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Physical Review A

Dynamics of a Rabi oscillation under a pulsed perturbation

Jai Min Choi, Gee-Na Kim, D. Cho

Published Jan 22, 2008• 6 citations
Publisher

Abstract

We study how a Rabi oscillation is affected by a periodic pulsed perturbation. Unlike a continuous perturbation, which simply shifts the resonance frequency, a pulsed perturbation splits the Rabi resonance into two lines separated by the pulse repetition rate. When the perturbation integrated over one pulse is equal to $\ensuremath{\pi}$, the resonance splits into two symmetrically placed lines at \ifmmode\pm\else\textpm\fi{} half the pulse repetition rate. When it is $2\ensuremath{\pi}$, the Rabi oscillation is unaffected by the perturbation. We demonstrate these behaviors using the ground hyperfine transition of cesium atoms in a magneto-optical trap. The pulsed perturbation is introduced by a periodic magnetic field pulse. The $2\ensuremath{\pi}$ case is compared with the self-induced transparency, and its implications for optical frequency metrology using a pulsed optical trap is discussed.

DOI
10.1103/physreva.77.010501

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We study how a Rabi oscillation is affected by a periodic pulsed perturbation. Unlike a continuous perturbation, which simply shifts the resonance frequency, a pulsed perturbation splits the Rabi resonance into two lines separated by the pulse repetition rate. When the perturbation integrated over one pulse is equal to \ensuremathπ\ensuremath{\pi}\ensuremathπ, the resonance splits into two symmetrically placed lines at \ifmmode\pm\else\textpm\fi{} half the pulse repetition rate. When it is 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ, the Rabi oscillation is unaffected by the perturbation. We demonstrate these behaviors using the ground hyperfine transition of cesium atoms in a magneto-optical trap. The pulsed perturbation is introduced by a periodic magnetic field pulse. The 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ case is compared with the self-induced transparency, and its implications for optical frequency metrology using a pulsed optical trap is discussed.
We present the first experimental observation of the Rabi splitting of M\"ossbauer resonance lines. A radio-frequency magnetic field is tuned to induce transitions between hyperfine sublevels of the Zeeman-split excited or ground state of 57Fe^{57}\mathrm{Fe}57Fe nuclei. The line splitting corresponding to the Rabi flopping frequency is observed using a magnetically soft 57FeNi^{57}\mathrm{FeNi}57FeNi absorber foil of composition with almost zero magnetostriction.
We perform spectroscopy on the hyperfine splitting of 85^{85}85Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then show how hyperfine spectroscopy can be used to study quantum dynamics of optically trapped atoms.
Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid matrix and coupled by magnetic dipole interactions is theoretically studied. It is shown that these interactions result in random shifts of spin transient nutation frequencies and thus lead to the decay of the transient signal. Averaging over random spatial distribution of spins within the solid and over their spectral positions within magnetic resonance line, we obtain analytical expressions for the decay of Rabi oscillations. The rate of the decay in the case when the half-width of magnetic resonance line exceeds Rabi frequency is found to depend on the intensity of resonant microwave field and on the spin concentration. The results are compared with the literature data for E ′ 1 centers in glassy silica and [AlO 4 ] 0 centers in quartz.
The influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.