Basic spectroscopic characterization of Pr3+ in YSO

In our laboratory we chose to excite Pr3+ to the 3P 0 state because its lifetime of 1.95 μs is shorter than 166 μs for the 1D 2 state, which has been used in the great majority of the published research5,7,11,12,13,22. Figure 1a sketches some of the energy levels of Pr3+ in the visible spectrum while Fig. 1b provides more details on the emission spectrum. The correspondingly broader natural linewidth of 82 kHz instead of 1 kHz sets a less-stringent requirement for the bandwidth of the laser to be used. When an ion is excited to the 3P 0 state, it can decay into each of the three ground state hyperfine levels via different pathways. The main channel involves a non-radiative relaxation to the 1D 2 state followed by fluorescence decay at a wavelength of 606 nm. In our work, we used long-pass filters to collect the fluorescence at wavelengths above 595 nm.

Figure 1: Spectroscopic properties of Pr:YSO. (a) Level scheme of Pr3+ in YSO. The ground (3H 4 ) and excited states (3P 0 ) show hyperfine splittings into three doubly degenerate levels. The hyperfine level splittings of 3P 0 were measured for the first time in this report, but their spin assignments remain unknown. The spin values of the ground-state levels are displayed. (b) Fluorescence emission spectrum of bulk Pr:YSO with excitation light polarized parallel to the D 1 axis measured at T=4.3 K. The main peak at 606 nm corresponds to the transition from 1D 2 to 3H 4 . The spectral features at longer wavelengths correspond to transitions from either 3P 0 or 1D 2 to other intermediate levels as indicated. (c) Hole burning spectrum measured on an ensemble of Pr3+ in a bulk YSO crystal. Side holes and anti-holes mark the excited and ground state hyperfine splittings, respectively. The orange spectrum presents a simulation (not a fit), assuming equal transition rates (see text). (d) Zoom of the main spectral hole at low-fluence excitation. Full size image

Considering the long lifetime of the ground state hyperfine levels, excitation at only one laser frequency would quickly transfer the population of any of the hyperfine levels into the other two. The resulting population trapping leads to the inhibition of fluorescence and is the mechanism that allows spectral hole burning10,11. In Fig. 1c we display an example of a hole-burning spectrum obtained from a bulk crystal at T=4.3 K. Here, a strong narrow-band laser beam at a fixed frequency was used to optically pump the population from one of the 3H 4 hyperfine levels of a subclass of ions, thus ‘burning’ a spectral hole in the absorption profile of the sample. A weak probe laser was subsequently scanned over the spectral hole to report on the homogeneous broadening and the separation of the hyperfine levels. The spectral dips on the sides of the central hole in Fig. 1c reveal the hyperfine splittings of the 3P 0 state at 2.9 MHz and 5.4 MHz, measured for the first time in Pr:YSO. The anti-holes appear at the expected frequency spacings of 10.19 MHz and 17.3 MHz for the hyperfine levels of the ground state9. The observed spectral features with linewidths of ~172 kHz in low-fluence hole-burning experiments (Fig. 1d) are consistent with a homogeneous width of 82 kHz and a laser linewidth below 10 kHz (see Methods section). Repeated scans verify that the hole depth and spectral position persist in the bulk sample for minutes, pointing to the absence of noticeable spectral diffusion in this system. The orange spectrum overlaid on the experimental hole-burning data presents a simulation, assuming equal weights for all nine possible transition rates involved in the 3H 4 –3P 0 transition and neglecting other intermediate states. This simplified assumption yields very good agreement with the measurements, but a quantitative assignment of the transition rates requires detailed spectroscopic studies that go beyond the scope of this work.

Detection of single ions via spectral selection

To detect single ions on a low background, it is desirable to reduce the observation volume and ion concentration by as much as possible. In our current work, we were restricted to commercially available Pr:YSO crystals with minimum doping of 0.005%. Therefore, we milled a small piece of such a crystal to obtain micro- and nanocrystals. As sketched in Fig. 2a, the crystallites were deposited on the flat side of a cubic zirconia solid immersion lens (SIL) with a refractive index of n=2.15. The SIL was thermally contacted to a cold finger in a liquid helium flow cryostat. A continuous-wave Ti:sapphire laser operating at 976 nm was locked to a high-finesse cavity to achieve a spectral linewidth below 10 kHz and long-term spectral stability (Fig. 2b). For addressing the 3H 4 –3P 0 transition, the resulting laser light was frequency doubled to 488 nm in a resonant cavity and could be scanned over 600 MHz using an acousto-optical modulator (AOM) in double-pass mode. Broader spectral investigations could be obtained by stitching these scans. The laser beam was then coupled to a microscope objective (numerical aperture 0.75) that was scanned by a three-dimensional (3D) piezoelectric actuator. We used a single-photon detector with very low dark counts to measure the fluorescence signal from the sample in reflection and employed another avalanche photodiode (APD) to detect the laser light in transmission through a bore in the cold finger.

Figure 2: Experimental setup and reflection scan image. (a) Schematic of the experimental setup. A frequency-stabilized Ti:sapphire laser is frequency-doubled and used for excitation. An acousto-optical modulator (AOM1) scans the frequency of the fundamental light. A second modulator (AOM2) produces the three frequencies f 1 , f 2 and f 3 described in the main text. Pr:YSO microcrystals are placed on the flat side of a hemispherical SIL inside a liquid helium flow cryostat. The 488-nm excitation light is focused onto the microcrystals by a high-NA objective mounted on a 3D piezo stage. Fluorescence and the reflected light are detected through the same objective. (b) Position of the spectral hole centre after a single burn pulse and repeated scans. The measurement confirms the long-term frequency stability. (c) Reflection scan image of the sample, visualizing the individual micro- and nanocrystals. (d) Cross section of the nanocrystal used in our measurements taken from the scan image in (c). Full size image

The first step of our measurements consisted of imaging individual YSO crystallites on the SIL surface. Here, we monitored the reflected excitation light on a photodetector to record the interference between the light fields scattered by the small crystals and the SIL surface. Figure 2c displays a scanning image of the crystallites using this interferometric scattering (iSCAT) contrast, which depends on the size and index of refraction of the object under illumination23. For the experiments discussed below, we used the nanocrystal in the middle of the image, which we estimate from the cross-section in Fig. 2d to be of the order of 100–200 nm in size. Considering the weak signal of an ion, even small sample drifts can complicate the measurements. We, thus, used the iSCAT signal to also actively lock the laser spot to the nanocrystal, making it possible to study a single ion for hours. To avoid population trapping in the hyperfine levels of the ground state, we used a second AOM to generate two frequencies at f 1 =f 2 −10.19 MHz and f 3 =f 2 +17.3 MHz in addition to the laser frequency (f 2 ). This allowed us to simultaneously excite all three hyperfine levels of the ground state.

Figure 3a shows an example of an excitation fluorescence spectrum when frequencies f 1 , f 2 and f 3 were scanned over 4 GHz. To reduce the measurement time, this spectrum was recorded with a laser linewidth of ~1 MHz without using external cavity locking. A background fluorescence as low as ~20–30 counts per second allows the detection of narrow spectral features. Figure 3b plots a zoom into three narrow resonances recorded with the narrow-band laser (<10 kHz). In most cases, such peaks were spectrally stable over measurement times of the order of hours although we also observed some spectral jumps. The sparse appearance of the observed narrow spectral lines lets us attribute them to the emission of single Pr3+ ions21.

Figure 3: Spectral detection and spatial localization of single ions. (a) Fluorescence excitation spectrum recorded at the speed of 1 MHz s−1 over several GHz. Narrow resonances are attributed to single ions. (b) An excitation fluorescence spectrum recorded over ~300 MHz, consisting of three ions. (c) Laser scanning fluorescence image of a single ion recorded on resonance. (d) Super-resolution colocalization image of the three ions detected in (b). The error bars depict the standard error of the mean ion position, calculated from eight measurements per ion. Full size image

Super-resolution imaging of ions

Each of the spectrally detected ions can be spatially mapped in fluorescence. Figure 3c presents a laser-scanning image of the fluorescence signal when the laser frequency was tuned to a narrow resonance. Fitting the image of the diffraction-limited spot lets us localize the ion with a precision of the order of 10 nm. By repeating this procedure for each resonance, one can colocalize all the ions in the sample beyond the diffraction limit. Figure 3d illustrates this idea for the three ions of Fig. 3b. Combination of this type of super-resolution microscopy and high-resolution spectral data will open the way for quantitative studies of near-field coupling among several ions24.

The effect of excited-state hyperfine levels

Up to this point, we treated the excited state as one level. However, one has to bear in mind that the 3P 0 state consists of three hyperfine levels at separations of 2.9 and 5.4 MHz (Fig. 1c), which become resonant with the three laser frequencies f 1 , f 2 and f 3 at different detunings. The blue spectrum in Fig. 4a plots the fluorescence signal that is expected from coupling the three ground-state hyperfine levels to the three excited-state hyperfine levels if one assumes a linewidth of 82 kHz. The three peaks occur whenever the laser detuning matches the transition of all ground state hyperfine levels to one of the excited state hyperfine levels. They are not affected by population trapping in one of the ground states. The displayed spectrum was calculated using a simple rate equation model, where the ion was described as a six-level system (see Methods section).

Figure 4: Some spectroscopic features of a single ion. (a) The blue trace depicts a simulated spectrum, assuming a transition linewidth of 82 kHz. The black curve plots an experimental high-resolution excitation spectrum of a single ion sampled at 0.1 s and averaged over 10 traces. The substructure originating from the excited state hyperfine splitting is clearly visible. The red curve displays a fit, assuming a full width at a half-maximum of 5.6 MHz. (b) Temperature dependence of the full width at half-maximum of the resonance, neglecting the underlying structure of the three hyperfine transitions. The error bars indicate the fit uncertainty of the Lorentzian linewidth. (c) Background-corrected fluorescence of a single ion as a function of the excitation power. The red curve denotes a fit assuming a three-level system. (d) Fluorescence signal recorded when addressing all hyperfine levels of the ground state (black) compared with the case where only the lower level was excited (red). In the latter case, population is trapped in the higher hyperfine levels. Full size image

The spectra in Fig. 3b do not mirror the expected multitude of narrow resonances in Fig. 4a, but spectra recorded at higher sampling resolution (see black curve in Fig. 4a) clearly show a substructure. We attribute this broadening to spectral diffusion caused by the strain in the milled crystallites. The red curve shows that the measured spectrum in Fig. 4a can be matched if we consider the individual transitions to be broadened to 5.6 MHz. We point out that although size-related deviations of the linewidth are expected in very small nanocrystals25, there is no fundamental reason for the existence of dephasing in crystallites. Proper preparation and handling can minimize26 or eliminate spectral diffusion. Furthermore, as shown in Fig. 4b, we have verified that the observed linewidths are not limited by temperature.

Figure 4c plots the fluorescence signal at the peak of a recorded resonance as a function of the excitation power. We report a measured saturation power of 98 pW in each of the three laser beams equivalent to an intensity of I sat ≈46 mW cm−2. We point out, however, that this is an approximate value because the overlapping broad transitions of various hyperfine levels make it difficult to assign a well-defined saturation power. The measurement also indicates a maximum detected count rate of ~60 photons per second. This is 6–8 times smaller than the count rate of 350–500 photons per second predicted by rate equations, when taking into account the upper 3P 0 , intermediate 1D 2 and ground state 3H 4 , as well as our measured detection efficiency of 11% and estimated collection efficiency of ~54–78% through the SIL (see Methods section). One possible explanation for this discrepancy is the existence of a transition to a long-lived state at energies below the 1D 2 state (Fig. 1a), which could act as bottle neck. Although the branching ratio of decay into such a state can be moderate (Fig. 1b), a lifetime of the order of 500 μs, which is typical for 4f-shell transitions, would suffice to rectify the observed discrepancy (see also discussion in Methods section). It should be noted that proper optical pumping out of these trap states would allow one to recover the maximum fluorescence rate.

Earlier we argued that we needed three laser frequencies to prevent shelving in various hyperfine levels of the ground state. While Fig. 4d verifies this statement, the black spectra in Fig. 5a–c illustrate that the fluorescence survives if one turns off one of the frequency components f 1 , f 2 or f 3 . To understand this observation, we simulated the excitation and fluorescence dynamics of the ion, using equally weighted branching ratios (as in the simulation shown in Fig. 1c). The blue traces in Fig. 5a–c show that one would expect very faint peaks for transition linewidths of 82 kHz. However, larger homogeneous linewidths make the various transitions overlap so that all three ground states can be partially addressed with only two laser frequencies. As a result, strict population trapping is avoided. Indeed, the fits in Fig. 5a–c presented by the red solid curves indicate that the recorded experimental data can be reproduced if a homogeneous linewidth of 3.3 MHz is assumed for this ion (different from the one examined in Fig. 4a). The simulated spectra in Fig. 5a–c also reveal that the influence of the transition linewidth on population trapping leads to a nontrivial effect on the line shapes. In Fig. 5a, for example, the most prominent spectral peak for the linewidth of 3.3 MHz is due to f 3 depopulating the lowest ground state, while f 2 depopulates the two higher lying ground states.

Figure 5: Two-frequency response. (a–c), Excitation spectra of a single ion illuminated by different combinations of only two laser frequencies. The legend in each plot denotes the frequencies that were turned on. The vertical green lines indicate the potential transitions for the given two-frequency excitation. The red curves were obtained by fitting all three experimental two-frequency spectra (black) simultaneously. The blue curves are simulations assuming interaction linewidths of 1 MHz and 82 kHz and are downshifted for better visibility. The zero of the horizontal axis denotes the frequency at which f 2 becomes resonant with the centre hyperfine levels of the ground and excited states. Full size image

State preparation and read out

The above measurements illustrate that a single ion can be prepared in a selected ground state by continuous optical pumping of the population to the desired state. To demonstrate the read out of the resulting quantum states, we implemented a pulsed excitation scheme sketched in Fig. 6a. The pulses were generated by a digital delay and a pulse generator and were applied independently to the three laser lines by the same AOM that produced f 1 , f 2 and f 3 . Two laser frequencies were turned on to pump the population out of two hyperfine levels to the third one. The pump duration of 344 μs was chosen to reach a population transfer of ~90%. A delay of 378 μs was implemented to allow the ion to decay from the excited state before applying the read-out pulse of 378 μs at the frequency of the third hyperfine level. This pulse drove the population for a few cycles until it was again trapped in the other two levels. We applied a gate pulse during the read out to discriminate against background and preparation pulse counts. Figure 6b displays the outcome of three sets of such measurements over 100 s. It is clear that if the read-out pulse is resonant with the state in which the ion was prepared, the fluorescence signal is maximized. These data exhibit the ease with which a single rare earth ion can be optically prepared in a hyperfine level of the electronic ground state, although in the current investigation the preparation efficiency was compromised due to the broadening and overlaps of the transitions.