Cavity-induced anticorrelated photon-emission rates of a single ion

We report on the alteration of photon-emission properties of a single trapped ion coupled to a high-finesse optical fiber cavity. We show that the vacuum field of the cavity can simultaneously affect the emissions in both the infrared (IR) and ultraviolet (UV) branches of the $\mathrm{\Lambda }$-type level system of ${}^{40}\mathrm{Ca}^{+}$ despite the cavity coupling only to the IR transition. The cavity induces strong emission in the IR transition through the Purcell effect resulting in a simultaneous suppression of the UV fluorescence. The measured suppression of this fluorescence is as large as 66% compared with the case without the cavity. Through analysis of the measurement results, we have obtained an ion-cavity coupling of ${\overline{g}}_0=2\pi \times (5.3\pm 0.1)$ MHz, the largest reported so far for a single ion in the IR domain.

Figure 1

(a) A close-up view of the ion-trap structure with an integrated FFPC. Only a cross section of the upper assembly is shown to reveal the internal structure: The fibers reside inside the inner electrodes and electrical isolation between the inner and outer electrodes is provided by ceramic spacer tubes. Four additional electrodes are located on the radial plane at the same height as the ion. (b) A simplified schematic of the experimental setup: AOM, acousto-optic modulator; BF, bandpass filter for 866 nm; DM, dichroic mirror; MMF, multimode fiber; OL, objective lens; PD, photodetector for the transmission of the 895-nm beam; PMT, photomultiplier tube; PZT, piezoelectric transducer; SMF, single-mode fiber; and SPCM, single-photon counting module. The output of the MMF is filtered with a DM which transmits the 895-nm beam used for cavity locking. The reflection is further filtered by a BF before being detected by the SPCM. The magnetic field (B) is controlled by external coils (not shown) and applied vertically along the cavity axis.

Figure 2

(a) Energy-level diagram of the ${}^{40}\mathrm{Ca}^{+}$ ion and driving lasers with relevant detunings. The cavity field operates on the 866-nm transition between the $4{}^2{P}_{1/2}$ and $3{}^2{D}_{3/2}$ states. The wavy lines indicate the UV fluorescence emissions to be detected with the PMT. The detunings are measured positive (negative) when the laser is blue (red) detuned. (b) Effective scheme for the three low-lying levels.

Figure 3

UV fluorescence detected with the PMT as the ion is shelved to the $D_{3/2}$ state with the cavity on the Raman resonance (red, lower) and with the cavity far detuned ($\gg 2\kappa$) from the Raman resonance (blue, upper). The solid black lines are exponential fits.

Figure 4

(a) Emission of the ion into the cavity as its detuning is scanned across the Raman resonance. Scatter from the repumping and locking lasers contribute to the background counts of $\sim 19$ 000 c/s. The solid black line is a fit by the Lorentzian function. The error bars show the statistical mean standard errors. (b) Normalized UV fluorescence measured simultaneously with (a). The solid black line is a numerical simulation using the measured experimental parameters.

Figure 5

(a) The ion is in a thermal distribution in the phase space spanned by the spatial ($z$) and momentum ($p_z$) coordinates. The delocalization in $z$ results in the averaging of $g_0$ whereas the distribution along $p_z$ results in the spectral inhomogeneous broadening due to the Doppler effect. (b) Numerical simulation of ${\tau }_{\mathrm{on}}$ (left) and $\delta$ (right) as a function of ${\overline{g}}_0$ and $\sigma$ shown as two-dimensional contour plots. The labels on the contour lines are in units of nanoseconds (left) and megahertz (right). The dashed red contour lines correspond to the measured values of ${\tau }_{\mathrm{on}}=292$ ns and $\delta =10.3$ MHz.

Figure 6

Maximum suppression in the normalized UV fluorescence spectra for various ${\mathrm{\Delta }}_{850}$. The solid (dashed) black line shows the numerical simulation including (excluding) the fluorescence at 393 nm. Apart from ${\mathrm{\Delta }}_{850}$, the same parameters as the ones in Table 1 are used.

Figure 7

Pulse sequence for the 850- and 854-nm beams in the ${\mathrm{\Omega }}_{850}$ measurement. The time durations are 170 $\mu \mathrm{s}$ in stage (i), 30 $\mu \mathrm{s}$ in stage (ii), and 200 $\mu \mathrm{s}$ in stage (iii).

Figure 8

Fluorescence counts as a function of time in stage (iii) of the sequence in Fig. 7. The solid black line is an exponential fit to the data.

Figure 9

Observed frequency shift of the fluorescence spectrum as a function of the 854-nm laser power. The solid line shows a linear fit to the data.