Delayed feedback control in quantum transport

Feedback control in quantum transport has been predicted to give rise to several interesting effects, amongst them quantum state stabilisation and the realisation of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system be affected instantaneously after the measurement of electronic jumps through it. In this contribution I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state-stabilisation and Maxwell's-daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.Comment: 13 pages, 5 figure

Revisiting quantum feedback control: disentangling the feedback‐induced phase from the corresponding amplitude

Coherent time‐delayed feedback allows the control of a quantum system and its partial stabilization against noise and decoherence. The crucial and externally accessible parameters in such control setups are the round‐trip‐induced delay time τ and the frequencies ω of the involved optical transitions which are typically controllable via global parameters like temperature, bias, or strain. They influence the dynamics via the amplitude and the phase= of the feedback signal. These quantities are, however, not independent. Here, the aim is to control the feedback phase via a microwave pump field. Using the example of a Λ‐type three‐level system, it is shown that the Rabi frequency of the pump field induces phase shifts on demand and therefore increases the applicability of coherent quantum feedback control protocols.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und AnwendungskonzepteEC/H2020/734690/EU/Localized Surface Plasmon Resonance in doped semiconductor nanocrystals/SONARTU Berlin, Open-Access-Mittel - 201

Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment

Quantum feedback can stabilize a two-level atom against decoherence (spontaneous emission), putting it into an arbitrary (specified) pure state. This requires perfect homodyne detection of the atomic emission, and instantaneous feedback. Inefficient detection was considered previously by two of us. Here we allow for a non-zero delay time $\tau$ in the feedback circuit. Because a two-level atom is a nonlinear optical system, an analytical solution is not possible. However, quantum trajectories allow a simple numerical simulation of the resulting non-Markovian process. We find the effect of the time delay to be qualitatively similar to that of inefficient detection. The solution of the non-Markovian quantum trajectory will not remain fixed, so that the time-averaged state will be mixed, not pure. In the case where one tries to stabilize the atom in the excited state, an approximate analytical solution to the quantum trajectory is possible. The result, that the purity ($P=2{\rm Tr}[\rho^{2}]-1$) of the average state is given by $P=1-4\gamma\tau$ (where $\gamma$ is the spontaneous emission rate) is found to agree very well with the numerical results.Comment: Changed content, Added references and Corrected typo

Effects of time delay in feedback control of linear quantum systems

We investigate feedback control of linear quantum systems subject to feedback-loop time delays. In particular, we examine the relation between the potentially achievable control performance and the time delays, and provide theoretical guidelines for the future experimental setup in two physical systems, which are typical in this research field. The evaluation criterion for the analysis is given by the optimal control performance formula, the derivation of which is from the classical control theoretic results about the input-output delay systems.Comment: 6 pages, 4 figure

Thermodynamics of Quantum-Jump-Conditioned Feedback Control

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such system and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.Comment: 12 pages, 6 figure

Rapid Steady State Convergence for Quantum Systems Using Time-Delayed Feedback Control

We propose a time-delayed feedback control scheme for open quantum systems that can dramatically reduce the time to reach steady state. No measurement is performed in the feedback loop, and we suggest a simple all-optical implementation for a cavity QED system. We demonstrate the potential of the scheme by applying it to a driven and dissipative Dicke model, as recently realized in a quantum gas experiment. The time to reach steady state can then reduced by two orders of magnitude for parameters taken from experiment, making previously inaccessible long time attractors reachable within typical experimental run times. The scheme also offers the possibility of slowing down the dynamics, as well as qualitatively changing the phase diagram of the corresponding physical system.Comment: 25 pages, 9 figures. Invited paper in "Focus on Coherent Control of Complex Quantum Systems", Eds. B. Whaley and G. Milburn. PS: Preview on OSX struggles with opening some of the figures with a lot of data in the