Gigahertz-Bandwidth Optical Memory in Pr^{3+}:Y_2SiO_5
M. Nicolle, J. N. Becker, C. Weinzetl, I. A. Walmsley, P. M. Ledingham
GGigahertz-Bandwidth Optical Memory inPr + :Y SiO M. N
ICOLLE
1, 2
J. N. B
ECKER
1, 3 , C. W
EINZETL , I. A.W ALMSLEY
1, 3 , P. M. L
EDINGHAM
1, 4 Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory & Department of Electrical andElectronic Engineering, University of Bristol, BS8 1FD, United Kingdom QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UnitedKingdom * Corresponding author: [email protected]
Abstract:
We experimentally study a broadband implementation of the atomic frequencycomb (AFC) rephasing protocol with a cryogenically cooled Pr + :Y SiO crystal. To allow forstorage of broadband pulses, we explore a novel regime where the input photonic bandwidthclosely matches the inhomogeneous broadening of the material (∼ ) , thereby significantlyexceeding the hyperfine ground and excited state splitting (∼
10 MHz ) . Through an investigationof different AFC preparation parameters, we measure a maximum efficiency of 10% after arephasing time of 12 . © 2021 Optical Society of America Quantum memories are crucial components of secure quantum communication networks [1].Their key function is to store and recall arbitrary quantum states of light on demand in an efficientand faithful fashion. This capability allows one to perform multiplexing, thereby enabling thesynchronisation of non-deterministic events, such as the generation, distribution, and distillationof entanglement throughout the quantum network [2–5]. For effective multiplexing, a storagetime 𝜏 much greater than the inverse clock-rate of the system is required, therefore a largetime-bandwidth product 𝛿𝜏 , where 𝛿 is the acceptance bandwidth of the quantum memory, isessential. For future quantum photonic networks, a high clock-rate is desirable, therefore placinga strict requirement on the acceptance bandwidth of the quantum memory.Many quantum memory protocols have been proposed (e.g. electromagnetically inducedtransparency, gradient echo memory, controlled reversible inhomogeneous broadening, off-resonant Raman) and demonstrated with various material platforms (e.g. trapped atoms, warmatomic vapours, rare-earth ion doped crystals) over the last decades, see [6, 7] for recent reviews.One of the promising protocol-platform combinations is the atomic frequency comb (AFC)quantum memory and cryogenically-cooled praseodymium doped yttrium oxyorthosilicate -Pr + :Y SiO . Like all rare earth ions, Pr + is characterised by a partially filled 4f shell spatiallylocated within the full 5s and 5p shells, resulting in relatively strong optical transitions with narrowhomogeneous linewidths (∼ kHz ) even when embedded in a solid [8]. The most commonlyutilised transition, the 𝐻 → 𝐷 zero-phonon line with wavelength of 605 . 𝛼 ∼
20 cm − for doping levels ∼ . 𝜇 s, a coherence time of 111 𝜇 s, and a crystal-field induced inhomogeneous broadening on theorder of ∼
10 GHz [8, 9]. The ground state coherence (population) lifetime is on the order of0 . + :Y SiO an ideal quantum memory platform, leading to manyimpressive experimental demonstrations. Heralded single photons [11], frequency-multiplexedsingle photons [12], and orbital-angular-momentum-encoded single photons [13] have been stored a r X i v : . [ qu a n t - ph ] F e b sing the AFC protocol. The spin-wave AFC protocol has been used to store and recall heraldedsingle photons on demand [14]. The controlled reversible inhomogenous broadening protocol hasbeen used to store weak coherent states with 69% efficiency [15]. Using external magnetic fieldsto operate at zero first-order Zeeman shift points [16] and dynamical decoupling techniques [17],strong coherent states have been stored and recalled 42s later employing electromagneticallyinduced transparency [18].Most approaches in Pr + :Y SiO focus on long storage times and map light to a hyperfineground state coherence, necessarily restricting the input pulse bandwidth to be narrow enough( ∼ MHz) to address individual transitions. So far, what is missing is a broadband implementationof a quantum memory with Pr + :Y SiO . Broadband AFC demonstrations so far includeTh [19], Er [20], with great potential for such a demonstration in Yb [21]. The potentially longstorage times of Pr + :Y SiO combined with the broad acceptance bandwidth give potentialfor unprecedented time-bandwidth-products. To maximise the bandwidth, we here adopt adifferent approach compared to previous studies, utilising a significant portion of inhomogeneousbroadened line to demonstrate for the first time a few-GHz bandwidth AFC optical memory in aPr + :Y SiO crystal. The AFC scheme involves the coherent mapping of a light pulse into anensemble of two-level atoms, where the atoms have been arranged into a series of absorbing peakswith a frequency separation of Δ and width 𝛾 . A collective coherence is established betweenthe ground state | 𝑔 (cid:105) and excited state | 𝑒 (cid:105) of the form √ 𝑁 (cid:205) 𝑁𝑗 = 𝑒 𝑖 𝛿 𝑗 𝑡 𝑒 − 𝑖 (cid:174) 𝑘 𝑝 ·(cid:174) 𝑧 𝑗 | 𝑔 , . . . , 𝑒 𝑗 , . . . , 𝑔 𝑁 (cid:105) where 𝑁 is the total number of atoms, (cid:174) 𝑘 𝑝 is the input photon wave vector, (cid:174) 𝑧 𝑗 is the 𝑗 th atomposition and 𝛿 𝑗 is the detuning of the 𝑗 th atom with respect to resonance. This collective staterapidly dephases as each term in the sum accumulates a phase 𝑒 𝑖 𝛿 𝑗 𝑡 . In the case where 𝛾 (cid:28) Δ ,the detuning can be approximated as 𝛿 𝑗 ≈ 𝑚 𝑗 Δ , where 𝑚 𝑗 are integers with the total numberof 𝑚 𝑗 being the number of absorbing peaks. This results in a rephasing of the collective stateat a time 𝜏 = 𝜋 / Δ with a corresponding coherent photon-echo re-emission of the light [22].The favourable spectral-hole-burning properties of rare earth-ion-doped media, in particularPr + :Y SiO , allows for the easy creation of atomic frequency comb structures.In our approach, we use an optical frequency comb created by a train of 70 ps-long opticalpulses from a synchronously pumped dye laser to simultaneously holeburn an AFC across alarge proportion of the inhomogeneously broadened ensemble. Spectral holes are created witha spacing of 2 𝜋 ×
80 MHz, matching the repetition rate of the laser, resulting in 𝜏 = . ± / state due to the hyperfine transition strengths (cf. Fig. 1b),creating antiholes in between the holes and giving the comb tooth a well-defined substructure(see below). In contrast, a typical AFC preparation would utilise atoms within a narrow spectralrange and starts with creating a spectral pit by sweeping a narrow-band laser across the hyperfinetransitions and emptying out the ± / and ± / ground states. Population in the form of combteeth is then transferred back into the pit by performing a modulated scan across the previouslycreated antihole region [23, 24].To generate the AFC we first apply a strong pulse train to the ensemble known as the ‘burn’.A small fraction of the light, referred to as the ‘probe’, can then be sent to either a scanningFabry-Perot interferometer (FSR=1.5 GHz, F=1500) to create a frequency-tunable, quasi-CWprobe beam to image the comb structure or sent to a Pockels cell to pick a single signal pulsethat can be read into the previously created AFC, the echoes of which can be monitored. Adouble-pass acousto-optic modulator (AOM) is used to rapidly frequency modulate the beamby ±
40 MHz during the probe period to avoid any comb structure in the probe. At the endof each experimental sequence, another strong pulse train is applied to the ensemble with theAOM modulation switched on to reset the population distribution. Switching between theindividual beam paths is accomplished using motorized shutters. The sample is kept at 2.5K requency A b s o r p ti on Frequency A b s o r p ti on Burn with narrowband laser
Scan Modulated Scan ~ Frequency I n t e n s it y Frequency A b s o r p ti on Burn with pulsed laser
Time I n t e n s it y Fourier Transform ∆ −1 ∆ δν −1 δν ~ 4 GHz ± / ± / ± / ± / ± / ± / StrongBurnWeakProbeAOMModulationDetectionStrongBeamWeakBeamAOMModulationDetection
Echo MeasurementsComb Measurements (a)(c) (d) (b)
Fig. 1. a) Broadband-AFC preparation scheme using an optical frequency comb. b) Typi-cal AFC preparation using narrowband laser. c) Level scheme of the 𝐻 ( ) → 𝐷 ( ) transition in Pr + :Y SiO . d) Experimental sequences used for AFC imaging as wellas echo measurements. inside a closed-cycle helium cryostat. Light transmitted through the sample is detected using a Siavalanche photodiode (APD). An additional shutter in front of the APD protects it during thepreparation reset protocols. The experimental sequences used to image the combs as well as torecord photon echoes are shown in Fig. 1c. A detailed experimental set-up is in the supplementarymaterial.We investigate comb characteristics as a function of burn time and power, as well as the effectof detuning from the center of the inhomogeneous line (i.e. effective OD of the ensemble).Across all measurements, we observe minimum hole widths of about 25 MHz, limited by thefrequency jitter of the laser, which was not actively stabilized for these experiments. Two distincteffects which lead to broadening of the comb have been observed: 1) Fluctuations in centerfrequency lead to a shift of the entire optical comb. 2) A change in laser repetition rate causes abreathing motion of the optical comb where teeth in the center of the comb shift less than teethfurther away. Both effects can, in principle, be overcome by using a more optimized, activelystabilized laser system.As shown in Fig. 2a, after an initial increase with burn time, the comb contrast plateaus ataround 30% after 2s ( 𝑃 𝐵 = . 𝑚𝑊 ). For longer burn times frequency instabilities of the laserbecome dominant, broadening the comb but not further increasing its contrast. Similarly, we findan optimum in burn power around 1 mW. For lower powers, the pumping takes too long and theaser frequency and repetition rate instabilities become more noticeable, broadening the combteeth. Higher powers lead to power broadening of the comb. Rel. Frequency (MHz)200-600 -400 -200 0 400 600 0.0 O p ti ca l D e p t h ( e ) P o w e r ( m W ) (a) (b) (c) O p ti ca l D e p t h ( e ) D e t un i ng ( GH z ) B u r n T i m e ( s ) O p ti ca l D e p t h ( e ) Fig. 2. Broadband atomic frequency comb structures depending on a) Burn time 𝑇 𝐵 i.e. length of the applied preparation pulse train ( 𝑃 𝐵 =1.1mW). b) Burn power of thepreparation pulse train 𝑃 𝐵 ( 𝑇 𝐵 =2s). c) Detuning from inhomogeneous line center( 𝑇 𝐵 =2s, 𝑃 𝐵 =1mW). We investigate the comb shape as a function of detuning from the center of the inhomogeneousline. We find that, up to a detuning of about 15 GHz the contrast first increases, while thepeak OD decreases following the ensemble density dictated by the inhomogeneous line shape.This is attributed to the increased effective optical pumping efficiency due to the reduced OD.At larger detunings however, it is not possible to burn even deeper holes while the peak ODfurther decreases, reducing the overall contrast again. This indicates that a steady state of opticalpumping rate and effective atomic relaxation rates is reached. We attribute this to the widthof the spectral holes which are wider than the difference of ground and excited state hyperfinesplittings ( ∼
17 MHz). This inevitably leads to repumping between the ground hyperfine states,thus limiting the comb contrast. As validated by simulations shown in Fig. 4a, addressing ofmultiple hyperfine states simultaneously also results in the asymmetric shape of the comb teeth.Simulation details can be found in the supplemental material. Both the contrast and the combshape can be further improved by using an actively stabilized laser system, which would allow toburn holes with width narrower than 17 MHz and allowing the holes to be burnt down to OD = 𝜂 ( ) 𝐴𝐹𝐶 ≈
10% whilethe maximum total efficiency is 𝜂 ( tot ) 𝐴𝐹𝐶 ≈ ff i c i e n c y ( % ) E ff i c i e n c y ( % ) E ff i c i e n c y ( % ) (a)(b) Fig. 3. Photon echoes recorded with broadband AFCs. a) Time traces for 0 and 8.8 GHzdetuning from the inhomogeneous line center (burn time=2s, burn power=1mW). b)Efficiencies of the first, second and third echoes as well as total efficiency (sum of allvisible echoes) for different detunings
In conclusion, we have demonstrated for the first time the preparation of broadband AFCsin Pr + :Y SiO using a novel technique employing optical frequency comb generated by abroadband modelocked laser. We evaluated their performance to absorb and rephase classicalbroadband pulses with a bandwidth of ∼ 𝜂 ( ) 𝐴𝐹𝐶 ≈ + with the -60 60-120 120 Rel. Frequency (MHz) O p ti ca l D e p t h ( e ) Exp. Data SimulationExp. DataSimulation25 50 75 100 125 150
Time (ns) I n t e n s it y ( a . u . ) (a)(b) Fig. 4. Simulations. a) Comparison of simulated and measured comb shapes. b)Comparison of simulated and measured photon echoes. Comb preparation for a) andb): 0 GHz detuning, 𝑇 𝐵 = 𝑠 , 𝑃 𝐵 = . 𝑚𝑊 . Details about simulations can be found inthe supplemental material. 𝐻 , 𝐹 and 𝐷 states [33]. The scheme would work as follows: after first preparing the AFC inthe ground state 𝐻 , one could map a single photon detuned from the 𝐻 → 𝐹 transition intoa coherence between the ground ( 𝐻 ) and excited ( 𝐷 ) state by a two-photon ladder processmediated with an off-resonant control pulse driving the 𝐹 → 𝐷 transition. The applicationof a second control pulse at precisely the AFC rephasing time will read out the memory. If thecontrol pulse is not applied or is mistimed, the memory will not be phase-matched for read-out.In fact, the coherence can now be read out at any time multiple of the rephasing time therebytransforming the AFC protocol to an on-demand quantum memory protocol modulo 𝜏 [34]. Afurther advantage with this approach is that the 𝐻 → 𝐹 transition is around 1550 nm whichwould enable Pr + :Y SiO to directly interface to telecommunication C-band quantum networks. Funding.
UK Engineering and Physical Sciences Research Council (EPSRC) Standard Grant No.EP/J000051/1, Programme Grant No. EP/K034480/1, the EPSRC Hub for Networked Quantum InformationTechnologies (NQIT), ERC Advanced Grant (MOQUACINO).
Acknowledgments.
We thank Margherita Mazzera for useful discussions and reading of the manuscript,and Hugues de Riedmatten for supplying the Pr + :Y SiO crystal. Disclosures.
The authors declare no conflicts of interest.
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1. Experimental Setup
For atomic frequency comb (AFC) preparation we use an optical frequency comb created bya train of 70ps-long optical pulses at 606 nm from a synchronously pumped dye laser (SirahGropius) using Rhodamine 6G in ethylene glycol. The laser is pumped by a frequency-doubledYb-doped fiber laser (NKT aeroPulse PS with APE Emerald Engine) with a fundamental pulsewidth of 5 ps and repetition rate of 80 MHz. This pulse train is sent through a 80 MHz double-passAOM setup with variable-frequency driver to optionally modulate the laser frequency by ± + :Y SiO crystal (0.05%Pr + , length=3 mm) kept at 2.5 K in a closed-cycle helium cryostat (Oxford Instruments OptistatDry) using custom-made copper heat shields. Light transmitted through the sample is detected byan AC-coupled 1 GHZ Si avalanche photodiode (Menlo Systems APD210). Switching betweenthe individual beam paths is accomplished using mechanical shutters controlled by a digital delaygenerator (Stanford Research Systems DG645) via an Arduino interface and sychronized to thetrigger signal generated by the pulsed laser. Fig. 5. Experimental setup used to conduct the experiments described in the main text. . Simulations
We model the hole burning process in order to calculate the simulated comb profile shown inFigure 4a of the main text. As the inhomogeneous linewidth is orders of magnitude wider thanthe linewidth of each individual ion, a monochromatic probe can address up to nine differenttransitions in different ions shifted in frequency with respect to each other. Optically pumpingthe ensemble with a single frequency then modifies the optical transmission at a multitude ofother frequencies by redistributing the relative hyperfine ground state populations. We calculatethis resulting absorption profile in our simulations using the relative oscillator strengths for theoptical transitions between the H and D hyperfine manifolds ( [9].The burning laser is modelled as a collection of narrowband probes separated by 80 MHzwhich jitters by a maximum of 40 MHz around a central frequency, inspired from measurementsof the laser spectrum. Each of the burning frequencies is taken into account in order to computethe redistribution of population along the inhomogeneous line and the resulting atomic frequencycomb profile. Within this framework, relaxation of the hyperfine states is neglected. In the AFC protocol, the temporal profile of the rephasing echoes is determined by the Fouriertransform of the atomic spectral distribution. For example, if the AFC profile is composed ofa set of evenly spaced delta-functions in frequency, the output will be a pulse train in the timedomain. What is observed in Figure 4b of the main text is not a simple pulse train, but onewhere the amplitude of each pulse is forms an interesting profile. The profile is down to thefinite peak width of the comb teeth leading to an exponential decay of the coherence, as wellas the interference between the multiple combs corresponding to different hyperfine levels ofPr + :Y SiO . In our simulation we assume that by the end of the comb preparation process,almost all of the ions are pumped into the ± //