Asymptotic Floquet states of a periodically driven spin-boson system in the nonperturbative coupling regime

Superradiant Quantum Phase Transition for an Exactly Solvable Two-Qubit Spin-Boson Model

A spin-boson-like model with two interacting qubits is analysed. The model turns out to be exactly solvable since it is characterized by the exchange symmetry between the two spins. The explicit expressions of eigenstates and eigenenergies make it possible to analytically unveil the occurrence of first-order quantum phase transitions. The latter are physically relevant since they are characterized by abrupt changes in the two-spin subsystem concurrence, in the net spin magnetization and in the mean photon number.

Open Quantum System Response from the Hierarchy of Pure States

The spectral properties of a quantum system are essential when probing theoretical predictions against experimental data. For an open quantum system strongly interacting with its environment, spectral features are challenging to calculate. Here we demonstrate that the stochastic Hierarchy of Pure States (HOPS) approach is well suited to calculate the response of an open quantum system to a, possibly strong, coherent probe driving. For weak driving, where Kubo's linear response theory is applicable, it turns out that the HOPS method is highly efficient since fluctuations inherent to the stochastic dynamics cancel for the response function and, thus, allow us to obtain the susceptibility easily. Our results are in agreement with experimental data for a strongly damped spin system showing that the transition from oscillatory to overdamped motion is also reflected by the transmission spectrum. As a further application we demonstrate that the susceptibility, quantifying the amplitude of the response, as a function of temperature exhibits a maximum which is the hallmark of stochastic resonance. Beyond the linear regime, the exact open system dynamics shows the asymptotic Floquet state. We use the topic of probe driving and response to present the HOPS approach in a novel and self-contained way. This includes the importance sampling scheme which yields the nonlinear HOPS as well as the stochastic treatment of a thermal initial environmental state within the zero temperature formalism. Special attention is given to the exponential representation of the algebraic Ohmic bath correlation function and the truncation condition for the hierarchy.

Application of Floquet theory to dynamical systems with memory

We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with infinite memory, i.e., a dependence on the whole previous history. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.

Discontinuities in Driven Spin-Boson Systems due to Coherent Destruction of Tunneling: Breakdown of the Floquet-Gibbs Distribution

If an open quantum system is periodically driven with high frequency and the driving commutes with the system-bath coupling operator, it is known that the system approaches a Floquet-Gibbs state, a generalization of Gibbs states to periodically driven systems. Here, we investigate the stationary state of an ac-driven system when the driving and dissipation are noncommutative. Then, the resulting stationary state does not obey the Floquet-Gibbs distribution, and the system dynamics is determined by inelastic scattering processes of the driving field. Based on the Floquet-Redfield formalism, we show that the probability distribution can exhibit population inversion and discontinuities, i.e., jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as intensity jumps in the emission into the bath.