Unraveling coherent quantum feedback for Pyragas control

Abstract

We present a Heisenberg operator based formulation of coherent quantum feedback and Pyragas control. This model is easy to implement and allows for an efficient and fast calculation of the dynamics of feedback-driven observables as the number of contributing correlations grows in systems with a fixed number of excitations only linearly in time. Furthermore, our model unravels the quantum kinetics of entanglement growth in the system by explicitly calculating non-Markovian multi-time correlations, e.g., how the emission of a photon is correlated with an absorption process in the past. Therefore, the time-delayed differential equations are expressed in terms of insightful physical quantities. Another considerate advantage of this method is its compatibility to typical approximation schemes, such as factorization techniques and the semi-classical treatment of coherent fields. This allows the application on a variety of setups, ranging from closed quantum systems in the few excitation regimes to open systems and Pyragas control in general.

Intensified antibunching via feedback-induced quantum interference

“…In the limit of high photon number, semiclassical approximations allow to derive manageable equations and establish the ties to the classical regime [20,21].…”

“…To solve this problem methods have been proposed employing the Liouville space [26], Matrix product state (MPS) evolution [27], and the Heisenberg picture [21].…”

A feedback scheme for control of single electron transport

“…This clearly involves some intrinsically classical, stochastic signals even if the system to be controlled is fully quantum. In contrast, passive feedback [6] (not discussed here) is essentially the embedding of a (quantum) system into a larger (quantum) system such that effectively, some parts of the enlarged system control the original system, without the need of permanent, external observation [7][8][9][10][11][12][13][14][15][16][17] .…”

Revisiting Quantum Feedback Control: Disentangling the Feedback‐Induced Phase from the Corresponding Amplitude

“…[37][38][39][40][41][42][43][44][45][46] Various setups to control quantum few-level systems via timedelayed feedback have been studied theoretically and it has been shown that it is possible to control characteristic quantities such as the photon-photon correlation and the concurrence which functions as a measure of entanglement. [47][48][49][50][51][52][53][54][55][56][57][58][59] In these systems, in general, the control parameters that can be used to evoke the desired behavior are the delay time and the characteristic frequency which, depending on the considered setup, can be, for example, the frequency of an involved optical transition or the frequency of a cavity mode. These parameters influence the dynamics via the feedback amplitude x(t − ) and the phase = .…”