Jürgen T. Stockburger

Exact c-number representation of non-Markovian quantum dissipation.

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schrödinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born-Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.

DYNAMICAL SIMULATION OF CURRENT FLUCTUATIONS IN A DISSIPATIVE TWO-STATE SYSTEM

Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over the real-time paths under the influence of colored noise. The nature of the transition from coherent to incoherent dynamics at low temperatures is re-examined.

Optimal control of open quantum systems: cooperative effects of driving and dissipation.

We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotovs iterative algorithm, with no need for Markovian or rotating-wave approximations. The application to a harmonic degree of freedom reveals cooperative effects of driving and dissipation that a standard Markovian treatment cannot capture. Remarkably, control can modify the open-system dynamics to the point where the entropy change turns negative, thus achieving cooling of translational motion without any reliance on internal degrees of freedom.

Stochastic Liouvillian algorithm to simulate dissipative quantum dynamics with arbitrary precision

An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon’s path-integral expression of the reduced density matrix, is used to describe the exact dynamics at any dissipative strength and for arbitrarily low temperatures. The utility of the method is demonstrated by applications to a damped harmonic oscillator and a double-well system immersed in an Ohmic bath at low temperatures.

Non-Markovian Dissipative Semiclassical Dynamics

The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low temperatures, where non-Markovian effects are substantial, this approach allows for the accurate description of dissipative dynamics in anharmonic potentials over many oscillation periods until thermalization is reached. The problem of convergence of the stochastic average at long times, which plagues full quantum mechanical implementations, is avoided through a joint sampling of the stochastic noise and the semiclassical phase-space distribution.

Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations

Abstract Based on recently derived exact stochastic Liouville–von Neumann equations, several strategies for the efficient simulation of open quantum systems are developed and tested on the spin-boson model. The accuracy and efficiency of these simulations is verified for several test cases including both coherent and incoherent dynamics, involving timescales differing by several orders of magnitude. Using simulations with a time-dependent field, the time evolution of coherences in the reduced density matrix is investigated. Even in the case of weak damping, pronounced preparation effects are found. These indicate hidden coherence in the interacting system which can only be indirectly observed in the basis of the reduced quantum dynamics.

Non-Markovian quantum state diffusion

Abstract We derive new time-local stochastic Schrodinger equations which offer a fully non-Markovian extension of conventional quantum state diffusion (QSD). The Feynman–Vernon influence functional of a linear heat bath is constructed as the stochastic mean value of time-local action terms, defining a linear stochastic Schrodinger equation. As a test, conventional QSD is recovered in limiting cases allowing the Born–Markov approximation. We further transform the dynamics to obtain a non-linear, norm-conserving Schrodinger equation with appealing properties: It is suitable for numerical simulations, and it has a well-defined classical limit even before noise averaging.

Negative Differential Conductance Induced by Spin-Charge Separation

Spin-charge states of correlated electrons in a one-dimensional quantum dot attached to interacting leads are studied in the nonlinear transport regime. With nonsymmetric tunnel barriers, regions of negative differential conductance induced by spin-charge separation are found. They are due to a correlation-induced trapping of higher-spin states without magnetic field and are associated with a strong increase in the fluctuations of the electron spin.

Almost local generation of Einstein-Podolsky-Rosen entanglement in nonequilibrium open systems

The generation of entanglement is studied in a minimal model consisting of two independent Gaussian parties embedded in a common heat bath. We consider the case of weak reservoir-induced interactions which themselves are insufficient to generate entanglement. Local driving by an external classical field, however, can promote this weak interaction to a source of entanglement. Presence or absence of the effect depends on the specific pulse shape of the external control, which we determine through optimal control techniques.

Semiclassical dynamics of nonadiabatic transitions in discrete-state systems using spin coherent-state path integrals

We present a semiclassical method for simulating the dynamics of nonadiabatic transitions in a discrete-state quantum system coupled to a bath of explicit continuous coordinates. This method employs a coherent-state formulation of the path integrals for the discrete system whose dynamics is described by spin operators. This spin coherent-state formulation allows the discrete system to be mapped onto a continuous coordinate. Stationary approximations of the resulting coherent-state path integrals of the system plus bath lead to quasiclassical equations of motion which can be solved numerically by direct integration. This algorithm reduces the problem to a number of simple classical trajectory calculations and does not require calculating any fluctuation determinants.