Single photon delayed feedback: a way to stabilize intrinsic quantum cavity electrodynamics

Heat production in a stochastic system with nonlinear time-delayed feedback

Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space [R. A. Kopp et al., Phys. Rev. E 107, 024611 (2023)2470-004510.1103/PhysRevE.107.024611]. Here we investigate, numerically and by analytical methods, the rate of heat production in the different regimes around the threshold to persistent motion. We find a nonzero average heat production rate, 〈q[over ̇]〉, already below the threshold, indicating the nonequilibrium character of the system even at small feedback. In this regime, we compare to analytical results for a corresponding linearized delayed system and a small-delay approximation which provides a reasonable description of 〈q[over ̇]〉 at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as a function of the delay time. In this regime, 〈q[over ̇]〉 can be approximated by that of a system subject to a constant force stemming from the long-time velocity in the deterministic limit. The distribution of dissipated heat, however, is non-Gaussian, contrary to the constant-force case.

PT-Symmetric Feedback Induced Linewidth Narrowing

Narrow linewidth is a long-pursued goal in precision measurement and sensing. We propose a parity-time symmetric (PT-symmetric) feedback method to narrow the linewidths of resonance systems. By using a quadrature measurement-feedback loop, we transform a dissipative resonance system into a PT-symmetric system. Unlike the conventional PT-symmetric systems that typically require two or more modes, here the PT-symmetric feedback system contains only a single resonance mode, which greatly extends the scope of applications. The method enables remarkable linewidth narrowing and enhancement of measurement sensitivity. We illustrate the concept in a thermal ensemble of atoms, achieving a 48-fold narrowing of the magnetic resonance linewidth. By applying the method in magnetometry, we realize a 22-times improvement of the measurement sensitivity. This work opens the avenue for studying non-Hermitian physics and high-precision measurements in resonance systems with feedback.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system's linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.

Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

Non-Markovian Collective Emission from Macroscopically Separated Emitters

We study the collective radiative decay of a system of two two-level emitters coupled to a one-dimensional waveguide in a regime where their separation is comparable to the coherence length of a spontaneously emitted photon. The electromagnetic field propagating in the cavity-like geometry formed by the emitters exerts a retarded backaction on the system leading to strongly non-Markovian dynamics. The collective spontaneous emission rate of the emitters exhibits an enhancement or inhibition beyond the usual Dicke superradiance and subradiance due to self-consistent coherent time-delayed feedback.

Stochastic polarization switching induced by optical injection in bimodal quantum-dot micropillar lasers

Mutual coupling and injection locking of semiconductor lasers is of great interest in non-linear dynamics and its applications for instance in secure data communication and photonic reservoir computing. Despite its importance, it has hardly been studied in microlasers operating at μW light levels. In this context, vertically emitting quantum dot micropillar lasers are of high interest. Usually, their light emission is bimodal, and the gain competition of the associated linearly polarized fundamental emission modes results in complex switching dynamics. We report on selective optical injection into either one of the two fundamental mode components of a bimodal micropillar laser. Both modes can lock to the master laser and influence the non-injected mode by reducing the available gain. We demonstrate that the switching dynamics can be tailored externally via optical injection in very good agreement with our theory based on semi-classical rate equations.

Exciting a Bound State in the Continuum through Multiphoton Scattering Plus Delayed Quantum Feedback

Excitation of a bound state in the continuum (BIC) through scattering is problematic since it is by definition uncoupled. Here, we consider a type of dressed BIC and show that it can be excited in a nonlinear system through multiphoton scattering and delayed quantum feedback. The system is a semi-infinite waveguide with linear dispersion coupled to a qubit, in which a single-photon, dressed BIC is known to exist. We show that this BIC can be populated via multiphoton scattering in the non-Markovian regime, where the photon delay time (due to the qubit-mirror distance) is comparable with the qubit's decay. A similar process excites the BIC existing in an infinite waveguide coupled to two distant qubits, thus yielding stationary entanglement between the qubits. This shows, in particular, that single-photon trapping via multiphoton scattering can occur without band edge effects or cavities, the essential resource being instead the delayed quantum feedback provided by a single mirror or the emitters themselves.

Tailoring the mode-switching dynamics in quantum-dot micropillar lasers via time-delayed optical feedback

Microlasers are ideal candidates to bring the fascinating variety of nonlinear complex dynamics found in delay-coupled systems to the realm of quantum optics. Particularly attractive is the possibility of tailoring the devices' emission properties via non-invasive delayed optical coupling. However, until now scarce research has been done in this direction. Here, we experimentally and theoretically investigate the effects of delayed optical feedback on the mode-switching dynamics of an electrically driven bimodal quantum-dot micropillar laser, characterizing its impact on the micropillar's output power, optical spectrum and photon statistics. Feedback is found to influence the switching dynamics and its characteristics time scales. In addition, stochastic switching is reduced with the subsequent impact on the microlaser photon statistics. Our results contribute to the comprehension of feedback-induced phenomena in micropillar lasers and pave the way towards the external control and tailoring of the properties of these key systems for the nanophotonics community.

Horizons of cybernetical physics

The subject and main areas of a new research field-cybernetical physics-are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control.This article is part of the themed issue 'Horizons of cybernetical physics'.

Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators

We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.

Feedback control of waiting times

Feedback loops are known as a versatile tool for controlling transport in small systems, which usually have large intrinsic fluctuations. Here we investigate the control of a temporal correlation function, the waiting-time distribution, under active and passive feedback conditions. We develop a general formalism and then specify to the simple unidirectional transport model, where we compare costs of open-loop and feedback control and use methods from optimal control theory to optimize waiting-time distributions.

Time-Delayed Quantum Feedback Control

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.

Hybrid Quantum Systems with Collectively Coupled Spin States: Suppression of Decoherence through Spectral Hole Burning

Spin ensemble based hybrid quantum systems suffer from a significant degree of decoherence resulting from the inhomogeneous broadening of the spin transition frequencies in the ensemble. We demonstrate that this strongly restrictive drawback can be overcome simply by burning two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Using this procedure we find an increase of the coherence time by more than an order of magnitude as compared to the case without hole burning. Our findings pave the way for the practical use of these hybrid quantum systems for the processing of quantum information.

Feedback between interacting transport channels

A model of particle transport through a large number of channels is introduced. Interactions among the particles can lead to a strong suppression of fluctuations in the particle number statistics. Within a mean-field-type limit, this becomes equivalent to a time-dependent (nonautonomous) collective feedback control mechanism. The dynamics can be interpreted as a diffusive spreading of a feedback signal across the channels that displays scaling, can be quantified via the flow of information, and becomes visible, e.g., in the spectral function of the particle noise.

Single photon transport along a one-dimensional waveguide with a side manipulated cavity QED system

An external mirror coupling to a cavity with a two-level atom inside is put forward to control the photon transport along a one-dimensional waveguide. Using a full quantum theory of photon transport in real space, it is shown that the Rabi splittings of the photonic transmission spectra can be controlled by the cavity-mirror couplings; the splittings could still be observed even when the cavity-atom system works in the weak coupling regime, and the transmission probability of the resonant photon can be modulated from 0 to 100%. Additionally, our numerical results show that the appearance of Fano resonance is related to the strengths of the cavity-mirror coupling and the dissipations of the system. An experimental demonstration of the proposal with the current photonic crystal waveguide technique is suggested.

Optical feedback-enhanced photon entanglement from a biexciton cascade

In a solid-state platform for quantum information science, the biexciton cascade is an important source of entangled photons. However, the entanglement is usually reduced considerably by the fine-structure splitting of the exciton levels. We show how to counteract this loss of entanglement by applying optical feedback. Substantial control and enhancement of photon entanglement can be achieved by coherently feeding back a part of the emitted signal, e.g., by a mirror, and by tuning the feedback phase and delay time. We present full quantum-mechanical calculations, which include the external photon mode continuum, and discuss the mechanisms leading to the above effects.