arXiv subjects

Anita Dabrowska

Publications and source records attributed to Anita Dabrowska.

8 recordsLinked to original sources

arXiv2025

Quantum trajectories and output field properties for two-photon input field

The excitation of atomic and molecular systems by propagating light in a two-photon state within the Wigner-Weisskopf approximation has been described using stochastic tools. The problem of a stochastic evolution of the quantum system, depending on the results of the measurement of the output field, was formulated and solved making use of the model of repeated interactions and measurement. We defined the discrete in-time interaction between the quantum system and its environment being the electromagnetic field approximated by a chain or chains of harmonic oscillators. We determined analytical formulae for quantum trajectories associated with one-dimensional and two-dimensional counting processes, corresponding respectively to unidirectional or bidirectional input field prepared in the two-photon states. We derived the formulae for the exclusive probability densities of photon counts that allow us to completely characterize the photon statistics of the output field. Finally, we showed how to apply the quantum trajectories to obtain the formula for the probability of the two-photon absorption for a three-level atom in a ladder configuration. The paper also includes a discussion on the optimal two-photon state that maximizes the two-photon absorption probability.

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arXiv2019

Quantum trajectories for environment in superposition of coherent states

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 a 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.

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arXiv2018

Quantum filtering equations for system driven by non-classical fields

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 chosen non-classical states of light. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the non-classical states of the field: a combination of vacuum and single photon states and a mixture of two coherent states. We describe the stochastic evolution conditioned on the results of the photon counting and quadrature measurements.

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arXiv2017

Quantum trajectories for a system interacting with environment in a single photon state: counting and diffusive processes

We derived quantum trajectories for a system interacting with the environment prepared in a continuous mode single photon state as the limit of discrete filtering model with an environment defined as series of independent qubits prepared initially in the entangled state being an analogue of a continuous mode state. The environment qubits interact with the quantum system and they are subsequently measured. The initial correlation between the bath qubits is the source of the non-Markovianity. The conditional evolutions of the quantum system for limit of the continuous in time observations together with the formulas for the photon counting probabilities are given.

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arXiv2014

Belavkin Filtering with Squeezed Light Sources

We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that, quantum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate $π_t (a)$ for the mode annihilator $a$ based on the homodyne quadrature observations up to time $t$.

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arXiv2012

A posterior quantum dynamics for a continuous diffusion observation of a coherent channel

We present the Belavkin filtering equation for the intense balanced heterodyne detection in a unitary model of an indirect observation. The measuring apparatus modelled by a Bose field is initially prepared in a coherent state and the observed process is a diffusion one. We prove that this filtering equation is relaxing: any initial square-integrable function tends asymptotically to a coherent state with an amplitude depending on the coupling constant and the initial state of the apparatus. The time-development of a squeezed coherent state is studied and compared with the previous results obtained for the measuring apparatus prepared initially in the vacuum state.

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arXiv2012

Continuous observation of a squeezed coherent state

The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The comparison of the a priori and a posteriori mean value of the optical quadrature operators and the photon number operator is given.

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arXiv2012

Counting Photons in the Lambda-Experiment

Dehmelt's Lambda-experiment for a three-level atom with simultaneously driven strong and weak transition is studied within quantum stochastic calculus approach. The statistics of the emitted photons is found by the method of generating functional of the corresponding two dimensional output counting process. In particular, the average waiting times for a count are calculated.

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