Driven dissipative dynamics and topology of quantum impurity systems

Karyn Le Hur; Loïc Henriet; Loïc Herviou; Kirill Plekhanov; Alexandru Petrescu; Tal Goren; Marco Schiro; Christophe Mora; Peter P. Orth

doi:10.1016/j.crhy.2018.04.003

Driven dissipative dynamics and topology of quantum impurity systems
[Dynamique dissipative et topologie dans des systèmes d'impuretés quantiques]

Karyn Le Hur ¹ ; Loïc Henriet ² ; Loïc Herviou ^1,³ ; Kirill Plekhanov ^1,⁴ ; Alexandru Petrescu ⁵ ; Tal Goren ¹ ; Marco Schiro ⁶ ; Christophe Mora ³ ; Peter P. Orth ⁷

¹ Centre de physique théorique, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau cedex, France
² ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
³ Laboratoire Pierre-Aigrin, École normale supérieure–PSL Research University, CNRS, Université Pierre-et-Marie-Curie, Sorbonne Universités, Université Paris-Sorbonne Paris Cité, 24, rue Lhomond, 75231 Paris cedex 05, France
⁴ LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
⁵ Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
⁶ Institut de physique théorique, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
⁷ Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA

Comptes Rendus. Physique, Quantum simulation / Simulation quantique, Volume 19 (2018) no. 6, pp. 451-483.

Résumé
Abstract

Dans cette revue, nous proposons une introduction et une vue d'ensemble de quelques progrès parmi les plus récents dans le domaine de la dynamique en temps réel des modèles d'impuretés quantiques et de leurs réalisations dans les dispositifs quantiques. Nous nous intéressons au modèle spin–boson avec dissipation ohmique et aux modèles associés, qui décrivent un seul spin 1/2 couplé à une collection infinie d'oscillateurs harmoniques. Les sujets abordés s'inspirent en grande partie de nos travaux de ces dernières années, mais nous présentons également quelques résultats nouveaux. Nous commençons la première partie de cette revue par une introduction pédagogique à la dynamique en temps réel d'un spin dissipatif à hautes et basses températures. Nous nous intéressons ensuite à la dynamique dirigée en régime quantique au-delà de la limite de faible couplage spin–bain. Dans ces situations, la méthode faisant appel à l'équation de Schroedinger stochastique non perturbative est idéale pour obtenir numériquement la dynamique de spin, car elle permet d'incorporer des champs de polarisation $h_{z} (t)$ de dépendance temporelle arbitraire dans le hamiltonien. Nous présentons différentes applications récentes de cette méthode : (i) comment les propriétés topologiques du spin telles que la courbure de Berry et le nombre de Chern peuvent être mesurées dynamiquement, et comment la dissipation affecte la topologie et le protocole de mesure ; (ii) comment les chaînes de spin quantiques suivent la dynamique de synchronisation par couplage avec un bain commun. Dans la deuxième partie de cette revue, nous discutons l'ingénierie quantique du modèle spin-boson et des modèles associés en électrodynamique quantique des circuits (cQED), des circuits électriques quantiques et des architectures d'atomes froids. Dans différentes réalisations, l'environnement ohmique peut être représenté par une longue ligne de transmission (micro-ondes), un liquide de Luttinger, un condensat de Bose–Einstein unidimensionnel, une chaîne de jonctions Josephson supraconductrices. Nous montrons que l'impureté quantique peut être utilisée comme un capteur quantique pour détecter les propriétés d'un bain au couplage minimal, et comment la dynamique de spin dissipative peut conduire à de nouvelles perspectives dans la transition Mott–superfluide.

In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_{z} (t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition.

Publié le : 2018-05-28

DOI : 10.1016/j.crhy.2018.04.003

Keywords: Quantum impurity model dynamics, Synchronization and spin topology, Light–matter and hybrid systems, Majorana quantum impurity models, Quantum materials, Quantum state engineering
Mots-clés : Dynamique du modèle d'impuretés quantiques, Synchronisation et topologie de spin, Systèmes lumière–matière et hybrides, Modèle d'impureté quantique de Majorana, Matériaux quantiques, Ingénierie de l'état solide

Affiliations des auteurs :

Karyn Le Hur ¹ ; Loïc Henriet ² ; Loïc Herviou ^{1, 3} ; Kirill Plekhanov ^{1, 4} ; Alexandru Petrescu ⁵ ; Tal Goren ¹ ; Marco Schiro ⁶ ; Christophe Mora ³ ; Peter P. Orth ⁷

¹ Centre de physique théorique, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau cedex, France
² ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
³ Laboratoire Pierre-Aigrin, École normale supérieure–PSL Research University, CNRS, Université Pierre-et-Marie-Curie, Sorbonne Universités, Université Paris-Sorbonne Paris Cité, 24, rue Lhomond, 75231 Paris cedex 05, France
⁴ LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
⁵ Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA
⁶ Institut de physique théorique, Université Paris-Saclay, CNRS, CEA, 91191 Gif-sur-Yvette, France
⁷ Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA

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     author = {Karyn Le Hur and Lo{\"\i}c Henriet and Lo{\"\i}c Herviou and Kirill Plekhanov and Alexandru Petrescu and Tal Goren and Marco Schiro and Christophe Mora and Peter P. Orth},
     title = {Driven dissipative dynamics and topology of quantum impurity systems},
     journal = {Comptes Rendus. Physique},
     pages = {451--483},
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Karyn Le Hur; Loïc Henriet; Loïc Herviou; Kirill Plekhanov; Alexandru Petrescu; Tal Goren; Marco Schiro; Christophe Mora; Peter P. Orth. Driven dissipative dynamics and topology of quantum impurity systems. Comptes Rendus. Physique, Quantum simulation / Simulation quantique, Volume 19 (2018) no. 6, pp. 451-483. doi : 10.1016/j.crhy.2018.04.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.04.003/

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