A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also exp
erience dephasing, or quantum diffusion. Here we show that the diffusion of quantum trajectories can also be of geometric nature as characterized by the imaginary part of the geometric phase. Such an imaginary geometric phase results from the interference of geometric phase dependent fluctuations around the quantum trajectory. As a specific example, we study the quantum trajectories of the optically excited electron-hole pairs, driven by an elliptically polarized terahertz field, in a material with non-zero Berry curvature near the energy band extremes. While the real part of the geometric phase leads to the Faraday rotation of the linearly polarized light that excites the electron-hole pair, the imaginary part manifests itself as the polarization ellipticity of the terahertz sidebands. This discovery of geometric quantum diffusion extends the concept of geometric phases.
Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to
understand extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz sideband generation (HSG). While HHG and ATI have been mostly studied in atoms and molecules, the HSG in semiconductors can have interesting effects due to possible nontrivial vacuum states of band materials. We find that in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field can accumulate Berry phases. Taking monolayer MoS$_2$ as a model system, we show that the Berry phases appear as the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.
We report high-temperature (300-1120 K) magnetization data of Fe and Fe3O4 nanoparticles embedded in multi-walled carbon nanotubes. The magnetic impurity concerntations are precisely determined by both high-energy synchrotron x-ray diffractometer and
inductively coupled plasma mass spectrometer. We unambiguously show that the magnetic moments of Fe and Fe3O4 nanoparticles are enhanced by a factor of about 3 compared with what they would be expected to have for free (unembedded) magnetic nanoparticles. The magnetization enhancement factor is nearly independent of the applied magnetic field but depends significantly on the cooling rate. What is more intriguing is that the enhanced moments were completely lost when the sample was heated up to 1120 K and the lost moments at 1120 K were completely recovered through several thermal cycles below 1020 K. Furthermore, there is a rapid increase or decrease in the magnetization below about 60 K. The anomalous magnetic properties cannot be explained by existing physics models except for the paramagnetic Meissner effect due to the existence of ultrahigh temperature superconductivity in the multi-walled carbon nanotubes.
