Dynamics of a Quantum Damped Oscillator with Relaxation

Robin Heveling, Jiaozi Wang, Christian Bartsch +1 more

Abstract There is an abundance of evidence that some relaxation dynamics, e.g., exponential decays, are much more common in nature than others. Recently, there have been attempts to trace this dominance back to a certain stability of the prevalent dynamics versus generic Hamiltonian perturbations. In the paper at hand, we tackle this stability issue from yet another angle, namely in the framework of the recursion method. We investigate the behavior of various relaxation dynamics with respect to alterations of the so-called Lanczos coefficients. All considered scenarios are set up in order to comply with the ‘universal operator growth hypothesis’. Our numerical experiments suggest the existence of stability in a larger class of relaxation dynamics consisting of exponentially damped oscillations. Further, we propose a criterion to identify ‘pathological’ perturbations that lead to uncommon dynamics.

A. L. De Brito, Fabio Cabral Carvalho, B. Baseia +1 more

Manel Bosch Aguilera, Raphaël Bouganne, Alexandre Dareau +4 more

We study the dynamics of a two-component Bose-Einstein condensate (BEC) of 174 Yb atoms coherently driven on a narrow optical transition. The excitation transfers the BEC to a superposition of states with different internal and momentum quantum numbers. We observe a crossover with decreasing driving strength between a regime of damped oscillations, where coherent driving prevails, and an incoherent regime, where relaxation takes over. Several relaxation mechanisms are involved: inelastic losses involving two excited atoms, leading to a non-exponential decay of populations; Doppler broadening due to the finite momentum width of the BEC and inhomogeneous elastic interactions, both leading to dephasing and to damping of the oscillations. We compare our observations to a two-component Gross-Pitaevskii (GP) model that fully includes these effects. For small or moderate densities, the damping of the oscillations is mostly due to Doppler broadening. In this regime, we find excellent agreement between the model and the experimental results. For higher densities, the role of interactions increases and so does the damping rate of the oscillations. The damping in the GP model is less pronounced than in the experiment, possibly a hint for many-body effects not captured by the mean-field description.

Dariusz Chruściński, Jacek Jurkowski

Anatoly Yu. Smirnov

The dissipative dynamics of a quantum bit driven by a strong resonant field and interacting with a heat bath is investigated. We derive generalized Bloch equations and find modifications of the qubit's damping rates caused by Rabi oscillations. The nonequilibrium decoherence and relaxation of a phase qubit inductively coupled to a resonant tank circuit is considered as an illustration of the general results.

Boris Ya Zel'dovich, A. M. Perelomov, В. С. Попов