Open quantum systems with delayed coherent feedback

Whalen, S. J.; Grimsmo, Arne L.; Carmichael, H. J.

doi:10.1088/2058-9565/aa8331

Cited by 51 publications

(57 citation statements)

References 32 publications

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“…In steady state the system is dynamically decoupled from the decay channel. This phenomenon of feedback-induced dynamical decoupling of an atom from a decay channel has been demonstrated previously [44,46,47].…”

supporting

confidence: 69%

Time-Delayed Quantum Feedback Control

2015

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A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a fictitious series of cascaded quantum systems, where the system is driven by past versions of itself. The derivation of this model relies on a tensor network representation of the system-reservoir time-propagator. For concreteness, this general theory is applied to a driven two-level atom scattering into a coherent feedback loop. We demonstrate how delay effects can qualitatively change the dynamics of the atom, and how quantum control can be implemented in the presence of time-delays. Introduction.-Delayed autonomous feedback, where a signal is directly fed back to a system after a controllable time-delay, is an important control tool for classical systems [1][2][3]. It is highly attractive as a tool for stabilizing non-equilibrium states of fast dynamical systems, where avoiding any time-costly signal-processing is crucial. Such stabilization is of great experimental and technological relevance [4][5][6]. In particular, delayed autonomous feedback has been used to stabilize the high frequency dynamics of optical systems and high speed electrical circuits [7, 8].Autonomous feedback is also receiving substantial and growing interest for controlling quantum systems [9][10][11][12][13][14][15][16]. Because of the relatively short coherence time and fast dynamics of quantum systems, very fast feedback control possible with autonomous feedback is highly desirable. In addition, any measurement of the feedback signal will necessarily destroy its quantum character, making a fully quantum mechanical feedback loop that preserves coherence attractive from a fundamental point of view. Compelling evidence that this type of coherent feedback can outperform any measurement-based counterpart for important quantum information processing tasks has been given [17,18].A natural way of implementing coherent feedback control loops is by coupling remote quantum systems via waveguides [19][20][21][22]. Time-delays are unavoidable in practice in such setups and are likely to become important if current experiments are scaled up to larger and more complex networks [23][24][25]. Despite of this, relatively little theoretical research has been done on delay effects for coherent quantum feedback. A major obstacle is the lack of tractable and general theoretical models for treating the highly non-Markovian dynamics induced by this type of feedback. The theoretical difficulty lies in the quantum correlations between the control target system and the in-loop quantum field: The field cannot simply be traced out, and one has to deal with a highly entangled quantum state over a continuum of degrees of freedom.Previous investigations have typically been limited to

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confidence: 69%

Time-Delayed Quantum Feedback Control

2015

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“…Still, the initial bath state is a product one which ensures that Eq. (17) holds in the present case as well (see Section 2.1.3) with the Hamiltonian and dissipator given by [cf. Eqs.…”

Section: Coherent Statementioning

confidence: 84%

Collision models in quantum optics

Ciccarello¹

2017

Quantum Measurements and Quantum Metrology

116

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Quantum collision models (CMs) provide advantageous case studies for investigating major issues in open quantum systems theory, and especially quantum non-Markovianity. After reviewing their general de nition and distinctive features, we illustrate the emergence of a CM in a familiar quantum optics scenario. This task is carried out by highlighting the close connection between the well-known input-output formalism and CMs. Within this quantum optics framework, usual assumptions in the CMs' literature -such as considering a bath of noninteracting yet initially correlated ancillas -have a clear physical origin.

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“…Due to complexities arising from the continuum of modes in the feedback reservoir and the non-Markovian dynamic, the majority of studies have been limited to the linear regime; although nonlinearity at the few-quanta level has been treated by employing fictitious cascading systems [22,23] or matrix product states [19,[24][25][26]. These treatments focus on particular model systems, however, and they can meet with severe computational limitations as photon numbers increase.…”

Section: Introductionmentioning

confidence: 99%

Quantum trajectory theory of few-photon cavity-QED systems with a time-delayed coherent feedback

2020

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We describe an efficient approach to modelling cavity quantum electrodynamics (QED) with a time-delayed coherent feedback using quantum trajectory simulations. An analytical set of equations is derived to exploit the advantages of trajectories in the presence of the non-Markovian dynamics, where adjustments to the standard stochastic dynamics are discussed. In the weak excitation regime, we first verify that our approach recovers known results obtained with other simulation methods and demonstrate how a coherent feedback loop can increase the photon lifetime in typical cavity-QED systems. We then explore the nonlinear few-photon regime of cavity-QED, under the restriction of at most one photon at a time in the feedback loop. In particular, we show how feedback affects the cavity photoluminescence (populations versus laser detuning), and describe how one must account for conditioning in the presence of feedback, specifically the system observables must be conditioned on no photon detections at the feedback output channel occurring.

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Open quantum systems with delayed coherent feedback

Cited by 51 publications

References 32 publications

Time-Delayed Quantum Feedback Control

Time-Delayed Quantum Feedback Control

Collision models in quantum optics

Quantum trajectory theory of few-photon cavity-QED systems with a time-delayed coherent feedback

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