Stochastic Schr Research Articles

Effect of feedback on the decoherence of a Schrödinger-cat state: A quantum trajectory description.

The linear stochastic Schr\odinger equation of a cavity mode subject to a homodyne measurement and to a phase-sensitive feedback loop realized with part of the output homodyne photocurrent is derived. We show that quantum feedback has stabilizing effects which manifest themselves in a significant retardation of the decoherence of a Schr\odinger-cat state. \textcopyright{} 1996 The American Physical Society.

Stochastic path integrals and open quantum systems.

The general theory of path integral propagators for the solution of linear quantum state diffusion (LQSD) stochastic Schr\"odinger equations describing open quantum systems is developed. Both Hamiltonian and, where possible, Lagrangian path integrals are derived and their connection established. The Hamiltonian version turns out to be more suitable. The results also show how the stochastic terms in the LQSD equation introduce a weight functional under the path integral, thus restricting the set of contributing paths. The center of this weight functional is determined by the stochastic processes governing the LQSD equation. In general, this picture holds in a semiclassical limit only. Some peculiarities of stochastic path integrals are pointed out. We evaluate the stochastic path integral in closed form for soluble models, gaining further insight into the behavior of the solutions of the LQSD equation. \textcopyright{} 1996 The American Physical Society.

Schrödinger cat states and single runs for the damped harmonic oscillator.

We discuss the fate of initial states of the Schr\"odinger cat type for the damped harmonic oscillator, mostly employing a linear version of the stochastic Schr\"odinger equation. We also comment on how such cat states might be prepared and on the relation of single realizations of the noise to single runs of experiments.

Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere.

It is shown that the evolution of an open quantum system whose density operator obeys a Markovian master equation can in some cases be meaningfully described in terms of stochastic Schr\"odinger equations (SSE's) for its state vector. A necessary condition for this is that the information carried away from the system by the bath (source of the irreversibility) be recoverable. The primary field of application is quantum optics, where the bath consists of the continuum of electromagnetic modes. The information lost from the system can be recovered using a perfect photodetector. The state of the system conditioned on the photodetections undergoes stochastic quantum jumps. Alternative measurement schemes on the outgoing light (homodyne and heterodyne detection) are shown to give rise to SSE's with diffusive terms. These three detection schemes are illustrated on a simple quantum system, the two-level atom, giving new perspectives on the interpretation of measurement results. The reality of these and other stochastic processes for state vectors is discussed.

Stochastic Schr�dinger operators and Jacobi matrices on the strip

We discuss stochastic Schrodinger operators and Jacobi matrices with wave functions, taking values in ℂ l so there are 2l Lyaponov exponents γ1≧...≧γl≧0≧γ l+1≧...≧γ2l =−γ1. Our results include the fact that if γ1=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j γ's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.