Figure 1

(a) A picosecond mode locked Ti:sapphire laser is tuned to 4 times the resonant wavelength of the ground state to the $5p{}^{2}P_{3/2}$ transition in ${}^{111}\mathrm{Cd}^{+}$. The 80 MHz pulse train is sent through an electro-optic pulse picker, allowing the selection of single pulses while blocking all other pulses with an extinction ratio of better than $100:1$ in the infrared. This single pulse is then frequency quadrupled through nonlinear crystals, filtered from the fundamental (IR) and second harmonic generated (SHG) pulses, and directed to the ion. The extinction ratio is expected to be on the order of ${10}^8:1$ in the UV. An amplified cw diode laser is also frequency quadrupled and tuned just red of the $S_{1/2}$ to $P_{3/2}$ transition for Doppler cooling of the ion within the trap, optical pumping to the dark state ($|\uparrow ⟩$) and ion state detection using the ${\sigma }^{+}$ cycling transition. Acousto-optic modulators (AOMs) are used to switch on and off the cw laser and to shift the optical pumping beam. Photons emitted from the ion are collected during state detection by an $f/2.1$ imaging lens and directed toward a photon counting photomultiplier tube (PMT). (b) The relevant energy levels of ${}^{111}\mathrm{Cd}^{+}$ where the $\pi$-polarized ultrafast laser pulse excites the ion from the ground state to the excited state. Selection rules prohibit both the $|\uparrow ⟩\to |{\downarrow }^{\prime }⟩$ and the $|\downarrow ⟩\to |{\uparrow }^{\prime }⟩$ transitions. The three possible decay channels for each excited state are shown with fluorescence branching ratios. (c) The first ultrafast laser pulse coherently excites and the second pulse coherently deexcites the ion.Reuse & Permissions

Figure 2

(a) The ion bright state population as a function of pulse energy. Each point represents a collection of 60 000 runs where the ion was prepared in the dark state ($|\uparrow ⟩$), a single laser pulse was applied, and then the ion state was measured. The collection of runs is fit to known bright/dark state histograms [19]. As the pulsed laser drives a $\pi$ pulse from the $S_{1/2}$ to $P_{3/2}$ states, the bright state population approaches $1/3$ (horizontal dashed line), determined by the spontaneous emission branching ratio [Fig. 1b]. The data are fit to a single parameter giving a value $a=0.42{\mathrm{pJ}}^{-1/2}$. (b) A second laser pulse, delayed by approximately 680 ps, further drives the ion, limited by the spontaneous emission probability (23%) and attenuation between the first and second laser pulse intensities. The solutions to the optical Bloch equations (OBE) are shown for a second pulse with 60% attenuation and no attenuation.Reuse & Permissions

Figure 3

(a) The contrast of the phase curve in a Ramsey experiment with the pulsed laser interjected between the two Ramsey zones as a function of pulse energy. The contrast disappears with a $\pi$ excitation because, on spontaneous emission, the photon is measured and coherence in the ion superposition is lost. The solid curve is the OBE solution for the single pulse. The inset shows the Ramsey fringes for no ultrafast pulse and for the maximum pulse energy. (b) A second laser pulse, coherently driving the population back down to the ground state, partially recovers the phase coherence of the ion with a phase shift of $18.9\pi$. The inset shows the Ramsey fringes for no laser pulses, a single $\pi$ pulse, and two ultrafast pulses. The OBE solution for 60% attenuation of the second pulse is shown as the dashed line. The dotted line is the same model for no attenuation of the second pulse.Reuse & Permissions

Figure 4

The phase of the Ramsey fringes as a function of the time delay between two ps laser pulses, set by the linear translation of the retroreflecting mirror. The uncertainty in the time delay of each point is 0.1 ps, and the uncertainty in the phase is 0.01 rad. The slope of the line gives the frequency difference between the ground state and excited state hyperfine splittings of $\Delta {\omega }_{\mathrm{HF}}=13.904\pm 0.004\mathrm{GHz}$. The inset figure shows three Ramsey fringes for three relative delays.Reuse & Permissions