One-hour coherent optical storage in an atomic frequency comb memory

Photon loss in optical fibers prevents long-distance distribution of quantum information on the ground. Quantum repeater is proposed to overcome this problem, but the communication distance is still limited so far because of the system complexity of the quantum repeater scheme. Alternative solutions include transportable quantum memory and quantum-memory-equipped satellites, where long-lived optical quantum memories are the key components to realize global quantum communication. However, the longest storage time of the optical memories demonstrated so far is approximately 1 minute. Here, by employing a zero-first-order-Zeeman magnetic field and dynamical decoupling to protect the spin coherence in a solid, we demonstrate coherent storage of light in an atomic frequency comb memory over 1 hour, leading to a promising future for large-scale quantum communication based on long-lived solid-state quantum memories.

In our previous work [1], we use Raman heterodyne detection method to probe the continuous-wave nuclear magnetic resonance (NMR) of the ground state 7 F 0 and excited state 5 D 0 of 151 Eu 3+ :Y 2 SiO 5 . However, in this work, although the ground-state resonances can be detected using the same method, the excited-state resonances are difficult to detect due to the weaker radiofrequency (RF) fields generated by the Helmholtz coils.
To overcome this problem, we use a pulsed Raman heterodyne detection approach [2]. Optical pumping is employed to isolate a single class of ions in a specific ground-state level via class cleaning and spin polarization described in the paper. Then a probe pulse with a duration of 200 µs and a power of 4 mW resonant with the populated ground state and an arbitrary excited state is sent into the crystal, and at the mean time an RF pulse with a duration of 100 µs is applied to drive the hyperfine transitions in the excited state. The RF pulse is generated by a local oscillator with an amplitude of 0.6 V, and amplified by an amplifier with an output of 300 W to ensure a strong enough interaction with the excited-state hyperfine levels. The transmitted optical pulse is accompanied with a Raman scattered field if the RF pulse is resonant with the hyperfine transitions. A beat signal between the transmitted and scattered field is then captured by a photodetector and demodulated with a lock-in amplifier.
The resonance of the hyperfine transitions can be identified by varying the frequency of RF pulses. At least five resonances need to be found in order to determine the excited-state structure with six hyperfine levels. An example of the |3 e ↔ |6 e transition at 124.52 MHz is shown in Supplementary Fig. 1. All the neighboring hyperfine transitions in the excited state are presented in Supplementary Table 1. As a comparison, we also provide the calculated results in the same field, based on the spin Hamiltonians determined in previous works [1,3]. Note that due to the experimental errors, the calculated strength and direction of the ZEFOZ field is slightly different based on these two works. But we verify that the first-order Zeeman coefficient S 1 is the same, which ensures that the fields are physically equivalent. According to the data presented in Supplementary  maximum error is larger than 1 MHz, which is the storage bandwidth of the memory. In addition, we note that the level structure of the 7 F 0 ground state obtained here is significantly different from the results that reported in Ref. [4]. These results indicate the necessity of this experiment before determining the optical pumping strategies.
Supplementary Note 2 -Atomic frequency comb The laser system at 580 nm is a specially-designed high-power laser. The seed laser is a semiconductor laser at 1160 nm (DL pro, Toptica) which is amplified to 30 W by a Raman fiber amplifier (PreciLasers). The laser at 580 nm is obtained by the single-pass second harmonic generation in a PPSLT crystal, with an output power of 6.2 W. The reference optical pulse for heterodyne detection is generated from another frequency-doubled semiconductor laser (TA-SHG, Toptica) with a locked frequency offset.
Before preparing the AFC in the |3 g level, optical pumping sequence called class cleaning and spin polarization [5] is used to select one class of ions. The six pumping lights are resonant with |1 g ↔ |1 e , |2 g ↔ |2 e , |3 g ↔ |3 e , |4 g ↔ |3 e , |5 g ↔ |3 e , |6 g ↔ |5 e , respectively, with a power of 100 µW and a duration of 2 ms.
The structure of the AFC is presented in Supplementary Fig. 2a. We use a single-photon detector to record the absorption profile of the AFC prepared in |3 g . The  Fig. 2. AFC structure and a photo of the sample. a The optical depth of the |4 g ↔ |3 e (green) and |3 g ↔ |3 e (blue) after the class cleaning and spin polarization, and the AFC structure with ten teeth prepared in the |3 g (red). b The photo of the sample, which is fixed on a specially-designed holder mounted on the goniometers. The helmholtz coils are placed at the two sides of the sample and the mirror is below the sample. The external magnetic field and the incident beams are along the vertical direction.
AFC is prepared using a parallel method [6] within the 1 MHz bandwidth. The AFC has a comb periodicity of 100 kHz and a single peak width (FWHM) of γ = 45 kHz, leading to a finesse F = 100/45 = 2.22. The two-level AFC efficiency can be calculated as follows: [7] where the optical depth after class cleaning and spin polarization is αL = 0.8. The calculated efficiency η is 4.4%, which is close to our experimental result of 4.5%. The control pulse used in the paper has a complex hyperbolic secant profile [8] to achieve efficient control over a large bandwidth. The transfer efficiency η control of a single control pulse is estimated by comparing the spin-wave AFC echo with the two-level AFC echo.
In Supplementary Fig. 2b, we present a photo of the cylindrical sample and its surroundings. The optical surface is cut perpendicularly to the direction of the known ZEFOZ magnetic field in order to easily align the sample to the magnetic field of the magnet, which is approximately in the vertical direction.

Supplementary Note 3 -Spin coherence time measurements
The width of the π pulse of 65.1 µs used in the dynamical decoupling and spin coherence time measurements is determined by implementing a spin nutation experiment [9]. The two-pulse phase memory time T M [10] is determined to be 21.5 s, which is shorter than the 47 s in the previous work [4]. The possible reason is the inhomogeneity of the magnetic field, considering the longer sample used here.
In order to take advantage of the long spin coherence time of the |3 g ↔ |4 g (|−3/2 g ↔ |+3/2 g ) transition in the ZEFOZ field, we measure the coherence times by spin echo experiments with different dynamical decoupling sequences applied as shown in Supplementary Fig. 3. The spin echo signals are detected by Raman heterodyne detection. CPMG and KDD x reach their longest coherence times of 2.68 ± 0.06 and 0.95 ± 0.03 hours respectively, when the interval τ between the π pulses is 20 ms. When τ is shorter than 20 ms, the heating of the Helmholtz coils and the infidelity of the π pulses will limit the spin coherence times. When τ = 100 ms, the coherence times are 50.6 ± 2.0 and 38.2 ± 2.0 minutes with CPMG and KDD x , respectively. The spin coherent lifetimes are essentially the same as the optical AFC storage lifetimes for τ = 100 ms. We note that, due to strong fluctuations of the signal for optical storage with storage time shorter than 5 minutes, the lifetimes are fitted using the data starting from 5 minutes in Fig. 3 in the main text.