Quantum jumps versus stochastic schrodinger equation. Applications in quantum optics

Peter Goetsch, R. Graham

John A. Vaccaro, Derek Richards

We derive stochastic Schr\"odinger equations describing the evolution of an optical linear amplifier conditioned on the state-selective detection of the source atoms. By applying a classical pulse to each atom immediately before the detection process we generate different stochastic Schr\"odinger equations including that of the quantum-jump method and quantum-state diffusion. We also study the transition from the distinct jumps of the quantum-jump method to the diffusive behavior of quantum-state diffusion and trace the effect of the information gained by the detection of the state of the atom on the state of the field.

Lue Bouten

B. Shore

Howard M. Wiseman, Gerard J Milburn

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.

Alberto Barchielli