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Fortschritte der Physik

A Realistic Proposal for the Observation of Zeno Phenomena in the Dynamics of Trapped Ions

Sabrina Maniscalco, Antonio Messina

Published Oct 1, 2001• 4 citations
Publisher

Abstract

A realistic experimental scheme for the observation of a continuous measurement Quantum Zeno Effect in the contest of single trapped ions is proposed. Our method relies on the nonlinearities characterizing the ionic Rabi frequency far from the Lamb-Dicke regime.
DOI
10.1002/1521-3978(200110)49:10/11<1027::aid-prop1027>3.0.co;2-8

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We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a blockade on the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We propose to use this blockade as a resource for the dissipative generation of high-number Fock states. Also, we compare the linear and nonlinear cases of the quantum Rabi model in the ultrastrong and deep strong-coupling regimes. Moreover, we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red- and blue-sideband interactions in a single trapped ion, yielding applications as a dynamical quantum filter.
We present an alternative scheme for the generation of a two-qubit quantum gate interaction between laser-cooled trapped ions. The scheme is based on the ac Stark shift (light shift) induced by laser light resonant with the ionic transition frequency. At specific laser intensities, the shift of the ionic levels allows the resonant excitation of transitions involving the exchange of motional quanta. We compare the performance of this scheme with respect to that of related ion-trap proposals and find that, for an experimental realization using traveling-wave radiation and working in the Lamb-Dicke regime, an improvement of over an order of magnitude in the gate switching rate is possible.
First order Doppler effects are usually ignored in laser driven trapped ions when the recoil frequency is much smaller than the trapping frequency (Lamb-Dicke regime). This means that the central, carrier excitation band is supposed to be unaffected by vibronic transitions in which the vibrational number changes. While this is strictly true in the Lamb-Dicke limit (infinitely tight confinement), the vibronic transitions do play a role in the Lamb-Dicke regime. In this paper we quantify the asymptotic behavior of their effect with respect to the Lamb-Dicke parameter. In particular, we give analytical expressions for the frequency shift, ``pulling'' or ``pushing,'' produced in the carrier absorption band by the vibronic transitions both for Rabi and Ramsey schemes. This shift is shown to be independent of the initial vibrational state.