Dynamics of a Rabi oscillation under a pulsed perturbation

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 $\pi$, the resonance splits into two symmetrically placed lines at ± half the pulse repetition rate. When it is $2\pi$, 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 $2\pi$ case is compared with the self-induced transparency, and its implications for optical frequency metrology using a pulsed optical trap is discussed.

Figure 1

(Color online) An electron spin $\vec{S}$ in a rotating frame. Curve $C_1$ represents a Rabi oscillation around $\vec{b}$ and curve $C_2$ represents precession around the $z$ axis due to a pulsed perturbation.

Figure 2

(Color online) Theoretical Rabi spectra under pulsed perturbations: (a) without a perturbation and (b) $\Delta \varphi =0.75\pi$, (c) $\Delta \varphi =\pi$, and (d) $\Delta \varphi =2\pi$. Frequency offset is normalized to the pulse repetition rate, and vertical offsets are added for clarity.

Figure 3

(Color online) Schematic diagram of the experimental apparatus. SC: $z$-axis shimming coil. PC: pulse coil. AHC: anti-Helmholtz coil. GPG: Gaussian pulse generator. ANT: antenna. PD: photodiode.

Figure 4

(Color online) Experimental Rabi spectra under pulsed perturbations: (a) without a perturbation and (b) to (i) with $\Delta \varphi$ increasing by $\pi ∕4$. In particular, (e) $\Delta \varphi =\pi$ and (i) $\Delta \varphi =2\pi$.