Fast Driving of a Particle in Two Dimensions without Final Excitation.

Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.

Thermalization with detailed-balanced two-site Lindblad dissipators.

The use of two-site Lindblad dissipators to generate thermal states and study heat transport was raised to prominence by Prosen and Znidaric [J. Stat. Mech. (2009) P020351742-546810.1088/1742-5468/2009/02/P02035]. Here we propose a variant of this method based on detailed balance of internal levels of the two-site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single- and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature, the steady state approaches closely a thermal state, with a relative error below 1% for the inverse temperature estimated from different observables.