Abstract:
We have studied the dissipative dynamics of a driven electronic spin trapped in a quantum dot. We consider the dissipative mechanism as due to the indirect coupling of the electronic spin to acoustic phonons via the spin-orbit/electron-phonon couplings. Using an effective spectral function of the dissipative phonon bath, we evaluated the expectation values of the spin components through the Bloch-Redfield theory. We show that due to a sharp bath resonance present in the effective spectral function, with typical energy much smaller than the electronic confinement energy, the dissipative spin has a rich dynamical behavior that helps us to determine some features of the spin-bath coupling. We also quantify the effects produced by the sharp bath resonance, and thus indicate the best regimes of operation in order to achieve the longest relaxation times for the spin.

Abstract:
We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. Starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary non-equilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest non-equilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems - underlying particle number conservation and detailed balance, respectively - is identified as the root of this new non-equilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.

Abstract:
We investigate the dynamical properties of low dimensional systems, driven by external noise sources. Specifically we consider a resistively shunted Josephson junction and a one dimensional quantum liquid in a commensurate lattice potential, subject to $1/f$ noise. In absence of nonlinear coupling, we have shown previously that these systems establish a non-equilibrium critical steady state [Nature Phys. 6, 806 (2010)]. Here we use this state as the basis for a controlled renormalization group analysis using the Keldysh path integral formulation to treat the non linearities: the Josephson coupling and the commensurate lattice. The analysis to first order in the coupling constant indicates transitions between superconducting and localized regimes that are smoothly connected to the respective equilibrium transitions. However at second order, the back action of the mode coupling on the critical state leads to renormalization of dissipation and emergence of an effective temperature. In the Josephson junction the temperature is parametrically small allowing to observe a universal crossover between the superconducting and insulating regimes. The IV characteristics of the junction displays algebraic behavior controlled by the underlying critical state over a wide range. In the noisy one dimensional liquid the generated dissipation and effective temperature are not small as in the junction. We find a crossover between a quasi-localized regime dominated by dissipation and another dominated by temperature. However since in the thermal regime the thermalization rate is parametrically small, signatures of the non-equilibrium critical state can be seen in transient dynamics.

Abstract:
Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions where times greater than a chosen cutoff time are suppressed. As a central result, a time evolution equation for the non-equilibrium effective action is derived, and the time-evolution of the Green functions is computed within a vertex expansion. It is shown that this agrees with the dynamics derived from the 1/N-expansion of the two-particle irreducible effective action.

Abstract:
The Rabi model considers a two-level system (or spin-1/2) coupled to a quantized harmonic oscillator and describes the simplest interaction between matter and light. The recent experimental progress in solid-state circuit quantum electrodynamics has engendered theoretical efforts to quantitatively describe the mathematical and physical aspects of the light-matter interaction beyond the rotating wave approximation. We develop a stochastic Schr\"{o}dinger equation approach which enables us to access the strong-coupling limit of the Rabi model and study the effects of dissipation, and AC drive in an exact manner. We include the effect of ohmic noise on the non-Markovian spin dynamics resulting in Kondo-type correlations, as well as cavity losses. We compute the time evolution of spin variables in various conditions. As a consideration for future work, we discuss the possibility to reach a steady state with one polariton in realistic experimental conditions.

Abstract:
We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the real-time evolution from an ordered phase of the Heisenberg or XY-model towards a disordered phase at late times, disregarding unitary Hamiltonian dynamics. The corresponding Kossakowski-Lindblad equation is solved via an efficient cluster algorithm. We find that the symmetry of the dissipative process determines the time scales which govern the approach towards a new equilibrium phase at late times. Most notably, we find a slow equilibration if the dissipative process conserves any of the magnetization Fourier modes. In these cases, the dynamics can be interpreted as a diffusion process of the conserved quantity.

Abstract:
We study the non-equilibrium many-body dynamics of a cold gas of ground state alkali atoms weakly admixed by Rydberg states with laser light. On a timescale shorter than the lifetime of the dressed states, effective dipole-dipole or van der Waals interactions between atoms can lead to the formation of strongly correlated phases, such as atomic crystals. Using a semiclassical approach, we study the long-time dynamics where decoherence and dissipative processes due to spontaneous emission and blackbody radiation dominate, leading to heating and melting of atomic crystals as well as particle losses. These effects can be substantially mitigated by performing active laser cooling in the presence of atomic dressing.

Abstract:
We study the coherent dynamics of relaxing qubits driven by a bichromatic radiation in the dispersive regime, when detuning of the frequency $\omega_{rf}$ of a longitudinal radiofrequency field from the Rabi frequency $\omega_{1}$ in a transverse microwave field is comparable in magnitude to $\omega_{rf}$ and $\omega_{1}$. We analytically describe this regime beyond the rotating wave approximation and find that the dominant feature of dynamics of qubits is the shift of the Rabi frequency caused by the dynamical Zeeman and Bloch-Siegert-like effects. These fundamental effects can be experimentally separated because, unlike the Bloch-Siegert effect, the dynamical Zeeman effect depends on the detuning sign. Our theoretical results are in a good agreement with the experimental data obtained in pulse EPR for the $E'_{1}$ centers in crystalline quartz.

Abstract:
When two isolated system are brought in contact, they relax to equilibrium via energy exchange. In another setting, when one of the systems is driven and the other is large, the first system reaches a steady-state which is not described by the Gibbs distribution. Here, we derive expressions for the size of energy fluctuations as a function of time in both settings, assuming that the process is composed of many small steps of energy exchange. In both cases the results depend only on the average energy flows in the system, independent of any other microscopic detail. In the steady-state we also derive an expression relating three key properties: the relaxation time of the system, the energy injection rate, and the size of the fluctuations.

Abstract:
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.