Geometric phases in multidirectional electromagnetic coupling theory

Yuchao Zhang, Kang Li B

Mustapha Maamache, Nadir Chaabi, J. R. Choi

Ludmila Viotti, Fernando C. Lombardo, Paula I. Villar

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.

Lei Xing

We have obtained the geometric phase of the tripartite spin-1/2 system with spin-spin coupling and discussed the influence of this coupling on the geometric phase. We have discovered the coupling-independent geometric phase and explained it. Based on this work, we propose the concept of quasimagnetic field and assimilate the coupling into the parameter space. By this theory, the relation between the geometric phase and the solid angle in parameter space still holds for a system with spin-spin coupling if the concept of the parameter is properly revised in the way we have elucidated.

Ludwig-Maximilians-Universität München, Detlef Dürr

Ravi Baijulal Bhandari