Generalized Ramsey Excitation Scheme with Suppressed Light Shift

We experimentally investigate a recently proposed optical excitation scheme V. I. Yudin et al. [Phys. Rev. A 82, 011804(R) (2010)] that is a generalization of Ramsey’s method of separated oscillatory fields and consists of a sequence of three excitation pulses. The pulse sequence is tailored to produce a resonance signal that is immune to the light shift and other shifts of the transition frequency that are correlated with the interaction with the probe field. We investigate the scheme using a single trapped ${}^{171}\mathrm{Yb}^{+}$ ion and excite the highly forbidden ${}^{2}S_{1/2}-{}^{2}F_{7/2}$ electric-octupole transition under conditions where the light shift is much larger than the excitation linewidth, which is in the hertz range. The experiments demonstrate a suppression of the light shift by four orders of magnitude and an immunity against its fluctuations.

Figure 1

Pulse sequence (a) and resulting excitation spectrum (b) of the Ramsey (green) and the HRS excitation scheme (blue). Here ${\nu }_{\mathrm{L}}$ is the probe laser frequency and ${\nu }_0$ the unperturbed transition frequency. The laser step frequency ${\Delta }_{\mathrm{S}}$ is assumed to be equal to the light shift ${\Delta }_{\mathrm{L}}$ and the intensity $I_0$ is chosen to obtain a pulse area $\pi /2$ for a pulse duration $\tau$. A discriminator signal can be generated by alternately stepping the phase of the first pulse by $\pm \pi /2$ as indicated by the dotted lines. The spectra are calculated for the parameters $T_1=2\tau$, $T_2=0$, ${\Delta }_{\mathrm{L}}=4.1/\tau$ with equal dark period durations in both schemes.

Figure 2

Calculated excitation probability as a function of the uncompensated light shift ${\Delta }_{\mathrm{L}}-{\Delta }_{\mathrm{S}}$ and of the laser detuning $\Delta {\nu }_0$ from the unperturbed transition frequency for (a) Ramsey and (b) HRS excitation. In accordance with typical parameters of the performed experiment, the duration of the $\pi /2$ pulse is $\tau =9\mathrm{ms}$ and that of the dark period $T=36\mathrm{ms}$.

Figure 3

Excitation spectra of the octupole transition in ${}^{171}\mathrm{Yb}^{+}$ using the HRS scheme with $\tau =9\mathrm{ms}$ and $T=36\mathrm{ms}$ with fully (${\Delta }_{\mathrm{L}}={\Delta }_{\mathrm{S}}$) and partially (${\Delta }_{\mathrm{L}}\ne {\Delta }_{\mathrm{S}}$) compensated light shift for ${\Delta }_{\mathrm{L}}\approx 1\mathrm{kHz}$. The laser detuning is relative to the unperturbed transition frequency and the data points are the result of 20 interrogations at each frequency step. The solid black lines show the calculated line shapes.

Figure 4

Frequency offset of the probe laser stabilized at ${\Delta }_{\mathrm{L}}-{\Delta }_{\mathrm{S}}$ relative to the fully compensated case ${\Delta }_{\mathrm{S}}={\Delta }_{\mathrm{L}}$, for conditions (a) $T=36\mathrm{ms}$, $\tau =9\mathrm{ms}$, and (b) $T=144\mathrm{ms}$, $\tau =36\mathrm{ms}$, corresponding to a linewidth of the central HRS fringe of 3.2 Hz. The solid red line indicates the predicted dependence if the discriminator signal of the stabilization is generated by alternately stepping the phase of the initial pulse by $\pm \pi /2$. The dashed line in (a) shows the position of the central minimum of the HRS spectrum. The inset in (b) is an enlarged view showing the frequency offset in units of the frequency ${\nu }_0$ of the ${\mathrm{Yb}}^{+}$ octupole transition.