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Chinese Physics Letters

Non-Adiabatic Geometric Phase in a Dispersive Interaction System

Ji-Bing Liu, Jiahua Li, Xin‐You Lü, Anshou Zheng

Published May 1, 2007• 1 citation
Publisher

Abstract

We investigate the geometric phase and dynamic phase of a two-level fermionic system with dispersive interaction, driven by a quantized bosonic field which is simultaneously subjected to parametric amplification. It is found that the geometric phase is induced by a counterpart of the Stark shift. This effect is due to distinct shifts in the field frequency induced by interaction between different states (| e ⟩ and | g ⟩) and cavity field, and a simple geometric interpretation of this phenomenon is given, which is helpful to understand the natural origin of the geometric phase.

DOI
10.1088/0256-307x/24/5/003

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We investigate the geometric phase and dynamic phase of a two-level fermionic system with dispersive interaction, driven by a quantized bosonic field which is simultaneously subjected to parametric amplification. It is found that the geometric phase is induced by a counterpart of the Stark shift. This effect is due to distinct shifts in the field frequency induced by interaction between different states (| e ⟩ and | g ⟩) and cavity field, and a simple geometric interpretation of this phenomenon is given, which is helpful to understand the natural origin of the geometric phase.
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We introduce a feasible scheme, considering nowadays available technology, to control and measure nonadiabatic geometrical phases in cavity quantum electrodynamics. Our proposal employs the dispersive interaction of a two-level atom with a quantized cavity field driving by a time dependent linear amplification process. A geometrical phase factor in the state of the system is introduced by such amplification process which depends on the atomic state (due to the Stark shift). We provide a geometrical interpretation of this effect that may be useful for implementation of geometric quantum computation. Finally, we show how to measure this effect in an interferometric experiment and to generate geometrical "Schrodinger cat"-like states.
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We consider a cavity field state, which is created by the atom-cavity field's interaction in the presence of a driven field. The two-level atom passes through the cavity and is driven by a weak classical field. A photon number dependent Stark shift is induced by the atom's dispersive interaction with the cavity field. When the atom is in excited state ∣a⟩|a\rangle∣a⟩, the output cavity field thus obtained is taken into consideration. With the help of the state evaluated, we investigate different statistical properties such as photon number distribution, Wigner function, Mandel's QQQ parameter and squeezing.
In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom–field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom–field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.