Language：Japanese   Publisher：The Physical Society of Japan  

<p>What is the gravity of a quantum system and what does it cause? This is a fundamental problem for unifying quantum mechanics and general relativity, which has not been elucidated yet. A key feature for elucidating the problem is the quantum superposition of a gravitational field, which may appear in the superposition of a quantum system with a mass. Interestingly, this quantum phenomenon of gravity generates entanglement in quantum systems. This gravity-induced entanglement can be a main target in the above context. In this article, we share the current studies on the gravity of a quantum system and on gravity-induced entanglement.</p>

DOI： 10.11316/butsuri.79.5_224

CiNii Research

Publisher：Physical Review D  

We investigate the quantum signature of gravity in optomechanical systems under quantum control. We analyze the gravity-induced entanglement and squeezing in mechanical mirrors in a steady state. The behaviors and the conditions for generating the gravity-induced entanglement and squeezing are identified in the Fourier modes of the mechanical mirrors. The condition of generating the entanglement between the mirrors found in the present paper is more severe than that of the gravity-induced entanglement between output lights. The gravity-induced entanglement in optomechanical systems is an important milestone toward verifying the quantum nature of gravity, which should be verified in the future.

DOI： 10.1103/PhysRevD.109.064090

Web of Science

Scopus

Publisher：Physical Review D  

Investigating the quantum nature of gravity is an important issue in modern physics. Recently, studies pertaining to the quantum superposition of gravitational potential have garnered significant interest. Inspired by Mari et al. [Sci. Rep. 6, 22777 (2016)SRCEC32045-232210.1038/srep22777] and Baym and Ozawa [Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)PNASA60027-842410.1073/pnas.0813239106], Belenchia et al. [Phys. Rev. D 98, 126009 (2018)PRVDAQ2470-001010.1103/PhysRevD.98.126009] considered a gedanken experiment involving such a quantum superposition and mentioned that the superposition renders causality and complementarity inconsistent. They resolved this inconsistency by considering the quantized dynamical degrees of freedom of gravity. This suggests a strong relationship between the quantum superposition of the gravitational potential and the quantization of the gravitational field. In our previous study [Phys. Rev. D 106, 125002 (2022)PRVDAQ2470-001010.1103/PhysRevD.106.125002], we have shown that the quantum uncertainty of a field guarantees the consistency between causality and complementarity. In this study, we focus on the entanglement between two particles' states due to the electromagnetic/gravitational potential and investigate its relationship with quantum uncertainty, causality, and complementarity. Our numerical analyses show that the quantum uncertainty of the electromagnetic/gravitational field results in vacuum fluctuations and prohibits the entanglement between two particles' states when causality is satisfied. We further demonstrate that complementarity holds when the particles do not get entangled. The uncertainty relation does not cause the entanglement between two particles' states, which guarantees complementarity.

DOI： 10.1103/PhysRevD.108.105019

Web of Science

Scopus

Publisher：Physical Review D  

No experimental evidence of the quantum nature of gravity has been observed yet and a realistic setup with improved sensitivity is eagerly awaited. We find two effects, which can substantially enhance the signal of gravity-induced quantum entanglement, by examining an optomechanical system in which two oscillators gravitationally couple and one composes an optical cavity. The first effect comes from a higher-order term of the optomechanical interaction and generates the signal at the first order of the gravitational coupling in contrast to the second-order results in previous works. The second effect is the resonance between the two oscillators. If their frequencies are close enough, the weak gravitational coupling effectively strengthens. Combining these two effects, the signal in the interference visibility could be amplified by a factor of 1024 for our optimistic parameters. The two effects would be useful in seeking feasible experimental setups to probe quantum gravity signals.

DOI： 10.1103/PhysRevD.108.106014

Web of Science

Scopus

Publisher：Physical Review A  

We consider how the reduced dynamics of an open quantum system coupled to an environment is realized in the Poincaré symmetry. The reduced dynamics is described by a dynamical map, which is a quantum channel (a completely positive and trace-preserving linear map) given by tracing out the environment from the total unitary evolution without initial correlations. We investigate the dynamical map invariant under the Poincaré transformations and discuss how the invariance constrains the form of the map. Based on the unitary representation theory of the Poincaré group, we develop a systematic way to construct the dynamical map with the Poincaré invariance. Using this method, we derive such a dynamical map for a spinless massive particle, and the conservation of the Poincaré generators is discussed. We then find the map with the Poincaré invariance and the four-momentum conservation. Further, we show that the conservation of the angular momentum and the boost operator makes the map of a spinless massive particle unitary.

DOI： 10.1103/PhysRevA.108.042217

Web of Science

Scopus

Publisher：Physical Review A  

Pendulums have long been used as force sensors due to their ultimately low dissipation (high-quality factor) characteristic. They are widely used in the measurement of the gravitational constant, detection of gravitational waves, and determination of ultralight dark matter. Furthermore, it is expected that the quantum nature of gravity will be demonstrated by performing quantum control for macroscopic pendulums. Recently, we have demonstrated that quantum entanglement between two pendulums can be generated using an optical spring [D. Miki, N. Matsumoto, A. Matsumura, T. Shichijo, Y. Sugiyama, K. Yamamoto, and N. Yamamoto, Phys. Rev. A 107, 032410 (2023)10.1103/PhysRevA.107.032410]; however, we have ignored that an optical spring can reduce the quality factor (Q factor) by applying normal-mode splitting between the pendulum and rotational modes possessing relatively high dissipation. Herein, we analyze a system composed of a cylinder suspended using a beam (a suspended mirror, i.e., a pendulum) and an optical spring to consider normal-mode splitting. The reduction in Q factor is determined only by the beam parameters: the ratio of the radius of the mirror to the length of the beam, and the ratio of the frequency of the rotational mode to the pendulum mode in the absence of cavity photons. In our analysis, we find that the reduction factor 4.38 is reproduced, which is consistent with the experimental result in Matsumoto et al. [N. Matsumoto, S. B. Cataño-Lopez, M. Sugawara, S. Suzuki, N. Abe, K. Komori, Y. Michimura, Y. Aso, and K. Edamatsu, Phys. Rev. Lett. 122, 071101 (2019)0031-900710.1103/PhysRevLett.122.071101]. Our analysis shows that low dissipation (high quality) can be reached using an optical spring for the realistic pendulum system considering the rotational degree of freedom.

DOI： 10.1103/PhysRevA.107.033515

Web of Science

Scopus

Publisher：Physical Review A  

This paper is aimed at investigating the feasibility of generating quantum conditional entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We consider the squeezing of the states of the mechanical common and the differential motions of the mirrors by the action of measuring the common and the differential output light beams in the Fabry-Pérot-Michelson interferometer. We carefully derive a covariance matrix for the mechanical mirrors in a steady state, employing the Kalman filtering problem with dissipative cavities. We demonstrate that Gaussian entanglement between the mechanical mirrors is generated when the states of the mechanical common and differential modes of the mirrors are squeezed with high purity in an asymmetric manner. Our results also show that quantum entanglement between 7-mg mirrors is achievable in the short term.

DOI： 10.1103/PhysRevA.107.032410

Web of Science

Scopus

Publisher：Physical Review D  

It has long been debated whether gravity should be quantized or not. Recently, the authors in [Sci. Rep. 6, 22777 (2016)SRCEC32045-232210.1038/srep22777; Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)PNASA60027-842410.1073/pnas.0813239106] discussed the inconsistency between causality and complementarity in a Gedankenexperiment involving the quantum superposition of massive/charged bodies, and Belenchia et al. [Phys. Rev. D 98, 126009 (2018)PRVDAQ2470-001010.1103/PhysRevD.98.126009; Int. J. Mod. Phys. D 28, 1943001 (2019)IMPDEO0218-271810.1142/S0218271819430016] resolved the inconsistency by requiring the quantum radiation and vacuum fluctuations of gravitational/electromagnetic field. Stimulated by their works, we reanalyze the consistency between the two physical properties, causality and complementarity, according to the quantum field theory. In this analysis, we consider a Gedankenexperiment inspired by [Sci. Rep. 6, 22777 (2016)SRCEC32045-232210.1038/srep22777; Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)PNASA60027-842410.1073/pnas.0813239106; Phys. Rev. D 98, 126009 (2018)PRVDAQ2470-001010.1103/PhysRevD.98.126009; Int. J. Mod. Phys. D 28, 1943001 (2019)IMPDEO0218-271810.1142/S0218271819430016], in which two charged particles coupled with a photon field are in a superposition of two trajectories. First, we observe that causality is satisfied by the retarded propagation of the photon field. Next, by introducing an inequality between visibility and which-path information, we show that the quantum radiation and vacuum fluctuations of the photon field ensure complementarity. We further find that the Robertson inequality associated with the photon field leads to the consistency between causality and complementarity in our Gedankenexperiment. Finally, we mention that a similar feature appears in the quantum field of gravity.

DOI： 10.1103/PhysRevD.106.125002

Web of Science

Scopus

Language：English   Publisher：Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  

CiNii Research

Publisher：Quantum  

We investigate the quantum nature of gravity in terms of the coherence of quantum objects. As a basic setting, we consider two gravitating objects each in a superposition state of two paths. The evolution of objects is described by the completely positive and trace-preserving (CPTP) map with a population-preserving property. This property reflects that the probability of objects being on each path is preserved. We use the `1-norm of coherence to quantify the coherence of objects. In the present paper, the quantum nature of gravity is characterized by an entangling map, which is a CPTP map with the capacity to create entanglement. We introduce the entangling-map witness as an observable to test whether a given map is entangling. We show that, whenever the gravitating objects initially have a finite amount of the `1-norm of coherence, the witness tests the entangling map due to gravity. Interestingly, we find that the witness can test such a quantum nature of gravity, even when the objects do not get entangled. This means that the coherence of gravitating objects always becomes the source of the entangling map due to gravity. We further discuss a decoherence effect and an experimental perspective in the present approach.

DOI： 10.22331/q-2022-10-11-832

Web of Science

Scopus

Publisher：Physical Review D  

The Bose-Marletto-Vedral experiment is a proposal for testing the quantum nature of gravity with entanglement due to Newtonian gravity. This proposal has stimulated controversy on how the entanglement due to Newtonian gravity is related to the essence of quantum gravity and the existence of gravitons. Motivated by this, we analyze the entanglement generation between two charged particles coupled to a photon field. We assume that each particle is in a superposition of two trajectories and that the photon field is initially in a coherent state. Based on covariant quantum electrodynamics, the formula for the entanglement negativity of the charged particles is derived for the first time. Adopting simple analytic trajectories of the particles, we demonstrate the entanglement between them. It is observed that the entanglement is suppressed by the decoherence due to the vacuum fluctuations of the photon field. We also find that the effect of quantum superposition of bremsstrahlung appears in the entanglement negativity formula. The similar structures between the gravity theory and electromagnetic theory suggests that a similar feature may be observed in the entanglement generation by quantum gravitational radiation.

DOI： 10.1103/PhysRevD.106.045009

Web of Science

Scopus

Publisher：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

Web of Science

Scopus

Publisher：Physical Review A  

We explore a general feature of the interaction mediated by the gravitational fields of spatially superposed masses. For this purpose, based on quantum information theory, we characterize the evolution of two particles each in a superposition state of paths. The evolution is assumed to be given by a completely positive trace-preserving (CPTP) map. We further assume that the probability of a particle being on each path is unchanged during the evolution. This property is called population preserving. We examine when a population-preserving CPTP map can create entanglement in terms of separable operations, which form a large class of local operations and classical communication (LOCC). In general, entanglement is not always generated by inseparable or non-LOCC operations, and one can consider a model of gravity described by an inseparable operation which does not create entanglement. However, we find that a population-preserving CPTP map is inseparable if and only if it can create entanglement. This means that the above model of gravity is incompatible with the possible evolution of spatially superposed masses.

DOI： 10.1103/PhysRevA.105.042425

Web of Science

Scopus

Publisher：Modern Physics Letters A  

Quantum coherence is one of the most striking features of quantum mechanics rooted in the superposition principle. Recently, it has been demonstrated that it is possible to harvest the quantum coherence from a coherent scalar field. In order to explore a new method of detecting axion dark matter, we consider a point-like Unruh-DeWitt detector coupled to the axion field and quantify a coherent measure of the detector. We show that the detector can harvest the quantum coherence from the axion dark matter. To be more precise, we consider a two-level electron system in an atom as the detector. In this case, we obtain the coherence measure C = 2.2 × 10-6γ(T/1s) where T and γ are an observation time and the Lorentz factor. At the same time, the axion mass ma we can probe is determined by the energy gap of the detector.

DOI： 10.1142/S0217732322500286

Web of Science

Scopus

Publisher：Physical Review D  

We develop an entanglement criterion with third- and fourth-order cumulants to detect the entanglement of non-Gaussian states. The efficiency of the entanglement criterion is investigated for gravitating mirrors in optomechanical systems. We show that the entangled regime of the mirrors is enlarged by the third- and fourth-order cumulants. We also discuss the limitations of the entanglement criterion for mirrors in a highly non-Gaussian state.

DOI： 10.1103/PhysRevD.105.026011

Web of Science

Scopus