Tailoring coupling in artificial superconducting quasi-spins
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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 hz(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. 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 hz(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.
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The global coupling of few-level quantum systems (``spins'') to a discrete set of bosonic modes is a key ingredient for many applications in quantum science, including large-scale entanglement generation, quantum simulation of the dynamics of long-range interacting spin models, and hybrid platforms for force and spin sensing. We present a general numerical framework for treating the out-of-equilibrium dynamics of such models based on matrix product states. Our approach applies for generic spin-boson systems: it treats any spatial and operator dependence of the two-body spin-boson coupling and places no restrictions on relative energy scales. We show that the full counting statistics of collective spin measurements and infidelity of quantum simulation due to spin-boson entanglement, both of which are difficult to obtain by other techniques, are readily calculable in our approach. We benchmark our method using a recently developed exact solution for a particular spin-boson coupling relevant to trapped ion quantum simulators. Finally, we show how decoherence can be incorporated within our framework using the method of quantum trajectories, and study the dynamics of an open-system spin-boson model with spatially nonuniform spin-boson coupling relevant for trapped atomic ion crystals in the presence of molecular ion impurities.
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We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized using time-dependent external forces. If the force depends on the spin state of the atoms, the dynamics will entangle the inner and outer degrees of freedom which offers unique opportunities for quantum information and quantum simulation. Here, we introduce a method to realize a quantum walker based on the state-dependent transport of spinor atoms and a coherent driving of the internal state. In the limit of weak driving the dynamics is equivalent to that of a Dirac particle in 1+1 dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.
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We develop the ideas of the quantum renormalization group and quantum information by exploring the low-energy-state dynamics of entanglement resources of a system close to its quantum critical point. We demonstrate that low-energy-state dynamical quantities of one-dimensional magnetic systems can show a quantum phase transition point and show scaling behavior in the vicinity of the transition point. To present our idea, we study the evolution of two spin entanglements in the one-dimensional Ising model in the transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We investigate the evolution of the generation of entanglement with increasing magnetic field. We obtain that the derivative of the time at which the entanglement reaches its maximum with respect to the transverse field diverges at the critical point and its scaling behaviors versus the size of the system are the same as the static ground-state entanglement of the system.
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We study the capacity of antiferromagnetic lattices of varying geometries to entangle two additional spin-$1/2$ probes. Analytical modeling of the quantum Monte Carlo data shows the appearance of a robust gap, allowing a description of entanglement in terms of probe-only states, even in cases where the coupling to the probes is larger than the gap of the spin lattice and cannot be treated perturbatively. We find a considerable enhancement of the temperature at which probe entanglement disappears as we vary the geometry of the bus and the coupling to the probes. In particular, the square Heisenberg antiferromagnet exhibits the best thermal robustness of all systems, whereas the three-leg ladder chain shows the best performance in the natural quantum ground state.
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Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.
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