We consider a quantum harmonic oscillator coupled with a graviton bath. We discuss the loss of coherence in the matter sector due to the matter-graviton vertex interaction, which leads to a loss of coherence provided that the matter-wave system is allowed to gravitons by the kinematics. Working in the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order ∼O(G) and ∼O(c−2) . We find that the decoherence rate is proportional to the cube of the harmonic trapping frequency and vanishes for a free particle, as expected for a system without a mass quadrupole. Furthermore, our quantum model of graviton emission recovers the known classical formula for gravitational radiation from a classical harmonic oscillator for coherent states with a large occupation number. In addition, we find that the quantum harmonic oscillator eventually settles in a steady state with of the ground and first excited states. While classical emission of gravitational waves would make the harmonic system loose all of its energy, our quantum field theory model does not allow the number states |1⟩ and |0⟩ to decay via graviton emission. In particular, the superposition of number states 12[|0⟩+|1⟩] is a steady state and never decoheres. Published by the American Physical Society 2024
We consider a quantum harmonic oscillator coupled with a graviton bath. We discuss the loss of coherence in the matter sector due to the matter-graviton vertex interaction, which leads to a loss of coherence provided that the matter-wave system is allowed to gravitons by the kinematics. Working in the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order ∼O(G) and ∼O(c−2) . We find that the decoherence rate is proportional to the cube of the harmonic trapping frequency and vanishes for a free particle, as expected for a system without a mass quadrupole. Furthermore, our quantum model of graviton emission recovers the known classical formula for gravitational radiation from a classical harmonic oscillator for coherent states with a large occupation number. In addition, we find that the quantum harmonic oscillator eventually settles in a steady state with of the ground and first excited states. While classical emission of gravitational waves would make the harmonic system loose all of its energy, our quantum field theory model does not allow the number states |1⟩ and |0⟩ to decay via graviton emission. In particular, the superposition of number states 12[|0⟩+|1⟩] is a steady state and never decoheres. Published by the American Physical Society 2024
We derive and investigate the reduced dynamics of a nonrelativistic quantum matter system interacting with quantized gravitational waves. Because gravitational radiation couples tidally to the mass quadrupole moment, we emphasize that the leading interaction is quadratic in the mechanical displacement. Rather than treating it as a complication to be removed by linearization, we retain this full quadratic dependence, which gives rise to two-phonon rather single-phonon processes typical in dipolar interactions. We clarify its relation to the effective linear coupling that often appears in optomechanical literature, but which conceals the delicate quantum signatures of the full quadratic coupling. Using the Born-Markov and secular approximations, we microscopically derive Lindblad master equations for the matter dynamics induced by graviton baths in multi-mode vacuum, coherent, number, thermal, and squeezed states. We treat the ultraviolet-divergent Lamb-shift Hamiltonian by an explicit renormalization procedure, with the mechanical frequency identified as the physical frequency. Remarkably, owing to the nature of the interaction, the matter Hilbert space decomposes into even- and odd-parity sectors for all bath states considered. For a coherent graviton bath, the decoherence is identical to that of the vacuum, while the bath one-point function produces a coherent-shift Hamiltonian that exactly reproduces the tidal interaction with a classical gravitational wave. For a vacuum graviton bath, we recover the coherence protection between the two lowest mechanical number states, while number and thermal graviton baths remove this protection and enhance decoherence, although the effect remains small for realistic parameters. By contrast, a squeezed graviton bath enlarges the coupled coherence structure, and gives rise to a novel, coherence-protected sector spanned by dressed dark states.
In this paper, we study the coherence/decoherence of a quantum harmonic oscillator in anti-de Sitter (AdS) spacetime by quantising the graviton in a curved background with a nontrivial boundary condition. In the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order in G and 1/omega^2, where omega is related to the trapped frequency of the harmonic oscillator. We will proceed with a semi-Markovian analysis to compute the Lindbladian equation and estimate the decoherence rate and selection rules at the leading order, which come in two kinds: one responsible for the local interaction between matter and graviton, and the other related to the AdS global curvature. The latter determines the recoherence of the quantum system for a certain choice of the trapped harmonic oscillator's frequency and the global curvature. We also demonstrate that we recover the flat spacetime limit by taking appropriate approximations.
In this paper we consider non-relativistic matter-wave interferometer coupled with a quantum graviton bath − and discuss the loss of coherence in the matter sector due to the matter-graviton vertex. First of all, such a process does not lead to any entanglement, but nonetheless the on-shell scattering diagram can lead to loss of coherence as we will show. Importantly, we will show that graviton emission is the only one-vertex Feynman-diagram ∼G which is consistent with the conservation of energy and momentum at the dominant order ∼O(c−2). We will find that the resulting dephasing is extremely mild and hardly places any constraints on matter-wave interferometers in the mesoscopic regime. In particular, the show that the corresponding loss of coherence in the recently proposed experiment which would test quantum aspects of graviton − via entanglement of two matter-wave interferometers − is completely negligible.
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.
Some collapse models proposed that gravitational effects cause the instability of mass distribution superpositions, leading to wave function collapse. In this paper, we utilize the quantum Boltzmann equation (QBE) to analyze the behavior of a fermion in a spatial superposition under graviton emission. We introduce a quantitative measure that links the stability of the superposition to the spatial separation, particle mass, and gravitational coupling. By examining the collision term in the QBE, we derive the decoherence rate and show how it depends on these parameters. Our results provide a detailed framework for understanding gravity induced decoherence, bridging the gap between quantum field theory and collapse models. We also discuss the implications of these findings for experimental tests of gravitationally induced wave function collapse and the broader class of collapse models known as dissipative continuous spontaneous localization (CSL) model.
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.