Single-photon coherent feedback control and filtering

Abstract

In this survey, we present single-photon states of light fields, discuss how a linear quantum system responds to a single-photon input, after that we show how a coherent feedback network can be used to manipulate the temporal shape of a single-photon state, finally we present a single-photon filter.Index Terms -Quantum control systems; single photon states; filtering; coherent feedback control * This survey is an extensive version of an article in the second edition of the Encyclopaedia of Systems and Control.† Guofeng Zhang is with the

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

“…Note that |ξ k | 2 τ is the probability of detecting a photon in the interval [kτ, (k + 1)τ ). Here we deal with a discrete version of a single photon state defined in [17,22,23,25,28,36] for the symmetric Fock space…”

“…is the probability of detecting a photon in the interval [kτ, (k + 1)τ ). Here we deal with a discrete version of a single photon state defined in [17,22,23,25,28,36] for the symmetric Fock space F L 2 (R + ) . We gain the information about the system S in indirect way, namely by performing a sequence of measurements on the bath qubits just after their interactions with S. The conditional state of S and the part of the environment chain which has not interacted with S up to time jτ is at the moment jτ given by [32] | Ψj|η η ηj = |Ψ j|η η ηj…”

“…Thus if we observed two photons we are certain that the system has already met the photon (|α t|t2,t1 = 0). The terms in (36) correspond respectively to the following scenarios:…”

“…The scattering process of N photons on a quantum system was described in the pure-state wavefunction approaches [10,11] and diagrammatic approaches [12][13][14]. Generalized master equations [15][16][17][18][19][20][21] and stochastic master equations [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] were used to study the excitation of the two-level atom interacting with a N photon packets.…”

Photon counting probabilities of the output field for a single-photon input

“…There are several theoretical techniques allowing to tackle this problem. The scattering in the waveguide can be studied by using Heisenberg picture approach [12], methods based on the Lippmann-Schwinger equation [13][14][15][16][17][18], generalized master equation [19,20], pure-state analysis [21,22] or stochastic approach [23][24][25][26][27][28][29][30][31][32][33][34]. In [35] one can find description of the method based on the operational translation of the system nonlinear response.…”