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

Abstract

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.

Photonic Berry curvature in double liquid crystal microcavities with broken inversion symmetry

“…On the other hand, the second cavity in our double LC cavity system is tuned to possess two polarization dependent mechanisms in correspondence with recent studies [10,11]. First, a splitting between the TE and TM polarized modes which results in a unique photonic SOC described by an effective in-plane magnetic field which winds itself twice around the momentum space origin, whereas, in comparison, Rashba and Dresselhaus SOCs wind only once.…”

“…Recently, flexible liquid crystal (LC) microcavites have displayed an amazing ability to tune their cavity photon dispersions between the TE and TM polarized modes, realizing synthetic spin-orbit coupling of light [10,11]. The flexibility stems from the voltage dependent orientation of the LC molecular director allowing one to control the dielectric tensor of the cavity by adjusting the voltage applied to the LC.…”

“…It was recently shown that a photonic equivalent of equal Rashba-Dresselhaus (RD) SOC can be synthesized in a single LC cavity [11] through voltage dependent tuning of its LC director. There, cavity modes of orthogonal polarizations and opposite parity were tuned into resonance by rotating the molecular director such that their coupling resulted in an effective RD SOC for the cavity photons.…”

Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

“…Nevertheless, remarkable progress has recently been made. In momentum space, non-Abelian gauge fields manifest as high-dimensional spin-orbit coupling 30,31 in atoms 32,33 , liquid crystals 34 and exciton-polaritons 35,36 . They also affect the wavepacket evolution in the momentum space of mechanical lattices 37 .…”

Manipulation of room-temperature valley-coherent exciton-polaritons in atomically thin crystals by real and artificial magnetic fields

“…Furthermore, it is straightforward to enhance and maximize the effect, e.g. by utilizing microcavities with a strong asymmetry 36 , yielding strongly extended TE-TM splitting, or by engineering the natural birefringence reversibly, as has been demonstrated recently by applying external stress to semiconductor microcavities 37 , or by utilizing strongly anisotropic liquid crystal filled DBR devices 38 . In such structures, it will be possible to gain control over the valley -pseudospin, its coherence, and finally the topology of valley polaritons in an unprecedented manner, by taking advantage of the coherent light-matter coupling.…”