Related papers: Comment on the Adiabatic Condition
We consider in sufficient detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties…
The standard quantum mechanical electronic state calculations for molecules and solids uses the Schroedinger representation where the momentum conjugate to the coordinate $q_r$ is given by $-hbar {partial over {partial q_r}}$. This…
We present measurements of the Berry Phase in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. Our results demonstrate the remarkable degree of coherent control achievable in the presence of a highly…
We argue the feasibility to study the phase structure of a quantum physical system on quantum devices via adiabatic preparation of states. We introduce a novel method and successfully test it in application to the Schwinger model in the…
We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons…
We make use of a superconducting qubit to study the effects of noise on adiabatic geometric phases. The state of the system, an effective spin one-half particle, is adiabatically guided along a closed path in parameter space and thereby…
We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the…
The effect of inter-subsystem couplings on the Berry phase of a composite system as well as that of its subsystem is investigated in this paper. We analyze two coupled spin-$\frac 1 2 $ particles with one driven by a quantized field as an…
Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting…
We study the role of different orientations of an applied magnetic field as well as the interplay of structural asymmetries on the characteristics of eigenstates in a quantum ring system. We use a nearly analytical model description of the…
Adiabatic invariants are introduced and shown to provide an approximate second integral of motion for the non-integrable Dicke model, in the energy region where the system exhibits a regular dynamics. This low-energy region is always…
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the…
Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general quantum states. For example, the Berry…
Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter.…
The aim of the present paper is to propose experiments for observing the significant features of Berry's phases for S>1, generated by spin-Hamiltonians endowed with two couplings, a magnetic dipole and an electric quadrupole one with…
We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled qubits…
We present the first measurements of the Berry phase in a superconducting Cooper pair pump. A fixed amount of Berry phase is accumulated to the quantum-mechanical ground state in each adiabatic pumping cycle, which is determined by…
We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry…
Adiabatic processes in the quantum Ising model and the anisotropic Heisenberg model are discussed. The adiabatic processes are assumed to consist in the slow variation of the strength of the magnetic field that environs the spin-systems.…
Within the context of very simple avoided crossing, we investigate the investigate the effect of a complex diabatic coupling in determining spin-dependent rate constants and scattering states. We find that, if the molecular geometry is not…