Symmetry Analysis of Geometric-Phase Effects in Quantum Dynamics

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more

Razmik G. Unanyan, Michael Fleischhauer

A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are accompanied by dynamical phases and are thus not robust, we show that in the more general case of an $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ symmetry it is possible to obtain a nonvanishing geometric phase without dynamical contributions. The scheme is illustrated for a phase gate using two systems with dipole-dipole interactions in external laser fields which form an effective four-level system.

Jincheng Zhang

Quantum-enhanced Geometric Phase Field Analysis presents a novel methodology for investigating complex geometric phase field dynamics. This research delves into the application of quantum algorithms to accelerate and refine the analysis of these fields, offering unprecedented insights into fundamental physics. The core mechanism centers around 'Quantum Geometric Phase Field Analysis,' a process designed to effectively navigate and understand intricate geometric phase field evolution. This work aims to provide a fundamentally new approach to solving problems currently challenging the intersection of quantum mechanics and geometric physics, potentially unlocking new discoveries and insights into complex systems.

Aron Kuppermann

Ali Mostafazadeh

We introduce the notion of the geometrically equivalent quantum systems (GEQSs) as quantum systems that lead to the same geometric phases for a given complete set of initial state vectors. We give a characterization of the GEQSs. These systems have a common dynamical invariant, and their Hamiltonians and evolution operators are related by symmetry transformations of the invariant. If the invariant is T -periodic, the corresponding class of GEQSs includes a system with a T -periodic Hamiltonian. We apply our general results to study the classes of GEQSs that include a system with a cranked Hamiltonian H ( t ) = e -i Kt H 0 e i Kt . We show that the cranking operator K also belongs to this class. Hence, in spite of the fact that it is time independent, it leads to nontrivial cyclic evolutions and geometric phases. Our analysis allows for an explicit construction of a complete set of nonstationary cyclic states of any time-independent simple harmonic oscillator. The period of these cyclic states is half the characteristic period of the oscillator.

A. Cabo, J. L. Lucio