Phonon Lasing from Optical Frequency Comb Illumination of Trapped Ions

We demonstrate the use of a frequency-doubled optical frequency comb to load, cool, and crystallize trapped atomic ions as an alternative to ultraviolet (UV) or even deep UV continuous-wave lasers. We find that the Doppler shift from the atom’s oscillation in the trap, driven by the blue-detuned comb teeth, introduces additional cooling and amplification which gives rise to steady-state phonon lasing of the ion’s harmonic motion in the trap. The phonon laser’s gain saturation keeps the optical frequency comb from continually adding energy without bound. This protection allows us to demonstrate loading and crystallization of hot ions directly with the comb, eliminating the need for a continuous-wave cooling laser, a technique that is extendable to the deep UV.

Figure 1

Fluorescence spectrum (in kilocounts per second) from a single trapped ion illuminated by an optical frequency comb. When the near-resonant tooth is red detuned, the ion is localized via Doppler cooling (b) and the spectrum (a) follows the rest-frame line shape from Eq. (1) (dashed, gray). When the near-resonant tooth is blue detuned, the ion oscillates with a fixed amplitude (c) and the fluorescence shows clear departure from the natural rest-frame resonance shape. The solid black curve is $\mathrm{\Gamma }(\delta ,x_0)$ with oscillation amplitude $x_0=0$ or $x_0=4.9\mu \mathrm{m}$ when the near-resonant comb tooth is red or blue detuned, respectively. The systematic increase in count rate from left to right is consistent with laser intensity drifts during the measurement.

Figure 2

Calculated net power delivered to the motion of a trapped ${\mathrm{Yb}}^{+}$ atom illuminated by an optical frequency comb as a function of the amplitude of the oscillations in the trap. The right side of Eq. (3) is plotted for the case where the near-resonant tooth is blue detuned with $\delta =\pi /2T_r$. Red (blue) shading indicates amplification (damping) of the ion’s motion. Stable fixed points are shown by circles. The red-detuned case ($\delta \to -\delta$) is similar but inverted with an additional fixed point near zero ($x_0^{*}=90\mathrm{nm}$).

Figure 3

Integrated ion fluorescence images when illuminated by an optical frequency comb whose nearest-resonant tooth is red detuned (upper) or blue detuned (lower) of rest-frame resonance. Hysteresis associated with the ion’s initial energy determines which fixed point the ion finds. The dashed lines indicate the fixed-point oscillation amplitudes extracted from fitting to classical harmonic oscillator distributions (solid black curves). The systematic fluorescence asymmetry is due to the intensity gradient of the ML laser beam.

Figure 4

Acoustic injection locking of the $x_1^{*}$ fixed point phonon laser when the near-resonant tooth is blue detuned. When the frequency of an injected signal is moved from outside (orange) to within (blue) the phonon laser’s gain bandwidth, it is amplified at the expense of other frequencies.