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arXiv:1604.05100 · Journal of Experimental and Theoretical Physics Letters

Non-adiabatic geometric phases and dephasing in an open quantum system

Aleksandr E. Svetogorov, Yu. Makhlin

Published Apr 1, 2016• 0 citations
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Abstract

We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of both weak short-correlated noise and slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit.

DOI
10.1134/s0021364016080129

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We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of both weak short-correlated noise and slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit.
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A quantum system interacting with its environment is subject to dephasing, which ultimately destroys the information it holds. Here we use a superconducting qubit to experimentally show that this dephasing has both dynamic and geometric origins. It is found that geometric dephasing, which is present even in the adiabatic limit and when no geometric phase is acquired, can either reduce or restore coherence depending on the orientation of the path the qubit traces out in its projective Hilbert space. It accompanies the evolution of any system in Hilbert space subjected to noise.
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The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus applicable to a quantitative analysis of transitional regions away from ideal adiabaticity. In view of the recent experimental observation of the Berry phase in a superconducting qubit, we illustrate our formulation for a concrete adiabatic case in the Ohmic dissipation. The correction to the total phase together with the geometry-dependent dephasing time is given in a transparent way. The behavior of the geometric phase away from ideal adiabaticity is also analyzed in some detail.
Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak-coupling limit, and it involves the phase information of the environment in general. In contrast with the geometric phase in dissipative systems, the geometric phase acquired by the system can be observed on a long time scale. We also show that with the system decohering to its pointer states, the geometric phase factor tends to a weighted sum over the phase factors pertaining to the pointer states.
The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus applicable to a quantitative analysis of transitional regions away from ideal adiabaticity. In view of the recent experimental observation of the Berry phase in a superconducting qubit, we illustrate our formulation for a concrete adiabatic case in the Ohmic dissipation. The correction to the total phase together with the geometry-dependent dephasing time is given in a transparent way. The behavior of the geometric phase away from ideal adiabaticity is also analyzed in some detail.