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Physical Review A

Microwave multiphoton Rabi oscillations

M. Gatzke, M. C. Baruch, R. B. Watkins, Thomas F. Gallagher

Published Dec 1, 1993• 22 citations
Publisher

Abstract

We have made direct observations of microwave multiphoton Rabi oscillations between two Rydberg states in potassium in the strong-radiation-field regime, where a perturbative treatment of the atom-field interaction becomes invalid. The results of measurements of the Rabi oscillation frequency are presented and compared with results calculated using Floquet theory, which predicts a very different field dependence for the Rabi frequency than is typical in the perturbation-theory limit.

DOI
10.1103/physreva.48.4742

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We have made direct observations of microwave multiphoton Rabi oscillations between two Rydberg states in potassium in the strong-radiation-field regime, where a perturbative treatment of the atom-field interaction becomes invalid. The results of measurements of the Rabi oscillation frequency are presented and compared with results calculated using Floquet theory, which predicts a very different field dependence for the Rabi frequency than is typical in the perturbation-theory limit.
We have applied a nonperturbative resonant theory to study the Rabi frequency of microwave multiphoton transitions between two Rydberg states of potassium in a static electric field. The Stark electric dipole moments used to calculate the Rabi frequency are determined by the Stark states' wave functions, which are obtained by the diagonalization method. The frequencies of the Rabi oscillations are in good agreement with either experimental ones or ones calculated by the time-dependent close-coupling method and the Floquet theory. Furthermore, we are able to show that the size of avoided crossings between the (n+2)s(n+2)s(n+2)s and (n,3)(n,3)(n,3) states can be predicted from the Stark electric dipole moment and the difference of the two Stark states' energy at a given resonance.
We report an experimental study of one- and two-photon Rabi oscillations and other coherent effects in microwave transitions between Rydberg states of calcium. Selective field ionization allows us to observe the time evolution of both the initial and final states with high discrimination. The experiments include measurements of the dependence of the one- and two-photon oscillation frequencies on microwave power and detuning from resonance. We have used the off-resonant behavior of the two-photon oscillation frequency to measure the ac Stark shift. In a magnetic field we have also observed the free evolution of the magnetic sublevels and the effect of Zeeman splitting on the one-photon Rabi oscillations. The theory for these experiments is presented; our results are in excellent agreement.
By using the B -spline expansion technique and a model potential of the alkali atoms, the properties of frequency-modulated excitation of Rydberg potassium atoms in a static electric field and a microwave field are investigated by using the time-dependent two-level approach. We successfully reproduce the square wave oscillations in the low frequency, the stair step population oscillations in the intermediate frequency, and the multiphoton transitions in the high frequency with respect to the unmodulated Rabi frequency, which have been observed experimentally by Noel et al. [ Phys. Rev. A 58 2265 (1998) ]. Furthermore, we also numerically obtain the discretized Rabi oscillations predicted in the Landau—Zener accumulation model.
We present a detailed experimental study of the frequency-modulated excitation of a two-level atom, using a microwave field to drive transitions between two Rydberg Stark states of potassium. In the absence of a modulation the interaction is the standard model of the Rabi problem, producing sinusoidal oscillations of the population between the two states. In the presence of a frequency modulation of the interacting field, however, the time evolution of the system is significantly modified, producing square wave oscillations of the population, sinusoidal oscillations at a different frequency, or even sinusoidal oscillations built up in a series of stair steps. The three responses described above are each found in a different regime for the frequency of the modulation with respect to the unmodulated Rabi frequency: the low-, high-, and intermediate-frequency regimes, respectively.
By using the B-spline expansion technique and a model potential of the alkali atoms, the properties of frequency- modulated excitation of Rydberg potassium atoms in a static electric field and a microwave field are investigated by using the time-dependent two-level approach. We successfully reproduce the square wave oscillations in the low frequency, the stair step population oscillations in the intermediate frequency, and the multiphoton transitions in the high frequency with respect to the unmodulated Rabi frequency, which have been observed experimentally by Noel et al. [Phys. Rev. A 58 2265 (1998)]. Furthermore, we also numerically obtain the discretized Rabi oscillations predicted in the Landau-Zener accumulation model.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.