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Physical Review A

Nonlinear motional effects in the spectroscopy of a trapped and laser-driven atom

Matthias Jakob, B. Kneer, Gagik Yu. Kryuchkyan

Published Dec 1, 1998• 5 citations
Publisher

Abstract

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 $\mathsf{V}$-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.

DOI
10.1103/physreva.58.4728

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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.
A single two-level atom, with quantized center-of-mass motion, is constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical traveling-wave light field. When the classical light field is tuned to the atom's lower vibrational sideband, cooling can occur. The strong-sideband and Lamb-Dicke perturbation regimes for the system are defined. The steady-state and time-evolution behaviors in the strong-sideband regime are discussed and, in particular, it is shown that the steady-state average trap number saturates when spontaneous emission is weak and that the steady-state average trap number depends more strongly on the trap frequency in the saturated regime than previously predicted. Finally, the possibility of observing quantum jumps between trap levels is discussed.
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.
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 dynamics of a two-level atom driven by a single laser beam and three-level atom (Lambda configuration) irradiated by two laser beams are studied taking into account of the quantized center-of-mass motion of the atom. It is shown that the trapped atom system under appropriate resonance condition exhibits the large time-scale revivals when the index of the vibrational sideband responsible for the atomic electronic transition is greater than unity. The revival times are shown to be dependent on the initial number of vibrational excitations and the magnitude of the Lamb-Dicke parameter. The sub-Poissonian statistics in vibrational quantum number is observed at certain time intervals. The minimum time of interaction for which the squeezed states of motional quadrature are generated is found to be decreasing with the increase in the Lamb-Dicke parameter.
Following the path of Bužek et al. in [Phys. Rev. A 56 2352 1997], we investigate the full intensity-dependent interaction between a motional two-level ion which is trapped in a f-deformed oscillator (so possessing vibrational modes too) with a single-mode nonlinear quantized field in the Lamb-Dicke limit. After finding the explicit form of the entire ion-field state vector in a general framework, we particularly restrict ourselves to an appropriate nonlinearity function (describing intensity-dependent interaction) corresponding to the center-of-mass motion of a trapped ion which explicitly depends on the Lamb-Dicke parameter as well as another well-known nonlinearity function in the form n. Then, we evaluate the effects of two different initial quantized field states as well as the considered nonlinearity function (via varying the Lamb-Dicke parameter) on a few physical properties of the system. For this purpose, we pay attention to the amount of entanglement, mean number of vibrational quanta (phonons), population inversion of the two-level ion and Q-distribution function. Finally, by comparing our results with the previously considered “linear” one which is pointed in the above Ref., we establish that, by tuning the Lamb-Dicke parameter, one can adjust the mentioned nonclassical properties of the system appropriately.