Search results for "Geometric phase"
showing 10 items of 40 documents
Geometric factors in the adiabatic evolution of classical systems
1992
Abstract The adiabatic evolution of the classical time-dependent generalized harmonic oscillator in one dimension is analyzed in detail. In particular, we define the adiabatic approximation, obtain a new derivation of Hannay's angle requiring no averaging principle and point out the existence of a geometric factor accompanying changes in the adiabatic invariant.
Revealing Anisotropy in a Paul Trap Through Berry Phase
2006
When an ion confined in an anisotropic bidimensional Paul trap is subjected to a laser beam oriented along an arbitrary direction, the interaction between its electronic and vibrational degrees of freedom is described by a time-dependent Hamiltonian model as a consequence of the lack of symmetry. Appropriately choosing the laser frequency, the Hamiltonian model turns out to be sinusoidally oscillating at the difference between the proper frequencies of the center of mass of the ion. Thus, if the anisotropy of the trap is sufficiently small, the evolution of the system can be considered as adiabatic. In the context of this physical situation we have calculated the Berry phase acquired in a c…
Orbiting Orbitals: Visualization of Vi-Bronic Motion at a Conical Intersection
2013
The Jahn-Teller (JT) active unpaired electron of single metalloporphyrin radical anions is imaged through scanning tunneling microscopy. It is demonstrated that the electron is delocalized over the porphyrin macrocycle and its topographic image is determined by vibronic motion: the orbital of the electron adiabatically follows the zero-point pseudorotation of skeletal deformations. Transformation of the polar graphs of the observed images allows visualization of the adiabatic vibrational density to which the electron is coupled. The vibronic potential at the conical intersection is visualized and the half-integer angular momentum characteristic of the Berry phase is revealed in the radial f…
Geometric phase induced by a cyclically evolving squeezed vacuum reservoir
2006
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As a specific scheme we analyse a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We propose also a scheme to measure such geometric phase by means of a suitable polarization detection.
Observable geometric phase induced by a cyclically evolving dissipative process
2006
In a prevous paper (Phys. Rev. Lett. 96, 150403 (2006)) we have proposed a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon. The basic idea was to force the ground state of the system to evolve ciclically by "adiabatically" manipulating the environment with which it interacts. The specific scheme we have previously analyzed, consisting of a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath whose squeezing parameters are smoothly changed in time along a closed loop, is here solved in a more direct way. This new solution emphasizes how the geometric phase on the ground state of the system is indeed du…
Connection between optimal control theory and adiabatic-passage techniques in quantum systems
2012
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum Principle. In a three-level quantum system, we show that the Stimulated Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.
Vacuum induced berry phase: Theory and experimental proposal
2003
We investigate quantum effects in geometric phases arising when a two-level system is interacting with a quantized electromagnetic field. When the system is adiabatically driven along a closed loop in the parameter space, signatures of the field quantization are observable in the geometric phase. We propose a feasible experiment to measure these effects in cavity QED and also analyse the semi-classical limit, recovering the usual Berry phase results.
Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
2018
Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets a…
Charge transport through spin-polarized tunnel junction between two spin-split superconductors
2019
We investigate transport properties of junctions between two spin-split superconductors linked by a spin-polarized tunneling barrier. The spin-splitting fields in the superconductors (S) are induced by adjacent ferromagnetic insulating (FI) layers with arbitrary magnetization. The aim of this study is twofold: On the one hand, we present a theoretical framework based on the quasiclassical Green's functions to calculate the Josephson and quasiparticle current through the junctions in terms of the different parameters characterizing it. Our theory predicts qualitative new results for the tunneling differential conductance, $dI/dV$, when the spin-splitting fields of the two superconductors are…
Purification of Lindblad dynamics, geometry of mixed states and geometric phases
2015
We propose a nonlinear Schr\"odinger equation in a Hilbert space enlarged with an ancilla such that the partial trace of its solution obeys to the Lindblad equation of an open quantum system. The dynamics involved by this nonlinear Schr\"odinger equation constitutes then a purification of the Lindbladian dynamics. This nonlinear equation is compared with other Schr\"odinger like equations appearing in the theory of open systems. We study the (non adiabatic) geometric phases involved by this purification and show that our theory unifies several definitions of geometric phases for open systems which have been previously proposed. We study the geometry involved by this purification and show th…