Nanophotonic quantum storage at telecommunications wavelength

TL;DR

This paper demonstrates on-chip quantum storage of telecommunications wavelength light using erbium-167 ions in a nanobeam resonator, achieving high bandwidth, fidelity, and multimode capacity for quantum networks.

Contribution

It introduces a novel on-chip quantum memory platform operating at telecom wavelengths with demonstrated storage times and multimode capabilities.

Findings

Storage times up to 10 microseconds achieved

High fidelity and bandwidth demonstrated

Multimode capacity confirmed

Abstract

Quantum memories for light are important components for future long distance quantum networks. We present on-chip quantum storage of telecommunications band light at the single photon level in an ensemble of erbium-167 ions in an yttrium orthosilicate photonic crystal nanobeam resonator. Storage times of up to 10 $\mu$s are demonstrated using an all-optical atomic frequency comb protocol in a dilution refrigerator under a magnetic field of 380 mT. We show this quantum storage platform to have high bandwidth, high fidelity, and multimode capacity, and we outline a path towards an efficient erbium-167 quantum memory for light.

Full text

Optical quantum memories can aid processes involving the transfer of quantum information via photons, with applications in long distance quantum communication and quantum information processing Kimble (2008); Heshami et al. (2016); Briegel et al. (1998); Kok et al. (2007); Monroe et al. (2014). Rare-earth ions in crystals are a promising solid-state platform for optical quantum memories due to their long-lived optical and spin transitions that are highly coherent at cryogenic temperatures Thiel et al. (2011); Zhong et al. (2015a). Among rare-earth ions, only erbium has been shown to possess highly coherent optical transitions in the telecommunications C-band, which allows for integration of memory systems with low loss optical fibers and integrated silicon photonics Miyazono et al. (2017).

Fixed delay quantum storage for less than 50 ns at telecommunications wavelengths has been demonstrated in erbium-doped fibers Saglamyurek et al. (2015), and lithium niobate waveguides Askarani et al. (2018) at efficiencies approaching $1\%$. The protocol used in both cases, the atomic frequency comb (AFC), requires spectrally selective optical pumping Afzelius et al. (2009). The storage efficiencies in these works were limited in part by the lack of suitable long-lived shelving states in the erbium ions in these hosts. Moving to isotopically purified erbium-167 in a yttrium orthosilicate host (YSO) offers the prospect of long-lived shelving states in the form of hyperfine levels Rančić et al. (2018). While optical storage has been realized in erbium-doped YSO Lauritzen et al. (2010, 2011); Dajczgewand et al. (2014), including efficiencies approaching $50\%$ at storage times of $16\>\mu$s (revival of silenced echo protocol Dajczgewand et al. (2014)) quantum storage has yet to be demonstrated in this material.

In this work, we demonstrate on-chip quantum storage of telecommunications light at the single photon level. We used a nanophotonic crystal cavity milled directly in 167Er3+ doped YSO (167Er3+:YSO) to couple to an ensemble of erbium ions and realize quantum storage using the AFC protocol Afzelius et al. (2009). The cavity increased the absorption of light by the ion ensemble, allowing on-chip implementation of the memory protocol Afzelius and Simon (2010). By working in a dilution refrigerator and using permanent magnets to apply a field of 380 mT, we accessed a regime in which the ions have optical coherence times of $\sim 150\>\mu$s and long lived spin states to allow spectral tailoring. For the shortest measured storage time of 165 ns, we achieved an efficiency of $0.2\%$, with lower efficiencies for longer storage times, up to $10\>\mu$s. We demonstrated storage of multiple temporal modes and measured a high fidelity of storage, exceeding the classical limit. Lastly, we identified the limits on the storage efficiency and proposed avenues for overcoming them to achieve an efficient 167Er3+ quantum memory for light.

Memories using spectral tailoring such as the AFC protocol require a long-lived level within the optical ground state manifold, where population can be shelved. Hyperfine levels in the optical ground state in 167Er3+:YSO have been shown to have long lifetimes at 1.4 K and a magnetic field of 7 TRančić et al. (2018). In general, these levels can be long-lived when the erbium electron spin is frozen, which occurs when $\hbar\omega_{e}\gg k_{B}T$, where $\omega_{e}$ is the electron Zeeman splitting Rančić et al. (2018). In this work, we satisfied this inequality by using a moderate magnetic field of 380 mT parallel to the D1 axis of the crystal $(\omega_{e}=2\pi\times 80\>\textrm{GHz})$ and a nanobeam temperature of $\sim$400 mK. The nanobeam temperature was estimated via the electron spin population at a lower magnetic field SOM ; Kukharchyk et al. (2018). The hyperfine lifetime in the bulk crystal was measured to be 29 minutes, enabling the long-lived, spectrally selective optical pumping required for the AFC protocol (see supplementary material SOM ).

Figures 1a-c describe the nanoresonator used in this experiment. A triangular nanobeam photonic crystal cavity Zhong et al. (2016) was milled in a YSO crystal doped with isotopically purified 167Er3+ ($92\%$ purity) at a nominal concentration of 50 ppm. The width of the nanobeam was $1.5\>\mu$m, and the length $\sim 20\>\mu$m. The slots in the nanobeam created a photonic crystal bandgap, and the periodic pattern (lattice constant = 590 nm, groove width = 450 nm) was modified quadratically in the center to create a cavity mode. Figure 1a shows a scanning electron micrograph of the nanobeam and Fig. 1b shows a finite element analysis simulation of the TM cavity mode.

The coherence time of the 1539 nm optical transition, which provides an upper bound on all-optical storage time, was measured to be $149\>\mu\mathrm{s}\pm 4\>\mu\mathrm{s}$ in the nanobeam. The bulk optical coherence time of this transition under similar cooling conditions was measured to be $760\>\mu\mathrm{s}\pm 41\>\mu\mathrm{s}$. The reduction in coherence time as measured in the nanobeam is likely caused by a combination of higher temperature in the nanobeam during measurement and the impact of the focused ion beam milling process SOM . We note that the fabrication method has not significantly impacted the coherence properties of ions in similar devices Zhong et al. (2015b, 2017), although the bulk crystal coherence times measured in those works were also lower, preventing a direct comparison. The optical coherence time did not limit the storage time achieved in this work.

Figure 1d shows a schematic of the optical testing setup. Figure 1c shows the reflection spectrum of the nanobeam cavity, which has a measured loaded quality factor of $7\times 10^{3}$. The cavity was tuned onto resonance with the 1539 nm transition of the 167Er3+ ions by freezing nitrogen gas onto the nanobeam at cryogenic temperatures Mosor et al. (2005). The coupling of the ensemble of ions to the cavity is seen as a peak in the cavity reflection dip. The inset shows a close-up of the ion-cavity coupling (in black) and a fit to theory Diniz et al. (2011). The ensemble cooperativity was estimated from the fit to this curve to be 0.1 SOM . For high efficiency storage using ions coupled to a cavity, the ensemble cooperativity (after spectral tailoring) should equal one Afzelius and Simon (2010); Moiseev et al. (2010). An increased ensemble cooperativity of 0.3, as shown in red in the inset of Fig. 1c, was obtained using a partial hyperfine initialization procedure. The spectral density of erbium ions in the center of the inhomogeneous line (zero detuning) was increased from its thermal equilibrium value by sweeping the laser frequency between 350 MHz and 820 MHz on both sides of the inhomogeneous line. This procedure can be optimized to further increase the ensemble cooperativity, but was limited here by the relatively weak magnetic field, which allows only partial hyperfine initialization SOM . At 7 T, initialization into one hyperfine state with an efficiency of $95\%$ has been demonstrated Rančić et al. (2018).

The nanobeam device was used to demonstrate quantum optical storage using the AFC protocol Afzelius et al. (2009). In this protocol, a pulse of light that is absorbed by an AFC with an inter-tooth spacing of $\Delta$ is stored for $t=1/\Delta$. Frequency selective optical pumping was used to create a comb within the inhomogeneous linewidth, as shown in Fig. 2a. Figure 2b shows a schematic of the protocol. First, a long pulse with strong frequency modulated sidebands was used for partial hyperfine initialization. The next 15 pulses, repeated $n_{\mathrm{pump}}=20$ times, created the comb: the laser frequency was swept through 15 values, separated by $\Delta=6.1$ MHz, to optically pump away ions and create 15 spectral transparencies. The following $n_{\mathrm{input}}=60$ pulses were zero-detuning weak coherent states which were stored in the frequency comb. The full experiment was repeated $\sim 10^{4}$ times. As shown in Fig. 2c, 60 ns wide pulses with an average photon number of $\bar{n}=0.60\pm 0.09$ were stored for 165 ns with an efficiency of $0.2\%$. Despite the partial initialization, the storage efficiency was limited by the ensemble cooperativity of the device SOM .

Coherent pulses could be stored in the device for up to $10\>\mu$s, although with a lower efficiency of $10^{-5}$, as shown in Fig. 3. For this experiment, as for all storage times longer than 165 ns, we used an accumulated AFC method SOM ; de Riedmatten et al. (2008) to create the comb. As shown in the inset of Fig. 3, weak pairs of pulses separated by $t_{\mathrm{storage}}=10\>\mu$s were repeatedly sent into the cavity. The Fourier transform of each pulse pair is a frequency comb, which imprinted onto the 167Er3+ inhomogeneous line to create the AFC. The efficiency at this long storage time was limited by laser frequency jitter and by superhyperfine coupling to the yttrium ions in YSO. Superhyperfine coupling limits the narrowest spectral feature to $\sim 1$ MHz Guillot-Noël et al. (2007); Car et al. (2018). Since this exceeds the period of the comb needed for this storage time ($\Delta=1/t_{\mathrm{storage}}=0.1$ MHz), the resulting AFC will have a lower contrast, leading to lower storage efficiency SOM .

The AFC protocol is capable of storing multiple temporal modes Afzelius et al. (2009). Ten coherent pulses were stored in this device, as shown in Fig. 4a. Multiplexing in frequency is also possible Sinclair et al. (2014). The AFC comb in Figure 2a has a bandwidth of $\sim 90$ MHz (see Fig. 2a) which can accommodate storage in multiple frequency modes. An inhomogeneous linewidth of 150 MHz limits the bandwidth of storage in this system. Although there exist methods to increase this linewidth Welinski et al. (2017), the bandwidth cannot be increased much further before being limited by overlapping optical transitions from other hyperfine levels.

In quantum storage protocols, the phase of the stored state must be preserved. A double AFC was used as an interferometer in order to characterize the coherence of the storage process de Riedmatten et al. (2008). Two overlapping AFCs with tooth spacing $\Delta_{1},\Delta_{2}$ and with frequency detuning $\delta_{1},\delta_{2}$, were created, so that each input pulse was mapped to two output pulses at times $1/\Delta_{1},1/\Delta_{2}$ and with a relative phase $\phi_{\mathrm{rel}}=2\pi\left(\frac{\delta_{2}}{\Delta_{2}}-\frac{\delta_{1}}{\Delta_{1}}\right)$Afzelius et al. (2009). An input state encoded into two pulses, $|\psi_{\mathrm{in}}\rangle=\frac{1}{\sqrt{2}}\left(|\mathrm{early}\rangle+|\mathrm{late}\rangle\right)$, was therefore mapped to a total of four output pulses. By appropriately selecting the time interval between the early and late input pulses, two of the four output pulses were made to overlap and either constructively or destructively interfere, depending on $\phi_{\mathrm{rel}}$ (see inset of Fig. 4b). Using an input state with mean photon number $\bar{n}=0.6\pm 0.09$, and sweeping $\phi_{\mathrm{rel}}$ via the detuning $\delta_{2}$, the interference fringe shown in Fig. 4b was obtained (see caption for details). The measured visibility of $91.2\%\pm 3.4\%$ demonstrates the high degree of coherence of this on-chip storage process. The visibility was limited by the 12 counts in the total destructive interference case $\left(\delta_{2}=\frac{\Delta_{2}}{2}\rightarrow\phi_{\mathrm{rel}}=\pi\right)$. This was due in part to imperfect cancellation of the two overlapping output pulses, resulting from the slightly different efficiencies of storage in the two AFCs, and in part to a dark count rate of 18.5 Hz, leading to a baseline of 7 counts. The dark-count-subtracted visibility is $97.0\%\pm 3.6\%$.

The double comb method was also used to estimate a lower bound for the fidelity of storing single photon time bin states, $F^{(n=1)}$. The fidelity of storage was measured for four input states $|\mathrm{early}\rangle$, $|\mathrm{late}\rangle$,$\frac{|\mathrm{early}\rangle+|\mathrm{late}\rangle}{\sqrt{2}}$ and $\frac{|\mathrm{early}\rangle-|\mathrm{late}\rangle}{\sqrt{2}}$, using two mean photon numbers $\bar{n}=0.30$ and $\bar{n}=0.60$. With these values, the decoy state method SOM ; Sinclair et al. (2014); Ma et al. (2005) was used to calculate a bound on the fidelity for storing single photon states $F^{(n=1)}\geq 93.7\%\pm 2.4\%$, which exceeds the classical limit of $F=2/3$. Similar to the case for visibility discussed above, the measured fidelity was limited in part by dark counts and in part by the double comb protocol being an imperfect interferometer SOM . Although the pulses stored in this experiment were weak coherent pulses, single Zargaleh et al. (2018); Wang et al. (2018); Rieländer et al. (2016); Dibos et al. (2018); Paul et al. (2017); Atzeni et al. (2018) and entangled photon Niizeki et al. (2018); Zhou et al. (2018) sources are available at telecommunications wavelengths. Notably, sources in the telecommunications C-band Dibos et al. (2018); Paul et al. (2017); Atzeni et al. (2018); Niizeki et al. (2018) including individual erbium-ion emitters Dibos et al. (2018), are compatible with this device. Storing photons of any frequency is enabled by quantum frequency conversion Dréau et al. (2018). The bandwidth of compatible photons is bounded by the AFC periodicity of $\gtrsim$ 1 MHz and the $\lesssim$ 100 MHz bandwidth of the AFC.

While the storage presented here was limited in efficiency, a nanophotonic cavity coupled to 167Er3+ ions in YSO promises to be an efficient quantum storage system. The main limitations to the storage efficiency in this work were a low ensemble cooperativity of 0.3 and loss from the optical nanobeam cavity. The cooperativity can be increased using higher 167Er3+ doping and better hyperfine initialization, which would require increasing the applied magnetic field or changing its angle SOM ; Rančić et al. (2018). A higher intrinsic quality factor resonator would serve to both increase cooperativity and decrease cavity loss. For example, using a YSO crystal with 200 ppm 167Er3+ doping, optimal hyperfine initialization, and a resonator with an intrinsic quality factor of 2 million, the theoretical efficiency of the AFC quantum storage is $90\%$ (see supplementary material for analysis SOM ). Mature silicon nanofabrication technology can be leveraged to achieve this goal by using a silicon resonator evanescently coupled to 167Er3+ ions in YSO Dibos et al. (2018); Miyazono et al. (2017). With this efficiency level and a storage time of $10\>\mu$s, the device would outperform a delay line composed of standard telecommunications fiber Cho et al. (2016), an important benchmark on the way to achieving a quantum memory suitable for scalable quantum networks.

With the optical AFC protocol alone, it will be difficult to achieve efficient storage for this duration due to superhyperfine coupling. However, the AFC spin-wave protocol, where the stored information is reversibly transferred from the optical to the hyperfine manifold Afzelius et al. (2009), would enable even longer storage without the same requirements for narrow spectral features, as well as enabling on-demand recall. The availability of hyperfine states with coherence times exceeding 1 second Rančić et al. (2018) make 167Er3+:YSO a promising system for spin-wave storage.

In conclusion, we have demonstrated on-chip quantum storage of telecommunications band light at the single photon level. The storage had a bandwidth of $\sim 90$ MHz, and a storage fidelity for single photon states of at least $93.7\%\pm 2.4\%$. 167Er3+:YSO at temperatures of $\sim$ 400 mK and moderate magnetic field was shown to be a promising material for AFC quantum memories. A clear path exists for creating a high efficiency quantum memory using this material and a nanoscale resonator.