Bernd Kappler

Stochastic wave function method for non-markovian quantum master equations

A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space and it is shown, that this method is capable of simulating quantum master equations with negative transition rates. Non-Markovian effects in the reduced systems dynamics can be treated within this approach by employing the time-convolutionless projection operator technique. This ansatz yields a systematic perturbative expansion of the reduced systems dynamics in the coupling strength. Several examples such as the damped Jaynes Cummings model and the spontaneous decay of a two-level system into a photonic band gap are discussed. The power as well as the limitations of the method are demonstrated.

Real-time monitoring of ethene/1-hexene copolymerizations: determination of catalyst activity, copolymer composition and copolymerization parameters

High-throughput development of catalysts, initiators, and polymeric materials combines automated parallel catalyst synthesis and automated polymerization reactors. The reactors can be additionally equipped with on-line monitoring (ReactIR from Mettler) based on ATR-FT-IR technique. This powerful tool has proven to be a very valuable probe for high-throughput experiments. During copolymerizations of ethene and 1-hexene monomers, the ReactIR was used to monitor the 1-hexene conversion as well as polymer formation, polymer concentration, and polymer composition. This gives access to information on catalyst activity, activation and deactivation times of the catalyst, polymerization kinetics, copolymerization parameters, and the degree of homogeneity of the resulting copolymers. The technology is especially useful for solution copolymerization. The spectrometer can be applied in the lab as well as in pilot plants and production facilities where rapid on-line analyses are useful for product quality control.

Non-Markovian dynamics in pulsed- and continuous-wave atom lasers

The dynamics of atom lasers with a continuous output coupler based on two-photon Raman transitions is investigated. With the help of the time-convolutionless projection operator technique the quantum master equations for pulsed- and continuous-wave (cw) atom lasers are derived. In the case of the pulsed atom laser the power of the time-convolutionless projection operator technique is demonstrated through comparison with the exact solution. It is shown that in an intermediate coupling regime where the Born-Markov approximation fails, the results of this algorithm agree with the exact solution. To study the dynamics of a continuous-wave atom laser a pump mechanism is included in the model. Whereas the pump mechanism is treated within the Born-Markov approximation, the output coupling leads to non-Markovian effects. The solution of the master equation resulting from the time-convolutionless projection operator technique exhibits strong oscillations in the occupation number of the Bose-Einstein condensate. These oscillations are traced back to a quantum interference which is due to the non-Markovian dynamics and which decays slowly in time as a result of the dispersion relation for massive particles.

STOCHASTIC WAVE-FUNCTION APPROACH TO THE CALCULATION OF MULTITIME CORRELATION FUNCTIONS OF OPEN QUANTUM SYSTEMS

Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\bf 68}, 580 (1992)]. By means of a standard example the suggested algorithm is shown to be more efficient numerically and to converge faster. Finally, some specific examples from quantum optics are presented in order to illustrate the proposed method, such as the coupling of a system to a vacuum, a squeezed vacuum within a finite solid angle, and a thermal mixture of coherent states.

Time-Convolutionless Stochastic Unraveling of Non-Markovian Quantum Master Equations

Employing the time-convolutionless projection operator technique a stochastic wave function dynamics is derived which describes the time evolution of an open quantum system beyond the Born-Markov approximation. The method yields a systematic perturbation expansion in the coupling strength between system and environment. The performance of the method is tested with the help of the damped Jaynes-Cummings model and shown to be more efficient than other approaches based on the generalized master equation.

Heisenberg picture operators in the quantum state diffusion model

A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum-state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of the quantum master equation to a doubled Hilbert space which is then unravelled by a stochastic differential equation.

Stochastic Wave Function Approach to Generalized Master Equations

A generalization of the stochastic wave function method is presented that allows the unraveling of arbitrary linear quantum master equations that are not necessarily in Lindblad form and, moreover, the explicit treatment of memory effects by employing the time-convolutionless projection operator technique. The crucial point of this construction is the description of the open system in a doubled Hilbert space, which has already been successfully used for the computation of multitime correlation functions.