Optical coherence and energy-level properties of a Tm^{3+}-doped LiNbO_{3} waveguide at sub-Kelvin temperatures
Neil Sinclair, Daniel Oblak, Erhan Saglamyurek, Rufus L. Cone, Charles W. Thiel, Wolfgang Tittel
OOptical coherence and energy-level properties of a Tm -doped LiNbO waveguide atsub-Kelvin temperatures Neil Sinclair,
1, 2, 3, ∗ Daniel Oblak, Erhan Saglamyurek,
1, 4
Rufus L. Cone, Charles W. Thiel, and Wolfgang Tittel
1, 6 Institute for Quantum Science and Technology, and Department of Physics & Astronomy,University of Calgary, Calgary, Alberta T2N 1N4, Canada John A. Paulson School of Engineering and Applied Sciences,Harvard University, Cambridge, Massachusetts 02138, USA Division of Physics, Mathematics and Astronomy, and Alliance for Quantum Technologies (AQT),California Institute of Technology, Pasadena, California 91125, USA Department of Physics, University of Alberta, Edmonton, Alberta, T6G 2E1, Canada Department of Physics, Montana State University, Bozeman, Montana 59717, USA QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands
We characterize the optical coherence and energy-level properties of the 795 nm H to H tran-sition of Tm in a Ti :LiNbO waveguide at temperatures as low as 0.65 K. Coherence propertiesare measured with varied temperature, magnetic field, optical excitation power and wavelength,and measurement time-scale. We also investigate nuclear spin-induced hyperfine structure and pop-ulation dynamics with varying magnetic field and laser excitation power. Except for accountabledifferences due to difference Ti and Tm -doping concentrations, we find that the propertiesof Tm :Ti :LiNbO produced by indiffusion doping are consistent with those of a bulk-dopedTm :LiNbO crystal measured under similar conditions. Our results, which complement previ-ous work in a narrower parameter space, support using rare-earth-ions for integrated optical andquantum signal processing. I. INTRODUCTION
Rare-earth-ion-doped crystals (REICs) cooled to cryo-genic temperatures offer several exceptional propertiesfor optical and radio-frequency processing tasks thatrange from amplifier development to quantum signal ma-nipulation [1, 2]. These properties include desirableenergy-level structures and population dynamics, long-lived optical and spin coherence, as well as their abilityto be integrated on a chip [3, 4]. Of the many crys-tals that can host REIs, LiNbO is attractive due to itstransparency at optical wavelengths, high second-ordernonlinearity, and ability to be modified to allow opticalguiding, among other properties [5]. These attributes un-derpin the use of LiNbO for several optical applications,including modulators that are used by the telecommuni-cation industry [6].An early study of an ensemble of Tm ions in a Ti-indiffused LiNbO waveguide (Tm :Ti :LiNbO ) at 3K demonstrated properties that were inferior to thosemeasured in a Tm -doped LiNbO bulk crystal undersimilar conditions [7]. This difference was attributed tothe perturbation of Tm ions by Ti , which is usedto raise the index of refraction of LiNbO for waveguid-ing. However, a study of Tm :Ti :LiNbO at 0.8 K re-vealed a tenfold improvement of properties compared tothose measured at 3 K, matching those of a Tm -dopedbulk LiNbO crystal under similar conditions [8]. Herewe complement this study by measuring detailed coher-ence properties, population dynamics and sub-level struc- ∗ Corresponding author email: [email protected] ture of the H to H transition of a Tm :Ti :LiNbO waveguide at temperatures as low as 0.65 K.More precisely, using two- and three-pulse photon echotechniques, we measure coherence properties with var-ied laser excitation power and wavelength, temperature,magnetic field, and measurement time-scale [1, 2, 9]. Wethen characterize excited-level population dynamics andlifetimes using spectral hole burning. We also quantifynuclear spin-induced hyperfine energy level structure un-der the application of a magnetic field and with varyinglaser wavelength. The hyperfine structure is probed fur-ther by coherent excitation and emission of light. Finally,we quantify the dependence of spectral hole widths andlifetimes on laser excitation power, both of which impactthe suitability of Tm :Ti :LiNbO for the aforemen-tioned applications.Overall, we find equivalent properties to those mea-sured using a 0.1%-doped Tm :LiNbO bulk crystal attemperatures of less than 1 K except for accountable dif-ferences due to different Ti - and Tm -doping concen-trations. Our results are relevant for integrated quan-tum and classical light processing, and clarify how prop-erties of REIs are affected by crystal modification andmeasurement conditions in the technologically-significantLiNbO material system. II. EXPERIMENTAL METHODS
Measurements are carried out using a 15.7 mm-longTm :Ti :LiNbO waveguide. It is created by raisingthe index of refraction of a ∼ µ m-wide strip by thermallyindiffusing Ti into a 0.9 mm-thick, up to 0.7% Tm -indiffused, lithium niobate crystal wafer. More details a r X i v : . [ phy s i c s . a t o m - ph ] J a n regarding the composition and fabrication of the waveg-uide can be found in Ref. [8]. The crystal is mountedinside an adiabatic demagnetization refrigerator on anoxidized Cu stage and held down by a Macor lid that isattached to the Cu stage by spring-tensioned Ti screws.The Cu stage is mounted on an Au-coated Cu plate thatis attached to a magnetically-shielded GGG paramag-netic salt pill that generates temperatures as low as 0.65K by adiabatic demagnetization. The temperature ismeasured on the Macor lid using RuOx thermoelectricsensors. Light is directed into, and out of, the waveg-uide by butt-coupling single-mode fiber at around 800nm wavelength to the waveguide end facets. Each fiberis mounted on a three-axis nanopositioning stage to op-timize the efficiency of the butt-coupling. Transmissionthrough the entire cryogenic setup is 10-20% due to im-perfect overlap between the spatial modes of the fiberand the waveguide, reflections from uncoated surfaces,and imperfect fiber splices. Magnetic fields of up to 20kG are applied parallel to the c-axis of the crystal usinga superconducting solenoid. The magnetic field strengthis determined using a Hall sensor mounted directly abovethe Macor lid.We employ a continuous-wave external-cavity diodelaser with an output power of up to 50 mW, an es-timated linewidth of a few hundred kHz over millisec-ond timescales, and producing linearly-polarized lightoriented approximately normal to the c-axis of the crys-tal (sigma polarization). The laser operating wavelengthis tuned between 791 and 798 nm (vac.) by a diffractiongrating that forms part of the laser cavity and moni-tored using a HeNe-referenced wavemeter featuring anaccuracy better than 1 GHz. A 400 MHz acousto-opticmodulator is used to produce pulses as short as 50 ns forphoton echo measurements, or as long as 100 ms for holeburning and spectral tailoring of the absorption profile ofthe transition. Spectral features are probed by varyingthe laser detuning through serrodyne modulation usinga standard 20 GHz-bandwidth LiNbO phase modula-tor for frequency sweeps of >
20 MHz. A field-effect-transistor wired in parallel with the laser diode is used forfrequency sweeps of <
20 MHz. The laser power is var-ied from ∼ ≤ III. RESULTSA. Optical coherence properties
Frequency-selective modification of the lineshape of aninhomogeneously-broadened transition of an ensemble ofREIs is necessary for many optical processing applica-tions [3, 4]. The maximum spectral resolution of themodification is ultimately determined by the homoge-neous linewidth Γ h of the transition, which is inversely-proportional to the coherence lifetime T = 1 /π Γ h [10].Accordingly, decoherence can be interpreted as a broad-ening of the homogeneous linewidth [2]. This broadeningis due to a time-varying detuning of the transition fre-quency of each REI due to dynamic perturbations causedby the lattice or neighboring ions [1]. These perturba-tions depend on the REIC and the experimental condi-tions used in the measurement. Thus, to better under-stand the nature of coherence in Tm :Ti :LiNbO , wequantify Γ h as a function of laser excitation power andwavelength, temperature, magnetic field, and measure-ment time scale (i.e. we perform time-dependent spectraldiffusion).
1. Wavelength dependence
The large inhomogeneous linewidth Γ inh of REIs incrystals is one of their unique features, which allowsbroadband or spectrally-multiplexed light-matter inter-actions [2, 4]. Therefore, we quantify the inhomogeneouslineshape and probe optical coherence at various wave-lengths to determine the bandwidth for which coherenceproperties are invariant. This lineshape may be deter-mined using the Beer-Lambert relation I out = I off e − d in units of optical absorbance d . At 0.9 K, we generate aweak laser pulse, direct it into the waveguide, and detectits intensity I out ( λ ) at the output as a function wave-length λ of the laser light. The laser is then tuned to anoperating wavelength of 800 nm, off-resonant from theTm transition, and the intensity I off of the weak pulseis recorded to yield the absorption lineshape (Fig. 1, cir-cles). Note that the absorbance between 793 and 795 nmis too high to resolve the profile. This is expected dueto the large oscillator strength of Tm :Ti :LiNbO ,waveguide length, and doping concentration [7, 11–13].To compliment the measured data, Fig. 1 also shows aabsorbance profile (dotted line) measured using a 0.1%-doped Tm :LiNbO bulk crystal under similar condi-tions [12] that has been vertically scaled by a factor oftwo. This absorbance profile predicts a high d >
10 be-tween 793 and 795 nm for the waveguide while the scal-ing factor suggests an effective doping concentration of0.2%, which is consistent with the results of Ref. [7].Future measurements using a shorter sample or a lowerTm concentration will allow better characterization ofthe optical lineshape of Tm :Ti :LiNbO . Nonethe-less, our measurements unambiguously reveal d < W a v e l e n g t h ( n m )
Absorbance
Two-pulse photon echo intensity (a.u.)
FIG. 1: Measured optical absorbance spectra from theTm :Ti :LiNbO waveguide is shown using circles. Thedotted line indicates the absorption lineshape of a 0.1%-dopedTm :LiNbO bulk crystal that has been vertically scaled bya factor of two. Two-pulse photon echo intensity (log scale)measured from the waveguide is shown using squares withlines added to guide the eye. wavelengths between 795 and 797 nm, which is within thezero-phonon line [1, 2] and hence suitable for efficient andbroadband signal processing.We now characterize wavelength-dependent decoher-ence at 0.9 K using two-pulse photon echos. Specifically,two pulses, each separated by a time duration of t , aredirected into the waveguide and, due to the coherent re-sponse of the ions, a photon echo is produced a time t later [10]. The intensity of the echo I e is described by[12, 14] I e ≈ [ e − d sinh( d/ e − t /T . (1)Re-absorption inhibits observation of an echo in the pres-ence of high optical absorbance ( d >> ∼
300 MHz-wide spectral pit of reduced optical absorbance by opti-cally pumping Tm ions to long-lived nuclear-hyperfinelevels (see Sec. III B 2) [2, 15]. To avoid stimulated de-cay of population in the H excited level, we wait 5 ms,which is an order of magnitude longer than the ∼ µ slifetime of this level (see Sec. III B 1), and perform twopulse photon echo excitation for a fixed t and variedwavelength to determine I e ( λ ) (Fig. 1, squares).Our optical pumping sequence is performed with max-imum laser power for all measurements, resulting in avarying residual absorbance as a function of wavelengthat the bottom of the spectral pit. Yet this absorbanceis still high ( d >>
1) for wavelengths around 794 nmwhere we expect maximum absorbance. Accordingly, I e is reduced for wavelengths around 794 nm likely due tore-absorption rather than reduced T [12], an effect thatis not taken into account in Eq. 1. Consequently, we are unable to accurately determine T ( λ ) using Eq. 1.Note that T was found to be invariant over ∼
300 GHzof bandwidth around 794.5 nm using bulk Tm :LiNbO at 1.6 K [12]. Nonetheless, we observe photon echoes over >
100 GHz of bandwidth, suggesting coherence over thisrange.As a last step, we vary the laser power and detuningto generate a spectral population grating [2, 8] instead ofa spectral pit. After a time delay of 5 ms, we generatea laser pulse that scatters from the grating to producean echo 200 ns later. This protocol is similar to three-pulse photon echo excitation (see Sec. III A 5) [2]. Werepeat this procedure at various wavelengths, finding thatthe intensity of the echo varies with wavelength similarto that of the two-pulse photon echos shown in Fig. 1.This suggests that the coherence properties along withthe underlying level structure and dynamics are suitablefor wide-band optical processing.
2. Temperature dependence
Phonon interactions are a fundamental cause of deco-herence of REIs [1]. Therefore, temperature-dependentmeasurements are critical for determining the limitationsof coherence properties of REICs. Here we tune the laseroperating wavelength to 795.0 nm and measure Γ h as afunction of temperature by measuring the decay of two-pulse photon echo intensities as the time delay t be-tween the two excitation pulses is varied. This wave-length is used to ensure strong light-matter interactionwithout the reduction of signal intensity due to reab-sorption. This and similar wavelengths are also used forseveral other measurements in this work (e.g. photonecho excitation and hole burning) for the same reasons.The echo intensity I is measured and fit using the Mimsexpression I ( t ) = I e −
2( 2 t T ) x , (2)where I is the echo intensity at t = 0, and x is an em-pirical parameter determined by spectral diffusion (alsodiscussed in Secs. III A 3 and III A 5) [10]. At 4 K thedecay is exponential (i.e. x = 1), indicating that it isdominated by phonon scattering [1, 12], with Γ h ≈ ∼
100 kHz, which is similar tothat measured using bulk Tm :LiNbO at 1.7 K and a T = 4 9 ± 5 m sT = 5 1 ± 9 m sT = 1 0 ± 1 m s z e r o f i e l d 2 T f i e l d Two-pulse photon echo intensity (a.u.) t ( m s ) FIG. 2: Example two-pulse photon echo decays using zero(circles) and 20 kG (squares) magnetic field on a log scale.All data is taken at 0.89 K with excitation pulse powers of ∼ wavelength of 794.26 nm [11, 12]. The decay for t < µ s is used for the temperature-dependent characteriza-tion and, from fits to Eq. 2, the temperature-dependenthomogeneous linewidth is determined (Fig. 3). G h- 33.6 (kHz) Homogeneous linewidth (kHz)
T e m p e r a t u r e ( K )
FIG. 3: Temperature dependence of homogeneous linewidthmeasured using two-pulse photon echoes. A fit of the datausing Eq. 3 is shown by the red line. Inset: data and fitshown in the main figure (log scale) against 1 /T to highlightthe exponential dependence of Γ h − Γ . We expect Γ h to be limited by direct phonon excitation to a higher-lying crystal field level in the ground statemanifold [1, 12]:Γ h = Γ + Γ ph e ∆ E/k B T − , (3)where Γ is the homogeneous linewidth at zero temper-ature, Γ ph is the phonon coupling coefficient, ∆ E is thephonon energy, T is temperature, and k B is the Boltz-mann constant. A fit of Eq. 3 to the data in Fig. 3,yields an intrinsic linewidth of 33 . ± . :LiNbO crystal at a wavelength of 794.26 nm [12].We also find ∆ E = 7 . ± . − and Γ ph = 3 . ± . − of bulk Tm :LiNbO whilethe latter is three times higher than the 1.1 MHz ob-served using the bulk crystal at 795.01 nm [12]. Thissupports our previous observation of non-ideal coher-ence properties of Tm :Ti :LiNbO compared to bulkTm :LiNbO at 3 K [7]. The large phonon couplingmay be due to the higher, up to 0.7%, doping concen-tration of Tm :Ti :LiNbO compared to 0.1%-dopedbulk Tm :LiNbO [16]. Since ∆ E (cid:29) kT for all of ourmeasurements, Γ h − Γ exhibits an exponential depen-dence with respect to 1 /T (Fig. 3 inset, the fit using Eq.3 is also shown).
3. Magnetic field dependence
Decoherence beyond that induced by direct phonon-ion interactions is due to spectral diffusion. This may becaused by fluctuating fields within the host crystal thatare generated by dynamic interactions between host spinsor impurities [1]. Spectral diffusion results in a broad-ening of the measured homogeneous linewidth becauseeach ion experiences a slightly-different dynamic environ-ment. A magnetic field is expected to reduce the impactof spectral diffusion by increasing the energy-splitting be-tween magnetic levels beyond the phonon energy, induc-ing spin polarization and reducing the number of spinflips [1]. Furthermore, the applied field reduces decoher-ence through the ’frozen core’ effect in which the largemagnetic moment of REIs create a localized magneticfield gradient that inhibits spin flips of nearby nuclearspins, creating a spin diffusion barrier [17]. Spectral dif-fusion is expected due to coupling between Tm and Nb, Li, other Tm , and possibly Ti nuclear spinsin Tm :Ti :LiNbO [11–13].We apply a magnetic field of 20 kG and measure atwo-pulse photon echo decay at a temperature of 0.89 Kand wavelength of 795.0 nm. We find an exponential de-cay that is free of time-dependent spectral diffusion (Fig.2, squares), consistent with Tm :LiNbO bulk crystalmeasurements at a wavelength of 794.26 nm [11, 12].Moreover, fitting this decay using Eq. 2 reveals a co-herence lifetime of 49 ± µ s, which is consistent withthe 51 ± µ s observed in the motional narrowing regimeof the zero field data. We attribute the reduction of co-herence lifetimes compared to the 117 µ s reported in Ref.[8] to non-zero excitation-induced decoherence during ourmeasurement (see Sec. III A 4 for an analysis of this ef-fect).To further investigate magnetic field-dependent deco-herence, we measure two-pulse photon echo decays forvarying magnetic fields at a temperature of 0.86 K andfit the decays using Eq. 2 to determine Γ h (Fig. 4).For reliable fits, we perform echo decays for t > µ s Photon echo intensity (a.u.) t ( m s ) Homogeneous linewidth (kHz)
M a g n e t i c f i e l d i n t e n s i t y ( k G )
FIG. 4: Magnetic field dependence of Γ h (linear-log scale).Inset: two-pulse photon echo decay and fit (log scale) using a200 G magnetic field. when echo modulation has diminished (see Sec. III B 3).We find little field dependence and that 100 G of fieldis enough to achieve coherence properties comparable tothat of the zero-field motional narrowing regime. Notethat we observe a similar field dependence when perform-ing the measurement using three times less excitationpower in order to avoid the impact of excitation-inducedspectral diffusion.
4. Excitation-induced spectral diffusion
One source of spectral diffusion is due to optical excita-tion. Its effect on reducing coherence lifetimes is referredto as instantaneous spectral diffusion (ISD) [18, 19]. AsREIs are excited, the change in their permanent elec-tric dipole moment perturbs the resonance frequencies ofneighboring ions via electric dipole interactions. Con-sequently, the coherence lifetime that is inferred froma two-pulse photon echo decay may be underestimatedif intense excitation pulses are employed. To determinethe limitations of the coherence lifetime due to ISD, weset the temperature to be between 0.81 and 0.89 K and measure two-pulse photon echo decays at a wavelengthof 795.6 nm with varying excitation powers and magneticfields of 300 G and 20 kG. The echo decays are fit usingEq. 2, and we observe that the homogeneous linewidthrises with excitation power until saturation (Fig. 5).This behavior is supported by the following rate equa-
Homogeneous Linewidth (kHz)
E x c i t a t i o n p o w e r ( m W )
B = 3 0 0 G
B = 2 0 k G
Homogeneous linewidth (kHz)
E x c i t a t i o n P o w e r ( m W )
FIG. 5: Excitation power-dependence of the homogeneouslinewidth. Measurements using a 20 kG (300 G) field is shownin the main figure (inset). Excitation power refers to the peakpower of the second excitation pulse at the beginning of thewaveguide, accounting for any insertion loss. tion model for ISD:Γ h = Γ P =0 + 12 Γ ISD (1 − e − c P P ) , (4)where Γ P =0 is the homogeneous linewidth at zero exci-tation power, Γ ISD is the full-width at half maximumspectral broadening due to ISD and c P is a constant [19].A fit of our data using this model yields Γ P =0 = 2 . ± . . ± . ISD = 8 . ± . . ± . c P is related to a parameter β ISD that only depends onthe strength and the nature of the ion-ion interaction. Itis intrinsic to the material. For our measurements, β ISD may be estimated using β ISD = 3 πω hc λαt p c P Γ ISD , (5)where ω is the radius of waveguide mode, λ is the opti-cal excitation wavelength, α is the absorption coefficientand t p is the duration of the excitation pulse [19]. Thewaveguide features ω = 6 . µ m and α = 1 . − at λ = 795 . π -)pulses of du-ration t p = 25 . β ISD = 5 . ± . × − Hz · cm (5 . ± . × − Hz · cm ) for the 300 G (20kG) data, which is consistent with the 6 × − Hz · cm measured using bulk Tm :LiNbO at 1.7 K and a wave-length of 794.27 nm [19]. Note that the effects of ISDcould not be quantified at zero field due to a weak pho-ton echo intensity. Furthermore, varying amounts ofISD are measured at different wavelengths around 795.6and 794.2 nm, consistent with observations using bulkTm :LiNbO [16]. This suggests more complicated ion-ion or spin-spin interactions that go beyond the modeldiscussed here [13, 19], and should be addressed in fu-ture work.
5. Time-dependent spectral diffusion with magnetic field
In the presence of a magnetic field, spectral diffusion isknown to occur over timescales longer than the maximumvalue of t = 50 µ s used for our two pulse photon echoexcitation measurements [1, 2]. Since many optical signalprocessing applications using REIs rely on spectral fea-tures being created and probed over long timescales [2–4],we study spectral diffusion on such timescales. Towardsthis end, we use three-pulse photon echos at magneticfields of 300 G and 20 kG. Specifically, we generate twopulses that are separated by a time duration of t tocreate a population grating. Here, this grating is formedby optical pumping and trapping of population in the H , nuclear-hyperfine, or superhyperfine levels (see Secs.III B 1, III B 2, and III B 3). A third pulse, generated t after the second pulse, is scattered from the grating toproduce a photon echo of intensity I ( t ) = I I pop ( t ) e − t Γ h ( t ) , (6)where Γ h ( t ) is the time-dependent homogeneouslinewidth, I is a normalization constant, and I pop ( t )represents the reduction in echo intensity due to popula-tion decay [20]. For Tm :Ti :LiNbO at low tempera-tures and under magnetic fields, I pop ( t ) ≈ C e − t /T + C B e − t /T B + C H e − t /T H , where each C i are constantsand T = 109 µ s is the population lifetime of the H level, T B = 2 . T H > t .Specifically, at temperature of 0.80 K, a wavelength of795.3 nm, and using a magnetic field of 300 G, we vary t , and fit the echo decay using Eq. 2 ( x = 1) to de-termine Γ h ( t ) up to t = 300 µ s (Fig. 6, triangles).We find that spectral diffusion is negligible over the en-tire measurement timescale. An ∼ ∼
10 kHz measuredusing bulk Tm :LiNbO at 1.7 K and 794.26 nm wave-length, perhaps due to lowered temperature [11–13].Next, we increase the field to 20 kG and repeat themeasurement at 0.95 K (Fig. 6, circles). We find a T Z > 1 s Three-pulse echo intensity (a.u.) t ( m s ) T B ~ 3 . 8 m s Homogeneous linewidth (kHz) t ( m s ) FIG. 6: Time-dependent decoherence revealed by three-pulsephoton echoes. Variation of the homogeneous linewidth with t (linear-log scale) at 300 G (20 kG) magnetic field is shownusing triangles (circles). Note that the increasing uncertaintyof Γ h with t is due to decreasing echo intensities as a result ofthe decay of the H level (see Sec. III B 1) and the restrictionof echo decays to timescales beyond which echo modulationhas subsided ( t >
500 ns, see Sec. III B 3). Inset: variationof the three pulse photon echo intensity with t for t > T (double-log scale). linewidth that grows to ∼
50 kHz after 10 ms, indicat-ing a small rate of nuclear spin flips in the host, whichmay be due to the frozen core effect.To quantify the processes driving spectral diffusion, wefit our data using a spin fluctuation modelΓ h ( t ) = Γ + 12 Γ SD (1 − e − R SD t ) , (7)where Γ is the homogeneous linewidth at t = 0,and Γ SD is the maximum linewidth broadening due tospin fluctuations at a rate R SD [10, 20–22]. We findΓ = 7 . ± . h shownin Figs. 4 and 5, respectively. Our fit also yieldsΓ SD = 67 . ± . :LiNbO with zeromagnetic field at 1.7 K and 794.26 nm wavelength [12].Moreover, we also find R SD = 3 . ± . :LiNbO ,the increased maximum broadening may be due to addi-tional (and not yet understood) dynamics under strongfields, at long timescales, and at this wavelength, whichwill be explored in future studies.Note that despite the strong excitation powers usedin this measurement, we do not observe the distinctincrease (decrease) in decoherence over 1 µ s < t < µ s (at t ∼ µ s) that was observed using bulkTm :LiNbO at a wavelength of 794.27 nm and zeromagnetic field [13, 19]. This decoherence was ascribed tothe magnetic character of the H multiplet and popula-tion decay of these levels. The strong magnetic field andlow temperature used here likely inhibits these magneticinteractions by spin polarization.To examine the effects of spectral diffusion beyondtimescales of 10 ms, we perform three pulse photon echoexcitation and measure the echo intensity with t var-ied from 0.2 to 100 ms for fixed t = 500 ns (Fig. 6inset). A fit using Eq. 6 reveals that the echo inten-sity depends only on I pop with C ≈ t > T ), T B ≈ . T H > t >
10 ms, Γ h remains constant and any reduction inecho intensity is solely due to population decay from thehyperfine levels. This is consistent with the model of Eq.7 to describe the spectral diffusion dynamics in which thehomogeneous linewidth saturates at long time delays. B. Population dynamics and energy level structure
In addition to long coherence lifetimes of the opticaltransition, long-lived energy levels are required to re-alize optical technology with REIs [1–3]. For instance,these levels are used as a population reservoir for spectraltailoring of diffraction gratings or quantum memories.Therefore, we characterize both the energy-level struc-ture and population dynamics of the H to H transi-tion of the Tm :Ti :LiNbO waveguide under varyingconditions.
1. Lifetimes and dynamics of excited levels
We perform time-resolved spectral hole burning, inwhich interaction of a short laser pulse excites a subsetof ions and, after a varying time delay t d , the resultantincrease in optical transmission is assessed by varying thelaser frequency and measuring the depth of the spectralhole [2, 9]. We aim to determine the population lifetimesof the H excited level ( T ) and the F ‘bottleneck’level ( T B ) as shown in the simplified energy level dia-gram of the inset of Fig. 7 [1]. The H level has alifetime much shorter than T B and cannot be observedin the hole decay. Our measurements are performed atzero field, a temperature of 0.85 K, and at a wavelengthof 795.50 nm. Note that, in accordance with the resultsof Ref. [13], measurements at this wavelength probe ionsthat experience more local strain or those that occupymultiple sites.The variation of spectral hole depth with time delayreveals the expected double-exponential (Fig. 7). Notethat the hole depth is proportional to the number of ex- Spectral hole depth (a.u.)
T i m e d e l a y ( m s )
FIG. 7: Transient spectral hole decay and fit (log scale). Inset:Simplified electronic level structure and approximate transi-tion wavelengths of Tm . cited ions because spectral diffusion has saturated after10 µ s. A fit of the decay using e − t /T + β T B T B − T ( e − t /T B − e − t /T ) , (8)where β is the branching ratio to the bottleneck level[12], revealing T = 109 ± µ s, T B = 2 . ± . β = 62 ± T = 82 µ s, β = 44%, and T B = 2 . :LiNbO [11], where T = 160 µ s, β = 27%, and T B = 4 . :Ti :LiNbO . Increased dopingenhances the Tm -Tm cross-relaxation rate via de-cay through the H and F level [23]. For example,measurements using a 2% Tm -doped LiNbO crystalrevealed T ≈ µ s and T B ≈ .
2. Structure of Tm nuclear-hyperfine levels We apply a magnetic field and perform spectral holeburning to investigate field-activated atomic-level struc-ture and dynamics [1, 9]. We expect to observe anatomic-level structure that arises from
Tm hyperfinesplitting of the H and H levels. This is due to cou-pling between the nuclear spin and the enhanced elec-tronic magnetic moment, combined with a weaker nu-clear Zeeman effect contribution [11, 12]. Previous mea-surements of Tm :Ti :LiNbO have shown these lev-els to have lifetimes of up to several hours at 795.5 nmand 0.85 K with 600 G field [8], matching that of bulkTm :LiNbO measured under similar conditions [24].Exposing the Tm-doped crystal at non-zero magneticfield to narrow-band laser light will result in one addi-tional pair of side-holes and up to three pairs of anti-holesin the observed transmission spectrum due to populationredistribution among the Tm nuclear-hyperfine groundlevels [2]. The depth of the side-holes and anti-holesdepends on the measurement timescale and the relativetransition rates between hyperfine levels within the ex-cited and ground manifolds. However, if strong selectionrules prevent optical transitions involving a change in theTm nuclear spin, the spectral hole structure is simpli-fied so that only a single pair of anti-holes appears. Fur-thermore, if magnetic anisotropy or contributions frommagneticially-inequivalent sites exist in the crystal, thenholes and anti-holes may be broadened or non-resolvable.Previous work using bulk Tm :LiNbO indicates thatseveral different Tm sites may be probed at any givenexcitation wavelength [12, 13].We do not immediately resolve anti-holes or side-holesarising from Tm hyperfine splitting at a temperatureof 0.85 K and field of 600 G for excitation between 794.26and 795.50 nm wavelengths. This is likely due to a strongbroadening of the (anti-)hole structure or the high opti-cal absorbance at wavelengths close to 794 nm (see Fig.1). Anti-hole broadening has been observed using bulkTm :LiNbO [12, 13] as well as bulk and waveguidingEr :LiNbO [25, 26].To determine the anti-hole structure, we perform amodified hole-burning method. We simultaneously ex-cite narrow-band subsets of ions at laser frequencies re-ferred to as reference ( ω r ) and control ( ω c ) and measurethe resulting absorbance spectrum at zero magnetic field(i.e. we burn and measure spectral holes at frequenciesof ω r and ω c ). A conceptual example of the absorbancespectrum with non-zero magnetic field depicts exagger-ated holes and anti-holes for clarity, where a single pairof anti-holes is ascribed to each hole (Fig. 8a, grey).Next, the magnetic field strength is increased to 1 kGwhile monitoring the shape of the hole at ω r . When theanti-hole generated by the light at ω c begins to spec-trally overlap with the hole at ω r , the reference holedepth decreases (Fig. 8a, dotted line). Subsequently, thefrequency difference between the two holes, ω c − ω r atminimum hole depth, gives the value of the median sep-aration ∆ sep between the hole and anti-hole. Repeatingthis process for varying frequency differences of ω c − ω r gives rise to anti-hole profiles that broaden with increas-ing field due to spin inhomogeneous broadening (Fig. 8cand d for wavelengths of 795.50 nm and 794.26 nm, at3.5 K and 0.85 K, respectively). Detuning ω c ω r A b s o r ban c e Control Reference (a) (b) (c) (d)
0 100 200 300 400 500 600 700 800020406080100 Magnetic field intensity (G) H o l e - A n t i - ho l e s epa r a t i on / A n t i - ho l e b r oadn i ng ( M H z ) separationbroadening Magnetic field intesity (G)0510152025 R e f e r en c e ho l e dep t h ( a . u ) Magnetic field intensity (G)0510152025 R e f e r en c e ho l e dep t h ( a . u . ) No control excitation ω c – ω r = 25 MHz ω c – ω r = 50 MHz ω c – ω r = 75 MHz ω c – ω r = 100 MHz795.50 nm 794.26 nm .26 nm .50 nm FIG. 8: Determination of the anti-hole structure due to theTm nuclear-hyperfine interaction. (a) Illustration of theconcept (see main text for a description). (b) Anti-hole sep-arations and widths with varied magnetic fields at 795.50 nmand 794.26 nm extracted from data shown in (c) and (d).Solid and dashed lines are used to guide the eye. (c) and (d),Reference hole depths as a function of magnetic field for vary-ing frequency differences ( ω c − ω r ), at wavelengths of 795.50nm and 794.26 nm, respectively. The legend for (c) is identi-cal to that shown in (d) and solid lines are used to guide theeye. We determine ∆ sep to vary linearly with field (Fig. 8b),finding ∆ sep / π = 136 ±
14 kHz/G and 155 ± sep to the difference betweenthe hyperfine energy splitting in the H excited leveland H ground level. Our result is consistent withthe 140 kHz/G measured directly from field-dependentanti-hole shifts in bulk Tm :LiNbO at 794.28 nm and1.8 K, indicating a similar electronically-enhanced effec-tive nuclear moment in the Tm :Ti :LiNbO waveg-uide [11, 12]. The differences in ∆ sep with wavelength isattributed to inequivalent Tm sites [13]. In addition,our analysis reveals the anti-holes to be Gaussian-shaped,with an inhomogeneous broadening of δ ∆ sep / π = 109 ±
36 kHz / G and 59 ±
13 kHz / G for measurements at wave-lengths of 795.50 nm and 794.26 nm, respectively (Fig.8b). This indicates a variation of splittings in either theground or excited state, and similar to what was observedusing bulk Tm :LiNbO , also likely due to inequivalentTm sites [13]. More studies are needed to determineif this broadening can be reduced or how this limits theapplicability of Tm :Ti :LiNbO for broadband signalprocessing.
3. Structure of superhyperfine sub-levels
Spectral hole burning measurements. With increasedmagnetic fields beyond 1 kG, we expect to resolvemore holes and anti-holes due to superhyperfine split-ting caused by the weak coupling of the ions of the hostcrystal to the electronic levels of the REIs [2]. Superhy-perfine ground levels in Tm :Ti :LiNbO can have life-times of at least several minutes at 0.85 K for these fields[8], similar to those of bulk Tm :LiNbO under similarconditions [24]. We probe the superhyperfine structureof the H to H transition using spectral hole burningat a temperature of 0.90 K, with magnetic fields of up to19 kG, and at wavelengths of 794.26 nm and 795.46 nm. - 3 0 - 2 0 - 1 0 0 1 0 2 0 3 00908090504 - 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0 D e t u n i n g f r o m 7 9 4 . 2 6 n m ( M H z )
10 kG 12 kGOptical transmission (a.u.) 15 kG
19 kG
FIG. 9: Hole burning transmission spectra at a wavelengthof 794.26 nm for varying magnetic fields (as indicated). Tri-angles, squares, and circles indicate the side holes associatedwith the | ∆ m I | = 1 transitions of Li, Nb, and Li nu-clear spins, respectively. Distortions are due to the large ab-sorbance.
The resultant spectra (Figs. 9 and 10) reveal no dis-tinct anti-hole structure but rather side-holes due to tran-sitions to different superhyperfine levels in the H ex-cited state [2]. To identify the spin transitions that areassociated with the side-holes, a linear fit of each set - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 00605050504 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 D e t u n i n g f r o m 7 9 5 . 4 6 n m ( M H z )
10 kG 12 kGOptical transmission (a.u.) 15 kG
19 kG
FIG. 10: Hole burning transmission spectra at a wavelengthof 795.46 nm for varying magnetic fields (as indicated). Trian-gles, squares, circles, diamonds, open squares, open diamonds,and open circles, indicate the side holes associated with the | ∆ m I | = 1 transitions of Li, Nb, and Li nuclear spins, aswell as the | ∆ m I | = 2 transitions of , Ti, Nb (site 1), Nb (site 2), and Li nuclear spins, respectively. Note theincrease in the range of detuning compared to Fig. 9. of field-dependent side-hole detunings (relative to themain hole) is performed to determine all effective spingyromagnetic ratios. We find that the hole structureoriginates from , Li, Nb, and , Ti nuclei in theTi :LiNbO crystal. The ascribed nuclei and transi-tions, indicated by the difference in magnetic quantumnumber | ∆ m I | , average gyromagnetic ratios γ , associateduncertainties from our fits δγ are indicated in Table I (II)for measurements at a wavelength of 794.26 (795.46) nm.At 794.26 nm, the splittings are distinctive and matchwell with those observed using bulk Tm :LiNbO ata similar wavelength [27] despite the presence of morespin inhomogeneous broadening or laser-power broaden-ing (see Sec. III B 4).At 795.46 nm, the structure is different, likely dueto ions experiencing enhanced local strain compared tothose probed at 794.26 nm [12, 13]. Side-holes corre-sponding to | ∆ m I | = 1 transitions of Nb and , Lihave profiles and detunings that are easily identifiable0since they compose the two main lattice constituents,and are similar to those observed from measurements us-ing bulk Tm :LiNbO [27] and the results at 794.26nm. The remaining side-holes are attributed to the nor-mally forbidden | ∆ m I | = 2 transitions for Nb, Li, and , Ti spins. Moreover, the Nb sideband is split intotwo – likely corresponding to different relative positionsto Tm ions – with relative detunings and areas of thetwo holes giving a center-of-gravity that is similar to thefree-ion gyromagnetic ratio. Further studies, such as spindouble-resonance measurements [28], are required to fullycharacterize the nature of the observed superhyperfinesplitting and confirm our assignments of spins. element ∆ m I γ δγ Li 1 0.57 0.03 Nb 1 1.11 0.05 Li 1 1.71 0.01TABLE I: Results of analysis of side-hole structure at varyingmagnetic fields at a wavelength of 794.26 nm, see main text fordetails. Units of effective gyromagnetic ratios and associateduncertainties is kHz/G.element ∆ m I γ δγ , Ti 2 0.50 0.01 Li 1 0.60 0.03 Nb 1 1.04 0.01 Li 1 1.65 0.01 Nb Nb Li 2 3.31 0.01TABLE II: Results of analysis of side-hole structure at varyingmagnetic fields at a wavelength of 795.46 nm, see main text fordetails. Units of effective gyromagnetic ratios and associateduncertainties is kHz/G. The subscript on the Nb spin denotesthe site associated with its sideband splitting, see main text.
Next, we set the magnetic field to 19 kG and performspectral hole burning with varying laser wavelengthacross the inhomogeneous line to further probe varia-tions of the superhyperfine structure (Fig. 11). We findthat the hole structure varies across the inhomogeneousline, with more complex structure at detunings farthestfrom 794.2 nm, corresponding to Tm ions that likelyexperience higher local strain or are positioned in alter-native sites [12, 13]. At 794.23 nm, the hole spectrumis dominated by the Nb splitting, similar to that inFig. 9. This is likely due to the strong absorbancethat limits observation of the other weaker transitions.Varying the excitation wavelength towards either 794.9or 793.6 nm increasingly reveals the splittings from Liand Li as well as the ∆ m I = 2 transition of Nb.The side-hole corresponding to , Ti is hidden, owingto power broadening of the holes. As the detuning isvaried more, either to 796.1 or 792.7 nm (addressing ions - 1 0 0 - 5 0 0 5 0 1 0 001 002 102 202 101 801 20801 701 902 302 102 1 - 1 0 0 - 5 0 0 5 0 1 0 0
D e t u n i n g f r o m t h e m a i n h o l e ( M H z )
Optical transmission (a.u.)
FIG. 11: Hole burning transmission spectra with 19 kG fieldfor varying laser wavelength (as indicated). Each measure-ment is optimized to reduce distortions compared to mea-surements of Figs. 9 and 10, yet holes experience greaterpower broadening at wavelengths where the absorbance islower. Vertical scale is optimized for clarity. experiencing higher strain) more side holes than those inFig. 10 appear. Although ascribing transitions to theseadditional holes is challenging without a measurementwith varied magnetic field, we tentatively attributethe split side-hole, corresponding to the | ∆ m I | = 2transition of the Nb ion, to different transitions.Specifically, we ascribe these two holes to the | ∆ m I | = 2and | ∆ m I | = 3 transitions of Nb, acknowledging thelimited resolution of Fig. 10. This new assignmentis consistent with the additional side-holes being fromthe | ∆ m I | = 4 and | ∆ m I | = 5 transitions of Nb.Nevertheless, further studies are required for a completeinterpretation of the hole structure.Photon echo measurements. If a broad optical inhomo-geneous distribution obscures transitions that have smalldifferences in energy splitting, such as the superhyper-fine levels in our case, then a two-pulse photon echo de-cay may feature a modulation due to the interferencebetween any of the sublevels [2, 29, 30]. Similarly, echomodulations may be observed in a three-pulse photon1echo decay. In the simple case of two doublets with asplitting of ω g ( e ) in the ground (excited) state, the sys-tem is composed of four optical transitions, leading to atwo- or three-pulse photon echo decay described by I ( t ) = I e −
2( 2 t T ) x (cid:2) σ σ F ( t , t ) (cid:3) . (9)Here the first part is the Mims decay function of Eq. 2, σ ≡ σ diff /σ same is the ratio of absorption cross-sectionsbetween spins of same or different m I , and F ( t , t ) isa modulation function that describes the quantum inter-ference between the four possible optical transitions: F ( t , t ) = e − π Γ g t { cos[ ω g t ] + cos[ ω g ( t + t )] } + e − π Γ e t { cos[ ω e t ] + cos[ ω e ( t + t )] }− e − π (Γ e +Γ g ) t cos[ ω e t ]cos[ ω g ( t + t )] − e − π (Γ e +Γ g ) t cos[ ω g t ]cos[ ω e ( t + t )] . (10)Finally, Γ g ( e ) is the nuclear transition linewidths for theground (excited) states [11, 29, 30].We perform two- and three-pulse photon echo decaymeasurements using 300 G field at a wavelength of 795.5nm and temperature of 0.65 K. For the latter, t wasfixed at 300 µ s. The results are depicted in Fig. 12(circles and squares, respectively). B ~ 6 0 G s = 1 ± 6 G e = 0 . 1 ± 1 . 2 M H z w e / 2 p = 0 . 1 ± 0 . 4 M H z G g = 0 . 1 ± 0 . 6 M H z w g / 2 p = 7 0 ± 1 6 1 k H z Photon echo intensity (a.u.) t ( m s ) B = 3 0 0 G G e = 1 7 ± 6 6 k H z w e / 2 p = 5 1 7 ± 2 4 k H z s = 0 . 0 9 ± 0 . 0 5 G g = 1 5 ± 6 0 k H z w g / 2 p = 4 8 5 ± 2 4 k H z FIG. 12: Echo decay modulation (log scale) observed usingtwo- (circles, triangles) and three-pulse (squares) photon echoexcitation (log scale). A field of 300 G results in a highermodulation frequency (circles, squares) compared to that ob-tained using 60 G (triangles). Parameters extracted from fitsusing Eq. 9 are shown, with large uncertainties due to thelarge number of fitting parameters or, for the case of the de-cay with 60 G field, the observation of only one period ofmodulation.
We simultaneously fit both decays using Eq. 9. Ourfour-transition model describes the observed behavior likely because the ∆ m I > ω g ( e ) / π = 485 ± ±
24) kHz that, considering the results presented inTable II, correspond to the | ∆ m I | = 1 splitting of the Li nucleus (495 kHz) with a nuclear quadrupole shift of22 kHz [11]. Linewidths Γ g ( e ) = 15 ±
60 (17 ±
66) kHz anda cross-section ratio of 0.09 ± ω g ( e ) / π = 498 (520) kHz, Γ g = Γ e = 18 kHz, and σ = 0 .
06, measured using a Tm :LiNbO bulk crystalat 1.8 K, a wavelength of 794.26 nm, and the same field[11, 27], which was also ascribed to the same Li transi-tion.Finally, to verify the field-dependence of the mod-ulation, we reduce the magnetic field to ∼
60 G, andmeasure a two-pulse photon echo decay shown in Fig.12 using triangles. For these measurements, the tem-perature is 0.8 K. A fit using Eq. 9 yields ω g ( e ) / π =70 ±
161 (100 ± :LiNbO at 794.26 nm. This may be due to similarsuperhyperfine splittings from different ∆ m I transitionsof Li in the H and H levels, or weak emission fromlevels split by other nuclear spins [11, 27].Measurements using continuous coherent excitation.Superhyperfine structure may also be revealed by con-tinuous coherent narrow-band excitation of the opticaltransition. Due to inhomogeneous broadening, thisresults in coherent emission by optical transitions thatdiffer in energies given by the superhyperfine splittings.This produces a modulation of the transmitted field,sometimes referred to as a quantum beat [31].To this end, for two different laser excitation wave-lengths, three different magnetic fields, and using varyingoptical excitation power, we observe the modulation of along optical pulse after being transmitted through thewaveguide. These measurements are performed at 1 K.Figs. 13a and insets show that the modulation is similarfor all optical powers. This modulation cannot be re-lated to optical nutation, which is the coherent driving,and hence modulation, of atomic population between op-tical transitions, which has a rate that is proportional tothe square root of the excitation power. Further, we ob-serve the amplitude and periodicity of the modulationat the same magnetic field to be similar for both wave-lengths (Figs. 13a and b). As the field is increased, themodulation becomes damped, while the modulation fre-quency increases and becomes more complex. As shownin the inset of Fig. 13b, fits of the most discernible modu-lation frequency for both excitation wavelengths reveal alinear and identical dependence with respect to the mag-netic field, with a slope of 1 . ± .
04 kHz/G and zerooffset (within error). The modulation frequency is simi-lar to that observed using photon echoes, and, according2 T (cid:85) (cid:68)(cid:81) (cid:86) (cid:80) (cid:76) (cid:86)(cid:86) (cid:76) (cid:82)(cid:81) (cid:3) (cid:11) (cid:68) (cid:17) (cid:88) (cid:17) (cid:12) (cid:37)(cid:3)(cid:32)(cid:3)(cid:21)(cid:19)(cid:3)(cid:78)(cid:42)(cid:3) (cid:26)(cid:28)(cid:24)(cid:17)(cid:24)(cid:19)(cid:3)(cid:81)(cid:80) (cid:26)(cid:28)(cid:24)(cid:17)(cid:24)(cid:19)(cid:3)(cid:81)(cid:80)Pulse(cid:3)(cid:76)(cid:81)(cid:87)(cid:72)(cid:81)(cid:86)(cid:76)(cid:87)(cid:92)(cid:3)(cid:11)(cid:68)(cid:17)(cid:88)(cid:17)(cid:12) (cid:3) M odu l a t i on (cid:3)(cid:73) (cid:85) (cid:72)(cid:84)(cid:88)(cid:72)(cid:81) (cid:70)(cid:92) (cid:3) (cid:11) (cid:48) (cid:43) (cid:93) (cid:12) (cid:26)(cid:28)(cid:23)(cid:17)(cid:21)(cid:19)(cid:3)(cid:81)(cid:80) (cid:24)(cid:3)(cid:78)(cid:42)(cid:20)(cid:3)(cid:78)(cid:42) (cid:48)(cid:68)(cid:74)(cid:81)(cid:72)(cid:87)(cid:76)(cid:70)(cid:3)(cid:73)(cid:76)(cid:72)(cid:79)(cid:71)(cid:3)(cid:76)(cid:81)(cid:87)(cid:72)(cid:81)(cid:86)(cid:76)(cid:87)(cid:92)(cid:3)(cid:11)(cid:78)(cid:42)(cid:12) M odua l a t i on (cid:3)(cid:73) (cid:85) (cid:72)(cid:84)(cid:88)(cid:72)(cid:81) (cid:70)(cid:92) (cid:3) (cid:11) (cid:48) (cid:43) (cid:93) (cid:12) (cid:26)(cid:28)(cid:23)(cid:17)(cid:21)(cid:19)(cid:3)(cid:81)(cid:80)(cid:20)(cid:17)(cid:25)(cid:26)(cid:3)(cid:147)(cid:3)(cid:19)(cid:17)(cid:19)(cid:22)(cid:3)(cid:78)(cid:43)(cid:93)(cid:18)(cid:42) (cid:17) (cid:3)(cid:147)(cid:3)(cid:19)(cid:17)(cid:19) (cid:78) Hz/ (cid:42)
0 20 40 60 80 100 0 20 40 60 80 100
0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.0 (cid:83) ulse (cid:3)(cid:76)(cid:81)(cid:87)(cid:72)(cid:81)(cid:86)(cid:76)(cid:87)(cid:92)(cid:3)(cid:20)(cid:19)(cid:19)(cid:3)(cid:11)(cid:68)(cid:17)(cid:88)(cid:17)(cid:12) pulse (cid:3)(cid:76)(cid:81)(cid:87)(cid:72)(cid:81)(cid:86)(cid:76)(cid:87)(cid:92)(cid:3)(cid:20)(cid:24)(cid:3)(cid:11)(cid:68)(cid:17)(cid:88)(cid:17)(cid:12) (cid:37)(cid:3)(cid:32)(cid:3)(cid:21)(cid:19)(cid:3)(cid:78)(cid:42)(cid:3) (cid:37)(cid:3)(cid:32)(cid:3)(cid:20)(cid:3)(cid:78)(cid:42) (cid:37)(cid:3)(cid:32)(cid:3)(cid:24)(cid:3)(cid:78)(cid:42) pulse (cid:3)(cid:76)(cid:81)(cid:87)(cid:72)(cid:81)(cid:86)(cid:76)(cid:87)(cid:92)(cid:3)(cid:23)(cid:19)(cid:3)(cid:11)(cid:68)(cid:17)(cid:88)(cid:17)(cid:12) (cid:26)(cid:28)(cid:23)(cid:17)(cid:21)(cid:19)(cid:3)(cid:81)(cid:80) (cid:20)(cid:17)(cid:19)(cid:3)(cid:3)(cid:3) (cid:3)(cid:55)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11) (cid:99) (cid:86)(cid:12)
0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.0 (cid:11)(cid:68)(cid:12)(cid:11)(cid:69)(cid:12) (cid:21)(cid:19)(cid:3)(cid:78)(cid:42) (cid:24)(cid:3)(cid:78)(cid:42)(cid:20)(cid:3)(cid:78)(cid:42)(cid:21)(cid:19)(cid:3)(cid:78)(cid:42) T (cid:85) (cid:68)(cid:81) (cid:86) (cid:80) (cid:76) (cid:86)(cid:86) (cid:76) (cid:82)(cid:81) (cid:3) (cid:11) (cid:68) (cid:17) (cid:88) (cid:17) (cid:12) (cid:3)(cid:55)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11) (cid:99) (cid:86)(cid:12) (cid:20)(cid:17)(cid:19)(cid:3)(cid:3)(cid:3) FIG. 13: Intensity modulation of a narrowband pulse of lightcaused by superhyperfine levels. (a) The transmitted intensityof pulses with varying input powers (vertically displaced) at awavelength of 795.50 nm and a magnetic field of 20 kG. Theinset depicts the most discernible modulation frequencies andtheir dependence on magnetic field, wavelength, and the inputpulse intensity. (b) The transmitted intensity for pulses offixed intensities with varying magnetic field at a wavelengthof 794.20 nm. The inset shows that the frequencies of the mostdiscernible modulation varies linearly with magnetic field andis independent of wavelength. Fits, represented by dottedlines, reveal the modulation to be from Li superhyperfinesplitting. to Tables I and II, consistent with the splitting causedby coupling to Li. Moreover, the weak intensity of themodulation is consistent with the small absorption cross-sections predicted by the echo data. The damping ofthe modulation is due to spin inhomogeneous broaden-ing, occurs faster for higher magnetic fields, and is more pronounced at a wavelength of 795.5 nm, consistent withthe broadening of the nuclear-hyperfine levels. The addi-tional frequency components of the modulation at highfields could be due to the similar ∆ m I transitions causedby Li in the H and H levels. However, more mea-surements are required to evaluate this interpretation.
4. Excitation-power dependence of spectral hole widths anddepths
Spectral tailoring of an optical inhomogeneous line iskey to realizing optical applications with REICs such asoptical filters or dispersion elements [3, 9]. Narrow-bandexcitation will produce a spectral hole whose depthand width depend not only on the level structure anddynamics, but also on the intensity and the duration ofthe excitation pulse [9]. Here we investigate the effectsof laser power on the widths and depths of spectral holesusing the Tm :Ti :LiNbO waveguide.Power dependence of hole width. Strong laser pow-ers can rapidly drive transitions. This leads tolaser-induced broadening of a spectral hole, an effectreferred to as power broadening [32]. To measure powerbroadening, we perform spectral hole burning at 0.85K, zero magnetic field, and 795.5 nm wavelength withvarying laser power.Ions are excited using a pulse of 1 ms duration and,by varying the laser detuning after a delay of 400 µ s, theshape of the spectral hole is measured. The full-width-at-half-maximum width Γ hole of the hole is fit using aLorentzian (Fig. 14). For excitation powers of <
100 nW,we observe no power dependence of the hole width, indi-cating that our narrowest spectral hole width is limitedby laser frequency jitter and spectral diffusion. Powerbroadening increases with excitation power according toΓ hole = Γ L (cid:2) (1 + (cid:112) L K ) ) × (1 + (cid:113) L K ) e − d i ) (cid:3) , (11)where the initial absorbance of the transition is d i , Γ L isthe fitted homogeneous linewidth that includes linewidthbroadening due to laser frequency instability, and K isproportional to the excitation power [32]. We fit our datausing Eq. 11, yielding d i = 2 . ± . d = 2 . L = 106 ± <
100 kHz laser linewidth, is compatible withthe ∼
50 kHz measured using bulk Tm :LiNbO at 1.7K and 794.27 nm wavelength [11, 12, 19].Power dependence of hole depth. It is a recurrent ob-servation when spectrally tailoring Tm :Ti :LiNbO that wide spectral features may not be burned to fulltransparency. This may be due to accumulation of pop-ulation in near-detuned inhomogeneously broadened hy-perfine levels, which results in a reduction of hole depth,or ISD that also results in hole broadening and depth re-duction [19]. However, as described below, we rule out all3 Transmission (a.u.)
L a s e r d e t u n in g ( M H z )
Deconvolved spectral hole width (MHz)
P e a k p o w e r a t t h e i n p u t o f t h e c r y o s t a t ( m W )
FIG. 14: Power broadening of a spectral hole. Linear-logscale is used to clearly reveal the zero-excitation intercept.The hole width is deconvolved from 70 kHz of broadeningdue to the laser frequency variation. Inset: Spectral hole andfit of the data taken using 16 nW of excitation power. of these causes and attribute the limitation to spin-latticerelaxation that is induced by laser excitation.To investigate this effect, we perform the following ex-periment using a 3 kG field at 3 K and a wavelength of795.5 nm (Fig. 15a). We consecutively burn two spec-tral holes, first one at 700 MHz detuning using a fixedexcitation power and then one at 0 MHz detuning withvarying excitation power, starting with none. The de-tuning avoids the impact of anti-holes from populationaccumulation in nuclear-hyperfine levels. After a 2 msdelay, we record the optical absorbance profile and fit thehole depths and widths at the two detunings with vary-ing excitation power used to burn the 0 MHz detunedhole (Figs. 15b, c, d).As expected, we observe that the depth of the hole at0 MHz initially increases as the increased power allowsmore ions to be optically pumped. However, a furtherincrease in optical power results in a decrease in holedepth. Note that the width of this hole increases withthe square-root of the power, as expected from powerbroadening. Meanwhile, the hole at 700 MHz detuningdecreases as soon as optical power is applied to burnthe 0 MHz hole. Since the power employed to burn the700 MHz hole is constant, we do not expect any powerbroadening of that hole. Specifically, we observe that thewidth of the hole at 700 MHz detuning is constant withexcitation power at 0 MHz detuning. Since the area ofthe hole at 700 MHz detuning is not conserved, we cannotascribe the reduction of this hole to ISD. Although itswidth is increased by power broadening, we expect thatthe reduction of the hole at 0 MHz detuning also cannotbe explained by ISD. (cid:19)(cid:19)(cid:19)(cid:16)(cid:20)(cid:19)(cid:19)(cid:19)(cid:20)(cid:19)(cid:19)(cid:19) H o l e dep t h ( a . u . ) (cid:239)(cid:21)(cid:19)(cid:19) I nen s i t y o f l a s e r a t z e r o de t un i ng ( a . u . ) (a)(b) (c)(d) Intensity of laser at zero detuning (a.u.) H o l e w i d t h ( M H z ) Intensity of laser at zero detuning (a.u.) L aser detuning ( MHz ) FIG. 15: Excitation power-dependence of the depth of a spec-tral hole. (a) Timing sequence of the experiment. Opti-cal intensity in (out) indicates the light that is generated(detected) before (after) the waveguide. (b) Hole burningabsorbance spectrum for varying excitation powers at zerodetuning. Dark (light) color corresponds to high (low) ab-sorbance. (c) Depths of both holes are reduced with increasedburning power. (d) Width of hole at 700 MHz detuning re-mains nearly constant, while the other is power broadened.
We note that this measurement procedure has alsobeen performed using an Er :Ti :LiNbO waveguide,with similar conclusions (i.e. ruling out population re-distribution in hyperfine levels and ISD) [26]. However,excitation-power dependence of hole depth has not beenobserved in bulk REI-doped LiNbO [16], likely becauseits effect is significantly enhanced by light confinement ina waveguide. Following the discussion in Ref. [26], thereduction in hole depth is furthermore not caused by ac-celerated spin diffusion, i.e. spin flip-flops due to nuclearspin excitation and decay during the burning procedure,and likely not by coupling of laser-excited two-level tun-neling systems (TLSs) to nuclear spins as we have not ob-served any clear signature of TLS in any of our previous(coherence) measurements. Alternatively, spin-lattice re-laxation from non-equilibrium phonon dynamics duringthe laser excitation [1, 33], in which phonons are gen-erated due to electron-phonon interactions and the de-cay of optically-excited levels of REIs, could play a role.Nonetheless, further measurements are needed to clarifythe presence of these dynamics, (e.g. using varying laserdetuning and magnetic fields) or using laser excitationthat is far detuned from the REI transition to determineif the effects are caused by the Ti :LiNbO crystal itself.4 IV. CONCLUSION
We analyzed the coherence and energy-level prop-erties of the H to H optical transition of aTm :Ti :LiNbO waveguide at temperatures as lowas 0.65 K, with fields up to 20 kG, over varying measure-ment timescales as well as laser excitation wavelengthsand powers. Complementing our previous work, we char-acterize properties that limit the performance of this ma-terial for optical signal processing applications, sheddinglight on underlying mechanisms behind important pa-rameters such as optical coherence or hole spectra.Importantly, we find properties that are consistentwith those of a Tm :LiNbO bulk crystal at tem-peratures of less than 1 K except for differences thatcan be explained by Tm or Ti -doping concentra-tion. For example, Tm -doping appears to impact thetemperature-dependence of homogeneous linewidth andreduces the excited-level lifetime compared to that mea-sured in the bulk crystal, while mode confinement pro-vided by Ti -doping yields additional side-holes whilefacilitating strong laser intensities that enhance the spin-lattice relaxation rate of the hyperfine levels. Still, someproperties could not be compared because they were notmeasured in the bulk crystal, e.g. time-dependent spec-tral diffusion using a 20 kG field or wavelength-dependentsuperhyperfine structure.Our study indicates that REIs retain their properties when the crystal is co-doped for integrated applications,thereby establishing new directions for optical signal pro-cessing in this widely-used electro-optic crystal. V. ACKNOWLEDGMENTS
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