Realizing Optical Persistent Spin Helix and Stern-Gerlach Deflection in an Anisotropic Liquid Crystal Microcavity.

Spin-orbit interactions which couple the spin of a particle with its momentum degrees of freedom lie at the center of spintronic applications. Of special interest in semiconductor physics are Rashba and Dresselhaus spin-orbit coupling. When equal in strength, the Rashba and Dresselhaus fields result in SU(2) spin rotation symmetry and emergence of the persistent spin helix only investigated for charge carriers in semiconductor quantum wells. Recently, a synthetic Rashba-Dresselhaus Hamiltonian was shown to describe cavity photons confined in a microcavity filled with optically anisotropic liquid crystal. In this Letter, we present a purely optical realization of two types of spin patterns corresponding to the persistent spin helix and the Stern-Gerlach experiment in such a cavity. We show how the symmetry of the Hamiltonian results in spatial oscillations of the spin orientation of photons traveling in the plane of the cavity.

Engineering spin-orbit synthetic Hamiltonians in liquid-crystal optical cavities.

Spin-orbit interactions lead to distinctive functionalities in photonic systems. They exploit the analogy between the quantum mechanical description of a complex electronic spin-orbit system and synthetic Hamiltonians derived for the propagation of electromagnetic waves in dedicated spatial structures. We realize an artificial Rashba-Dresselhaus spin-orbit interaction in a liquid crystal-filled optical cavity. Three-dimensional tomography in energy-momentum space enabled us to directly evidence the spin-split photon mode in the presence of an artificial spin-orbit coupling. The effect is observed when two orthogonal linear polarized modes of opposite parity are brought near resonance. Engineering of spin-orbit synthetic Hamiltonians in optical cavities opens the door to photonic emulators of quantum Hamiltonians with internal degrees of freedom.

Anomalous Rashba spin-orbit interaction in electrically controlled topological insulator based on InN/GaN quantum wells.

We study theoretically the topological phase transition and the Rashba spin-orbit interaction in electrically biased InN/GaN quantum wells. We show that that for properly chosen widths of quantum wells and barriers, one can effectively tune the system through the topological phase transition applying an external electric field perpendicular to the QW plane. We find that in InN/GaN quantum wells with the inverted band structure, when the conduction band s-type level is below the heavy hole and light hole p-type levels, the spin splitting of the subbands decreases with increasing the amplitude of the electric field in the quantum wells, which reveals the anomalous Rashba effect. Derived effective Rashba Hamiltonians can describe the subband spin splitting only for very small wave vectors due to strong coupling between the subbands. Furthermore, we demonstrate that for InN/GaN quantum wells in a Hall bar geometry, the critical voltage for the topological phase transition depends distinctly on the width of the structure and a significant spin splitting of the edge states lying in the 2D band gap can be almost switched off by increasing the electric field in quantum wells only by a few percent. We show that the dependence of the spin splitting of the upper branch of the edge state dispersion curve on the wave vector has a threshold-like behavior with the on/off spin splitting ratio reaching two orders of magnitude for narrow Hall bars. The threshold wave vector depends weakly on the Hall bar width, whereas it increases significantly with the bias voltage due to an increase of the energetic distance between the s-type and p-type quantum well energy levels and a reduction of the coupling between the subbands.

Operator expansions for polarization mode dispersion analysis and compensation.

We present analytic third- and fourth-order expansions of the Jones matrix as products of exponentials of individual matrices. In our first formalism, these are polarization mode dispersion (PMD) matrices of definite orders. We then discuss an alternative procedure that instead employs exponentials of general skew-Hermitian matrices with a low-order dependence on the deviation of the optical frequency from a central reference frequency. Our expressions correspond to PMD compensators formed from a succession of relatively simple optical components each of which has the frequency response of a single operator in the product.

Spectral density matrix description of polarization mode dispersion.

We introduce a power spectral density matrix formalism that incorporates both the pulse shape and the field polarization and can therefore easily describe averages over random fluctuations of the local birefringence vector. We demonstrate that quantities such as the differential time delay, power diffusion, and decoherence effects can be obtained directly from the equations of motion for the power density matrix. This approach can be applied to pulses with arbitrary frequency-dependent polarization and intensity distributions and in particular makes possible the minimization of the eye-opening penalty through the proper choice of the initial pulse profile.