Hot accelerated qubits: decoherence, thermalization, secular growth and reliable late-time predictions

Abstract

We compute how an accelerating qubit coupled to a scalar field -i.e. an Unruh-DeWitt detector -evolves in flat space, with an emphasis on its late-time behaviour. When calculable, the qubit evolves towards a thermal state for a field prepared in the Minkowski vacuum, with the approach to this limit controlled by two different time-scales. For a free field we compute both of these as functions of the difference between qubit energy levels, the dimensionless qubit/field coupling constant, the scalar field mass and the qubit's proper acceleration. Both time-scales differ from the Candelas-Deutsch-Sciama transition rate traditionally computed for Unruh-DeWitt detectors, which we show describes the qubit's early-time evolution away from the vacuum rather than its late-time approach to equilibrium. For small enough couplings and sufficiently late times the evolution is Markovian and described by a Lindblad equation, which we derive in detail from first principles as a special instance of Open EFT methods designed to handle a breakdown of late-time perturbative predictions due to the presence of secular growth. We show how this growth is resummed in this example to give reliable information about late-time evolution including both qubit/field interactions and field self-interactions. By allowing very explicit treatment, the qubit/field system allows a systematic assessment of the approximations needed when exploring late-time evolution, in a way that lends itself to gravitational applications. It also allows a comparison of these approximations with those -e.g. the 'rotating-wave' approximation -widely made in the open-system literature (which is aimed more at atomic transitions and lasers).

Hot cosmic qubits: late-time de Sitter evolution and critical slowing down

“…We here apply open-system tools to a similarly simple late-time question: what happens to such a qubit (again coupled to a scalar field) moving for very long times along a co-moving trajectory in de Sitter space. We again identify the relevant master equation for differential qubit evolution once the field is integrated out, and again find that a Markovian approximation works at sufficiently late times, asymptotically approaching a thermal state in much the same manner as in [21]. de Sitter space brings an important complication, however: the length of time required for this Markovian limit to apply grows like an inverse power of the scalar mass if this mass is sufficiently small.…”

“…This section reviews for later use some basic properties of de Sitter space, with details of the qubit/field system to be studied. The section then closes with a statement -following [21] -of the Nakajima-Zwanzig equation that governs qubit evolution once the scalar field is integrated out.…”

“…To this field we couple a qubit, following the construction used in [21]. The result is an Unruh-DeWitt detector coupled to a scalar field, along the lines of that first introduced in [22,23].…”

“…They thereby promise controlled and reliable approximations for late-time behaviour that straight-up perturbative methods cannot. This work accompanies a companion paper [21], which uses these tools to track the late-time evolution of an Unruh-DeWitt detector [22,23]: a simple two-level system (or qubit) as it uniformly accelerates in flat space while coupled to a simple quantum scalar field (prepared in its Minkowski vacuum). Such a simple system allows these open-system tools to be explored in a very concrete and explicit way (see also [24][25][26][27][28][29][30][31][32][33][34][35]).…”

“…Ref. [21] treats the field as an environment and integrates it out to set up the Nakajima-Zwanzig equation [36,37] describing its perturbative effects for the qubit. This is an integro-differential equation that is difficult to solve, but which simplifies at late times under certain assumptions to give an approximate late-time Markovian evolution.…”