun function. We determine the ERE by tuning the behavior of the Heun function such that it becomes consistent with the geometry of the replica manifold. We find the same two saddle points as previous studies for (Formula presented.) in the above system. Then, we provide the ERE for the large but finite c and the (Formula presented.) in case that all the saddle points contribute comparably to the ERE. In particular, the ERE is the summation of these two saddle points by the same weight, due to the symmetry of the system. Based on this work, it shall be of interest to reconsider EE in other semi-classical physical systems with multiple saddle points.

DOI： 10.3390/e24121758

Deep learning metric detectors in general relativity 査読有り

Katsube Ryota, Tam Wai-Hong, Hotta Masahiro, Nambu Yasusada

PHYSICAL REVIEW D 106 巻 ( 4 ) 2022年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

We consider conceptual issues of deep learning (DL) for metric detectors using test particle geodesics in curved spacetimes. Advantages of DL metric detectors are emphasized from a viewpoint of general coordinate transformations. Two given metrics (two spacetimes) are defined to be connected by a DL isometry if their geodesic image data cannot be discriminated by any DL metric detector at any time. The fundamental question of when the DL isometry appears is extensively explored. If the two spacetimes connected by the DL isometry are in superposition of quantum gravity theory, the postmeasurement state may be still in the same superposition even after DL metric detectors observe the superposed state. We also demonstrate metric-detection DL methods in 2dimensional anti-de Sitter (AdS) spacetimes to estimate the cosmological constants and Brown-Henneaux charges. In the AdS/CFT correspondence dictionary, it may be expected that such metric detectors in the AdS bulk region correspond to quantum measurement devices in the conformal field theory at the AdS boundary. +ACY-copy+ADs- 2022 American Physical Society.

DOI： 10.1103/PhysRevD.106.044051

Leggett-Garg inequalities for testing quantumness of gravity

Matsumura Akira, Nambu Yasusada, Yamamoto Kazuhiro

PHYSICAL REVIEW A 106 巻 ( 1 ) 2022年7月

記述言語：日本語出版者・発行元：Physical Review A

In this study, we determine a violation of the Leggett-Garg inequalities due to gravitational interaction in a hybrid system consisting of a harmonic oscillator and a spatially localized superposed particle. The violation of the Leggett-Garg inequalities is discussed using the two-time quasiprobability in connection with the entanglement negativity generated by gravitational interaction. It is demonstrated that the entanglement suppresses the violation of the Leggett-Garg inequalities when one of the two times of the quasiprobability t1 is chosen as the initial time. Further, it is shown that the Leggett-Garg inequalities are generally violated due to gravitational interaction by properly choosing the configuration of the parameters, including t1 and t2, which are the times of the two-time quasiprobability. The feasibility of detecting violations of the Leggett-Garg inequalities in hybrid systems is also discussed.

DOI： 10.1103/PhysRevA.106.012214

Expanding edges of quantum Hall systems in a cosmology language: Hawking radiation from de Sitter horizon in edge modes 査読有り

Hotta Masahiro, Nambu Yasusada, Sugiyama Yuuki, Yamamoto Kazuhiro, Yusa Go

PHYSICAL REVIEW D 105 巻 ( 10 ) 2022年5月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free fields decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum field theory in 1+1-dimensional curved spacetimes to analyze the edge dynamics. We propose methods to address the following questions using edge waveforms from the expanding region: Does the conformal symmetry survive? Is the nonlinear interaction of the edge excitations induced by edge expansion? Do the edge excitations interact with the bulk excitations? We additionally show that the expanding edges can be regarded as expanding universe simulators of two-dimensional dilaton-gravity models, including the Jackiw-Teitelboim gravity model. As an application, we point out that our theoretical setup might simulate emission of analog Hawking radiation with the Gibbons-Hawking temperature from the future de Sitter horizon formed in the expanding-edge region.

DOI： 10.1103/PhysRevD.105.105009

その他リンク： http://arxiv.org/pdf/2202.03731v2

Alfvénic superradiance for a monopole magnetosphere around a Kerr black hole 査読有り

Noda S., Nambu Y., Takahashi M., Tsukamoto T.

Physical Review D 105 巻 ( 6 ) 2022年3月

担当区分：責任著者記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

Herein, we explore superradiance for Alfvén waves (Alfvénic superradiance) in an axisymmetric rotating magnetosphere of a Kerr black hole within the force-free approximation. On the equatorial plane of the Kerr spacetime, the Alfvén wave equation is reduced to a one-dimensional Schrödinger-type equation by separating variables of the wave function and introducing a tortoise coordinate mapping the inner and outer light surfaces to -∞ and +∞, respectively, and we investigate a wave scattering problem for Alfvén waves. An analysis of the asymptotic solutions of the wave equation and conservation of the Wronskian provides the superradiant condition for Alfvén waves, and it is shown that the condition coincides with that for the Blandford-Znajek process. This indicates that when Alfvénic superradiance occurs, the Blandford-Znajek process also occurs in the force-free magnetosphere. Then, we evaluate the reflection rate of Alfvén waves numerically and confirm that Alfvénic superradiance is indeed possible in the Kerr spacetime. Moreover, we will discuss a resonant scattering of Alfvén waves, which is related to a "quasinormal mode"of the magnetosphere.

DOI： 10.1103/PhysRevD.105.064018

Interferometry of black holes with Hawking radiation 査読有り

Nambu Yasusada, Noda Sousuke

PHYSICAL REVIEW D 105 巻 ( 4 ) 2022年2月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review D

We investigate the wave optical imaging of black holes with Hawking radiation. The spatial correlation function of Hawking radiation is expressed in terms of transmission and reflection coefficients for scalar wave modes and evaluated by numerically summing over angular quantum numbers for the Unruh-Hawking state of the Kerr-de Sitter black hole. Then, wave optical images of an evaporating black hole are obtained by the Fourier transformation of the spatial correlation function. For a short wavelength, the image of the black hole with the outgoing mode of the Unruh-Hawking state has the appearance of a star with its surface given by the photon sphere. It is found that interference between incoming modes from the cosmological horizon and reflected modes due to the scattering of the black hole can enhance brightness of images in the vicinity of the photon sphere. For a long wavelength, the entire field of view is bright, and the emission region of Hawking radiation cannot be identified.

DOI： 10.1103/PhysRevD.105.045022

Qubit Clock in Quantum Cosmology 招待有り査読有り

Nambu Yasusada

UNIVERSE 8 巻 ( 2 ) 2022年2月

担当区分：責任著者記述言語：英語出版者・発行元：Universe

We investigate the emergent time scenario in quantum cosmology based on the Page– Wotters approach. Using a quantum cosmological model with a qubit clock, it is demonstrated how the entanglement between the qubit clock and the geometry derives emergence of a time parameter, which defines evolution of the timeless quantum state of the universe. We show that the universe wave function conditioned by a qubit clock obeys the standard Schrödinger equation and the Fisher information for the clock state, which quantifies entanglement between the universe and the clock, and contributes as a negative energy density.

DOI： 10.3390/universe8020099

Blandford-Znajek process as Alfvenic superradiance 査読有り

Noda Sousuke, Nambu Yasusada, Tsukamoto Takuma, Takahashi Masaaki

PHYSICAL REVIEW D 101 巻 ( 2 ) 2020年1月

Wave optics in spacetimes with compact gravitating object 査読有り

Nambu Yasusada, Noda Sousuke, Sakai Yuichiro

PHYSICAL REVIEW D 100 巻 ( 6 ) 2019年9月

Large scale quantum entanglement in de Sitter spacetime 査読有り

Matsumura Akira, Nambu Yasusada

PHYSICAL REVIEW D 98 巻 ( 2 ) 2018年7月

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