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arXiv:quant-ph/0607015 · Physical Review A

Vibronic Rabi resonances in harmonic and hard-wall ion traps for arbitrary laser intensity and detuning

Ion Lizuain, Juan Gonzalo Muga

Published Mar 26, 2007• 11 citations
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Abstract

We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard-wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well-isolated Rabi resonances, where the detuning-adapted Rabi frequency coincides with the transition frequency between vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.

DOI
10.1103/physreva.75.033613

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We investigate laser-driven vibronic transitions of a single two-level atomic ion in harmonic and hard-wall traps. In the Lamb-Dicke regime, for tuned or detuned lasers with respect to the internal frequency of the ion, and weak or strong laser intensities, the vibronic transitions occur at well-isolated Rabi resonances, where the detuning-adapted Rabi frequency coincides with the transition frequency between vibrational modes. These vibronic resonances are characterized as avoided crossings of the dressed levels (eigenvalues of the full Hamiltonian). Their peculiarities due to symmetry constraints and trapping potential are also examined.
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.
The interaction of a cold trapped ion with a strong laser field is studied in a configuration in which quasienergetic levels become important but heating of the system is unessential. Absorption spectroscopy of the quasienergetic states of a strongly confined and laser-driven trapped ion is analyzed by probing vibrational transitions. Calculations are carried out analytically by using the master equation in quasienergetic state representation. We consider a V\mathsf{V}V-level scheme for the ion with a resonant strong pump field and a weak probe field. The steady-state and time-evolution behavior of the system is discussed and the probe-field absorption spectrum for various initial population distributions of the motional state is calculated. It is found that the absorption spectrum displays vibrational sidebands with multipeak splitting due to the nonlinear dependence of the Rabi frequencies on both the Lamb-Dicke parameter and the trap occupation number. This multipeak splitting has interesting consequences and can be useful for the measurement of the initial trap number population distribution.
It is well known that electronic transitions driven by nearly resonant travelling- or standing- wave lasers are often accompanied with vibrational sideband transitions of a single trapped ion undergoing quantized center-of-mass motion [1], Our previous studies showed that quantum statistics of radiation fields can be used to manipulate the vibronic motion of a trapped ion localised within the Lamb-Dicke limit (LDL) [2]. The present paper addresses quantum manipulating vibronic motion of an ion trapped far beyond the LDL.
We investigate the resonance fluorescence emission and absorption spectra for a one-dimensional harmonically trapped two-level ion. The master equation is used to generate the atomic polarizations from which the spectra are derived. Because of their size, the final density matrix equations are investigated numerically. The calculations are carried out in the Lamb-Dicke limit of tight localization of the ion. Sharp peaks are found to appear in the spectra at frequencies detuned from line centre by steps of the trap frequency. The frequency of the peaks and their superposition with Rabi sidebands above saturation are analysed for a variety of parameter ranges. Moreover, new features of the absorption spectra of a weak probe such as sharp gain regions around the trap sidebands are also discussed.
The resonance fluorescence from a vibronic system with displaced potential-energy surfaces is studied. Because of the equal vibrational frequencies in the two electronic quantum states, a large number of vibronic transitions can be excited by a strong laser field. Even in the case of weaker driving fields, nonperturbative effects may be observed provided that the vibrational relaxation is slow enough. If the vibronic coupling is not extremely strong, the Rabi oscillations will arise mainly from the excitation of the vibrationless transition. Furthermore, the damping of the Rabi oscillations may be accompanied by a substantial decrease in intensity.
The nonlinear interaction of three ions in a linear trap with laser light is studied by taking into account the three vibrational modes within a rotating-wave approximation. It is demonstrated that, for localization conditions far from the Lamb-Dicke limit, all three modes have a significant impact on the dynamics of the system. Preparations of vibrational Fock states can be used to realize two different regimes with an exactly solvable three-atom dynamics. The first one corresponds to a nonlinear version of the Tavis-Cummings coupling, whereas the Tavis-Cummings type interactions are suppressed in the second one.