# Project B7

### Real Time Dynamics of Driven, Dissipative Quantum Systems

## PIs: Prof. J. von Delft, Prof. S. Kehrein

In the field of quantum information processing, most theoretical studies of the real-time dynamics of driven, damped qubits employ perturbative and/or Markovian approximations. Such strategies work well if the qubit is damped only very weakly and if bath memory effects are negligible. These typically are the conditions sought out by experimental groups for proof-of-principle demonstrations of new qubit realizations, where one of the first goals is to demonstrate long decoherence times.

However, to manipulate and measure qubits it is often necessary to enter parameter regimes where standard theoretical approaches fail. Examples are dispersive readout schemes leading to qubit-Duffing oscillator models, dissipative Landau-Zener transitions at zero and low temperatures, or quantum telegraph noise, which constitutes a non-Gaussian environment.

To deal with such situations, we plan to employ two many-body techniques that have proven to be very powerful for solving qubit-bath models (or more generally, “quantum impurity models” describing a few discrete degrees of freedom coupled to a continuous bath of excitations). The first technique is numerical: it combines ideas from the numerical renormalization group (NRG) for studying qubit-bath models with ideas from the time-dependent density matrix renormalization group (tDMRG), exploiting the fact that both are formulated in terms of matrix product states. The second, largely analytical, technique employs the flow equation renormalization group (FRG) to diagonalize the Hamiltonian governing the dynamics.

These methods will be developed to the point that they can describe the dynamics of driven, dissipative quantum systems governed by a Hamiltonian H(t) with arbitrary time dependence. They will be used to study a number of important qubit-bath models, for both bosonic and fermionic bath, and for a qubit coupled to quantum telegraph noise. We will in particular focus on questions that are of interest also to other projects in this SFB, including dissipative Landau-Zener tunneling (A5), non-linear damping (A2,A5), non-Gaussian noise (A5), and coherent transport through quantum dots by adiabatic passage (A1). We will also employ our methods to study the dynamics of ultracold atomic gases near a quantum phase transition (also pursued in B6), with a view to shedding light on how the entanglement properties (such as the entanglement entropy) change as the system is driven through the phase transition.