12 research outputs found
Creating number states in the micromaser using feedback
We use the quantum theory of feedback developed by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] and Wiseman [Phys. Rev. A 49, 2133 (1994)] to investigate the photon-number noise properties of the micromaser with direct detection feedback. We find that the feedback can significantly reduce the amount of noise in the photon number. Under the right conditions the feedback locks the systems onto a number state. As opposed to other schemes in the past [P. Meystre, Opt. Lett. 12, 669 (1987); J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987)], we can fix the number states to which the system evolves. We also simulate the micromaser using the quantum-trajectories method and show that these results agree with the quantum theory of feedback. We show that the noise of quantum island states [P. Bogar, J. A. Bergou, and M. Hillary, Phys. Rev. A 50, 754 (1994)] can be significantly reduced by the feedback
A perturbative approach to non-Markovian stochastic Schr\"odinger equations
In this paper we present a perturbative procedure that allows one to
numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations,
for a wide range of memory functions. To illustrate this procedure numerical
results are presented for a classically driven two level atom immersed in a
environment with a simple memory function. It is observed that as the order of
the perturbation is increased the numerical results for the ensembled average
state approach the exact reduced state found via
Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure
The interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory
Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open
quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A
66, 012108 (2002)] we investigated this question using the orthodox
interpretation of quantum mechanics. We found that the solution of a
non-Markovian SSE represents the state the system would be in at that time if a
measurement was performed on the environment at that time, and yielded a
particular result. However, the linking of solutions at different times to make
a trajectory is, we concluded, a fiction. In this paper we investigate this
question using the modal (hidden variable) interpretation of quantum mechanics.
We find that the noise function appearing in the non-Markovian SSE can
be interpreted as a hidden variable for the environment. That is, some chosen
property (beable) of the environment has a definite value even in the
absence of measurement on the environment. The non-Markovian SSE gives the
evolution of the state of the system ``conditioned'' on this environment hidden
variable. We present the theory for diffusive non-Markovian SSEs that have as
their Markovian limit SSEs corresponding to homodyne and heterodyne detection,
as well as one which has no Markovian limit.Comment: 9 page
Non-Markovian Decay of a Three Level Cascade Atom in a Structured Reservoir
We present a formalism that enables the study of the non-Markovian dynamics
of a three-level ladder system in a single structured reservoir. The
three-level system is strongly coupled to a bath of reservoir modes and two
quantum excitations of the reservoir are expected. We show that the dynamics
only depends on reservoir structure functions, which are products of the mode
density with the coupling constant squared. This result may enable pseudomode
theory to treat multiple excitations of a structured reservoir. The treatment
uses Laplace transforms and an elimination of variables to obtain a formal
solution. This can be evaluated numerically (with the help of a numerical
inverse Laplace transform) and an example is given. We also compare this result
with the case where the two transitions are coupled to two separate structured
reservoirs (where the example case is also analytically solvable)
Time-reversed quantum trajectory analysis of micromaser correlation properties and fluctuation relations
The micromaser is examined with the aim of understanding certain of its properties based on a time-reversed quantum trajectory analysis. The background theory of master equations derived from a repeated interaction model perspective is briefly reviewed and extended by taking into account the more general renewal process description of the sequence of interactions of the system with incoming ancilla, and results compared with other recent (and not so recent) approaches that use this generalisation. The results are then specialised to the micromaser, and a quantum trajectory unravelling of the micromaser dynamics is formulated that enables time-reversed quantum trajectories, defined according to the Crooks approach, to, first, be shown to arise naturally in the analysis of micromaser and atomic beam correlations, and second used in the formulation of a fluctuation relation for the probabilities of trajectories and their time-reversed counterparts
Resolvent operator theory of sequential quantum processes
The Mower sequential decay theory of quantum processes has been extended in order formally to remove certain spurious poles in the matrix elements of the resolvent operator, and to recast the results into a more symmetrical general form. A special choice of intermediate manifolds of states leads to a further simplification. An illustrative application of the theory is given
Quantum theory of friction
We present a Markovian quantum theory of friction. Our approach is based on the idea that collisions between a Brownian particle and single molecules of the surrounding medium constitute, as far as the particle is concerned, instantaneous simultaneous measurements of its position and momentum