Optical spin-wave storage in a solid-state hybridized electron-nuclear spin ensemble

TL;DR

This paper demonstrates optical storage in a rare-earth ion system using hybridized electron-nuclear spins, achieving a balance of long storage time and high bandwidth, advancing quantum memory technology.

Contribution

First demonstration of optical storage using spin states in a rare-earth ion with electronic spin, combining long storage time and high bandwidth.

Findings

Storage time of 1.2 ms achieved

Optical bandwidth of 10 MHz demonstrated

Memory efficiency around 3%

Abstract

Solid-state impurity spins with optical control are currently investigated for quantum networks and repeaters. Among these, rare-earth-ion doped crystals are promising as quantum memories for light, with potentially long storage time, high multimode capacity, and high bandwidth. However, with spins there is often a tradeoff between bandwidth, which favors electronic spin, and memory time, which favors nuclear spins. Here, we present optical storage experiments using highly hybridized electron-nuclear hyperfine states in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$, where the hybridization can potentially offer both long storage time and high bandwidth. We reach a storage time of 1.2 ms and an optical storage bandwidth of 10 MHz that is currently only limited by the Rabi frequency of the optical control pulses. The memory efficiency in this proof-of-principle demonstration was about 3%. The experiment constitutes the first optical storage using spin states in any rare-earth ion with electronic spin. These results pave the way for rare-earth based quantum memories with high bandwidth, long storage time and high multimode capacity, a key resource for quantum repeaters.

Full text

Solid-state impurity spins play an increasingly important role in quantum information technologies, with applications in communication, computing and sensing Bussières et al. (2014); Degen et al. (2017); Awschalom et al. (2018). In quantum communication, solid-state spins that can be interfaced with photons are promising candidates for nodes in quantum networks and quantum repeaters. In such systems, optical transitions are used to convert quantum information between internal spin states and optical photons, where spins store and possibly process quantum information within the solid Atatüre et al. (2018); Awschalom et al. (2018).

There is a current interest in using both the electronic and nuclear degrees of freedom of solid-state spin systems Awschalom et al. (2018); Bradley et al. (2019), with the goal of simultaneously achieving efficient manipulation and long-duration storage. Electronic spins couple strongly to external fields, making them ideal for high-bandwidth operations and highly sensitive sensors. The weaker coupling of the nuclear spins shields them from the environment, allowing long-duration quantum storage. However, finding spin systems that simultaneously possess good optical, electronic and nuclear spin properties is challenging. A prominent example is the nitrogen vacancy (NV) center in diamond, where the electron spin of the NV can be coupled to photons Doherty et al. (2013), while the hyperfine interaction with neighbouring 13C nuclear spin provides a long-duration memory Maurer et al. (2012); Bradley et al. (2019). Similar hybrid electron-nuclear systems are investigated using 31P phosphor donors in silicon Steger et al. (2012); Saeedi et al. (2013) and quantum dots Gangloff et al. (2019).

Rare-earth-ion (RE) doped crystals represent another prominent example of solid-state impurities with excellent optical Thiel et al. (2011) and spin properties Zhong et al. (2015). RE crystals have emerged as strong candidates for ensemble-based quantum memories (QMs) Hedges et al. (2010); Clausen et al. (2011); Saglamyurek et al. (2011); Zhou et al. (2012), and more recently for single ion/spin Kolesov et al. (2012); Dibos et al. (2018); Zhong et al. (2018); Casabone et al. (2018) quantum information processing. For ensemble-based QMs, thus far only RE nuclear spin systems have been used for storing optical pulses using spin states Ferguson et al. (2016); Laplane et al. (2017); Kutluer et al. (2017); Seri et al. (2017), based on the nuclear quadrupole states of either Pr3+ or Eu3+ ions. While these non-Kramers RE ions with quenched electronic spin provide excellent memory times, the purely nuclear states limit the memory bandwidth to $<10~{}\textrm{MHz}$. RE ions with non-zero electronic spins, so-called Kramers ions, could potentially provide a solution to the bandwidth limit, provided that long coherence times can be engineered in such electronic spin systems.

Recently, it has been shown that such long spin coherence times can be found in some Kramers RE ions with electron spin  S Kindem et al. (2018); Rančić et al. (2018); Rakonjac et al. (2018); Ortu et al. (2018) and non zero nuclear spin I by exploiting the hyperfine coupling $\textbf{S}\cdot\textbf{A}\cdot\textbf{I}$, where A is the hyperfine tensor. In Refs Rakonjac et al. (2018); Ortu et al. (2018) it was particularly shown that at zero applied magnetic field, an anisotropic hyperfine interaction leads to strong mixing of S and I, resulting in highly hybridized electron-nuclear states with zero first-order Zeeman (ZEFOZ) effect Fraval et al. (2004). Using this feature we showed simultaneous long optical and spin coherence times of $T^{o}_{2}=180$ µs and $T^{s}_{2}=1.5$ ms, respectively, in 171Yb3+:Y2SiO5 Ortu et al. (2018). We also showed that, while the hybridized states are insensitive at first order to slowly fluctuating magnetic DC fields (at the ZEFOZ point), the magnetic AC transition moment between the hybridized states remains electronic, resulting in high Rabi frequency and fast operations. These results are promising for broadband and long-duration optical quantum memories, but thus far there has been no demonstration of optical storage using spin states in any Kramers RE ion system.

In this Letter we demonstrate an optical memory using the hybridized electron-nuclear states at zero field in 171Yb3+:Y2SiO5, based on the atomic frequency comb (AFC) memory scheme Afzelius et al. (2009). We reach a spin storage time of 1.2 ms and a bandwidth of 10 MHz, which is only limited by the current optical Rabi frequency. In addition, we show efficient optical AFC echoes with delays one order of magnitude longer than previously achieved in any Kramers system, which we attribute to reduced superhyperfine coupling in the zero-field ZEFOZ point.

The AFC memory is based on a $\Delta$-periodic structure of highly absorbing peaks within an inhomogeneously broadened optical transition Afzelius et al. (2009). An input pulse then produces an optical AFC echo, with a delay of $1/\Delta$. The AFC echo process allows high temporal multimode storage, provided that $1/\Delta$ is much longer than the input pulse duration Jobez et al. (2016). To achieve on-demand read out, an optical control pulse can be applied before the AFC echo, thereby converting the optical coherence into a spin coherence. This spin-wave memory Afzelius et al. (2010); Gündoğan et al. (2015); Jobez et al. (2015); Seri et al. (2017) is read out by applying another control pulse after a time $T_{\text{S}}$, which results in an output pulse with a storage time of $T_{\text{M}}=1/\Delta+T_{\text{S}}$. The spin-wave storage time can be extended to the spin coherence time $T_{2}^{\text{s}}$ by applying a spin echo sequence Jobez et al. (2015).

The memory puts specific demands on the atomic system. It requires an excited state coupled to two spin states, a so-called $\Lambda$ system, where the optical memory bandwidth is ultimately limited by the spin-state energy split Afzelius et al. (2009). Efficient AFC echoes and long $1/\Delta$ delays require an optically deep and high resolution comb, which in turn requires a long optical coherence time and efficient optical pumping. Finally, long memory lifetime requires a long $T_{2}^{\text{s}}$ and efficient spin manipulation through microwave (MW) pulses.

The optical transition we use in 171Yb3+:Y2SiO5 connects the lowest crystal field levels in the electronic 2F7/2 ground and 2F5/2 excited states, at 978.854 nm (in vacuum) for site II in Y2SiO5 Welinski et al. (2016). The highly anisotropic hyperfine tensors splits both levels into four non-degenerate hyperfine states at zero applied magnetic field Tiranov et al. (2018), as shown in Figure 1a. Many different combinations of transitions could be used as the $\Lambda$ system for optical storage, with corresponding microwave frequencies from 529 to 3026 MHz. Here we focus on the particular $\Lambda$ system formed by the $\nu_{1}$ and $\nu_{2}$ transitions, see Figure 1a, with a spin transition at $\nu_{\text{MW}}=655$ MHz, which has the required optical and spin coherence times Ortu et al. (2018). A crucial first step towards optical spin-wave storage is then to demonstrate efficient optical pumping and optical AFC echoes.

Optical pumping of all hyperfine states requires addressing transitions involving all four hyperfine states. Our setup (Figure 1d) is based on two lasers (master and slave), where the master is locked to a high-finesse cavity at the frequency of the $\nu_{1}=306263.0$ GHz transition. The slave is locked to the master laser with an offset $\nu_{2}=\nu_{1}+0.6547$ GHz using an optical phase lock loop (PLL). Additionally the slave laser addresses the $\nu_{3}=\nu_{2}+6.2594$ GHz and $\nu_{4}=\nu_{2}+7.0762$ GHz transitions by phase modulation (Figure 1a and d).

The Y2SiO5 crystal is doped with 5 ppm of 171Yb3+, with an isotopic purity of $\approx 95$%. The optical inhomogeneous broadening is 1.3 GHz, hence there is clear overlap between optical transitions (Figure 1b). This issue can be solved by standard pumping sequences for RE crystals, refereed to as class cleaning Rippe et al. (2005); Lauritzen et al. (2012). By class cleaning for 400 ms with all $\nu_{1}$-$\nu_{4}$ frequencies and then state initializing into state $\ket{4}_{g}$ using frequencies $\nu_{2}$-$\nu_{4}$, we obtain the absorption spectrum in Figure 1b. The strong optical absorption on the $\nu_{1}$ transition and the deep holes on the $\nu_{2}$-$\nu_{4}$ transitions are evidence of efficient state initialization.

A measurement of the lifetime of the absorption structure showed that it rethermalizes with two different exponential time constants (Figure 1c); a faster 36(6) ms decay and a longer 390(55) ms decay. The double decay is due the different relaxation rates between hyperfine states, as also observed in 145Nd3+ Zambrini Cruzeiro et al. (2018). The population relaxation lifetimes are significantly longer than in the 10 ppm doped 171Yb3+:Y2SiO5 sample used in Ref. Ortu et al. (2018), which indicates that the population relaxation is due to flip-flops between ions in different hyperfine states Zambrini Cruzeiro et al. (2017, 2018); Car et al. (2018). A more detailed investigation of optical pumping and hyperfine flip-flop relaxation processes in this material will be presented elsewhere Welinski et al. (2019).

In a first set of storage experiments the optical AFC echo was studied (Figure 2), without applying the optical control pulses. The AFC was created on the $\nu_{1}$ transition, which has the strongest absorption in the $\Lambda$ system. In particular we measured the AFC echo efficiency $\eta_{AFC}$ as a function of the AFC delay $1/\Delta$, which depends strongly on the contrast and shape of the comb. The ideal shape of the comb teeth is squarish, with an optimal comb finesse given only by the maximum optical depth Bonarota et al. (2010). To create such combs we use the optical pumping method presented in Ref. Jobez et al. (2016), which was specifically designed to create optimal AFCs over a large frequency bandwidth. The AFC bandwidth was set to 20 MHz, and the 60 ms long comb preparation sequence directly followed the state initialization and class cleaning sequences.

An example of an optical AFC echo is shown in Figure 2a, and the echo efficiencies are plotted in Figure 2b. At the shortest delay of $1/\Delta=1$ µs, the AFC echo reaches a combined storage and retrieval efficiency of $\eta_{AFC}=24$%. The associated comb is shown in Figure 2c, and it features a high contrast, squarish shape that is close to optimal. The theoretical efficiency for an optimal comb for an optical depth of $d=4$ is 32% Bonarota et al. (2010). But the experimental comb at $1/\Delta=1$ µs has a background optical depth of about $d_{0}\approx 0.3$, which reduces the efficiency to $0.32\exp(-d_{0})=24$% de Riedmatten et al. (2008), consistent with the experimental data. Higher efficiencies should be achieved by improving the optical pumping, which requires a lower 171Yb3+ concentration to reduce the flip-flop rate Zambrini Cruzeiro et al. (2017), and using optical cavities Sabooni et al. (2013); Jobez et al. (2014).

The decay of the AFC echo as a function of $1/\Delta$ is due to a reduction in contrast and a small deviation in shape from the optimal square one, as exemplified for $1/\Delta=5$ µs in Figure 2c. The decay curve can be fitted using the formula $\exp(-4/(\Delta\cdot T_{2}^{{}^{\prime}}))$, where ideally the $T_{2}^{{}^{\prime}}$ is the optical coherence time Jobez et al. (2016). However, shorter $T_{2}^{{}^{\prime}}$ are typically obtained due to technical noise such as laser coherence time limitations and cryostat vibrations. The data in Figure 2b shows a double exponential decay with $T_{2}^{{}^{\prime}}=15$ and 165 µs, respectively, while the optical coherence time in this material we measured to be as long as 600 µs with photon echoes. We believe the laser spectrum to be the main limitation to the observed decay constants.

The timescale of the AFC delays shown in Figure 2b is up to two orders of magnitude longer than previously achieved delays ($0.1-1$ µs) in RE ions with electronic spin degrees of freedom, such as in Nd3+ Usmani et al. (2010); Clausen et al. (2011) or Er3+ Craiciu et al. (2019) doped crystals. Those short decays have been explained Usmani et al. (2010); Craiciu et al. (2019) by invoking superhyperfine interaction between the RE electronic spin and the nuclear spin of Y3+ ions in the host, which causes spectral nuclear spin-flip sidebands Wannemacher et al. (1991) and effectively enlarges the homogeneous linewidth of the RE ion. The efficient AFC echoes at long delays suggest that superhyperfine interaction is strongly suppressed at the zero-field ZEFOZ point. The delays are similar to those achieved in the purely nuclear RE spin systems Eu3+ Jobez et al. (2016) and Pr3+ Seri et al. (2018), which yet again highlights the interest of the hybridization of the electronic and nuclear spins at zero field in 171Yb3+:Y2SiO5.

We now turn to the optical spin-wave storage experiments, which in addition require coherent manipulation of the optical and microwave transitions, see Figure 3. Optically one requires an efficient population transfer of the control pulse on the $\nu_{2}$ transition, see Figure 1a, which has a dipole moment about 3 times weaker than the $\nu_{1}$ transition (see Supplemental materials Bus ). On the $\nu_{1}$ transition we achieved an optical Rabi frequency of $\Omega_{\text{O}}=2.0$ MHz, see Figure 3a, which gives an estimated Rabi frequency of $\Omega_{\text{O}}=0.6$ MHz on $\nu_{2}$. The resulting $\pi$-pulse duration of 0.8 $\mu$s implies an efficient population transfer over less than its Fourier limited bandwidth of $1.2$ MHz, clearly insufficient for the 10 MHz bandwidth of the 100 ns input pulse. To increase the bandwidth over which efficient population transfer can be achieved, one can employ longer frequency-chirped adiabatic pulses Minář et al. (2010). In this case we employ hyperbolic-square-hyperbolic (HSH) pulses Tian et al. (2011) of duration 5 µs, chirped over 10 MHz, which resulted in a measured population transfer efficiency of about 90% per HSH pulse. To reach larger memory bandwidths would require higher control pulse Rabi frequencies (see Supplemental materials Bus ).

On the microwave transition $\nu_{\text{MW}}$, the stored spin coherence induced by the optical control pulse will dephase with the inverse of the inhomogeneous spin linewidth $1/\Gamma_{\text{MW}}$. We measured a spin linewidth of $\Gamma_{\text{MW}}=0.7$ MHz (see Supplemental materials Bus ), which practically makes it impossible to read out the memory given the duration of the optical control pulse. But the spin coherence can be rephased with a spin echo sequence Heinze et al. (2013); Jobez et al. (2015), in this case a pair of MW $\pi$ pulses greatly extends the storage time. Using a simple coil wrapped around the crystal we reached a Rabi frequency of $\Omega_{\text{MW}}=0.65$ MHz, see Figure 3b. We note that with respect to pure nuclear non-Kramers systems, the spin linewidth is significantly larger. But this is more than compensated for by the electronic spin transition moment, as reflected by the large Rabi frequency. Using adiabatic MW pulses with a duration of 10 µs and a chirp bandwidth of 3 MHz, we readily reach an estimated transfer efficiency of $>$95%.

The final AFC spin-wave storage experiment data is shown in Figure 3d, as a function of the total storage time $T_{\text{M}}=1/\Delta+T_{\text{S}}$. Memory output pulses were detectable beyond 1 ms and the memory lifetime is consistent with previous measurements of the spin coherence time in 171Yb3+:Y2SiO5 Ortu et al. (2018). It should be emphasized that we reach spin-wave storage times presently only achieved in Eu3+:Y2SiO5 crystals using nuclear states. For the shortest spin storage time of $T_{\text{S}}=100$ µs, the total memory efficiency was $\eta_{\text{M}}=3.3\%$. While the AFC echo efficiency could be understood by the optical depth, see Figure 2, the total memory efficiency falls short of our predictions by a factor of 4, given the optical and MW control pulse efficiencies given above (see Supplemental materials Bus ). Possibly these were overestimated and/or their phase coherence was not sufficient.

To summarize, in this Letter we have demonstrated storage of optical pulses using the electronic-nuclear hyperfine states in 171Yb3+:Y2SiO5, which constitutes the first demonstration of spin-wave storage in any RE ion with electronic spin. Moreover, the AFC echo delay (which is related to temporal multimode capacity) and the total spin-wave storage time reach similar performance as in the pure nuclear 151Eu3+:Y2SiO5 system, but with 5 times larger optical bandwidths Laplane et al. (2016).

To conclude, we briefly discuss current limitations and future prospects of the memory. The memory bandwidth of 10 MHz is currently limited by the 0.6 MHz Rabi frequency of the control pulses. Simulations show (see Supplemental materials Bus ) that a 2 MHz Rabi frequency could increase the memory bandwidth to 100 MHz. Other $\Lambda$ systems could reach such Rabi frequencies using different polarization modes. To efficiently excite microwave transitions at $>1$ GHz in these $\Lambda$ systems, one can use lumped-element MW cavities Chen et al. (2016); Angerer et al. (2016). The optical Rabi frequency can also be greatly increased by using laser-written waveguides Corrielli et al. (2016); Seri et al. (2018) and could potentially allow memory bandwidths in the range of 100 MHz to 1 GHz. This would facilitate interfacing with quantum photon pair sources Saglamyurek et al. (2011); Clausen et al. (2014), and possibly allow interfacing with quantum dot single photon sources Grange et al. (2017); Kiršanskė et al. (2017); Schweickert et al. (2018). There is also the prospect of greatly increasing the AFC multimode capacity, which would increase the rate of a quantum repeater Simon et al. (2007). By increasing the bandwidth and by achieving AFC echo delays only limited by the long optical coherence time in 171Yb3+:Y2SiO5, the temporal multimode memory capacity could potentially reach 1000 modes. An important future step will be to demonstrate storage of weak coherent states, a strong requirement for a quantum memory. This will crucially depend on the efficiency with which one can optically pump ions out of the storage state, to decrease unwanted photon emission noise due to the control pulses. Recent work has shown that optical pumping of hyperfine states can be particularly efficient Zambrini Cruzeiro et al. (2018).

ACKNOWLEDGEMENTS

We acknowledge funding from FNS Research Project No 172590, EUs H2020 programme under the Marie Skłodowska-Curie project QCALL (GA 675662), IMTO Cancer AVIESAN (Cancer Plan, C16027HS, MALT).