Control of a single-particle localization in open quantum systems

Abstract

We investigate the possibility to control localization properties of the asymptotic state of an open quantum system with a tunable synthetic dissipation. The control mechanism relies on the matching between properties of dissipative operators, acting on neighboring sites and specified by a single control parameter, and the spatial phase structure of eigenstates of the system Hamiltonian. As a result, the latter coincide (or near coincide) with the dark states of the operators. In a disorder-free Hamiltonian with a flat band, one can either obtain a localized asymptotic state or populate whole flat and/or dispersive bands, depending on the value of the control parameter. In a disordered Anderson system, the asymptotic state can be localized anywhere in the spectrum of the Hamiltonian. The dissipative control is robust with respect to an additional local dephasing.

Quantum jumps on Anderson attractors

“…The switch from diffusive to ballistic propagation for non-zero α can be understood as an interplay between disorder and dissipation. As we already pointed it out, dissipation selects Anderson modes from a particular part of the spectrum, and they borrow spatial phase properties of the zero-disorder plain wave eigenstates, with wave numbers 16,32 k ≈ α. Overlapping in space (Figs. 1 and 2), the exponentially localized modes interact due to dissipative coupling.…”

“…Second, it was shown that a one-dimensional quantum system with a Hamiltonian exhibiting Anderson localization can be driven into a steady state, an "Anderson attractor", which retains localization properties 15 . Such an asymptotic state can be engineered with a set of local dissipative operators [17][18][19][20] , the corresponding mechanism is based on the robust spatial phase-structure of Anderson modes 16 .…”

“…which produce non-trivial asymptotic states featuring localization, coined "Anderson attractors" 15,16 . The dissipators are parametrized by 30 α, making them phaseselective.…”

“…. N/2 is a dark state of the dissipators for α = k. As Anderson modes inherit spatial phase properties from the seeding plain waves 32 , asymptotic states of the open disordered lattice are dominated by a respective part of the Anderson spectrum, controlled by 15,16 α.…”

Prominent interference peaks in the dephasing Anderson model

“…Decoherence will generally allow initially localized states to expand as destructive interference is lifted [4,5]. The details of such dynamics [6] and their stationary solutions [7,8] depend on the specific properties of the environment coupling, as encoded, for example, in a Lindblad operator. Quite generically, decoherence rates are particularly high for states that can easily be distinguished by the environment, whereas they tend to be low for states that can hardly be distinguished by the environment.…”