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Nanophotonic rare-earth quantum memory with optically controlled retrieval

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Science  29 Sep 2017:
Vol. 357, Issue 6358, pp. 1392-1395
DOI: 10.1126/science.aan5959

A rare-earth quantum memory

The development of global quantum networks will require chip-scale optically addressable quantum memories for quantum state storage, manipulation, and state swapping. Zhong et al. fabricated a nanostructured photonic crystal cavity in a rare-earth-doped material to form a high-fidelity quantum memory (see the Perspective by Waks and Goldschmidt). The cavity enhanced the light-matter interaction, allowing quantum states to be stored and retrieved from the memory on demand. The high fidelity and small footprint of the device offer a powerful building block for a quantum information platform.

Science, this issue p. 1392; see also p. 1354

Abstract

Optical quantum memories are essential elements in quantum networks for long-distance distribution of quantum entanglement. Scalable development of quantum network nodes requires on-chip qubit storage functionality with control of the readout time. We demonstrate a high-fidelity nanophotonic quantum memory based on a mesoscopic neodymium ensemble coupled to a photonic crystal cavity. The nanocavity enables >95% spin polarization for efficient initialization of the atomic frequency comb memory and time bin–selective readout through an enhanced optical Stark shift of the comb frequencies. Our solid-state memory is integrable with other chip-scale photon source and detector devices for multiplexed quantum and classical information processing at the network nodes.

Quantum memories for light play a vital role in optical quantum networks (1) for long-distance secure communications and interconnecting future quantum computers. Although optical quantum memories—devices that faithfully store input photonic qubits—have already been implemented in macroscopic systems such as atomic ensembles (2), solid-state crystals (35), and waveguides (68), realizing scalable networks requires integration of micro- or nanoscale memories with other guided-wave components for on-chip quantum information routing and processing. Crystals doped with rare-earth ions (REIs) are appealing solid-state materials for quantum storage because of their highly coherent optical transitions between 4f levels, which are further split into Zeeman and hyperfine levels with coherent transitions in the microwave regime (4, 9, 10). So far, memories based on macroscopic rare-earth crystals have been realized with electromagnetically induced transparency (11), gradient echo, controlled reversible inhomogeneous broadening (CRIB) (12), and atomic frequency comb (AFC) protocols (3, 13). REI-doped waveguide quantum memories have also been developed (68), but the macroscopic lengths of these devices are not ideal for on-chip integration. Coherent coupling of a mesoscopic REI ensemble to a nanophotonic cavity has been achieved recently (14, 15). To show the versatile functionality of this nanoscale platform, we demonstrate storage of photonic quantum bits with high fidelity, fast memory initialization, and a method for dynamically controlling the storage time.

Our optical quantum memory is based on a triangular nanobeam photonic crystal resonator (14, 16) fabricated in a Nd:YVO crystal nominally doped at 100 parts per million [materials and methods (17)] (Fig. 1). The device is a one-sided cavity; the input mirror (left side in Fig. 1, B and C) was fabricated using a smaller number of photonic crystal lattice periods and thus has a lower reflectivity. The optical coupling in and out of the device was implemented by means of a 45°-angled coupler at one end of the nanobeam that totally internally reflects light into the device. An aspheric doublet lens matched the mode of the single-mode fiber to the mode of the nanobeam waveguide (Fig. 1A). The coupling efficiency was optimized to 27% (from fiber to waveguide) by positioning the device using a three-axis nano-positioner. The nanocavity fundamental mode volume is Vmode = 0.52(λ/n)3 = 0.0564 μm3 (simulated, where λ is the resonance wavelength and n is the effective modal refractive index), with a measured, near-critically coupled quality factor Q = 3700 (energy decay rate κ = κin + κsc + κleak = 2π × 90 GHz). The waveguide-cavity coupling rate κin through the input mirror was ~50% of κ. κsc is the intrinsic scattering loss, and κleak is the leakage through the long mirror. The device was cooled to ~0.5 K in a helium-3 refrigerator. The laser used to prepare and probe the memory was modulated by two double-pass acousto-optic modulators (AOMs) and two electro-optic modulators (EOMs) connected in series, and it was delivered to the sample by means of a single-mode fiber. The reflected signal from the device was sent via a circulator and an optical switch to either a spectrometer for characterization or an 82%-efficient superconducting nanowire single-photon detector (18) [supplementary text (17)] mounted in the same refrigerator.

Fig. 1 Schematics of the experiment.

(A) The Nd:YVO device was cooled to 480 mK in a helium-3 refrigerator. Laser light was modulated by a combination of AOMs and EOMs and was delivered to the device with a single-mode fiber. An aspheric doublet lens focused the fiber output to the nanobeam coupler (close-up view shown in the red dashed box). The reflected light was sent either to a room-temperature apparatus for characterization or to a WSi superconducting nanowire detector in the same refrigerator. Scale bar, 1 μm. a, b, and c are crystallographic axes. SNSPD, superconducting nanowire single-photon detector; MEMS, micro-electromechanical system; SMF, single-mode fiber; pol., polarization; PM, phase modulation; AM, amplitude modulation. (B) A scanning electron microscope image of the one-sided nanobeam optical cavity. (C) Simulated fundamental transverse-magnetic (electric field polarization along c) mode profiles. The black dashed line defines the input-output boundary for characterizing the memory device efficiency.

Compared with macroscopic bulk memories that rely on long crystals (for large optical depth) to achieve high storage efficiency, memories based on nanocavities exploit the enhanced light-matter interaction at the single-photon level and thus can achieve high efficiency using a very small volume of material containing a mesoscopic ensemble of atoms (1921). Moreover, to efficiently map a photon in and out of the ensemble, the device needs to be impedance-matched so that the atoms are coupled to the cavity with a collective cooperativity C = 4Ng2/κΓh close to unity (20, 21). Here g is the atom-cavity coupling rate, Γh is the atomic homogeneous linewidth, and N is the number of atoms per Γh bandwidth. This impedance-matching condition applies to a pulsed operation to maximize the efficiency of absorbing a pulse in the atomic ensemble. The reflection spectrum of the cavity on resonance with the Nd ensemble shows a center peak (Fig. 2A, red dashed box) resulting from the coupling between the cavity field and the Nd3+ 4F3/2(Y1)–4I9/2(Z1) transition at 880 nm. From the contrast of the peak, we extracted an effective C = 0.75 at the center frequency of the ensemble absorption [materials and methods (17)]. Figure 2B plots the photoluminescence lifetime (optical T1) in the cavity (blue), showing a 1/e decay time of 4.5 μs that is 20 times as fast as that of the bulk (red). This Purcell enhancement increases the branching ratio of the Y1-to-Z1 transition from initially 27% (22) to ~97%, which facilitates an efficient Λ system for optical pumping experiments. The optical coherence time T2 from two-pulse photon echo measurements was 3.1 ± 0.3 μs [Γh = 1/(πT2) = 100 kHz] for cavity-coupled ions when the cavity was detuned from the ensemble resonance by ~50 GHz (blue curve in Fig. 2C), which is close to the 3.2 ± 0.2 μs found for the bulk crystal. When the cavity was on resonance, the strong Purcell enhancement modified the T2 to Embedded Image = 2.3 ± 0.3 μs. With an inhomogeneous broadening of ~2 GHz, our nanocavity contained a total of ~4 × 105 ions, with a peak spectral density of N ~ 20 ions per Γh estimated from the cooperativity and a maximum single-photon Rabi frequency gmax = 2π × 30 MHz (22).

Fig. 2 Cavity-enhanced impedance-matched light-matter interface.

(A) Cavity reflection spectra for an empty cavity (dotted blue line, frequency shifted to overlap with the on-resonance spectrum) and a cavity on resonance with the Nd transition (solid blue line). The peak (red dashed box) results from collective coupling of the Nd ensemble with the cavity. The flat spectrum (brown line) is the reflection from the right coupler, indicating that the cavity is dominantly one-sided. λ, wavelength. (B) Photoluminescence (PL) decays (optical T1) for ions coupled to the nanocavity (blue) and in the bulk crystal (red). The decay in the nanocavity is not a single exponential (inset), because the ions randomly distributed in the cavity experience different Purcell enhancement. t, time; a.u., arbitrary units. (C) Two-pulse photon echo decays in the nanocavity that is on resonance with the ensemble (gray), detuned by ~50 GHz (blue), and in the bulk (red). The inset shows a typical photon echo signal from the nanocavity. The vertical axis is in linear scale and arbitrary units. The horizontal axis is in microseconds. τ, delay between the first and second pulse.

Ensemble-based optical quantum memory protocols such as AFC and CRIB require preparing high-contrast spectral features within the inhomogeneous profile by means of persistent hole-burning. In REI-doped crystals, this preparation step is typically slow because of the long excited-state optical lifetimes T1. Additionally, the resultant spin polarization, measured by the ratio of two spin-ground-state populations, can be poor for Kramers ions that, compared with non-Kramers ions, have shorter Zeeman lifetimes Tz relative to optical T1 (e.g., erbium) (23). Here we show that the nanocavity increases the optical pumping efficiency and spin polarization by enhancing the spontaneous decay rate from excited states to the Zeeman shelving states (transitions b and d in Fig. 3A). The experimental magnetic field (B = 340 mT) configuration is illustrated in Fig. 3A. The misalignment of the magnet with respect to the sample caused a slight deviation θ of the field orientation from the c axis (crystal symmetry axis). From the bulk optical pumping measurement [supplementary text (17)], we estimated this deviation to be ~8.2°. A representative spectrum for the four transitions is plotted next to the Zeeman-level splitting (24) in Fig. 3A. The spin-preserving transitions a and c overlapped, which favored higher optical depth and better impedance-matching when using their overlapped spectral region as a photon-atom interface. The b and d transitions had smaller branching ratios, but both were enhanced, similar to the a and c transitions in the cavity. Using the pulse modulation sequence shown in the inset of Fig. 3C, we verified that the Zeeman spin lifetime in the cavity, Embedded Image = 12.5 ± 1.0 ms, was not degraded relative to the bulk, Embedded Image = 12.7 ± 1.5 ms (Fig. 3B). Figure 3C plots the spin population as a function of optical pumping time tpump. In the nanocavity, a maximum spin polarization of ρ21 ≈ 20 (ρ1 < 5%) was achieved with tpump less than 1 ms, whereas in the bulk, it took more than 10 ms to reach ρ21 ≈ 3. This enhancement can be understood from a rate-equation model taking into account the field angle–dependent branching ratios given by the spin Hamiltonian (23, 24) [supplementary text (17)].

Fig. 3 Efficient optical pumping and quantum storage in a Nd:YVO nanocavity.

(A) Magnetic field configuration with Zeeman spin levels and transitions (a to d) of Nd3+ (only isotopes with 0 nuclear spins). (B) Spectral hole decays from which spin lifetimes were extracted. tw, wait time between optical pumping and the probe pulse. (C) Optical pumping dynamics showing an enhanced spin polarization in the nanocavity [ρ1 < 5% (blue), versus ~20% (red) in the bulk]. The inset shows the AOM modulation sequence. The bulk spin population was measured by the transmission of the probe pulse (red). The cavity was probed using photoluminescence counts after the probe excitation (blue). (D) An AFC with F = 3.3 and ~400 ions in each tooth. Gray, 100-kHz resolution; black, 500-kHz resolution. (E) Input (black line), reflected (blue area), and AFC echo signal of a coherent state (mean photon number α = 0.58) time-bin mode Embedded Image from the nanocavity. The inset shows the lower bounds on the qubit storage fidelity for a set of inputs, with an arithmetic mean fidelity of 96.8%. Error bars, standard deviation.

To demonstrate storage of photonic qubits by means of the AFC protocol, we sent a sequence of 10-ns pulse pairs separated by a time interval t = 1/Δ, where Δ is the frequency spacing of the comb. The number of pulses in the sequence was optimized for the best echo efficiencies for a given t, which effectively controlled the finesse F of the comb. Figure 3D shows an AFC with F = 3.3, Δ = 13.3 MHz, and a vanishing absorption background. The peaks of the comb appeared to be slightly eroded because of power broadening of the burning pulses. The narrowest tooth width was 3.2 MHz full-width-at-half-maximum (FWHM), which was likely to be limited by the superhyperfine interactions in Nd:YVO and spectral diffusion during comb preparation.

Given the comb profile, we estimate an expected device storage efficiency ηdev—defined as the probability that an AFC echo photon will be emitted back into the waveguide terminating the cavity for a photon sent into the cavity—to be 4%, on the basis of ηdev = [4κinΓcomb/(κ + Γcomb + Γbg)2]2Embedded Image [supplementary methods (17)], where Γcomb and Γbg are the cavity-enhanced absorption rates for ions contributing to the comb and the background, respectively. The storage of a single coherent pulse was first measured to characterize the AFC efficiency and noise performance [supplementary text (17)]. Figure 3E plots the reflected input and AFC echo signal of coherent photons prepared in a time-bin state Embedded Image (where Embedded Image and Embedded Image are early and late time-bin states, respectively), with a mean photon number of α = 0.58. The input intensity was determined from a signal (black line) that was detuned 1 nm from the cavity resonance (i.e., 879 nm in Fig. 2A). The AFC device efficiency was 2.5% for a storage time of 75 ns. This efficiency was measured 200 μs (~40 times the T1 in the cavity) after the preparation sequence. The discrepancy from theory is likely due to an elevated background density in the comb at large detunings, which reduces the echo efficiency by not rephasing the input excitation. This effect is caused by the limited bandwidth of current AFC preparation pulses, which can be eliminated by shortening the pulses to 1 ns with a faster arbitrary-wave generator.

To assess the performance of this nanophotonic memory at the single-photon level, we measured the recalled state fidelity for test input qubit states Embedded Image, Embedded Image, Embedded Image, and Embedded Image [supplementary text (17)] at two mean photon numbers α1 = 0.58 and α2 = 0.26. We then calculated the lower bounds on the qubit storage fidelity, following a decoy-state strategy in quantum key distribution that was recently adopted to gauge the quantum storage process (25) [supplementary text (17)]. The results of this analysis are plotted in the inset of Fig. 3E, in which the mean fidelity of a time-bin qubit is 96.8%, considerably above the classical limit of two-thirds and on par with the state-of-the-art bulk AFC memories (3, 26).

The ability to store photons in multiple time bins and to retrieve one at an arbitrary bin is a key functionality in proposed multiplexed quantum repeater networks (25). Upon successful Bell-state measurement, a feedforward signal will be sent to retrieve the stored photon at a desired time bin for subsequent entanglement swap. Here we demonstrate time bin–selective readout of a coherent pulse, using the cavity-enhanced ac Stark shift. Two Stark pulses detuned at ±Δst = 1 GHz (Embedded Image) from the center of the AFC [supplementary methods (17)] uniformly compressed the comb spacing by Embedded Image (27) (Fig. 4A) over the Stark pulse duration of tst = 16 ns (where nst is the average number of photons in the cavity while the Stark pulse passes through it, and gst is the Stark Rabi frequency per single photon in the cavity). This comb compression resulted in an additional delay of the echo by δΔtst/Δ. Figure 4C plots the measured echo retrieval time with increasing Stark pulse intensities from nst = 0 to ~170 photons per pulse. The relative timing of the echo peaks is plotted against the Stark pulse photon number in Fig. 4D, with a linear fit of ~50 ps per photon (red dashed line). As the Stark pulse intensity increased, the echo efficiency gradually dropped (Fig. 4E), owing to broadening and distortion of the AFC teeth as a result of inhomogeneous ac Stark frequency shifts produced by random locations of ions in the cavity. Nevertheless, the echo signal (Fig. 4C) was still 12.3 dB above the background at the highest Stark pulse intensity. The maximum delay of the measured echo was 10 ± 1 ns, which is comparable to the FWHM of the echo pulse—that is, a time bin. In the current device, inhomogeneous Rabi frequencies cause a smearing of the comb teeth while the Stark pulses are applied. This results in a weaker echo, thus limiting the maximum time shift without severely attenuating the echo intensity. Such limitations can be lifted if ions are selectively doped at the cavity antinodes by site-controlled implantation (28). Alternatively, isolating subensembles with more homogeneous Rabi frequencies could be possible by optical pumping with repeated 2π pulses, as demonstrated in (29).

Fig. 4 Temporal-mode selective pulse retrieval using ac Stark pulses.

(A) Schematic spectral configuration of two Stark pulses with respect to the AFC comb. The symmetric, far-detuned Stark pulses induce uniform compression of the AFC. (B) Stark pulses cause an additional delay in echo retrieval times. (C) Measured AFC echoes with increasing photon number in 16-ns Stark pulses. Here Δst = 1 GHz and Δ = 13.3 MHz. The blue shaded area overlays the echo envelope with no Stark pulses. (D) AFC echo delay against Stark pulse intensity. A linear fit (red dashed line) corresponds to 50 ps per photon. (E) Decrease of AFC echo efficiency with Stark pulse intensity, caused by AFC distortion resulting from inhomogeneous Stark shifts in the nanocavity.

The nanocavity scheme demonstrated here enables versatile engineering of the quantum light-matter interface and offers the distinctive advantage of faster and more efficient memory preparation. An on-demand quantum memory will require the incorporation of the spin-wave storage in long-lived hyperfine levels of REIs (30) or the use of controlled reversible inhomogeneous broadening. Both of these can benefit from the nanoscale platform—for instance, by adding microwave striplines or microelectrodes in proximity to the nanocavity device for control of the rare-earth spins. With advances in nanofabrication of the REI host crystals, medium- to large-scale quantum memory arrays can be envisioned, which would enable highly multiplexed repeater schemes. Furthermore, our platform also allows direct integration with single rare-earth qubits (31) and interfacing to superconducting quantum devices (32).

Supplementary Materials

www.sciencemag.org/content/357/6358/1392/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S4

Table S1

References (3335)

References and Notes

  1. See the supplementary materials.
Acknowledgments: This work was funded by a National Science Foundation (NSF) Faculty Early Career Development Program (CAREER) award (1454607), an Air Force Office of Scientific Research (AFOSR) Young Investigator Award (FA9550-15-1-0252), 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. J.G.B. acknowledges the support of the American Australian Association’s Northrop Grumman Fellowship. We thank A. Ferrier and P. Goldner for providing Nd:YSO crystals for initial quantum memory experiments. 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.
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