Quantum Correlations and Speed Limit of Central Spin Systems

In this article, single, and two-qubit central spin systems interacting with spin baths are considered and their dynamical properties are discussed. The cases of interacting and non-interacting spin baths are considered and the quantum speed limit (QSL) time of evolution is investigated. The impact of the size of the spin bath on the quantum speed limit for a single qubit central spin model is analyzed. The quantum correlations for (non-)interacting two central spin qubits are estimated and their dynamical behavior with that of QSL time under various conditions are compared. How QSL time could be availed to analyze the dynamics of quantum correlations is shown.     

Environment induced entanglement in many-body mesoscopic systems

We show that two, non-interacting, infinitely long spin chains can become globally entangled at the mesoscopic level of their fluctuation operators through a purely noisy microscopic mechanism induced by the presence of a common heat bath. By focusing on a suitable class of mesoscopic observables, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of the dissipation strength and bath temperature.     

Quantum dynamics of Gaudin magnets

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment. The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging. In this paper, using the Bethe ansatz wave function, we study the quantum dynamics of an inhomogeneous Gaudin magnet. We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins, such as: the spin distribution function, the spin–spin correlation function, and the Loschmidt echo. We also numerically study the relaxation behavior of these dynamic properties, gaining considerable insight into coherence and entanglement between the central spin and the bath. In particular, we find that the spin–spin correlations relax to their steady value via a nearly logarithmic scaling, whereas the Loschmidt echo shows an exponential relaxation to its steady value. Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.     

Quantum coherence and correlation dynamics of two-qubit system in spin bath environment

The quantum entanglement,discord,and coherence dynamics of two spins in the model of a spin coupled to a spin bath through an intermediate spin are studied.The effects of the important physical parameters including the coupling strength of two spins,the interaction strength between the intermediate spin and the spin bath,the number of bath spins and the temperature of the system on quantum coherence and correlation dynamics are discussed in different cases.The frozen quantum discord can be observed whereas coherence does not when the initial state is the Bell-diagonal state.At finite temperature,we find that coherence is more robust than quantum discord,which is better than entanglement,in terms of resisting the influence of environment.Therefore,quantum coherence is more tenacious than quantum correlation as an important resource.     

Hybridization and spin decoherence in heavy-hole quantum dots

We theoretically investigate the spin dynamics of a heavy hole confined to an unstrained III-V semiconductor quantum dot and interacting with a narrowed nuclear-spin bath. We show that band hybridization leads to an exponential decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips, and that the accordant single-hole-spin decoherence time T2 can be tuned over many orders of magnitude by changing external parameters. In particular, we show that, under experimentally accessible conditions, it is possible to suppress hyperfine-mediated nuclear-pair-flip processes so strongly that hole-spin quantum dots may be operated beyond the "ultimate limitation" set by the hyperfine interaction which is present in other spin-qubit candidate systems.     

Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (In,Ga)As quantum dots

The problem of how single central spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying time scales and dynamical responses (exponential, power-law, gaussian, etc.). Here we detect the small random fluctuations of central spins in thermal equilibrium [holes in singly charged (In,Ga)As quantum dots] to reveal the time scales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at a zero magnetic field that increase to ～5 μs as dominant hole-nuclear relaxation channels are suppressed with small (100 G) applied fields. Concomitantly, the noise line shape evolves from Lorentzian to power law, indicating a crossover from exponential to slow [～1/log(t)] dynamics.     

Quantum oscillations without quantum coherence

We study numerically the damping of quantum oscillations and the dynamics of the density matrix in model many-spin systems decohered by a spin bath. We show that oscillations of some density matrix elements can persist with considerable amplitude long after other elements, along with the entropy, have come close to saturation, i.e., when the system has been decohered almost completely. The oscillations exhibit very slow decay, and may be observable in experiments.     

Dynamics and protection of tripartite quantum correlations in a thermal bath

We study the dynamics and protection of tripartite quantum correlations in terms of genuinely tripartite concurrence, lower bound of concurrence and tripartite geometric quantum discord in a three-qubit system interacting with independent thermal bath. By comparing the dynamics of entanglement with that of quantum discord for initial GHZ state and W state, we find that W state is more robust than GHZ state, and quantum discord performs better than entanglement against the decoherence induced by the thermal bath. When the bath temperature is low, for the initial GHZ state, combining weak measurement and measurement reversal is necessary for a successful protection of quantum correlations. But for the initial W state, the protection depends solely upon the measurement reversal. In addition, the protection cannot usually be realized irrespective of the initial states as the bath temperature increases.     

Random quantum states: recent developments and applications

We review the methods and use of random quantum states with particular emphasis on recent theoretical developments and applications in various fields. The guiding principle of the review is the idea that random quantum states can be understood as classical probability distributions in the Hilbert space of the associated quantum system. We show how this central concept connects questions of physical interest that cover different fields such as quantum statistical physics, quantum chaos, mesoscopic systems of both non-interacting and interacting particles, including superconducting and spin–orbit phenomena, and stochastic Schrödinger equations describing open quantum systems.     

量子气体中的输运行为

输运测量是了解物质性质的一个重要手段.本文简单介绍最近在量子气体中实现的输运实验及其主要结论,包括在类似于介观物理器件中的Landauer输运和强相互作用费米气体中的自旋输运行为.我们着重讨论自旋动力学的特殊性以及其由于全同粒子相互作用所导致的特殊自旋扩散流的形式.     

Hidden Caldeira-Leggett dissipation in a Bose-Fermi Kondo model

We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy-fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe physical quantities close to the quantum phase transition.     

Driven dissipative dynamics and topology of quantum impurity systems

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.     

Influences of Initial States on Entanglement Dynamics of Two Central Spins in a Spin Environment

We investigate the entanglement dynamics of two electronic spins coupled to a bath of nuclear spins for two special cases, one is that two central spins both interact with a common bath, and the other is that one of two spins interacts with a bath. We consider three types of initial states with different correlations between the system and the bath, i.e., quantum correlation, classical correlation, and no-correlation. We show that the initial correlations (no matter quantum correlations or classical correlations) can effectively avoid the occurrence of entanglement sudden death. Irrespective of whether both two spins or only one of the two spins interacts with the bath, the system can gain more entanglement in the process of the time evolution for initial quantum correlations. In addition, we find that the effects of the distribution of coupling constants on entanglement dynamics crucially depend on the initial state of the spin bath.     

Long-Lived Mesoscopic Entanglement Between Two Damped Infinite Harmonic Chains

We consider two chains, each made of N independent oscillators, immersed in a common thermal bath and study the dynamics of their mutual quantum correlations in the thermodynamic, large-N limit. We show that dissipation and noise due to the presence of the external environment are able to generate collective quantum correlations between the two chains at the mesoscopic level. The created collective quantum entanglement between the two many-body systems turns out to be rather robust, surviving for asymptotically long times even for non vanishing bath temperatures.     

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.     

The two-qubit amplitude damping channel: Characterization using quantum stabilizer codes

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.     

Phase coherent transmission through interacting mesoscopic systems

This is a review of the phase coherent transmission through interacting mesoscopic conductors. As a paradigm we study the transmission amplitude and the dephasing rate for electron transport through a quantum dot in the Coulomb blockade regime. We summarize experimental and theoretical work devoted to the phase of the transmission amplitude. It is shown that the evolution of the transmission phase may be dominated by non-universal features in the short-time dynamics of the quantum dot. The controlled dephasing in Coulomb-coupled conductors is investigated. Examples comprise a single or multiple quantum dots in close vicinity to a quantum point contact. The current through the quantum point contact “measures” the state of the dots and causes dephasing. The dephasing rate is derived using widely different theoretical approaches. The Coulomb coupling between mesoscopic conductors may prove useful for future work on electron coherence and quantum computing.     

Interacting quantum dot coupled to a kondo spin: a universal Hamiltonian study

We study a Kondo spin coupled to a mesoscopic interacting quantum dot that is described by the "universal Hamiltonian." The problem is solved numerically by diagonalizing the system Hamiltonian in a good-spin basis and analytically in the weak and strong Kondo coupling limits. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground-state spin (Stoner staircase), which is modified nontrivially by the Kondo interaction. We find that the spin-transition steps move to lower values of the exchange coupling for weak Kondo interaction, but shift back up for sufficiently strong Kondo coupling. The interplay between Kondo and ferromagnetic exchange correlations can be probed with experimentally tunable parameters.