Mixed-Order Symmetry-Breaking Quantum Phase Transition Far from Equilibrium.

We study the current-carrying steady state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the nonequilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady states with a nonvanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilibrium case. Our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.

Dephasing due to Nuclear Spins in Large-Amplitude Electric Dipole Spin Resonance.

We analyze effects of the hyperfine interaction on electric dipole spin resonance when the amplitude of the quantum-dot motion becomes comparable or larger than the quantum dot's size. Away from the well-known small-drive regime, the important role played by transverse nuclear fluctuations leads to a Gaussian decay with characteristic dependence on drive strength and detuning. A characterization of spin-flip gate fidelity, in the presence of such additional drive-dependent dephasing, shows that vanishingly small errors can still be achieved at sufficiently large amplitudes. Based on our theory, we analyze recent electric dipole spin resonance experiments relying on spin-orbit interactions or the slanting field of a micromagnet. We find that such experiments are already in a regime with significant effects of transverse nuclear fluctuations and the form of decay of the Rabi oscillations can be reproduced well by our theory.

Diabolical points in multi-scatterer optomechanical systems.

Diabolical points, which originate from parameter-dependent accidental degeneracies of a system's energy levels, have played a fundamental role in the discovery of the Berry phase as well as in photonics (conical refraction), in chemical dynamics, and more recently in novel materials such as graphene, whose electronic band structure possess Dirac points. Here we discuss diabolical points in an optomechanical system formed by multiple scatterers in an optical cavity with periodic boundary conditions. Such configuration is close to experimental setups using micro-toroidal rings with indentations or near-field scatterers. We find that the optomechanical coupling is no longer an analytic function near the diabolical point and demonstrate the topological phase arising through the mechanical motion. Similar to a Fabry-Perot resonator, the optomechanical coupling can grow with the number of scatterers. We also introduce a minimal quantum model of a diabolical point, which establishes a connection to the motion of an arbitrary-spin particle in a 2D parabolic quantum dot with spin-orbit coupling.

Characterization of spin-orbit interactions of GaAs heavy holes using a quantum point contact.

We present transport experiments performed in high-quality quantum point contacts embedded in a GaAs two-dimensional hole gas. The strong spin-orbit interaction results in peculiar transport phenomena, including the previously observed anisotropic Zeeman splitting and level-dependent effective g factors. Here we find additional effects, namely, the crossing and the anticrossing of spin-split levels depending on subband index and magnetic field direction. Our experimental observations are reconciled in a heavy-hole effective spin-orbit Hamiltonian where cubic- and quadratic-in-momentum terms appear. The spin-orbit components, being of great importance for quantum computing applications, are characterized in terms of magnitude and spin structure. In light of our results, we explain the level-dependent effective g factor in an in-plane field. Through a tilted magnetic field analysis, we show that the quantum point contact out-of-plane g factor saturates around the predicted 7.2 bulk value.

Spin-echo dynamics of a heavy hole in a quantum dot.

We develop a theory for the spin-echo dynamics of a heavy hole in a quantum dot, accounting for both hyperfine- and electric-field-induced fluctuations. We show that a moderate applied magnetic field can drive this system to a motional-averaging regime, making the hyperfine interaction ineffective as a decoherence source. Furthermore, we show that decay of the spin-echo envelope is highly sensitive to the geometry. In particular, we find a specific choice of initialization and π-pulse axes which can be used to study intrinsic hyperfine-induced hole-spin dynamics, even in systems with substantial electric-field-induced dephasing. These results point the way to designed hole-spin qubits as a robust and long-lived alternative to electron spins.

Anomalous spin-resolved point-contact transmission of holes due to cubic Rashba spin-orbit coupling.

Evidence is presented for the finite wave vector crossing of the two lowest one-dimensional spin-split subbands in quantum point contacts fabricated from two-dimensional hole gases with strong spin-orbit interaction. This phenomenon offers an elegant explanation for the anomalous sign of the spin polarization filtered by a point contact, as observed in magnetic focusing experiments. Anticrossing is introduced by a magnetic field parallel to the channel or an asymmetric potential transverse to it. Controlling the magnitude of the spin splitting affords a novel mechanism for inverting the sign of the spin polarization.

Quantum Hall ferromagnetic states and spin-orbit interactions in the fractional regime.

The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for fractional quantum Hall states by including correlation effects. A transition of the direction of the spin polarization is predicted at specific values of the Zeeman energy. We show that these values can be expressed in terms of the pair-correlation function, and thus provide information about the microscopic ground state. We examine the particular examples of the Laughlin wave functions and the 5/2-Pfaffian state. We also include effects of the nuclear bath.