scholarly journals The quantum trajectory approach to quantum feedback control of an oscillator revisited

2012 ◽  
Vol 370 (1979) ◽  
pp. 5338-5353 ◽  
Author(s):  
Andrew C. Doherty ◽  
A. Szorkovszky ◽  
G. I. Harris ◽  
W. P. Bowen
Keyword(s):  
Master Equation ◽  
Quantum Trajectory ◽  
Measurement Sensitivity ◽  
Position Measurement ◽  
Stochastic Master Equation ◽  
Trajectory Approach ◽  
Quantum Feedback ◽  
Master Equation Approach ◽  
Rotating Wave ◽  
Parametric Driving

We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.

scholarly journals An analysis of reading out the state of a charge quantum bit

2003 ◽  
Vol 3 (2) ◽  
pp. 121-138
Author(s):  
H-S. Goan
Keyword(s):  
Density Matrix ◽  
Master Equation ◽  
The State ◽  
Qubit State ◽  
Reduced Density Matrix ◽  
Quantum Trajectory ◽  
Single Shot ◽  
Quantum Bit ◽  
Trajectory Approach ◽  
Reduced Density

We provide a unified picture for the master equation approach and the quantum trajectory approach to a measurement problem of a two-state quantum system (a qubit), an electron coherently tunneling between two coupled quantum dots (CQD's) measured by a low transparency point contact (PC) detector. We show that the master equation of ``partially'' reduced density matrix can be derived from the quantum trajectory equation (stochastic master equation) by simply taking a ``partial'' average over the all possible outcomes of the measurement. If a full ensemble average is taken, the traditional (unconditional) master equation of reduced density matrix is then obtained. This unified picture, in terms of averaging over (tracing out) different amount of detection records (detector states), for these seemingly different approaches reported in the literature is particularly easy to understand using our formalism. To further demonstrate this connection, we analyze an important ensemble quantity for an initial qubit state readout experiment, P(N,t), the probability distribution of finding N electron that have tunneled through the PC barrier(s) in time t. The simulation results of P(N,t) using 10000 quantum trajectories and corresponding measurement records are, as expected, in very good agreement with those obtained from the Fourier analysis of the ``partially'' reduced density matrix. However, the quantum trajectory approach provides more information and more physical insights into the ensemble and time averaged quantity P(N,t). Each quantum trajectory resembles a single history of the qubit state in a single run of the continuous measurement experiment. We finally discuss, in this approach, the possibility of reading out the state of the qubit system in a single-shot experiment.

A MEASURE OF ENTANGLEMENT THROUGH QUANTUM TRAJECTORY APPROACH

2008 ◽  
Vol 06 (02) ◽  
pp. 403-410 ◽  
Author(s):  
X. L. HUANG ◽  
L. C. WANG ◽  
X. X. YI
Keyword(s):  
Master Equation ◽  
Time Evolution ◽  
Physical System ◽  
Quantum Trajectory ◽  
Mixed States ◽  
Trajectory Approach

We propose a measure of entanglement through the quantum trajectory approach. The advantage of this measure is that it can avoid the problem of finding all possible decompositions for mixed states, which is usually complicated. This method can be applied to any physical system whose time evolution is governed by the master equation. As an example, we calculate the entanglement of the following cases: (A) entangled system composed of a pair of two-level atoms coupling to two separate baths and, (B) two entangled modes subjected to two separate baths.

scholarly journals Stepwise introduction of model complexity in a generalized master equation approach to time-dependent transport

2012 ◽  
Vol 61 (2-3) ◽  
pp. 305-316 ◽  
Author(s):  
V. Gudmundsson ◽  
O. Jonasson ◽  
Th. Arnold ◽  
C-S. Tang ◽  
H.-S. Goan ◽  
...  
Keyword(s):  
Master Equation ◽  
Time Dependent ◽  
Model Complexity ◽  
Equation Approach ◽  
Master Equation Approach ◽  
Dependent Transport ◽  
Generalized Master Equation

scholarly journals Intrinsic Friction of Monolayers Adsorbed on Solid Surfaces.

2003 ◽  
Vol 790 ◽  
Author(s):  
O. Bénichou ◽  
A.M. Cazabat ◽  
J. De Coninck ◽  
M. Moreau ◽  
G. Oshanin
Keyword(s):  
Density Distribution ◽  
Master Equation ◽  
Vapor Phase ◽  
Tracer Particle ◽  
Hard Core ◽  
Solid Surfaces ◽  
Equation Approach ◽  
Frictional Properties ◽  
Master Equation Approach ◽  
Frictional Forces

ABSTRACTWe review recent results on intrinsic frictional properties of adsorbed monolayers, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of a dynamical master equation approach we determine the velocity of a biased impure molecule - the tracer particle (TP), constrained to move inside the adsorbed mono-layer probing its frictional properties, define the frictional forces exerted by the monolayer on the TP, as well as the particles density distribution in the monolayer.

THE QUANTUM TRAJECTORY APPROACH TO GEOMETRIC PHASE FOR OPEN SYSTEMS

2005 ◽  
Vol 20 (22) ◽  
pp. 1635-1654 ◽  
Author(s):  
ANGELO CAROLLO
Keyword(s):  
Quantum System ◽  
Open System ◽  
Geometric Phase ◽  
Open Systems ◽  
Quantum Trajectory ◽  
Operational Method ◽  
Markovian Approximation ◽  
Physical Systems ◽  
Quantum Jump ◽  
Trajectory Approach

The quantum jump method for the calculation of geometric phase is reviewed. This is an operational method to associate a geometric phase to the evolution of a quantum system subjected to decoherence in an open system. The method is general and can be applied to many different physical systems, within the Markovian approximation. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. It is shown that the geometric phase is to very large extent insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.

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