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

Abstract

We present the analytical formulas for the conditional and unconditional states of a two-level atom interacting with a single-photon wavepacket. We express the a priori state of the system by means of the quantum trajectories related to the process of detection of photons in the output field. We give the formulas for the mean number of photons detected up to the given time and we derive the expressions for the mean time of detection of the photons.

Quantum collision models: Open system dynamics from repeated interactions

“…Due to the natural connection of CMs with quantum trajectories (see Section 6, another promising application of the collisional mapping are non-Markovian extensions of photon counting and quantum trajectories (usually formulated for Markovian dynamics [10,76]). Examples are non-Markovian dynamics induced by single-photon states (see Section 9.11) [205,206,207] and delayed coherent feedback [182,57].…”

Control engineering of continuous-mode single-photon states: a review

“…quantum filtering theory was pioneered by Belavkin in the early 1980s [67]. More developments can be found in [26,27,31,35,64,65,[68][69][70][71][72][73][74][75][76][77][78] and references therein.…”

Collisional picture of quantum optics with giant emitters

“…(20) and (25). This can be expressed in terms of original ladder operators j through (7), (13), and (27). The master equation (23) for a unidirectional field is retrieved for γ = 0.…”

“…This indeed rules out that the evolution of the emitters (open system) at each elementary collision be described by a CPTP quantum map [66], which is the key requirement for a Lindblad master equation to hold. A typical instance is a single-photon wave packet of bandwidth comparable to γ [10,12,13,63,67].…”

“…A somewhat unconventional method to tackle quantum optics problems is a collision-model description, an approach adopted in a growing number of works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Much like in standard theories of photon counting statistics, the basic idea (see Fig.…”