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

Abstract

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.

12 pages, Accepted for publishing in Physical Review A

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• From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket
• Quantum non-Markovian collision models from colored-noise baths
• Quantum trajectories for environment in superposition of coherent states
• Collisional-model quantum trajectories for entangled qubit environments
• Photon counting probabilities of the output field for a single-photon input
• Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket
• Stochastic approach to evolution of a quantum system interacting with a wave packet in squeezed number state
• Control of continuous-mode single-photon states: a review