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arXiv:2309.07236 · Physical review. D/Physical review. D.

Open quantum system approach to the gravitational decoherence of spin- 1/2 particles

M. Sharifian, Moslem Zarei, Mehdi Abdi, N. Bartolo, S. Matarrese

Published Feb 8, 2024• 17 citations
arXivHTMLPDF

Abstract

This paper investigates the decoherence effect resulting from the interaction of squeezed gravitational waves with a system of massive particles in spatial superposition. This paper investigates the decoherence effect resulting from the interaction of squeezed gravitational waves with a system of massive particles in spatial superposition. We first employ the open quantum system approach to obtain the established decoherence in a spatial superposition of massive objects induced by squeezed gravitational waves. Subsequently, we focus on the spin-$1/2$ particle system, and our analysis reveals that the decoherence rate depends on both the squeezing strength and the squeezing angle of the gravitational waves. Our results demonstrate that squeezed gravitational waves with squeezing strengths of ${r}_{p}\ensuremath{\ge}1.2$ and a squeezing angle of ${\ensuremath{\varphi}}_{p}=\ensuremath{\pi}/2$ can induce a 1% decoherence within 1 s free falling of a cloud of spin-$1/2$ particles. This investigation sheds light on the relationship between squeezed gravitational waves and the coherence of spatial superposition states in systems of massive particles and their spin. The dependence of decoherence on squeezing strength and, in the case of spin-$1/2$ particles, on the squeezing angle paves the way for further exploration and understanding of the quantum-gravity connection. We suggest that such an experimental setup could also be employed to eventually investigate the level of squeezing effect (and hence quantum-related properties) of gravitational waves produced in the early universe from inflation.

DOI
10.1103/physrevd.109.043510

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This paper investigates the decoherence effect resulting from the interaction of squeezed gravitational waves with a system of massive particles in spatial superposition. This paper investigates the decoherence effect resulting from the interaction of squeezed gravitational waves with a system of massive particles in spatial superposition. We first employ the open quantum system approach to obtain the established decoherence in a spatial superposition of massive objects induced by squeezed gravitational waves. Subsequently, we focus on the spin-1/21/21/2 particle system, and our analysis reveals that the decoherence rate depends on both the squeezing strength and the squeezing angle of the gravitational waves. Our results demonstrate that squeezed gravitational waves with squeezing strengths of rp\ensuremath≥1.2{r}_{p}\ensuremath{\ge}1.2rp​\ensuremath≥1.2 and a squeezing angle of \ensuremathφp=\ensuremathπ/2{\ensuremath{\varphi}}_{p}=\ensuremath{\pi}/2\ensuremathφp​=\ensuremathπ/2 can induce a 1% decoherence within 1 s free falling of a cloud of spin-1/21/21/2 particles. This investigation sheds light on the relationship between squeezed gravitational waves and the coherence of spatial superposition states in systems of massive particles and their spin. The dependence of decoherence on squeezing strength and, in the case of spin-1/21/21/2 particles, on the squeezing angle paves the way for further exploration and understanding of the quantum-gravity connection. We suggest that such an experimental setup could also be employed to eventually investigate the level of squeezing effect (and hence quantum-related properties) of gravitational waves produced in the early universe from inflation.
We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of large masses (to be quantified) would be prevented by their coupling to the gravitational field. We discuss how to experimentally discriminate between decoherence due to entanglement, decoherence due to classical dephasig as well as a genuine collapse of quantum superpositions (if such a process exists at all).
We consider the effect of gravity on extended quantum systems (EQS) in the low energy regime. We model the gravitational effect due to a nearby source mass as a redshift in the internal Hamiltonian of the EQS. Due to the dependence of the energy spectrum of the EQS on the position of the massive particle (via the redshift) at zero temperature, our model predicts gravitational decoherence of the massive particle in the position basis. We show that the decoherence effect is multiplicative, in the sense that the increase in number of EQS gravitationally interacting with a single massive particle leads to an increase in its decoherence. If the considered model of gravitational redshift holds alongside the linearity of quantum mechanics (as an appropriate limit of an accepted theory for coupling quantum matter with gravity) to allow for a spatial superposition of the source mass, we propose that the same methodology can be applied to continuous fields, which are essentially EQS. This could provide an upper limit on the number of undiscovered fields by observing coherent superpositions of masses, e.g., in a matter wave interferometer. Besides, by taking a spin chain as a toy model of an EQS, we analyse the dependence of the new effect on relevant system parameters and identify the number of independent spin chains that can cause a detectable effect.
We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.
Abstract Understanding the interplay between quantum mechanical systems and gravity is a crucial step towards unifying these two fundamental ideas. Recent theoretical developments have explored how global properties of spacetime would cause a quantum spatial superposition to lose coherence. In particular, this loss of coherence is closely related to the memory effect, which is a prominent feature of gravitational radiation. In this work, we explore how a burst of gravitational radiation from a far-away source would decohere a quantum superposition. We identify the individual contributions to the decoherence from the memory and oscillatory components of the gravitational wave source, corresponding to hard and soft graviton emissions, respectively. In general, the memory contributions dominate, while the oscillatory component of the decoherence is strongly dependent on the phase of the burst when it is switched off. This work demonstrates how quantum systems can lose coherence from interactions with a classical gravitational field. We also comment on the electromagnetic analogue of this effect and discuss its correspondence to the gravitational case.
This thesis investigates the role of gravitational waves in quantum systems, motivated by advances in our understanding of the quantum–gravity interface and efforts to identify experimental signatures of quantum gravity. It focuses on gravitational decoherence and the interplay between internal energy and centre-of-mass dynamics in composite quantum systems, complemented by a study of internal-energy effects in gravitationally mediated entanglement. First, we develop relativistic Hamiltonian formulations showing that changes in a composite system’s internal energy increase its gravitational mass rather than alter its momentum. This removes earlier ad hoc arguments for eliminating “anomalous friction forces”. We show that gravitational waves act as a dynamical background, inducing curvature-dependent forces that modify total momentum. Second, we revisit a thought experiment in which tensions between causality and complementarity arise. We identify a scenario in which these tensions follow from energy–mass equivalence, making the effect specific to gravitational interactions. In a gravitationally mediated entanglement experiment using Newtonian gravity as mediator, we investigate whether decohering gravitational radiation can resolve the apparent conflict. Finally, we build upon a model of gravitational decoherence consistent with general relativity. This requires deriving a higher-derivative quantum Langevin equation and master equation. The resulting dynamics show that gravitational interactions induce decoherence in the canonical momentum basis of the quadrupole and generate acceleration- and jerk-dependent corrections absent in electrodynamics. Together, these results show that weak-field gravitational interactions leave distinct relativistic imprints on quantum systems, including effects unique to gravitational waves, providing potential signatures that distinguish gravity from other interactions.
The fact that gravitational environments cannot be shielded (since gravity is universal) makes them of great theoretical interest to decoherence mechanisms and to the quantum-to-classical transition. While past results seemed to indicate that graviton-induced decoherence of spatial superpositions happens only for macroscopic systems, recently it was shown that this mechanism can be enhanced through the system's own dynamical internal structure. In this work, we extend this analysis by including the interaction with a classical Newtonian potential. We show that, although the graviton bath alone dominates the mechanism for short times compared to a timescale established by the size of the quantum spatial superposition, the interaction between the gravitons and the internal degrees of freedom of the system renders decoherence inevitable in the long-time limit, even for microscopic masses. We also show that this mechanism is slightly slowed down by the interplay with the classical Newtonian potential, which, for systems without dynamical internal degrees of freedom, can even lead to recoherence-like behaviour, at least in principle.