Driven dissipative dynamics and topology of quantum impurity systems

Abstract

In this review, we provide an introduction and overview to 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 describes a single spin-1/2 coupled to 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 Schroedinger 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 to 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, 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.

Tunable phonon-induced steady-state coherence in a double-quantum-dot charge qubit

“…Such models can generically be used to describe dissipa-tive two-level systems, and can be engineered in various platforms (for examples, see Refs. [38,39] and citations therein). The DQD charge qubit provides an especially promising example, since the required parameter regime corresponds to current state-of-the-art experiments [10][11][12][13][14].…”

Environment-induced synchronization of two quantum oscillators

“…We have found that this effect can be triggered by the coupling of the relative motion of the two clouds to a quantum dissipative environment, extending results obtained in Refs. [29,30] in the case of two spins 1/2. In that regime, the overall amplitude of the oscillations decay in time to reach the steady-state x j = 0.…”

Phase-Coherent Dynamics of Quantum Devices with Local Interactions

“…Additionally, we mention that the relation ( 40 ) also affects the phase-shift of reflected or transmitted light through a mesoscopic system in the Kondo LFL regime [ 150 , 151 , 152 ]. Such situations have been recently realized with quantum-dot devices embedded in circuit-QED architectures [ 153 , 154 , 155 , 156 , 157 , 158 , 159 ], in which the driving input signal can be modeled by an AC potential of the form ( 35 ).…”

“…Such an effect was distinctly observed in carbon nanotube devices coupled to high-quality-factor microwave cavities [ 145 ]. These systems efficiently probe the admittance ( 30 ) also in quantum dots with more than two internal degrees of freedom [ 150 , 152 ], such as extensions of the AIM to SU(4) regimes, relevant for quantum dots realized with carbon nanotubes [ 68 , 171 , 172 , 173 , 174 , 175 , 176 , 177 ].…”