Unraveling mirror properties in time-delayed quantum feedback scenarios

Abstract

We derive in the Heisenberg picture a widely used phenomenological coupling element to treat feedback effects in quantum optical platforms. Our derivation is based on a microscopic Hamiltonian, which describes the mirror-emitter dynamics based on a dielectric, a mediating fully quantized electromagnetic field, and a single two-level system in front of the dielectric. The dielectric is modeled as a a system of identical two-state atoms. The Heisenberg equation yields a system of describing differential operator equations, which we solve in the Weisskopf-Wigner limit. Due to a finite round-trip time between emitter and dielectric, we yield delay differential operator equations.Our derivation motivates and justifies the typical phenomenological assumed coupling element and allows, furthermore, a generalization to a variety of mirrors, such as dissipative mirrors or mirrors with gain dynamics. * E-mail me at: faulstich@math.tu-berlin.de; Visit: http://page.math.tu-berlin.de/˜faulstich/ 1 arXiv:1703.05928v2 [quant-ph]

Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model

“…The other method involves solving the delayed differential equation (19) instead of (16) and (17), thus directly incorporating the influence of the discrete environment. In FIG.…”

“…A fundamental example of this is a two-level system in front of a mirror or, in other words, the half-cavity setup. In this case, the presence of the mirror imposes a coherent time-delayed feedback for the atom and thus alters the quantum statistics and spontaneous emission spectrum of the system [11][12][13][14][15][16][17][18][19]. Signatures of non-Markovian behaviour for this setup were also demonstrated experimentally [20][21][22].…”

Stabilizing quantum coherence against pure dephasing in the presence of time-delayed coherent feedback at finite temperature

“…The goal of the modification of the LB-reservoir dynamics, g k : g 0 → g 0 sin(kL) [36,[71][72][73]80], is to restore/stabilize as much of the initial coherence for as long as possible. As there is no direct driving considered for the TLS, we haveP…”

“…This coherent feedback [86], originally introduced as an all-optical feedback [87] for quantum systems, has been proven an efficient way to recover lost quantum information from a reservoir with infinite degrees of freedom. Besides introducing a distant mirror, as just described [36], it can also be considered as a special case of cascaded quantum systems, as illustrated in Fig. 1(d) and described in [88] For optical excitations, the effect of feedback first manifests itself as a reduction in the effective cavity linewidth.…”

“…1(c) can be realized by phononic Bragg mirrors [28][29][30][32][33][34]. This way, the infinite degrees of freedom of the solid state reservoir amount either to enhanced or suppressed dephasing of the TLE [18,35] and may even introduce, e.g., timedelayed feedback for the system's dynamics [36].…”