Optical tuning of Berry phase effect in topological insulators

We theoretically discuss the influence of driving laser field on the topological nature, one of the manifestation of the electron Berry phase effect, in two-dimensional electronic systems. Adiabatic change of the laser amplitude with circular polarization alters the “order parameter”, termed the Chern number, in topological insulator with broken time-reversal symmetry, resulting in photo-induced phase transition. The finding is an optical analog of the integer quantum Hall effect, that is triggered by the laser field instead of magnetic field. This parallelism suggests the similarity of effects to electron dynamics between circularly polarized light and magnetic field.     

Optical anisotropy of volume phase gratings

A propagation of zero diffraction order through a volume phase grating is analysed. It is shown that a phase shift between S and P polarization components arises, thus providing optical anisotrpy of the grating. Experimental verification of theoretical predictions is presented.     

Optical anisotropy as a technique for studying ultrafast phase transformations at solid surfaces

A new technique for testing long-range order in high-absorption anisotropic crystals has been developed using conversion of an incident p-(s-)wave to an s-(p-)wave due to optical anisotropy. The technique yields time-resolved measurements of parameters related to phase transformations in thin (10⁻⁶–10⁻⁵ cm) layers with a high resolution (10⁻¹² s). Using picosecond laser pulses and an “Agat” streak camera, the technique has been applied to an experimental investigation of melting and recrystallization kinetics at zinc and graphite surfaces. It was found that the process of melting takes less than 3 ps and the recrystallization time is about 100 ps. Zh. éksp. Teor. Fiz. 113, 2162–2173 (June 1998)     

Spin Hall effect and Berry phase of spinning particles

We consider the adiabatic evolution of the Dirac equation in order to compute its Berry curvature in momentum space. It is found that the position operator acquires an anomalous contribution due to the non-Abelian Berry gauge connection making the quantum mechanical algebra noncommutative. A generalization to any known spinning particles is possible by using the Bargmann–Wigner equation of motions. The noncommutativity of the coordinates is responsible for the topological spin transport of spinning particles similarly to the spin Hall effect in spintronic physics or the Magnus effect in optics. As an application we predict new dynamics for nonrelativistic particles in an electric field and for photons in a gravitational field.     

Berry phase in a nonisolated system

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin + environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on time scales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin states or the dressed spin resonances. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits.     

Berry phase in a composite system

The Berry phase in a composite system with one driven subsystem has been studied in this Letter. We choose two coupled spin-1 / 2 systems as the composite system; one of the subsystems is driven by a time-dependent magnetic field. We show how the Berry phases depend on the coupling between the two subsystems, and the relation between the Berry phases of the composite system and those of its subsystems.     

Topological Hall effect and Berry phase in magnetic nanostructures

We discuss the anomalous Hall effect in a two-dimensional electron gas subject to a spatially varying magnetization. This topological Hall effect does not require any spin-orbit coupling and arises solely from Berry phase acquired by an electron moving in a smoothly varying magnetization. We propose an experiment with a structure containing 2D electrons or holes of diluted magnetic semiconductor subject to the stray field of a lattice of magnetic nanocylinders. The striking behavior predicted for such a system (of which all relevant parameters are well known) allows one to observe unambiguously the topological Hall effect and to distinguish it from other mechanisms.     

Berry phase and de Haas-van Alphen effect in LaRhIn5

We explain the experimental data on the magnetization of LaRhIn5 recently published by Goodrich et al. [Phys. Rev. Lett. 89, 026401 (2002)]]. We show that the magnetization of a small electron group associated with a band-contact line was detected in that Letter. These data provide the first observation of the Berry phase of electrons in metals via the de Haas-van Alphen effect.     

Polarization as a Berry Phase

The macroscopic polarization of a crystalline dielectric is best defined as a Berry phase of the electronic Bloch wavefunctions, a feature that is best exemplified by the spontaneous polarization of a ferroelectric crystal for which a microscopic theory was previously unavailable.     

Non-Abelian Berry phase in a quantum mechanical environment

We investigate a quantum physical system that can be naturally separated into fast and slow moving components. A modification of the conventional molecular Born-Oppenheimer approximation is considered by taking the intermolecular position vector to be a slowlyvarying quantum mechanical parameter. It is found that the fast motion (electronic degrees of freedom) induces a non-Abelian vector potential (Berry connection) into the dynamics of the slow system (nucleus), thereby modifying the commutation relations of the slow variables.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom--field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index $k$ is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom--field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Particle creation by a black hole as a consequence of the casimir effect

The accelerated-mirror results are applied to a black hole. As a consequence the hole produces black-body radiation. Its temperature exactly coincides with Hawking's result. An important difference between the energy-momentum tensors of scalar and electromagnetic fields near the horizon is discovered.     

Particle creation by a black hole as a consequence of the Casimir effect

Particle creation by a black hole is investigated in terms of temperature corrections to the Casimir effect. The reduction of the Hawking effect to more familiar effects observed in the laboratory enables us to reveal the mechanism of particle creation. The blackbody nature of the Hawking radiation is due to the interaction of virtual particles with the surface of a cavity formed by the Schwarzschild gravitational field potential barrier. These particles are squeezed out by the contraction of the potential barrier and appear to an observer atJ ⁺ as the real blackbody ones.     

Particle creation by a black hole as a consequence of the Casimir effect

It is shown that the effect of particle creation by a black hole is a consequence of the Casimir effect for a spherical shell. The temperature of black-body radiation coincides with that obtained by Hawking.     

Quantized Berry phase in twisted Bloch momentum space as a topological order parameter for spin chains

We show that a quantized Berry phase in Bloch momentum space can serve as a topological order parameter to the quantum phases of a gapped spin chain system with time-reversal invariance. Specifically, we study this approach analytically in a class of XY spin-1/2 chain with multiple sites interactions in a transverse field. In order to derive a proper definition of the Berry curvature in a two-dimensional parameter space, we performed a local gauge transformation to the spin chain system by a twist operator, which endows the Hamiltonian of the system with the topology of a torus T²$T^2$ without changing its energy spectrum. We show that a topological _Z2$Z_2$ order parameter can be obtained as a quantized Berry phase by a loop integral of the Berry gauge potential along quarter of the Brillouin zone, which determines the zero-temperature phase diagram of the system.     

Berry phase generation and measurement in a single trapped ion

In this work, we propose a new design of an ion trap which can enable us to generate state specific Berry phase for a single trapped ion. This allows the study of the underlying Abelian and non-Abelian gauge symmetries and could also have significant implications in quantum computation.