Abstract
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol for the fast thermalization of a quantum oscillator.
Highlights
We provide details to establish the equivalence of the different master equations for the fast thermalization of a quantum oscillator
The thermal state of a harmonic oscillator is known to be described by a Gaussian density matrix, (x, x, t)= x| (t)|x =Nte−At(x2+x 2)−2Ctxx, (52)
The dissipator admits the operator form of the dissipator given in the main text, Eq (41)
Summary
N and can be recast as a Liouville-von Neumann equation, ∂t (t) = −i[H1(t), (t)] (with = 1), whenever the dynamics is generated by the Hamiltonian. CD assumes that |nt are the eigenstates of a reference system H0(t) that can be controlled by the auxiliary field H1(t) so that the full dynamics is generated by H0(t) + H1(t). Where Z0(t) = Tr[e−βH0(t)] denotes the partition function, and β is the inverse temperature (assuming kB = 1). With this definition, the spectral decomposition of the reference Hamiltonian reads.
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