Oscillatory dynamics and non-Markovian memory in dissipative quantum systems

Radiative decay of an emitter due to non-Markovian interactions with dissipating matter

It is known that the more tractable Markovian models of coupling suited for weak interactions may overestimate the Rabi frequency notably when applied to the strong-coupling regime. Here, a more significant consequence of the non-Markovian interaction between a photon emitter and dissipating matter such as resonant plasmonic nanoparticles is described. A large increase of radiative decay and a diminished non-radiative loss is shown, which unravels the origin of unexpected large enhancements of surface-enhanced-Raman-spectroscopy, as well as the anomalous enhancements of emission due to extremely small fully absorbing metal nanoparticles less than 10 nm in dimensions. We construct the mixture of pure states of the coupled emitter-nanoparticle system, unlike conventional methods that rely on the orthogonal modes of the nanoparticle alone.

Non-Markovian dynamics of a two-level system in the presence of hierarchical environments

Dynamics of an open system is vividly influenced by the structure of environments. This paper studies in detail the dynamics of a two-level atom in the presence of an overall environment composed of two hierarchies. The first hierarchy is just a single lossy cavity while the second hierarchy consists of a number of other lossy cavities. The atom is coupled directly to the first hierarchy but indirectly to the second one via the couplings between the two hierarchies. We show that even when the coupling between the atom and the first hierarchy is weak the atom's dynamics can become non-Markovian if the number of cavities in the second hierarchy or/and the coupling between the two hierarchies are large enough. We also analyze the case when the coupling between the atom and the first hierarchy is strong and show that the non-Markovian dynamics exhibits different patterns depending on both the number of cavities in the second hierarchy and the coupling between the two hierarchies.

Modeling the metastable dynamics of correlated structures

Metastable quantum dynamics of an asymmetric triangular cluster that is coupled to a reservoir is investigated. The dynamics is governed by bath-mediated transitions, which in part require a thermal activation process. The decay rate is controlled by tuning the excitation spectrum of the frustrated cluster. We use the master equation approach and construct transition operators in terms of many-body states. We analyze dynamics of observables and reveal metastability of an excited state and of a magnetically polarized ground state.

Chaos driven by interfering memory

The transmission of information can couple two entities of very different nature, one of them serving as a memory for the other. Here we study the situation in which information is stored in a wave field and serves as a memory that pilots the dynamics of a particle. Such a system can be implemented by a bouncing drop generating surface waves sustained by a parametric forcing. The motion of the resulting "walker" when confined in a harmonic potential well is generally disordered. Here we show that these trajectories correspond to chaotic regimes characterized by intermittent transitions between a discrete set of states. At any given time, the system is in one of these states characterized by a double quantization of size and angular momentum. A low dimensional intermittency determines their respective probabilities. They thus form an eigenstate basis of decomposition for what would be observed as a superposition of states if all measurements were intrusive.

A perturbative renormalization group approach to driven quantum systems

We use a perturbative momentum shell renormalization group (RG) approach to study the properties of a driven quantum system at zero temperature. To illustrate the technique, we consider a bosonic ϕ(4) theory with an arbitrary time dependent interaction parameter λ(t) = λ f(ω0t), where ω0 is the drive frequency and we derive the RG equations for the system using a Keldysh diagrammatic technique. We show that the scaling of ω0 is analogous to that of temperature for a system in thermal equilibrium and its presence provides a cutoff scale for the RG flow. We analyze the resultant RG equations, derive an analytical condition for such a drive to take the system out of the gaussian regime, and show that the onset of the non-gaussian regime occurs concomitantly with the appearance of non-perturbative mode coupling terms in the effective action of the system. We supplement the above-mentioned results by obtaining them from equations of motion of the bosons and discuss their significance for systems near critical points described by time-dependent Landau-Ginzburg theories.

Dissipative dynamics of a driven quantum spin coupled to a bath of ultracold fermions

We explore the dynamics and the steady state of a driven quantum spin coupled to a bath of fermions, which can be realized with a strongly imbalanced mixture of ultracold atoms using currently available experimental tools. Radio-frequency driving can be used to induce tunneling between the spin states. The Rabi oscillations are modified due to the coupling of the quantum spin to the environment, which causes frequency renormalization and damping. The spin-bath coupling can be widely tuned by adjusting the scattering length through a Feshbach resonance. When the scattering potential creates a bound state, by tuning the driving frequency it is possible to populate either the ground state, in which the bound state is filled, or a metastable state in which the bound state is empty. In the latter case, we predict an emergent inversion of the steady-state magnetization. Our work shows that different regimes of dissipative dynamics can be explored with a quantum spin coupled to a bath of ultracold fermions.