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Publication# Quantum dynamics of dissipative Kerr solitons

Fabrizio Minganti, Riccardo Rota, Vincenzo Savona, Kilian Robert Seibold

*AMER PHYSICAL SOC, *2022

Journal paper

Journal paper

Abstract

Dissipative Kerr solitons arising from parametric gain in ring microresonators are usually described within a classical mean-field framework. Here, we develop a quantum-mechanical model of dissipative Kerr solitons in terms of the Lindblad master equation and study the model via the truncated Wigner method, which accounts for quantum effects to leading order. We show that, within this open quantum system framework, the soliton experiences a finite coherence time due to quantum fluctuations originating from losses. Reading the results in terms of the theory of open quantum systems allows us to estimate the Liouvillian spectrum of the system. It is characterized by a set of eigenvalues with a finite imaginary part and a vanishing real part in the limit of vanishing quantum fluctuations. This feature shows that dissipative Kerr solitons are a specific class of dissipative time crystals.

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Nathan Rafaël Bernier, Tobias Kippenberg, László Dániel Tóth

Isolation of a system from its environment is often desirable, from precision measurements to control of individual quantum systems; however, dissipation can also be a useful resource. Remarkably, engineered dissipation enables the preparation of quantum states of atoms, ions or superconducting qubits as well as their stabilization. This is achieved by a suitably engineered coupling to a dissipative cold reservoir formed by electromagnetic modes. Similarly, in the field of cavity electro- and optomechanics, the control over mechanical oscillators utilizes the inherently cold, dissipative nature of the electromagnetic degree of freedom. Breaking from this paradigm, recent theoretical work has considered the opposite regime in which the dissipation of the mechanical oscillator dominates and provides a cold, dissipative reservoir to an electromagnetic mode. Here we realize this reversed dissipation regime in a microwave cavity optomechanical system and realize a quasi-instantaneous, cold reservoir for microwave light. Coupling to this reservoir enables to manipulate the susceptibility of the microwave cavity, corresponding to dynamical backaction control of the microwave field. Additionally, we observe the onset of parametric instability, i.e. the stimulated emission of microwaves (masing). Equally important, the reservoir can function as a useful quantum resource. We evidence this by employing the engineered cold reservoir to implement a large gain (above 40 dB) phase preserving microwave amplifier that operates 0.87 quanta above the limit of added noise imposed by quantum mechanics. Such a dissipative cold reservoir forms the basis of microwave entanglement schemes, the study of dissipative quantum phase transitions, amplifiers with unlimited gain-bandwidth product and non-reciprocal devices, thereby extending the available toolbox of quantum-limited microwave manipulation techniques.

2017Jean-Philippe Ansermet, François Reuse, Jacques Van Der Klink

We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and the bathed system. The statistical states of the ensemble are described in terms of density matrices. Supposing the bath to be held at some - not necessarily thermal - statistical equilibrium and tracing over the bath degrees of freedom, we obtain reduced density matrices defining the statistical states of the bathed system. The master equations describing the evolution of these reduced density matrices are derived under the most general conditions. On time scales that are large with respect to the bath correlation time τB corr and with respect to the reciprocal transition frequencies of the bathed system, the resulting evolution of the reduced density matrix of the bathed system is of Markovian type. The detailed balance relations valid for a thermal equilibrium of the bath are derived and the conditions for the validity of the fluctuation-dissipation theorem are given. Based on the general approach, we investigate the non-linear response of the bathed subsystem to a time-periodic perturbation. Summing the perturbation series we obtain the coherences and the populations for arbitrary strengths of the perturbation. © 2003 Springer-Verlag Berlin/Heidelberg.

2003The exploration of open quantum many-body systems -systems of microscopic size exhibiting quantum coherence and interacting with their surrounding- has emerged as a key research area over the last years. The recent advances in controlling and preserving quantum coherence at the level of a single particle, developed in a wide variety of physical platforms, have been a major driving force in this field. The driven dissipative nature is a common characteristic of a wide class of modern experimental platforms in quantum science and technology, such as photonic systems, ultracold atoms, optomechanical systems, or superconducting circuits. The interplay between the coherent quantum dynamics and dissipation in open quantum systems leads to a wide range of novel out-of-equilibrium behaviours. Among them, the emergence in these systems of dynamical phases with novel broken symmetries, topological phases and the occurrence of dissipative phase transitions are of particular interest. This thesis aims at establishing a theoretical framework to engineer, characterize and control nonclassical states of light in photonic quantum optical networks in different regimes. The emphasis is put on its implementation, in particular with respect to integration and scalability in photonic platforms. In this thesis, we tackle some interesting aspects arising in the study of the dynamics of driven dissipative coupled nonlinear optical resonators. In that context, we consider the dynamics of two coupled nonlinear photonic cavities in the presence of inhomogeneous coherent driving and local dissipations using the Lindblad master equation formalism.We show that this simple open quantum many-body system can be subject to dynamical instabilities. In particular, our analysis shows that this system presents highly nonclassical properties and its dynamics exhibits dissipative Kerr solitons (DKSs), characterized by the robustness of its specific temporal or spatial waveform during propagation.In a second step, our intuition gained from this system composed of only few degrees of freedom is expanded to the study of systems of bigger size. In particular, we study DKSs originating from the parametric gain in Kerr microresonators. While DKSs are usually described using a classical mean-field approach, our work proposes a quantum-mechanical model formulated in terms of the truncated Wigner formalism. This analysis is motivated by the fact that technological implementations push towards the realization of DKSs in miniaturized integrated systems. These are operating at low power, a regime where quantum effects are expected to be relevant. Using the tools provided by the theory of open quantum systems, we propose a detailed investigation of the impact of quantum fluctuations on the spectral and dynamical properties of DKSs. We show that the quantum fluctuations arising from losses engender a finite lifetime to the soliton, and demonstrate that DKSs correspond to a specific class of dissipative time crystals.