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.

arXiv comment12 pages, Accepted for publishing in Physical Review A

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• Qubit models of weak continuous measurements
• Divisibility of quantum dynamical maps and collision models
• Collisional picture of quantum optics with giant emitters
• Quantum master equations for entangled qubit environments
• Collision model for non-Markovian quantum trajectories
• Quantum trajectories for a system interacting with environment in N-photon state
• Master equations and quantum trajectories for squeezed wave packets
• Quantum master equations for a system interacting with quantum gas in the low density limit and for the semiclassical collision model
• From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket
• Quantum trajectories for environment in superposition of coherent states
• Quantum non-Markovian collision models from colored-noise baths
• Quantum filtering equations for system driven by non-classical fields
• Collisional-model quantum trajectories for entangled qubit environments
• Photon counting probabilities of the output field for a single-photon input
• Stochastic approach to evolution of a quantum system interacting with a wave packet in squeezed number state
• Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket
• Control of continuous-mode single-photon states: a review