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Acta Physica Polonica A

Quantum Filtering Equation for System Driven by Field in a Mixture of Vacuum and Coherent State

Anita Magdalena Dąbrowska

Published Jul 1, 2017• 0 citations
Publisher

Abstract

We consider the problem of optimal estimation of a state of a quantum system interacting with the Bose field being in a mixture of the vacuum and coherent state.The system and electromagnetic field are described by making use of quantum stochastic unitary evolution.We derive stochastic master equation using Gardiner and Collet's input-output theory and the concept of cascade systems.To find the stochastic evolution of the system conditioned on the result of the quadrature measurement of the output field, we extend the compound system by an ancilla driven by the vacuum and generating the desired non-classical state of light.

DOI
10.12693/aphyspola.132.112

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We consider the problem of optimal estimation of a state of a quantum system interacting with the Bose field being in a mixture of the vacuum and coherent state.The system and electromagnetic field are described by making use of quantum stochastic unitary evolution.We derive stochastic master equation using Gardiner and Collet's input-output theory and the concept of cascade systems.To find the stochastic evolution of the system conditioned on the result of the quadrature measurement of the output field, we extend the compound system by an ancilla driven by the vacuum and generating the desired non-classical state of light.
Using Gardiner and Collet’s input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by light in some specific nonclassical states. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the nonclassical states of field: a combination of vacuum and single photon states and a mixture of two coherent states. The stochastic evolution conditioned on the results of the photon counting and quadrature measurements is described.
A major component of establishing quantum technologies in the quantum optic platform is the cavity. This paper concerns state estimation (filtering) of a quantum one-sided cavity driven by a vacuum field while the output field is monitored by either Homodyne or photodetector. The stochastic master equation in the schrödinger picture is presented for Homodyne and photon measurements. Then, the infinite state space of the cavity is truncated by considering some reasonable simplifying assumptions. Finally, the number of photons in the cavity is estimated using the derived equations. Simulation results are validated by demonstrating that the average of several paths of the derived filter matches the corresponding master equation.
We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system, we use a collision model with an environment given as an infinite chain of not interacting between themselves qubits prepared initially in an entangled state being a discrete analogue of a superposition of coherent states of the Bose field. The elements of the environment chain interact with the quantum system in turn one by one, and they are subsequently measured. We determine a conditional evolution of the quantum system for continuous in time observations of the output field as a limit of discrete recurrence equations. We consider the stochastic master equations for a counting as well as for a diffusive stochastic process.