Antisymmetric PT-photonic structures with balanced positive and negative index materials

We propose a new class of synthetic optical materials in which the refractive index satisfies n(-\bx)=-n^*(\bx). We term such systems antisymmetric parity-time (APT) structures. Unlike PT-symmetric systems which require balanced gain and loss, i.e. n(-\bx)=n^*(\bx), APT systems consist of balanced positive and negative index materials. Despite the seemingly PT-symmetric optical potential V(\bx)\equiv n(\bx)^2\omega^2/c^2, APT systems are not invariant under combined PT operations due to the discontinuity of the spatial derivative of the wavefunction. We show that APT systems can display intriguing properties such as spontaneous phase transition of the scattering matrix, bidirectional invisibility, and a continuous lasing spectrum.Comment: 5 pages, 4 figure

Spin-orbit interaction in quantum dots in the presence of exchange correlations

We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different symmetries of the spin-orbit coupling, the problem has no closed solution. A conventional choice of a many-particle basis in a numerical diagonalization is the set of Slater determinants built from the single-particle eigenstates of the one-body Hamiltonian (including the spin-orbit terms). We develop a different approach based on the use of a good-spin many-particle basis that is composed of the eigenstates of the universal Hamiltonian in the absence of spin-orbit scattering. We introduce a complete labelling of this good-spin basis and use angular momentum algebra to calculate in closed form the matrix elements of the spin-orbit interaction in this basis. Spin properties, such as the ground-state spin distribution and the spin excitation function, are easily calculated in this basis.Comment: 14 pages, 3 figure

Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks

The quantum dynamics of open many-body systems poses a challenge for computational approaches. Here we develop a stochastic scheme based on the positive P phase-space representation to study the nonequilibrium dynamics of coupled spin-boson networks that are driven and dissipative. Such problems are at the forefront of experimental research in cavity and solid state realizations of quantum optics, as well as cold atom physics, trapped ions and superconducting circuits. We demonstrate and test our method on a driven, dissipative two-site system, each site involving a spin coupled to a photonic mode, with photons hopping between the sites, where we find good agreement with Monte Carlo Wavefunction simulations. In addition to numerically reproducing features recently observed in an experiment [Phys. Rev. X 4, 031043 (2014)], we also predict a novel steady state quantum dynamical phase transition for an asymmetric configuration of drive and dissipation.Comment: 15 pages, 8 figure