Gravity-induced decoherence has been discussed in recent years both theoretically and experimentally. Neighboring papers in the archive have already examined weak gravitational influence on quantum superpositions, quantum clocks as a test of the equivalence principle, and gravitational noise erasing quantum entanglement. This article continues that line but shifts the focus to photons as the system rather than a scalar field, and does so in a formalism suitable for future use in loop quantum gravity.
The authors formulate the classical Maxwell model coupled to linearized gravity in Ashtekar-Barbero variables and in the post-Minkowskian approximation. Then, within the relational formalism, dynamical reference fields (clocks) are chosen for all constraints, including the photon's U(1) gauge constraint. Combining the observable map with the dual map makes it possible to construct Dirac observables that, to linear order, coincide with the transverse components of the photon field and the symmetric transverse traceless degrees of freedom of gravitational waves. After Fock quantization of the reduced system, a second-order TCL master equation is derived.
A master equation is obtained for photons interacting with a thermal gravitational environment. It contains unitary evolution with a Hamiltonian that includes free parts, a true interaction, and a gravity-induced self-interaction, plus a dissipator with time-dependent coefficients. The structure of the equation agrees with earlier results for a scalar field and with a model of photons in ADM variables, but here the Markovian and rotating-wave approximations are not applied, which leaves the equation in a more general form. Key numbers: the temperature of the thermal gravitational background is taken to be 0.9 K, and the coupling is characterized by the gravitational constant κ=16πG_N.
The work stands out from its neighbors in that it is the first to derive a master equation for photons in Ashtekar-Barbero variables using relational clocks rather than gauge fixing. This makes it possible to obtain Dirac observables directly as transverse degrees of freedom, without manually introducing projectors. Such an approach opens the possibility of comparison with quantization inspired by loop quantum gravity and of testing how the choice of quantization affects decoherence.
The model can be extended to fermions, which would allow it to be linked to phenomenological models of neutrino decoherence. There are also plans to apply renormalization methods developed for a scalar field and to study the one-particle sector of the photon. In the longer term, LQG-like quantization might be applied to the gravitational environment.
The results will influence the theory of gravitational decoherence and quantum field theory in curved spacetime, as well as the interpretation of quantum information experiments in the presence of gravity.
The next step will be to renormalize the master equation and study the dynamics of a one-photon state, as well as to build a similar model for fermions.
For the theory of open quantum systems, the question of whether the Markovian approximation is applicable in relativistic field models with gravity remains open. This work keeps the time-dependent coefficients, which will make it possible in the future to test the conditions for that applicability.
In cosmological models the temperature of the thermal gravitational background is estimated at 0.9 K, only slightly above the temperature of the cosmic microwave background.