SO (SO) interactions give a spin-dependent correctionrso to the position operator, referred to as the anomalous position operator. We study the contributions ofrso to the spin-Hall effect (SHE) in quasi two-dimensional (2D) semiconductor quantum wells with strong band structure SO interactions that cause spin precession. The skew scattering and side-jump scattering terms in the SHE vanish, but we identify two additional terms in the SHE, due torso, which have not been considered in the literature so far. One term reflects the modification of spin precession due to the action of the external electric field (the field drives the current in the quantum well), which produces, viarso, an effective magnetic field perpendicular to the plane of the quantum well. The other term reflects a similar modification of spin precession due to the action of the electric field created by random impurities, and appears in a careful formulation of the Born approximation. We refer to these two effects collectively as anomalous spin precession and we note that they contribute to the SHE to the first order in the SO coupling constant even though they formally appear to be of second order. In electron systems with weak momentum scattering, the contribution of the anomalous spin precession due to the external electric field equals 1/2 the usual side-jump SHE, while the additional impurity-dependent contribution depends on the form of the band structure SO coupling. For band structure SO coupling linear in wave vector the two anomalous spin precession contributions cancel. For band structure SO coupling cubic in wave vector, however, they do not cancel, and the anomalous spin precession contribution to the SHE can be detected in a high-mobility 2DEG with strong SO coupling. In 2D hole systems both anomalous spin precession contributions vanish identically.
We propose a sub-Doppler laser cooling mechanism that takes advantage of the unique spectral features and extreme dispersion generated by the phenomenon of electromagnetically induced transparency (EIT). EIT is a destructive quantum interference phenomenon experienced by atoms with multiple internal quantum states when illuminated by laser fields with appropriate frequencies. By detuning the lasers slightly from the "dark resonance", we observe that, within the transparency window, atoms can be subject to a strong viscous force, while being only slightly heated by the diffusion caused by spontaneous photon scattering. In contrast to other laser cooling schemes, such as polarization gradient cooling or EIT-sideband cooling, no external magnetic field or strong external confining potential is required. Using a semiclassical approximation, we derive analytically quantitative expressions for the steady-state temperature, which is confirmed by full quantum mechanical numerical simulations. We find that the lowest achievable temperatures approach the single-photon recoil energy. In addition to dissipative forces, the atoms are subject to a stationary conservative potential, leading to the possibility of spatial confinement. We find that under typical experimental parameters this effect is weak and stable trapping is not possible.
Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a “magic” lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.
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