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arXiv:quant-ph/0407093 · Europhysics Letters (EPL)

Nonadiabatic geometric phase induced by a counterpart of the Stark shift

Eduardo I. Duzzioni, Celso J. Villas-Bôas, Salomon Sylvain Mizrahi, M. H. Y. Moussa, Roberto M. Serra

Published Aug 30, 2005• 8 citations
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Abstract

We analyse the geometric phase due to the Stark shift in a system composed of a bosonic field, driven by time-dependent linear amplification, interacting dispersively with a two-level (fermionic) system. We show that a geometric phase factor in the joint state of the system, which depends on the fermionic state (resulting form the Stark shift), is introduced by the amplification process. A clear geometrical interpretation of this phenomenon is provided. We also show how to measure this effect in an interferometric experiment and to generate geometric "Schrödinger cat"-like states. Finally, considering the currently available technology, we discuss a feasible scheme to control and measure such geometric phases in the context of cavity quantum electrodynamics.

DOI
10.1209/epl/i2005-10209-9

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We analyse the geometric phase due to the Stark shift in a system composed of a bosonic field, driven by time-dependent linear amplification, interacting dispersively with a two-level (fermionic) system. We show that a geometric phase factor in the joint state of the system, which depends on the fermionic state (resulting form the Stark shift), is introduced by the amplification process. A clear geometrical interpretation of this phenomenon is provided. We also show how to measure this effect in an interferometric experiment and to generate geometric "Schrödinger cat"-like states. Finally, considering the currently available technology, we discuss a feasible scheme to control and measure such geometric phases in the context of cavity quantum electrodynamics.
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.
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.
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing.