Persistent atomic frequency comb based on Zeeman sub-levels of an erbium-doped crystal waveguide
Mohsen Falamarzi Askarani, Thomas Lutz, Marcelli Grimau Puigibert, Neil Sinclair, Daniel Oblak, Wolfgang Tittel
PPersistent atomic frequency comb based on Zeeman sub-levels of an erbium-dopedcrystal waveguide
Mohsen Falamarzi Askarani,
1, 2
Thomas Lutz,
1, 3
Marcelli GrimauPuigibert,
1, 4
Neil Sinclair,
1, 5
Daniel Oblak, and Wolfgang Tittel
1, 2 Institute for Quantum Science and Technology, and Department of Physics & Astronomy,University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada QuTech, Delft University of Technology, 2600 GA Delft, The Netherlands ETH Zrich, Otto-Stern-Weg 1, 8093 Zrich, Switzerland University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland Division of Physics, Mathematics and Astronomy and Alliance for Quantum Technologies (AQT),California Institute of Technology, 1200 East California Boulevard, Pasadena, California 91125, USA (Dated: July 22, 2019)Long-lived sub-levels of the electronic ground-state manifold of rare-earth ions in crystals can beused as atomic population reservoirs for photon echo-based quantum memories. We measure thedynamics of the Zeeman sub-levels of erbium ions that are doped into a lithium niobate waveguide,finding population lifetimes at cryogenic temperatures as long as seconds. Then, using these levels,we prepare and characterize atomic frequency combs, which can serve as a memory for quantumlight at 1532 nm wavelength. The results allow predicting a 0.1% memory efficiency, mainly limitedby unwanted background absorption that we conjecture to be caused by the coupling between two-level systems (TLS) and erbium spins. Hence, while it should be possible to create an AFC-basedquantum memory in Er :Ti :LiNbO , improved crystal growth together with optimized AFCpreparation will be required to make it suitable for applications in quantum communication. I. INTRODUCTION
Cryogenically-cooled rare-earth-ion-doped (REI-doped) crystals have been extensively studied for theiruse in classical optical signal processing applications forseveral decades [1]. This is partially due to their conve-nient optical and spin-level structure, long populationand coherence lifetimes, large inhomogeneous broaden-ing, and their tunability with externally-applied fields[2]. More recently, this work has spawned applications inquantum signal processing, including photon echo-basedquantum memories for light [3–9].Several such protocols, including the widely-employedatomic frequency comb (AFC) protocol [10], requirefrequency-selective optical pumping (or persistent spec-tral hole burning) of REIs into a long-lived energy level,referred to as a shelving level (see Fig.1a). Typically,this level is a spin (hyperfine) level within the electronicground state manifold that features a much longer pop-ulation lifetime than that of the optically-excited level.This allows waiting for excited atoms to decay at theend of the optical pumping sequence without loosing thespectral population grating in the ground state, whichis key to quantum state storage with high fidelity andefficiency [11].Among the REIs, Er is the only one that featuresa transition from the ground level to an excited level attelecommunication wavelength of around 1.5 µ m. SinceEr is a Kramer’s ion, the ground level (more precisely,it’s lowest-lying crystal field level) is split into two elec-tronic Zeeman sub-levels under the application of a mag-netic field. If a host crystal contains nuclear spins, thesemay couple to the Zeeman sub-levels of Er , resultingin further splitting into superhyperfine levels [2]. Both Zeeman and superhyperfine levels are potentially usefulas shelving levels for the AFC memory preparation, withthe key requirement that they must feature a long pop-ulation lifetime. But since the memory bandwidth as-suming high-efficiency storage is limited by ground-statesplitting, optical pumping into electronic Zeeman levelsis preferred due to their larger splitting in a magneticfield.Partially motivated by its remarkably long optical co-herence lifetime of 4.4 ms [12], initial studies towardsa telecommunication-wavelength quantum memory havefocused on Er :Y SiO [13] and electronic Zeeman levelsfor spectral hole burning. However, their 130 ms popula-tion lifetime [14] (limited by Er spin flip-flops [15]) inconjunction with 11 ms optical population lifetime haveso far prevented reaching efficiencies in excess of 0.25%. Later, AFC-based storage of entangled photons inan Er-doped SiO fibre [16] was achieved by exploitingspin disorder, which reduces spin flip-flops between Zee-man levels compared to those in crystals. On the otherhand, the amorphous nature of SiO also leads to smalloptical coherence lifetimes, thereby restricting storagetimes to less than 100 nanoseconds. Furthermore, thedisorder-induced inhomogeneous broadening of the spin-transition has limited storage efficiencies to similar valuesas in Er :Y SiO [17, 18]. More recently, storage of her-alded single photons using AFCs in an Er- and Ti-dopedLiNbO (Er :Ti :LiNbO ) waveguide was achieved bytaking advantage of population shelving in superhyper-fine levels [19]. However, as before, the efficiency didnot exceed the percent level, this time due to remain-ing absorption in the AFC troughs caused by the com-plexity of the superhyperfine structure and excitation-induced spin relaxation [19]. In addition, the superhy- a r X i v : . [ qu a n t - ph ] J u l m s =+1/2e n m m s =-1/2m s =+1/2m s =-1/2 a c PM V(t)
PC AOMPD
Pump laser Er +3 :Ti +4 :LiNbO CryostatOscilloscope
T=0.7 K :4I13/2 g :4I15/2 t O p t i c a l d e p t h Freq. detuning (a.u.)
Background OD A F C O D b FIG. 1. a. Simplified energy level structure of the I / ↔ I / transition of Er . Exited and ground levels are indicated with | e (cid:105) and | g (cid:105) , respectively, and electronic Zeeman sub-levels with | m s = ± / (cid:105) . To create an atomic frequency comb (a periodicmodulation of the frequency-dependent optical depth into equally-spaced narrow peaks), persistent spectral holes are created(burned) by pumping all undesired population into shelving levels, e.g. | g, m s = +1 / (cid:105) . b. An example of an AFC, showingthe resulting spectral population grating. c. Experimental setup. Continuous-wave light at 1532 nm wavelength is directedthrough a phase-modulator (PM) and an acousto-optic modulator (AOM), which allow frequency and intensity modulation.After passing a polarization controller (PC), the light creates spectral holes and AFC structures in the erbium-doped lithiumniobate waveguide, and furthermore allows probing previously created structures with the help of a photo-detector (PD) andan oscilloscope. The PM is driven by a serrodyne voltage V(t) modulation similar to that depicted in the plot. perfine splitting limits the bandwidth for high-efficiencyAFCs to around 100 MHz, even assuming magnetic fieldsof several Tesla. Finally, AFC-based storage of qubits en-coded into attenuated laser pulses has been demonstratedusing Er :Y SiO . This work relied on spectral holeburning into nuclear spin levels of the Er isotope [20],and the use of a nanocavity to reduce the lifetime of theexcited level by means of the Purcell effect. However,the small storage bandwidth of 150 MHz, determined bythe inhomogeneous linewidth of Er :Y SiO , and thesmall efficiency of less than 1% supports the general con-clusion that the creation of a workable quantum mem-ory for telecommunication-wavelength photons remainsan open challenge. An interesting possibility is the useof the same crystal in a magnetic fields of several Tesla[21], but, so far, no storage experiment has been reported.Here we explore the generation of AFCs inEr :Ti :LiNbO using Zeeman sub-levels for popula-tion shelving. First, we quantify the population lifetimeof these levels using time-resolved spectral hole burningat a temperature of around 0.7 K and at magnetic fieldsof up to 1 kG. Next, we create AFCs that persist for upto a few seconds. However, the AFC structures are con-sistently marred by a significant absorption background,which restricts potential storage efficiencies. Probing theorigin of this background, we conjecture, after exclu-sion of other causes, that it is due to the coupling be-tween laser-induced excitation of two-level systems (TLS)and erbium spins, leading to decay of the ground-statepopulation grating. We conclude that improved crystalgrowth together with optimized AFC preparation will berequired to create an efficient and high-bandwidth quan-tum memory. II. EXPERIMENTAL DETAILS
Our experiments are performed using the I / ↔ I / transition of Er +3 :Ti :LiNbO , which is cooledto a temperature of around 0.7 K using an adiabaticdemagnetization refrigerator. Details of the waveguidefabrication can be found in Ref. [19]. The waveguide isexposed to magnetic fields up to 5 kG oriented parallelto the c-axis of the crystal. The field lifts the Kramer’sdegeneracy of the ground and excited electronic levelsof erbium, giving rise to Zeeman levels (see Fig. 1a fora simplified energy level scheme of Er ). To interactwith the erbium ions, we use light from a continuous-wave laser at around 1532 nm wavelength. As shown inFig. 1c, it is frequency and intensity modulated, andthen fibre butt-coupled into and out of the waveguide.For time-resolved spectral hole burning measurementswe first optically-excite erbium ions within a narrow spec-tral bandwidth, detuned by 250 MHz w.r.t the unmodu-lated laser light, using pulses of around 300 ms duration.The resulting decay redistributes the ions among the Zee-man sub-levels of the ground state, resulting in a spectralhole. After a varying time delay that exceeds the 2.1 mspopulation lifetime of the I / excited level, we mea-sure the decay of the area of the spectral hole (which isproportional to the number of shelved atoms) by linearlyvarying the frequency of the laser light during 1 ms overa 100 MHz-wide frequency window surrounding the hole.Frequency sweeps are achieved by using a phase modula-tor and serrodyning, resulting in a modulation efficiencyat 1 GHz detuning of approximately 50%.For AFC generation, we frequency and intensity mod-ulate the excitation light to burn up to 130 spectral pitsover a bandwidth of up to 6.4 GHz during 300 ms. Each t short = 0.06 ± 0.02 st long = 1.0 ± 0.1 s t short = 0.07 ± 0.02 st long = 1.36 ± 0.20 s t short = 0.06 ± 0.02 st long = 2.44 ± 0.30 s a b c Time delay (ms)Time delay (ms)Time delay (ms) H o l e a r ea H o l e a r ea H o l e a r ea B = 800 GB = 600 GB = 350 G d B(T) / t l ong ( S - ) FIG. 2. Time-resolved spectral hole decays at magnetic fields of a.
350 G, b.
600 G, and c.
800 G. d. Long-decay relaxationrate versus magnetic field. spectral pit is detuned by 50 MHz from its nearest neigh-bour to create a periodic modulation in the inhomoge-neously broadened atomic absorption spectrum. Thisfrequency spacing of the spectral pits corresponds to anAFC storage time of 20 ns [10]. The absorption profileof the comb is read after a time delay of 30 ms by per-forming a frequency sweep over bandwidths of up to 6.4GHz in 1 ms. All measurements are repeated 20 times,and hole and AFC absorption profiles are determined byaveraging.
III. RESULTS AND DISCUSSIONA. Population dynamics of ground state sub-levels
Time-resolved spectral hole burning is performed atfields of 350, 600, and 800 G. The time dependent decayof the hole area is plotted in Fig. 2, indicating the oc-cupation and the population lifetime of the ground-stateZeeman sub-levels along with those of any other shelv-ing level [17]. We find that the best fit corresponds to adouble exponential decay in which the shortest decay ex-hibits a e − population lifetime of t short ≈ .
06 s that isindependent of the magnetic field, whereas the e − pop-ulation lifetimes of the long decays are t long = 1 .
00, 1.36,and 2.44 s for magnetic fields of 350, 600, and 800 G,respectively. The relative weights of the exponentialsdo not change with field. Note that we are unable toburn the hole to transparency and we also do not resolveany side-holes or anti-holes, which arise from pumping ofatomic population between different, well defined, atomiclevels [22].The short, field independent decay is caused by popu-lation trapping in ground levels that couple only weaklyto magnetic fields. Previous hole burning measurements[19], in conjunction with the temperatures and fields usedhere, suggest that these levels are likely superhyperfinelevels arising from the coupling of Nb and Li spins ofLiNbO .The approximately linear field dependence of the pop-ulation lifetimes of the long decays ( t long ) suggests thatit is governed by spin flips [17]. An increasing mag-netic field causes more ions to become spin polarizedat low temperatures, which leads to a reduced spin flip- flop probability. Furthermore, the spin inhomogeneousbroadening increases with field and reduces the flip-floprate since it is less likely for two neighboring spins tobe resonant [17]. We fit the relaxation rate of the longdecays 1 /t long using a model that describes the temper-ature ( T ) and field ( B ) dependence of spin flip-flops andinhomogeneous broadening [17]:1 t long = α Γ s + γ s B sech ( gµ B B kT ) . (1)The magnitude of the spin inhomogeneous broadening isdescribed by a static term Γ s and a field-dependent term γ s B , g is the g-factor, µ B the Bohr magneton, and α ascaling coefficient.For a reliable fit of the limited experimental datashown in Fig. 2d, we assume g = 15 .
13, which was in-ferred from measurements of an Er :LiNbO bulk crys-tal [23, 24]. Furthermore, fixing the scaling factor of α at10 S − , as in [17], we find static and field-dependentspin inhomogeneous broadenings of Γ s =0.4 ± γ s =14.5 ± in a Ti :LiNbO waveguide [25]. Thesemeasurements imply significant magnetic disorder inTi :LiNbO , which is possibly due the inclusion of Ti ,near surface-related impurities, or the differences of con-gruent growth compared to other LiNbO crystals [25]. B. Creation of AFCs using Zeeman sub-levels
In order to assess the possibility for broadband quan-tum memory using Zeeman sub-levels as populationreservoir, we generate AFCs with bandwidths between0.2 and 6.4 GHz symmetrically around zero detuning.All AFCs are centred at 1532.05 nm (corresponding to aspectral region with an optical depth of 2 for light prop-agating perpendicular to the crystal c-axis), are createdunder the application of a 3 kG magnetic field (orientedalong the crystal c-axis), and feature peak spacings of50 MHz. Furthermore, the overall duration of the opti-cal pumping cycle is kept constant. Fig. 3 shows a 200-MHz section of a 6.4-GHz wide AFC. Note the significant -100 -50 0 50 1000.60.81.01.21.41.61.8 O p t i c a l dep t h Detuning (MHz)
FIG. 3. Absorption profile of 200 MHz-section of a 6.4 GHz-wide AFC at λ =1532.05 nm and B=3 kG. The grey shadedarea indicates remaining background absorption. Background optical depth (normalized)
A F C b a n d w i d t h ( G H z )
FIG. 4. Average background absorption as a function of AFCbandwidth. absorption background, which exponentially reduces thestorage efficiency of our AFCs compared to the case of nobackground [10]. The deep hole at zero detuning is dueto optical pumping by unmodulated light leaking throughthe phase modulator. As shown in Fig. 4, we find thatthe background absorption, which is assessed at detun-ings between -100 and +100 MHz, increases when thebandwidth of the AFC increases.
C. Determining the origin of the backgroundabsorption
1. Anti-hole broadening
One possible explanation for the bandwidth-dependentbackground absorption is that there is spectral over-lap between broad anti-holes (caused by optical pump-ing) and the AFC. Provided the frequency difference be-tween holes and anti-holes is larger than the anti-hole broadening, the spectral overlap—and hence the back-ground absorption—increases as the AFC bandwidth ap-proaches the hole-to-anti-hole splitting. This is the casein Er:LiNbO , for which the Zeeman level splitting at3 kG exceeds 50 GHz and the anti-hole broadening at thesame field is expected to be only around 5 GHz. However,the small AFC widths compared with the Zeeman split-ting makes spectral overlap between AFCs and antiholesunlikely.To fully rule out AFC background absorption due to in-homogeneous broadening of ground-state levels (whetherarising from Zeeman splitting or not), we generate, at anoptical depth of 0.8 (with light propagating parallel tothe c-axis of the crystal), pairs of 200 MHz-bandwidthAFCs with varying detuning between their centre fre-quencies, up to 1.4 GHz. If the broadened anti-holes,created by the second AFC, indeed overlap with the thefirst AFC, we expect to see an increase in backgroundoptical depth of the first AFC. This back-filling methodis similar to the one used for characterization of the in-homogeneous broadening of Zeeman sub-levels in an Er-doped fibre [17]. Table. I quantifies the background ab-sorption of the first AFC at different detunings betweenthe two AFCs. We find that measured values do not in-crease but rather scatter around a mean of around 0.66.This confirms that the anti-hole broadening does indeednot explain the observed increase of background shownin Fig. 4 – at least not for AFC bandwidths up to around1 GHz. Hence, another mechanism must be responsible,and we conjecture that it will also explain the backgroundfor large-bandwidths AFCs.We note that the inhomogeneous broadening of thesuperhyperfine levels is too small at the applied magneticfields to cause a constant absorption background [19], andtheir contribution to the observation in Fig. 4 can thusbe ignored. TABLE I.
Background absorption for 200 MHz-wideAFCs and varying frequency difference. The case ofa single AFC (zero detuning) is included for reference.
AFC backgrounddetuning (GHz) absorption0 0.66 ± ± ± ±
2. Instantaneous spectral diffusion (ISD)
An alternative reason for the increase of backgroundabsorption with AFC bandwidth stems from the relatedincrease of excited atoms during AFC preparation. (Eventhough the average laser power and pump-cycle-duration,i.e. the total energy of the pumping light, remain con-stant, the number of excited atoms grows due to thenon-linear dependence of the absorption rate with thelight power spectral density, which decreases with AFCbandwidth.) This may result in two undesired processes:instantaneous spectral diffusion (ISD) [26] (discussed be-low) and erbium spin flips [15] (discussed in the followingsections).Instantaneous spectral diffusion (ISD) can be intro-duced by optical pumping, during which Er ions arepromoted to the excited state, leading to a uncontrollableshift of the transition energies of nearby Er ions com-pared to their unperturbed values. The consequence ofaddressing the latter ions during subsequent hole burn-ing, is a smeared-out AFC with increased background.Indeed, as the cause for ISD—the presence of excitedions—will disappear at the end of the pumping sequence,transition frequencies will shift back to their unperturbedvalues, leading to a modification of the previously cre-ated absorption profile. ISD increases with the numberof excited ions [26], which is consistent with the observedincrease of the background absorption with bandwidth.To characterise broadening and AFC background,which could potentially be due to ISD, we burn two 25MHz-wide spectral holes with 200 MHz central frequencydifference. We vary the laser excitation power used tocreate one of the holes, which we refer to as the pumphole, while constant power is used to burn the other,which we refer to as the probe hole. The width of thepump hole is expected to increase due to power broad-ening [2], and ISD would manifest itself by simultane-ous broadening and shallowing of the probe hole. Weplot the widths and depths of the two holes as a func-tion of optical excitation power used for the pump holein Fig. 5a and b, and find that the width of the probehole increases by around 5 MHz. Additionally, we ob-serve decrease in the depths of the pump and probe holeswith increasing pump power (Fig. 5b). Note that dueto the optical pumping the reduction of the pump holedepth with increasing pump power is less than that ofthe probe hole, which decreases by factor of three. Theshallowing of the probe and pump holes is consistent withthe increase in the background absorption of the AFCswith their bandwidths as shown in Fig. 4. However,the level of probe hole broadening of only 5 MHz neitherexplains the large shallowing of the probe hole nor theincreased background optical depth observed in AFCswith 50 MHz tooth spacing (although it will impact thequality of AFCs with small peak spacing, i.e. AFCs thatallow for longer storage times).We also estimate the effect of ISD from measurementsof a 0.1%Er :LiNbO bulk crystal [23]. Assuming amaximum laser excitation power of ∼ concentration, and an ISD coefficient of ∼ × − Hz · cm /excited ion, we predict the maximum spectralbroadening to be on the order of kHz. This value is threeorders of magnitude smaller than the observed increaseof the width of the probe hole in Fig. 5a. Hence, our ex-perimental results and our estimate suggest that ISD isneither the cause for the observed spectral broadening ofthe probe hole, nor for the remaining background absorp- P r o b e h o l e P u m p h o l e
Hole width
P o w e r l e v e l ( a . u . )
P r o b e h o l e P u m p h o l e
Normalized hole depth
P o w e r l e v e l ( a . u . )
FIG. 5. Laser excitation-induced change of a spectral hole. a. Widths and b. depths of the pump and probe holes (seetext for details). tion of the probe hole and the AFCs. In the next sectionswe elaborate on two other power-dependent mechanismsthat may cause these observations.
3. Spin flip-flops
Another process that could be affected by the increaseof Er excitation when creating AFCs of larger band-widths is the number of spin flip-flops. In this case, spinsin one ground-state sub-level (Zeeman shelving level)that are within the AFC bandwidth resonantly exchangestate with other spins that are in the other ground-statesub-level and outside of the AFC bandwidth: onespin will be flipped up, the other flopped down. Thisleads to redistribution of the population within theAFC, and hence to background. However, as the spinflip-flop rate decreases with the sixth power of thedistance between ER-ions, we estimate its contributionto be small. In fact, if we extrapolate results from[27] to an approximate Er-doping concentration of3.6 × cm − (or 0.2%), we find a flip-flop rate ofa few Hz – by far to little to explain the AFC background.
4. TLS-driven spin-flips
Another power-dependent mechanism that may be re-sponsible for the increase of the width of the probe holeand the AFC background is light-induced two-level sys-tem (TLS) excitation, which, in turn, may drive spinflips. In this case, the laser field first excites TLSs inLiNbO [28]. The TLSs may subsequently decay intolower-energy states and emit phonons, which interactwith the electronic spins of Er , leading to spectral dif-fusion that can explain the observations in Fig. 4. Wenote that a similar effect was observed in Tm -dopedTi :LiNbO [25].In support of this hypothesis, we note that congru-ent LiNbO is known to contain various impurities andimperfections, and previous measurements of REI-dopedLiNbO suggest significant lattice disorder. Such dis-order could be the origin of the above-described TLSs[24, 25, 29, 30]. We also point out that laser-induced ex-citation and decay of TLS impurities determines photo-refraction in LiNbO . It is well-known that this effectis enhanced in waveguides compared to bulk crystalsdue to high confinement of the laser field and, conse-quently, larger light intensities. This is consistent withthe fact that the emergence of an absorption backgroundin AFCs due to spectral hole filling is not observed inbulk LiNbO . D. Discussion and conclusion
We experimentally study ground-state Zeeman sub-levels of Er ions doped into a Ti :LiNbO crys- talline waveguide as shelving levels for AFC-type quan-tum memory for light. Despite promising lifetimes in ex-cess of a second, several changes are required to increasethe storage efficiency for telecommunication-wavelengthphotons beyond the current state-of-the-art of around1%. Most importantly, the memory efficiency, whichis limited by the available optical depth (at most 2 inour waveguide) and the absorption background need tobe improved. The former can be addressed using animpedance-matched cavity [31], and the absorption back-ground may be reduced through optimization of the op-tical pumping procedure. This includes the use of opti-mized optical excitation power, laser scan rate, and mag-netic field strength and direction, which may result inlonger-lived Zeeman levels and a favourable branchingratio into the shelving level. But ultimately, it seemsnecessary to improve the LiNbO crystal itself, e.g. byvarying growth conditions, to reduce the number of two-level systems. IV. ACKNOWLEDGMENTS
The authors thank Wolfgang Sohler, Mathew George,and Raimund Ricken for providing the waveguide, andJacob H. Davidson for help with aligning the waveguideand Gustavo Amaral and Erhan Saglamyurek for use-ful discussions. The authors also acknowledge supportfrom Alberta Innovates (AI), the Alberta Major Inno-vation Fund, the Natural Sciences and Engineering andResearch Council of Canada (NSERC), and the DutchOrganisation for Scientific Research (NWO). N.S. ac-knowledges funding from the AQT’s Intelligent QuantumNetworks and Technologies (INQNET) research program,and W.T. support as a Senior Fellow of the Canadian In-stitute for Advanced Research (CIFAR). [1] W. Tittel, M. Afzelius, T. Chanelire, R. Cone, S. Kr¨oll,S. Moiseev, M. Sellars,
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