Universality of Boundary Charge Fluctuations.

We establish the quantum fluctuations ΔQ_{B}^{2} of the charge Q_{B} accumulated at the boundary of an insulator as an integral tool to characterize phase transitions where a direct gap closes (and reopens), typically occurring for insulators with topological properties. The power of this characterization lies in its capability to treat different kinds of insulators on equal footing, being applicable to transitions between topological and nontopological band, Anderson, and Mott insulators alike. In the vicinity of the phase transition, we find a universal scaling ΔQ_{B}^{2}(E_{g}) as a function of the gap size E_{g} and determine its generic form in various dimensions. For prototypical phase transitions with a massive Dirac-like bulk spectrum, we demonstrate a scaling with the inverse gap in one dimension and a logarithmic one in two dimensions.

Few-Mode Geometric Description of a Driven-Dissipative Phase Transition in an Open Quantum System.

By example of the nonlinear Kerr mode driven by a laser, we show that hysteresis phenomena in systems featuring a driven-dissipative phase transition can be accurately described in terms of just two collective, dissipative Liouvillian eigenmodes. The key quantities are just two components of a non-Abelian geometric connection, even though a single parameter is driven. This powerful geometric approach considerably simplifies the description of driven-dissipative phase transitions, extending the range of computationally accessible parameter regimes, and providing a new starting point for both experimental studies and analytical insights.

Nonreciprocity Realized with Quantum Nonlinearity.

Nonreciprocal devices are a key element for signal routing and noise isolation. Rapid development of quantum technologies has boosted the demand for a new generation of miniaturized and low-loss nonreciprocal components. Here, we use a pair of tunable superconducting artificial atoms in a 1D waveguide to experimentally realize a minimal passive nonreciprocal device. Taking advantage of the quantum nonlinear behavior of artificial atoms, we achieve nonreciprocal transmission through the waveguide in a wide range of powers. Our results are consistent with theoretical modeling showing that nonreciprocity is associated with the population of the two-qubit nonlocal entangled quasidark state, which responds asymmetrically to incident fields from opposing directions. Our experiment highlights the role of quantum correlations in enabling nonreciprocal behavior and opens a path to building passive quantum nonreciprocal devices without magnetic fields.

Scattering of two photons from two distant qubits: exact solution.

We consider the inelastic scattering of two photons from two qubits separated by an arbitrary distance R and coupled to a one-dimensional transmission line. We present an exact, analytical solution to the problem, and use it to explore a particular configuration of qubits that is transparent to single-photon scattering, thus highlighting non-Markovian effects of inelastic two-photon scattering: strong two-photon interference and momentum dependent photon (anti)bunching. This latter effect can be seen as an inelastic generalization of the Hong-Ou-Mandel effect.

Nonequilibrium Kondo model: crossover from weak to strong coupling.

We analyze the nonequilibrium Kondo model at finite voltage and temperature by using a new formulation of the real-time renormalization group method with the Laplace variable as the flow parameter. We evaluate the energy-dependent spin relaxation rate and nonlinear conductance, and derive an approximate form for the universal line shape for the latter in the whole crossover regime from weak to strong coupling. The results are shown to agree well with exact methods in equilibrium, Fermi-liquid theory, weak-coupling expansions, and recent experiments. For the transient spin dynamics we find a universal exponential decay in the long-time limit along with a truncation-dependent pre-exponential power law. For multichannel models a pure power-law decay typical for non-Fermi-liquid behavior is predicted.

Relaxation versus decoherence: spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field.

Using a nonequilibrium renormalization group method we study the real-time evolution of spin and current in the anisotropic Kondo model (both antiferromagnetic and ferromagnetic) at a finite magnetic field h(0) and bias voltage V. We derive analytic expressions for all times in the weak-coupling regime max{V, h(0),1/t} >> T(c) (T(c) is the strong-coupling scale). We find that all observables decay both with the spin relaxation and decoherence rates Gamma(1/2). Various V-dependent logarithmic, oscillatory, and power-law contributions are predicted. The low-energy cutoff of logarithmic terms is generically identified by the difference of transport decay rates. For small times t << max{V, h(0)}(-1), we obtain universal dynamics for spin and current.

Supersymmetry in quantum optics and in spin-orbit coupled systems.

Light-matter interaction is naturally described by coupled bosonic and fermionic subsystems. This suggests that a certain Bose-Fermi duality is naturally present in the fundamental quantum mechanical description of photons interacting with atoms. We reveal submanifolds in parameter space of a basic light-matter interacting system where this duality is promoted to a supersymmetry (SUSY) which remains unbroken. We show that SUSY is robust with respect to decoherence and dissipation. In particular, the stationary density matrix at the supersymmetric lines in parameter space has a degenerate subspace. The dimension of this subspace is given by the Witten index and thus is topologically protected. As a consequence, the dissipative dynamics is constrained by a robust additional conserved quantity which translates information about an initial state into the stationary state. In addition, we demonstrate that the same SUSY structures are present in condensed matter systems with spin-orbit couplings of Rashba and Dresselhaus types, and therefore spin-orbit coupled systems at the SUSY lines should be robust with respect to various types of disorder. Our findings suggest that optical and condensed matter systems at the SUSY points can be used for quantum information technology and can open an avenue for quantum simulation of SUSY field theories.