Open quantum dynamics induced by light scalar fields
  We consider the impact of a weakly coupled environment comprising a light
scalar field on the open dynamics of a quantum probe field, resulting in a
master equation for the probe field that features corrections to the coherent
dynamics, as well as decoherence and momentum diffusion. The light scalar is
assumed to couple to matter either through a nonminimal coupling to gravity or,
equivalently, through a Higgs portal. Motivated by applications to experiments
such as atom interferometry, we assume that the probe field can be initialized,
by means of external driving, in a state that is not an eigenstate of the light
scalar-field--probe system, and we derive the master equation for
single-particle matrix elements of the reduced density operator of a toy model.
We comment on the possibilities for experimental detection and the related
challenges, and highlight possible pathways for further improvements. This
derivation of the master equation requires techniques of non-equilibrium
quantum field theory, including the Feynman-Vernon influence functional and
thermo field dynamics, used to motivate a method of
Lehmann-Symanzik-Zimmermann-like reduction. In order to obtain
cutoff-independent results for the probe-field dynamics, we find that it is
necessary to use a time-dependent renormalization procedure. Specifically, we
show that non-Markovian effects following a quench, namely the violation of
time-translational invariance due to finite-time effects, lead to a
time-dependent modulation of the usual vacuum counterterms.
