Optically addressing single rare-earth ions in a nanophotonic cavity
Detection and control of single rare-earth dopants in solids is an important step towards quantum devices that take full advantage of the outstanding coherence properties of rare-earth ions in both optical and spin degrees of freedom. Coupling the 4f-4f transitions of ions to photonic resonators with highly confined optical modes provides an effective approach to overcome their weak photoluminescence emission and poor photon collection efficiency, which have so far hindered the experimental progress on optical isolation and control of single rare-earth emitters. Here we demonstrate a nanophotonic platform based on a yttrium orthovanadate (YVO) photonic crystal nanobeam resonator coupled to spectrally resolved individual neodymium (Nd) ions. The strong emission enhancement in the nanocavity enables optical addressing of single Nd ions. The ions show near-radiatively-limited single photon emissions. The measured high coupling strength between a single photon and the ion allows for optical Rabi oscillations and a high coupling cooperativity, which could enable optically controlled spin qubits, quantum logic gates, and spin-photon interfaces in future quantum networks.
Rare-earth dopants in solids exhibit long-lived coherence in both optical and spin degrees of freedom Thiel (); Sun (). The effective shielding of their 4f electrons leads to optical and radio-frequency transitions with less sensitivity to electronic and magnetic noise in their crystalline surroundings at cryogenic temperatures. Significant progress in rare-earth based quantum technologies has led to ensemble-based optical quantum memories Tittel (); Riedmatten (); Hedges (); Zhongsci () and coherent transducers Williamson (), with promising performance as efficient quantum light-matter interfaces for quantum networks. On the other hand, addressing single ions has remained an outstanding challenge, with the progress hindered by long optical lifetimes of rare-earth ions and resultant faint photoluminescence (PL). So far, only a few experiments have succeeded in isolating individual praseodymium KolesovNC (); Utikal (); Nakamura (), Cerium Kolesov (); Siyushev (); Xia (), and erbium Yin (); Dibos () ions, though majority of them were not probing ions via their highly coherent 4f-4f optical transitions. Recently, several works have demonstrated significant enhancement of spontaneous emissions of rare-earth emitters coupled to a nanophotonic cavity Zhong (); Zhongcavprot (); Zhongsci (); Dibos (), among which Zhong (); Zhongsci () also showed little detrimental effect on the coherence properties of ions in nanodevices. These results point at a viable approach to efficiently detect and coherently control individual ions in a chip-scale architecture.
Here we demonstrate a nanophotonic platform based on a yttrium orthovanadate (YVO) photonic crystal nanobeam resonator coupled to spectrally resolved individual neodymium (Nd) ions. While the system acts as an ensemble quantum memory when operating at the center of the inhomogeneous line Zhongsci (), it also enables direct optical addressing of single Nd in the tails of the inhomogeneous distribution, which show strongly enhanced, near-radiatively-limited single photon emissions. A measured vacuum Rabi frequency of 228.5 MHz significantly exceeds the linewidth of a Nd ion, potentially allowing coherent manipulation of single spins with optical pulses. Unlike prior experiments KolesovNC (); Utikal (); Nakamura (); Kolesov (); Siyushev (); Xia (), this technique does not hinge on spectroscopic details of a specific type of ion and can be readily extended to other rare-earths or defect centers. It opens up new opportunities of spectroscopy on single ions that are distinct from conventional ensemble measurements, which offers a probe for local nanoscopic environment around individual rare-earth ions and may lead to new quantum information processing, interconnect and sensing devices.
Our experiment builds upon a triangular nanobeam photonic crystal resonator Zhong (); Zhongfab () that was fabricated in a nominally 50 parts per million (ppm) doped Nd:YVO crystal using focused ion beam (FIB) milling Zhongfab (). The device is a one-sided cavity, as the input (left mirror in Fig.1(a,b)) has a lower reflectivity. The optical coupling in/out of the device was implemented via a 45-angled coupler Zhong (). An aspheric doublet matches the mode of the single mode fiber to that of the nanobeam waveguide (Fig.1(a)). The coupling efficiency was optimized to 19% (from fiber to waveguide) using a 3-axis nano-positioner. The nanocavity fundamental mode volume is = 0.056 m (simulated) with a measured quality factor = 3,900 (energy decay rate 90 GHz). The waveguide-cavity coupling through the input mirror was 45% of . The device was cooled to 20 mK base temperature in a dilution refrigerator, though the device effective temperature was estimated to be around 500 mK (by comparing the ground Zeeman level populations from the PL spectra). The elevated temperature was attributed to the diminishing thermal conductance in the nanobeam. The laser for probing the ions was modulated by two double-pass acousto-optic (AOM) modulators, and delivered to the sample via a single-mode fiber. The reflected signal from the device was sent via a circulator to a superconducting nanowire single photon detector (SNSPD) that measured a 82% detection efficiency at 880 nm and 2 Hz dark counts Zhongsci (). The SNSPD was mounted in the same fridge at the 100 mK stage. The overall photon detection efficiency including transmission from the cavity to the detector and the detection efficiency was 3.6% (Supplementary material SM ()).
A typical cavity reflection spectrum when it was tuned nearly on resonance with the Nd transition at 880 nm is shown in Fig.1(c). A 390 mT magnetic field was applied along the crystallographic a axis of YVO, giving rise to split Zeeman levels and four possible optical transitions Hastings () (labelled 1-4) shown in the inset. Symmetry considerations impose that the 2, 3 cross transitions are forbidden, and the 1, 4 transitions are close to cyclic AfzeliusYVO (); Zhongsci (). The PL emission spectrum (with a 200-ns pulsed resonant laser excitation) is shown in the lower part of Fig.1(c). Two weak lines labelled 1’ and 4’ were identified as emissions from Nd ions in the bulk substrate, which are red-detuned from ions coupled to the cavity by 2.5 GHz. This shift is due to a static strain in the nanobeam, which makes it easier to spectrally separate the ions in the cavity from the bulk. For subsequent experiments, we focus on the shorter wavelength tail of the inhomogeneous distribution. Figure 1(d) plots the resonant PL against frequency detuning from the peak of line 1 (340703.0 GHz). The PL and thus the atomic spectral density ( ions per excitation pulse bandwidth) fits with a power law of , where is the detuning from the center of line 1. The 2.9 power exponent corresponds to a strain-induced broadening according to Stoneham (). Statistical fine structures (SFS) Moerner () were also evident. By fitting the SFS with the projected shot noise of (i.e. indicated as the shaded area), it is projected that discrete single ion spectra () emerge at a detuning 25 GHz.
To search for spectrally resolved single ions, we scanned the center frequency of a 200-ns resonant excitation pulse around 30 GHz blue detuning from the peak of line 1, and measured the PL integrated over 5 s after the excitation. The repetition rate of the excitation pulses was 25 kHz, and the integration time was 20 seconds at each frequency. The laser was frequency stabilized to a vacuum can reference cavity attaining a narrowed linewidth of 5 kHz and a long term drift 100 kHz/day. Figure 2(a) shows the measured PL over a few GHz range. A handful of peaks, such as the one with close-up shown in Fig.2(c), were possible single Nd ions. The PL intensities were histogrammed in Fig.2(b) to reveal a distribution of ion-cavity coupling strengths, which is in good agreement with that from the finite difference time domain (FDTD) simulation as plotted in red. Thus, the PL intensity serves to correlate the coupling strength of each ion with its spatial position relative to the cavity anti-nodes: an ion located exactly at the antinode with the highest field intensity would have the strongest coupling and show the highest PL. The linewidth of the peak in Fig.2(c) was broadened by the Rabi frequency of the excitation pulse. The actual linewidth of single ions was expected to be considerably narrower. With the laser tuned on-resonance with one of the peak (marked with a red dot in Fig.2(a)), the intensity autocorrelation measurement using a single detector yielded a g(0) = 0.09 0.013 (Fig.2(e)), which was normalized to g() at large . The bunching behavior at 400s was expected from a multilevel emitter. The imperfect anti-bunching was partly due to a continuum of ions that is weakly coupled to the cavity, resulting in a background as in red in Fig.2(e). This background was measured with the excitation laser far detuned from the single ion resonance. The optical T of this ion was 2.10.2 s (Fig. 2(d)), which is strongly enhanced compared to the bulk T of 90 s. The lifetime enhancement corresponded to a Purcell factor of 156 of the probed Y-Z transition rate considering a branching ratio of =0.273 (the ground state splits into five Kramers doublets Z-Z) AfzeliusYVO (). The theoretically maximum Purcell factor was 189 Purcell (); Mcauslan () assuming a perfect alignment of the dipole with the cavity mode and is the local correction to the electric field since the ion is less polarizable than the bulk medium Dung (). The discrepancy is attributed to the non-optimal position of the ion with respect to the cavity anti-node, and the actual mode volume of the cavity being different from simulation because of fabrication imperfections.
The small mode volume of the nanocavity results in a significant enhancement of the coupling strength or the vacuum Rabi frequency . Focusing on the same ion in Fig.2(c), Fig.3(a) plots the PL excited by a square 250-ns resonant excitation pulse with increasing cavity mean photon number . The value of was calculated from the input pulse energy, all losses in the setup up to the device, and coupling rates of the photonic crystal mirrors (Supplementary Material SM ()). The PL shows Rabi oscillations similar to an optical nutation signal Gerhardt (). The inset plots the extracted Rabi frequencies versus square root of from the peaks (corresponding to odd integer of pulse areas) and valleys (even integer of pulses) of the Rabi oscillations. The slope corresponds to = 228.5 MHz, which is in agreement with the theoretical estimation of 28.0 MHz Mcauslan (), where =8.510 Cm is the transition dipole moment (calculated using an oscillator strength f=810Sun ()), =2.1785 is the refractive index of YVO, is the transition frequency, and is the vacuum permittivity. This value is orders of magnitude stronger than the linewidth of the emitter, which makes possible the use of hard optical pulses Pryde () to coherently control the single ion. Next, we applied two pulses to measure the Ramsey interference of the Nd as shown in Fig.3(b). The normalized Ramsey fridges (subtracting a T decay background) reveal a clear beating, which we believe corresponds to the superhyperfine interactions between Nd spins with the nuclear spins of yttrium in YVO. The measured superhyperfine splitting, confirmed by the two-pulse photon echo measurement (Supplementary materials), was 740 kHz, which is consistent with the 2 MHz/T observed in Usmani (). The decay of the Ramsey fringe envelope can be fitted (red curve in Fig. 3(b)) to extract a T = 4.00.2 s. From that, the spectral indistinguishability is calculated as =0.952, indicating that the linewidth of this ion approaches the radiatively-limited regime.
The use of single rare-earth ions as spin-photon interfaces to entangle remote quantum nodes requires each emitter’s linewidth to be radiatively limited. To further characterize the coherence of the ions coupled to the cavity, we performed additional ensemble two-photon echo measurements when the emitters have different detunings from cavity resonance. The ensemble T times are plotted against optical T decay times in Fig.4, including the single ion T data as denoted by the square. The experimental data were fitted with the relationship , where is the pure dephasing rate of the emitters. The fit (blue curve) gives a =9.70.6 kHz. While slow, this dephasing rate was attributed to the superhyperfine interactions since it closely matches the superhyperfine-limited T in Nd:YVO Sun (). The contribution from Nd spin flip-flops are expected to be small, because the measured T in an nominally undoped YVO crystal (residue doping estimated at 0.2 parts per million) was comparable to that measured in the current device (Supplementary material SM ()).
The full radiatively limited T=2T is plotted in red. With weak Purcell enhancement when the ions are detuned from the cavity resonance, the Nd ions exhibit poor indistinguishabilities as indicated by the sizeable gap between the red and blue curves. Only when the ions are coupled to the cavity resonantly, do the emitters become radiatively limited. A similar approach has been used to improve the single photon indistinguishabilities of quantum dots Grange (). To increase the indistinguishability, improving the cavity quality factor to further reduce T would be a straightforward step, which would also allow the device to operate at higher temperatures with stronger dephasing while still achieving radiatively limited emissions. The current linewidth of the single emitter was based on T values measured over a few s time scale (Fig.3(b)). For longer time scales (100 s to ms), as required in quantum memories for long-distance quantum network, the slow spectral diffusion of the emitter needs to be investigated. In general, rare-earth emitters in hosts with weaker nuclear spin baths such as yttrium orthosilicate and yttrium oxide are less susceptible to spectral diffusion. Furthermore, non-Kramers ions do not have superhyperfine couplings with the host spin baths, and may offer some advantages in terms of long term narrow linewidths.
In conclusion, we have optically detected single Nd ions coupled to a nanophotonic cavity, which enhanced the emitter spontaneous emission rate to the extent that the linewidth of the emitter became close to radiatively-limited. Optical Rabi oscillations of the single Nd yielded a vacuum Rabi frequency =228.5 MHz, and a linewidth of 12.5 kHz (=1/(T), where T=25.4 s is the emitter homogeneous linewidth without cavity enhancement (Supplementary material SM ())). Given the cavity decay of =290 GHz, the single ion cooperativity is =2.9. This value could be improved significantly by using cavities with higher Q (10 higher Q devices already demonstrated in Zhongfab () would attain an indistinguishability 99.5% and C30), thus making feasible the implementation of high-fidelity non-destructive detection of optical photons with a single rare-earth ion Brien16 (). Nevertheless, questions remain regarding the spin coherence and the qubit storage time of single ions Wolfowicz (), and spectral diffusion occurring at longer time scales. When two spectrally resolved ions are nearby, their dipole-dipole interaction can also be probed Longdell (). Single rare-earth ions could be used to probe the field and temperature of its nanoscopic surroundings. Finally, the large inhomogeneous linewidth of the emitters may facilitate spectral multiplexing of individual quantum emitters for expanded bandwidth of quantum communication networks.
This work was funded by a National Science Foundation (NSF) Faculty Early Career Development Program (CAREER) award (1454607), the AFOSR Quantum Transduction Multidisciplinary University Research Initiative (FA9550-15-1-002), and the Defense Advanced Research Projects Agency Quiness program (W31P4Q-15-1- 0012). Equipment funding was also provided by the Institute of Quantum Information and Matter, an NSF Physics Frontiers Center with support from the Moore Foundation. The device nanofabrication was performed in the Kavli Nanoscience Institute at the California Institute of Technology. Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. T. Zhong would like to thank Neil Sinclair, Ruffin Evans, Alp Sipahigil for experimental assistance and technical discussions.
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Appendix A Supplementary material for optically addressing single rare-earth ions in a nanophotonic cavity
a.1 More details on the experimental setup
Figure S1 illustrates the experimental setup with more details. The Nd:YVO sample crystal was soldered with indium onto a copper plate that was mounted on top of a 3-axis nanopositioner, and was thermally connected to the 20 mK base plate of the dilution refrigerator. Cavity tuning was realized by gas condensation using N gas. The gas tube (brown line in Fig. S1) was thermally anchored to the 3.8 K stage. When performing gas tuning, a heater on the gas tube heats it up to 30 K to allow gas to flow through. The heater was turned off after tuning. This configuration was to minimize the heat load generated by the tube, allowing the lowest possible temperature at the sample.
Fiber-waveguide coupling efficiency The fiber-waveguide coupling efficiency was characterized by measuring the reflection of a pulse far off resonance with the cavity (i.e. in the photonic bandgap). The pulse propagated from point 1 (marked in Fig.S1) to 2, 3, and was reflected back to 2, then 4. The transmission efficiency from 1 to 2 (64.1%), and from 2-4 (51.7%) were directly measured. The only unknown was the coupling efficiency from 2 to 3. Therefore, this coupling efficiency could be uniquely determined from the total pulse reflection, and was measured to be 19%.
Photon collection efficiency For each photon emitted by an ion into the cavity, the probability of that photon transmitted to the coupling waveguide was =45%. The photon then propagated from 3 to 2 (19% waveguide-fiber coupling), and from 2 to 4 (79.9% transmission through all fiber slices/connectors and 64.7% transmission through the optical circulator), and was finally detected by the 82%-efficient superconducting nanowire detector. Thus the overall collection efficiency for a cavity photon was 0.450.190.800.650.82 = 3.6%.
Cavity mean photon number To obtain the cavity mean photon number in Fig.3, we first calculate the peak power of the excitation pulse in the waveguide i.e. P with the knowledge of transmission from 1 to 2 and the coupling efficiency from 2 to 3. The cavity mean photon number was , where 40 GHz was the cavity in-coupling rate, 90 GHz was the total cavity decay rate, and is the photon frequency.
a.2 Photon echo measurements
Two pulse photon echo measurements were performed on an ensemble of ions in the cavity near the center of inhomogneous distribution (e.g.line 1). The cavity resonance was tuned to different frequencies using gas condensation technique to obtain homogeneous linewidths of ions at varying Purcell enhancement conditions. Fig.S2 plots photon echo decays at ensemble-cavity detuning of 22 and 50 GHz. Oscillations in the echo intensities correspond to syperhyperfine interactions between Nd spins and Y nuclear spins Usmani () at 740 kHz, which agree with the beat frequency observed in the Ramsey interference fringes. Note that the period of the oscillations appear to be twice long in the Ramsey fringes than the echo decays, because the photon echo is emitted after twice the delay between two pulses. The T were fitted from the linear section of the decay, which started after approximately 4 s.
a.3 OPTICAL DEPHASING IN Nd:YVO
Possible contributions to the optical dephasing =9.7 kHz include superhyperfine coupling between Nd spins and yttrium/vanadium nuclear spins, the Nd spin flip-flops, direct phonon couplings, and other higher order processes. Here we discuss contributions from two potentially dominant mechanisms.
Superhyperfine interaction The experimental condition in the current work closely reassembles that in Sun () in which optical T for a 10 ppm doped Nd:YVO sample was measured at varying magnetic field applied along the a-axis of the crystal. It was found in Sun () that with a field greater than 1.5 T, the T of 27 s became limited by the superhyperfine interaction. The corresponding dephasing rate could be calculated from = 10.0 kHz, which was very close to the currently measured dephasing. We thus expect that the superhyperfine interactions contribute substantially to the measured .
Nd spin flip-flops Dephasing due to the Nd spin flip-flops is a function of the Nd doping concentration and temperature. To better understand this process, we measured optical T times in both the 50 ppm doped (the same crystal on which the devices were fabricated) and a nominally undoped YVO crystal. From the absorption spectroscopy and secondary ion mass spectroscopy (SIMS), we estimated the doping concentration of Nd to be 0.2 ppm in the undoped YVO. Therefore, the dephasing owing to spin flip-flops are expected to be relatively small in that sample. Both crystals were soldered to a common sample holder. With the same magnetic field configuration as in the main text, the ground level splitting was =12.88 GHz where =2.36 is the ground state g-factor Hastings (); AfzeliusYVO (), and = 0.39 T. We then used the ratio between the absorptions of two Zeeman transitions to calibrate the crystal temperature. When both crystals were at 500 mK, we measured a T = 25.4 s and T = 27.0 s in 50 ppm doped and undoped YVO crystals, respectively. The difference in linewidths, which amounts to 1 kHz, serves as an upper bound on dephasing due to Nd spin flip-flops at 500 mK.
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