Open quantum dynamics induced by light scalar fields

Abstract

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 timedependent modulation of the usual vacuum counterterms.

Influence functionals, decoherence and conformally coupled scalars

“…Our starting point is the reduced density functional -the matrix element of the density operator in the basis of field eigenstates -of the 'atom' system (presented here in a simplified notation, cf. the full time-dependence and functional delta functions that appear in reference [32])…”

“…Inserting the explicit form of the influence-functional action for the model of section 2 (see reference [32]) into equation (32), we obtain the master equation…”

“…We recognize the first term on the right-hand side of equation (33) as the free-phase evolution, the remaining terms of the first and second lines as tadpole self-energy insertions, and the terms of the third to seventh lines as the contributions from the one-loop bubble diagram. The final line contains a disconnected vacuum diagram that we omit hereafter; for further details, see reference [32]. The self-energies of the second to fifth lines contain quadratic and logarithmic divergences.…”

“…Noticing, however, that all but the first of the self-energy insertions vanish in the limit t → 0, it follows that the contributions from any counterterms must vanish in the same limit. As a result, the renormalization procedure must be modified to reflect the fact that the external switching on and off of the interactions leads to violation of both time-translational invariance and Lorentz invariance, as described in detail in reference [32].…”

“…The fifth force can therefore be suppressed by dynamically modifying the mass M (X), as in the chameleon mechanism [15,16]; the coupling function A(X), as in the symmetron mechanism [17,18] (for related models, see references [19,20,21,22,23,24,25]), or the kinetic structure Z(X)c 2 s (X), as in the Vainshtein [26] mechanism (see also references [27,28,29,30,31]). In this note, we consider the impact of an environment composed of a light, screened scalar field on a probe system, reporting the results of reference [32]. Proceeding from first principles by means of the Feynman-Vernon influence functional [33] (see also reference [34]), we derive the quantum master equation for the reduced density matrix of a toy 'atomic' system (having in mind an atom-interferometry experiment).…”