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Nonadiabatic geometric phase induced by Stark shift

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

Published Jul 13, 2004• 0 citations
OpenAlex

Abstract

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 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 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 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.
We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr\"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which can generate a pair of dressed even and odd coherent states (i.e., Schr\"odinger cat states) for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, we show how to implement nonadiabatic geometric quantum computation with cat qubits. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, 1/f1/f1/f noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.
We propose a feasible experiment to investigate quantum effects in geometric phases, arising when a classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of the quantization of the electromagnetic field through a vacuum effect in Berry's phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasiclassical field. We also analyze the semiclassical limit recovering the usual Berry's phase results.
Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.