2023-03-22 15:00  P7F/Online

Quantum Fluctuations in Gravity: Gravitational Cat State, Graviton Noise and Stochastic Gravity

Prof. Bei-Lok Bernard Hu

The intersections or unions of gravity (G), quantum (Q) fields and quantum information (I) have sparked many interesting new directions of research in fundamental physics in the last decade, black hole information and wormhole physics are amongst the better known examples. In this talk I want to present two classes of low energy quantum fluctuation phenomena amenable to earth-environment laboratory or outer-space tests.  One is gravitational cat state, representing quantum entanglement in gravitating systems; the other, graviton noise, signifying the quantum nature of perturbative gravity.  In a quantum description of matter a single motionless massive particle can in principle be in a superposition state of two spatially-separated locations. This superposition state in gravity, or gravitational cat state, would lead to fluctuations in the Newtonian force exerted on a nearby test particle [1]. The centerpiece is the energy density correlation, corresponding to the noise kernel in stochastic semiclassical gravity theory [2], evaluated in the weak-field nonrelativistic limit.  It may come as a surprise that such a theory originally developed to describe quantum field effects in black holes and the early universe is actually needed for the description of gravitational entanglement in laboratory settings. For the graviton noise problem [3,4], we [5] consider the effects of gravitons and their fluctuations on the dynamics of two masses using the Feynman-Vernon influence functional formalism. The Hadamard function of the gravitons yields the noise kernel acting as a stochastic tensorial force in a Langevin equation governing the motion of the separation of the two masses. The fluctuations of the separation due to the graviton noise are then solved for various quantum states including the Minkowski vacuum, thermal, coherent and squeezed states, generalizing previous results of Parikh et al [3]. We end with a discussion of what would constitute a demonstration of the quantum nature of perturbative gravity, and a comment on the prospect of detecting these fluctuations in primordial gravitons using interferometers with long baselines in deep space experiments.

 

[1] Charis Anastopoulos and Bei-Lok Hu, “Probing a Gravitational Cat State” Class. Quant. Grav. 32 (2015) 165022 [arXiv:1504.03103] M. Derakhshani, C. Anastopoulos, B. L. Hu, [arXiv:1603.04430]
[2] B. L. Hu and E. Verdaguer, Semiclassical and Stochastic Gravity -- Quantum Field Effects on Curved Spacetime (Cambridge University Press 2020). “Stochastic gravity: Theory and Applications”, in Living Reviews in Relativity 11 (2008) 3 [arXiv:0802.0658]
[3] M. Parikh, F. Wilczek and G. Zahariade, Quantum Mechanics of Gravitational Waves, Phys. Rev. Lett. 127, 081602 (2021); Signature of the quantization of gravity at of gravitational wave detectors, Phys. Rev. D 104, 046021 (2021)
[4] S. Kanno, J. Soda, and J. Tokuda, Indirect detection of gravitons through quantum entanglement, Phys. Rev. D 104, 083516 (2021).
[5] H. T. Cho and B. L. Hu, Quantum noise of gravitons and stochastic force on geodesic separation, Phys. Rev. D 105, 086004 (2022). Graviton Noise on Tidal Forces and Geodesic Congruence, Phys. Rev. D107, (2023) [arXiv:2301.06325]