Publication: Photon Recoil Spectroscopy

Precision spectroscopy by photon-recoil signal amplification

Yong Wan, Florian Gebert, Jannes B Wübbena, Nils Scharnhorst, Sana Amairi, Ian D Leroux, Börge Hemmerling, Niels Lörch, Klemens Hammerer & Piet O Schmidt

Nature Communications 5, 3096 (2014)

Introduction

Precision optical spectroscopy of broad transitions reveals the properties of nature in various ways. It provides information on the structure of molecules, allows tests of quantum electrodynamics, and, through comparison with astrophysical data, probes for a possible variation of fundamental constants over cosmological scales. Nuclear properties are revealed through isotope shift measurements, or absolute frequency measurements. Simply by probing the energy difference between two levels, we are able to infer the internal structure of different kinds of microscopic systems. Trapped ions are particularly well suited for such high precision experiments. The ions are stored in an almost field-free environment and can be laser-cooled to eliminate Doppler shifts. These features have enabled record accuracies in optical clocks.

Laser spectroscopy is performed in two different flavors. For long-lived excited states efficient state detection is performed using the electron shelving technique, where quantum noise limited SNR can be achieved. But this technique requires a special level structure to perform the state preparation, cooling, and state detection. The invention of quantum logic spectroscopy (QLS) [1] removed the need to detect the signal on the spectroscopically investigated ion (spectroscopy ion) directly by transferring the internal state information through the motional state to the co-trapped logic ion where the signal is observed via the electron-shelving technique. However, this original implementation of QLS requires long-lived spectroscopy states to implement the transfer sequence. For transitions with a short-lived excited state, spectroscopy of trapped ions is typically implemented through detection of scattered photons in laser induced fluorescence (LIF) or detection of absorbed photons in laser absorption spectroscopy (LAS). Neither of the two techniques reaches the fundamental quantum projection noise limit as in the electron shelving technique [2] due to low light collection efficiency in LIF and small atom-light coupling in LAS.

Implementation

We combine the advantages of these techniques and demonstrate an extension of quantum logic spectroscopy which provides a highly sensitive, quantum projection noise-limited signal for the spectroscopy of broad transitions. It is based on detection of momentum kicks from a few absorbed photons near the resonance of a single spectroscopy ion through a co-trapped logic ion. In our implementation of photon recoil spectroscopy we use 25Mg+ as the logic ion and 40Ca+ as the spectroscopy ion. The investigated 2S1/22P1/2 transition in 40Ca+ has a natural linewidth of 21.6 MHz (Fig. 1).

Fig. 1: Experimental system for photon recoil spectroscopy

We start the experiment by preparing the two-ion crystal to the motional ground state with resolved sideband cooling along the axial direction (Fig. 2a). As the spectroscopy ion absorbs photons from the spectroscopy laser, the ion's motion will also be excited through the photon recoil (Fig. 2b). Owing to the strong Coulomb interaction, this excitation is shared by the logic ion where we convert this motional excitation into an electronic excitation using the electron-shelving technique (Fig. 2c). This allows us to amplify the signal of a few absorbed photons on the spectroscopy ion to thousands of scattered photons on the logic ion, providing quantum projection noise-limited detection of motional excitation (Fig. 2d).

 

Fig. 2: Principle of photon recoil spectroscopy.

Instead of the conventional CW spectroscopy, we enhance the photon sensitivity through application of short spectroscopy laser pulses which are synchronized to the ion's motion in the trap. The subsequent absorption events displace the ion out of the motional ground state constructively so that the population staying in the motional ground state after absorbing Na photons drops in a simple model exponentially with the square of the number of absorbed photons. This allows us to achieve an excitation of pe=0.5 with about 10 photons. This excitation level corresponds to a SNR of 1 in a single experiment limited by the quantum projection noise. Using laser induced fluorescence, about 1000 photons are neccesery to reach the same SNR level.

Precision spectroscopy

Photon recoil spectroscopy is demonstrated to be applicable for precision spectroscopy. Fig. 3a shows the scan across the resonance of the 2S1/22P1/2 transition. We are able to reach a resolution of 150 kHz in about 20 minutes. Combined with the high sensitivity of the technique, this means also that extremely limited number of photons are necessary to achieve the desired resolution. After absorbing 100 photons an uncertainty of 7.2 MHz is achieved.

Different systematic effects for the absolute frequency measurement are examined. These include the Zeeman shift, AC Stark shifts from the spectroscopy laser, the envelope shift of the short spectroscopy pulses and a lineshape error caused by the Doppler effect. The first three are determined experimentally, whereas the latter is modelled with an analytical and numerical model. In total, we determine the absolute frequency averaged over five individual measurement days to be 755,222,765,896 kHz with an uncertainy of 88 kHz (Fig. 3b). This result stays in agreement with the previous measurement [3], but the accuracy is improved by more than an order of magnitude.

 

Fig. 3: Absolute frequency measurement results.

Discussion

With the high photon sensitivity and high accuracy of photon recoil spectroscopy, the technique is well suited for systems with non-closed transitions or intrinsically low fluorescence rates, such as molecular ions, astro-physically relevant metal ions, and highly-charged ions. In these cases, photon recoil spectroscopy is an efficient extension of the original quantum logic spectroscopy, where long lifetime for the excited state is mandatory. For the opposite situations, where photons are the valuable resources such as in direct frequency comb, XUV, and x-ray spectroscopy, the single-photon sensitivity for high photon energies and the background-free detection make photon recoil spectroscopy an appreciable technique.

References

[1] Schmidt et al., Science 309, 749 (2005)

[2] Itano et al., PRA 47, 3554 (1993)

[3] Wolf et al., PRA 78, 032511 (2008)