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arXiv:1909.08972 · Advanced Quantum Technologies

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

Kisa Barkemeyer, Regina Finsterhoelzl, Andreas Knorr, Alexander Carmele

Published Oct 11, 2019• 15 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1002/qute.201900078

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Abstract 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.
Abstract The no-knowledge quantum feedback, introduced in Phys. Rev. Lett., 113, 020407 (2014), is a measurement-based feedback protocol for decoherence suppression in a quantum system coupled to noisy environment. By continuously measuring the environmental noise, without directly gathering any information about the system, the decoherence effect can be suppressed by feeding back quantum controls proportional to the measured signal. In the original work, the feedback control was assumed instantaneous, leading to perfect cancellation of noise backaction on the quantum system. However, the instantaneous feedback is difficult to achieve in practice, and close-loop feedback protocols are always associated with finite delayed time. Therefore, in this work, we consider the effects of the delay between the time at which the measurement signal is acquired and the time that such signal is fed back to the system. We investigate the problem with an example of a two-level system (qubit) coupled to a Markovian reservoir, via a Hermitian coupling operator, where a homodyne detection is used to measure the environmental noise. We numerically simulate quantum stochastic trajectories of the qubit and analyse their averaged dynamics. We find that the feedback control with time delay can either enhance or reduce the decoherence effects, depending on whether the delayed time is in-phase or out-of-phase with the unitary dynamics of the qubit system.
We numerically show that time-delayed coherent feedback controls the statistical output characteristics of driven quantum emitters. Quantum feedback allows us to enhance or suppress a wide range of classical and nonclassical features of the emitted quantum light. As an exemplary quantum system, we use a pumped cavity containing two emitters. By applying phase-selective feedback, we demonstrate that photon antibunching and bunching can be increased for a given set of parameters in orders of magnitude due to intrinsically and externally controllable quantum interferences. Our modeling is based on a fully non-Markovian quantum simulation of a structured photon continuum. We show that an approximative method in the Schr\"odinger picture allows a very good estimate for quantum feedback induced features for low pump rates.
Quantum information science relies on the feature of distant quantum entities (mostly "qubits") to form non-local states. A main challenge consists of generating such non-local entangled states between qubits. We exploit the fact that for coupled qubits, the eigenstates of the coupled system are usually highly entangled, and of different excitation energies. This allows to address the different entangled eigenstates by frequency-dependent control schemes. In our proposal, we present such a control mechanism, and demonstrate how it can be used to create entanglement from a fully separable initial state. The mechanism of our choice is time-delayed quantum-coherent feedback. If a qubit occupation decays via the emission of a photon, one can store this photon for a delay time τ and couple the radiation back into the qubit afterwards. Through the choice of τ, one can set the phase of the feedback, which will then lead to either an increased or decreased qubit decay. Since this phase depends on sin(ωτ), this effect strongly depends on the qubit frequency ω. In particular, it can be used to separate different entangled states in a quantum network by enhancing the decay of all entangled eigenstates except one. We discuss this protocol on the example of two coupled qubits, and analyze in detail its effectiveness depending on the feedback delay time τ.
We consider the feedback stabilization of Rabi oscillations in a superconducting qubit which is coupled to a microwave readout cavity. The signal is readout by homodyne detection of the in-phase quadrature amplitude of the weak-measurement output. By multiplying the time-delayed Rabi reference, one can extract the signal, with maximum signal-to-noise ratio, from the noise current. We further track and stabilize the Rabi oscillations by using Lyapunov feedback control to properly adjust the input Rabi drives. Theoretical and simulation results illustrate the effectiveness of the proposed control law.
In this theoretical thesis we apply the time-delayed Pyragas feedback scheme to several many-body quantum systems in order to control the quantum phases in a rather new way. The systems are the dissipative Dicke model, the dissipative Lipkin-Meshkov-Glick (LMG) model and a two-mode Tavis-Cummings laser. In the dissipative Dicke model our chosen way of feedback control, namely the modulation of the atom-field coupling by a difference of emitted photon numbers at different times, creates additional new quantum phases. These show up as an infinite sequence of super- and subcritical Hopf bifurcations of the stationary state by generation of stable and unstable limit cycles. We analyze and discuss the appearing bifurcations as a function of time delay and feedback strength and calculate an analytical expression for the phase boundaries. On top of this, we argue that our scheme is easy to implement within existing experimental setups, as in experiments the coupling is tuned by laser intensity. In the dissipative LMG model we investigate how the dissipation affects the excited state quantum phase transition (ESQPT). We show that with dissipative effects the ESQPT is directly visible in the spectrum of the effective Hamiltonian and not only in the density of states. Moreover, the ESQPT signal in the system observables gets smoothed. Then we use time delayed feedback control to restore the ESQPT signal by creation of new phases. We analyze and discuss the behavior of the system for different time delays. We argue that using our feedback scheme it is easier to measure ESQPT in the open LMG system than without it in the closed one. Then we use a 2-mode laser based on the Tavis-Cummings model with additional incoherent pumping and decay channels. Instead of the usually used rate-equation model, we describe the two-mode laser starting from a quantum mechanical description and present an analytical solution of the corresponding stationary mean-field equations in thermodynamic limit. We analyze the stationary solutions and their stability and obtain a complex phase diagram with up to 4 fixed points. In addition to this, we apply different time delayed Pyragas feedback control schemes, which allow us to influence the laser dynamic. The frequency of the emitted laser light can be controlled then or an unstable fixed point stabilized. In this way, our thesis links the topics of control, phase transitions and dissipation together which induce an interesting and unexpected dynamics in quantum many-body systems. Although all final calculations are at the mean-field level, we hold them to be valid in thermodynamic limit.
We investigate the stabilization of the dynamical state of a superconducting qubit. In a series of papers, A. Korotkov and his co-workers suggested that continuous weak measurement of the state of a qubit and applying an appropriate feedback on the amplitude of a Rabi drive, should maintain the coherence of the Rabi oscillations for arbitrary time. Here, in the aim of addressing a metrological application of these persistent Rabi oscillations, we explore a new variant of such strategies. This variant is based on performing strong measurements in a discrete manner and using the measurement record to correct the phase of the Rabi oscillations. Noting that such persistent Rabi oscillations can be viewed as an amplitude-to-frequency convertor (converting the amplitude of the Rabi microwave drive to a precise frequency), we propose another feedback layer consisting of a simple analog phase locked loop to compensate the low frequency deviations in the amplitude of the Rabi drive.