1. Introduction

The ⁷F₀ → ⁵D₀ f-f transition of Eu³⁺ in inorganic insulators has received vast interest, initially for its spectroscopic properties, and more recently for its potential application in quantum information processing and optical data storage. Just to give a few spectroscopic examples, Macfarlane and Shelby reported a sub kilohertz homogeneous linewidth of 760 Hz (∼8.5 × 10⁻¹⁰nm) for this transition in Y₂O₃:Eu³⁺ at ∼580 nm from photon echo measurements as early as 1981 [1]. In 1994 Equall et al. subsequently reported an ultra-narrow homogeneous linewidth of 102 Hz for a Y₂SiO₅:Eu³⁺ sample in a magnetic field of 10 mT, using again photon echo measurements [2]. Remarkably, the 102 Hz linewidth is ∼4·10⁷ times narrower than the 4 GHz inhomogeneous width. In another major achievement, Ahlefeldt et al. reported an ultra-narrow inhomogeneous linewidth of 25 MHz for a stoichiometric EuCl₃·6H₂O crystal [3].

It was realised early on that the ⁷F₀-⁵D₀ transition of Eu³⁺ in the solid state can be used as the medium for both frequency-domain optical storage (FDOS) by spectral hole-burning and time-domain optical storage (TDOS)⁴ by the photon echo effect [4,5]. TDOS overcomes the limited readout speed of FDOS, and hence has in principle more scope for practical applications. However, it is noted here that multilevel spectral hole-burning can greatly increase the readout speed in FDOS [6]. Photo-echo based memories have received renewed attention in recent years not just for the storage of classical data but also as quantum-memories i.e. by storing the quantum state of photons in the atom system. Possible storage schemes such a controlled reversible inhomogeneous broadening (CRIB), and their application in, for example, quantum repeaters, have been discussed in an excellent review [7].

In general, there are only a few host materials in which the Eu³⁺-isoelectronic divalent samarium ion is stable (Sm²⁺) and hence it is not surprising that the ⁷F₀→⁵D₀ transition in this latter ion has received much less attention compared to Eu³⁺. Notwithstanding this limitation, Sm²⁺ in the solid state was employed in the first demonstration of photon-gated spectral hole-burning [8] and room-temperature spectral hole-burning [9]. The Sm³⁺ to Sm²⁺ conversion in BaFCl upon exposure to ionising or UV radiation has also been demonstrated to have some potential in dosimetry and computed radiography [10], multilevel data storage [11], multilevel FDOS data storage [6] and for high-resolution grey scale images that could be used for anti-counterfeiting labels [12].

In this Article we report slow light and photon echo measurements for the ⁷F₀→⁵D₀ transition of Sm²⁺ in BaFCl. Slow and fast light phenomena have attracted a great deal of attention over the last three decades [13], again in the context of their potential in quantum memories and signal processing applications. Slow and fast light can be generated by electromagnetically induced transparency and transient and persistent spectral hole-burning [14]. The effect is based on the rapidly varying refractive index n in the vicinity of a spectral hole or a EIT induced transparency window. For example, if a spectral hole is burnt into an inhomogeneously broadened transition, the refractive index changes rapidly at the hole centre as follows from the Kramers-Kronig transformation. For a strongly frequency-dependent refractive index the group velocity v_G for a light pulse propagating through a material is given by Eq. (1)

The transmission spectrum T(ω) is determined experimentally, and the phase of the response function can be calculated by the Hilbert transform per Eq. (5).

The equations were evaluated by a MATLAB code with empirical values for all parameters.

BaFCl:Sm²⁺ (or other Sm²⁺ doped materials) may potentially provide a suitable platform for applications in quantum and classical data storage and related applications because in contrast to Eu³⁺ whose two stable isotopes (151 and 152) have a nuclear spin of 5/2 leading to quadrupole splittings of the ⁷F₀ and ⁵D₀ levels on the order of tens of MHz, only two stable (or very long-lived) Sm isotopes (147 and 149 with 15% and 13.8% abundances) have a nuclear spin with very small quadrupole splittings on the order of $\le $1 MHz as observed in BaFCl [20]. In addition, the peculiarity of the BaFCl structure and morphology facilitates a pronounced Stark effect which is a pre-requisite for CRIB and it may provide a true two-level atom system if the BaFCl is doped with ¹⁵²Sm only. Importantly, in contrast to Eu³⁺, the ⁷F₀-⁵D₀ transition of Sm²⁺ is in a wavelength region (∼690 nm) that is readily accessible by inexpensive and highly controllable diode lasers, which is a significant advantage for practical applications.

2. Experiment

BaFCl crystals, nominally doped with ∼0.5% Sm²⁺, were provided by Professors Hans Bill and Hans Hagemann, University of Geneva. The crystals were grown by the Kyropooulos method. The BaFCl:Sm²⁺ crystal (plate-like) was mounted with its c-axis perpendicular to the propagation direction of the light between two copper plates on a sample holder that was mounted on the cold finger of a closed-cycle refrigerator (Janis-Sumitomo SHI-4.5).

A MogLab Cateye laser was used as the light source for all experiments except for the measurement of the absorption spectrum for which a Toptica DL100 ECDL was employed (wider mode-hop free scan). The beam of the laser was pulsed/gated by an acousto-optic modulator (Isomet 1205C-1) and the light transmitted through the crystal was detected through a 688 nm 1-nm bandpass filter by a photomultiplier (EMI 9785B). The signal was averaged by a LeCroy waveSurfer 422 digital oscilloscope. The experiment is illustrated in Fig. 1.

3. Results and discussion

The host for Sm²⁺ used in the present Article, BaFCl, crystallizes in the tetragonal P4/nmm space group [21] with the peculiar feature of chloride anion double layers as is seen in the space filling model in Fig. 2(a). The crystals tend to grow as plates and easily cleave perpendicular to the crystal c-axis due to this chloride anion double layer and Sm²⁺ substitutes Ba²⁺ in a site of C_4v point symmetry. The z-axis of the C_4v site is parallel to the crystal c-axis and hence the electric dipole transition ⁷F₀(A₁)→⁵D₀(A₁) is expected to be fully polarized along the crystal c-axis, E||c, as is indicated in Fig. 2(b) in which a partial energy level diagram for Sm²⁺ in BaFCl is shown. Note that the very small [20] quadrupole splittings of the ⁷F_J and ⁵D_J multiplets for the ¹⁴⁷Sm (15% abundance) and ¹⁴⁹Sm (13.8% abundance) isotopes with nuclear spins of 7/2 are not shown in this figure.

 

Fig. 1. Schematic of the experimental setup. BS: beam splitter; ECDL: external cavity diode laser; CCR: closed-cycle refrigerator; FPI: Fabry-Perot interferometer (1.5 GHz or 300 MHz free spectral range); PMT: photomultiplier; AOM: acousto-optic modulator.

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Fig. 2. a) Representations of the matlockite crystal structure of BaFCl. Sm²⁺ substitutes the Ba²⁺ ion in the C_4v site. b) Energy level diagram showing the ⁷F_J levels and the two lowest excited states ⁵D₀ and ⁵D₁. The transition explored in the present Article is indicated with its polarization. c) polarized (E||c and E$\bot $c) absorption spectra of the ⁷F₀ → ⁵D₀ transition (center wavelength 688.10762 nm (vacuum wavelength); crystal thickness ∼5 mm). The dashed line in c is a fit by a Gaussian lineshape.

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Full E||c polarization is indeed observed as is illustrated in Fig. 2(c), where the absorption spectra are shown for E||c and E$\bot $c. These spectra were measured by scanning the frequency of an external cavity diode laser (ECDL) across the ⁷F₀(A₁) → ⁵D₀(A₁) transition. An absorbance A (A = log₁₀(I₀/I) = optical density) and a full width at half maximum (FWHM) of 1.7 and 7.65 ± 0.03 GHz (0.255 cm⁻¹) were observed, respectively, with a ∼5 mm optical pathlength through the crystal. From this measurement an oscillator strength f of ∼3 × 10⁻⁸ was calculated for this transition by using the well-known expression $f = 4.3 \times {10^{ - 9}}\smallint \varepsilon ({\bar{\nu }} )d\bar{\nu }$ with $\varepsilon ({\bar{\nu }} )$ being the molar decadic extinction coefficient as a function of wavenumber $\bar{\nu }$.

Transient hole-burning results are summarized in Fig. 3. In the hole-burning curve in 3a an absorbance change ${\Delta} $A of 1.6 was observed. The spectral hole could be fitted to a Lorentzian line shape and a hole-width of 690 ± 10 kHz was observed for this deep hole (94%) at an instrumentally limited readout delay of 114 $\mu $s. It is noted that this width is to some extent limited by the laser linewidth/ jitter (∼200 kHz). As follows from Fig. 3(c), the hole decays significantly faster than the excited state. Both decays fit very well to a single exponential function and lifetimes of $\tau $_hole = 0.77 ± 0.03 ms and $\tau $_ex =2.34 ± 0.01 ms were obtained for the hole decay and the excited state lifetime, respectively. The hole lifetime is just about 1/3 of the excited state and this is indicating relatively fast excitation energy transfer within the excited state lifetime. This can be expected because of the relatively high Sm²⁺ concentration of 0.5% in the employed crystal. For the very deep spectral holes (>90%) close to 50% of the ions resonant with the laser frequency are in the excited state after the burn pulse. It is important to realise that for energy transfer between ions that are in perfect resonance, i.e. 100% overlap of the homogenous linewidth, no hole decay would result but the wavefunctions would still be subject to dephasing. It is also important to realise that the relative concentrations of ions that are in perfect resonance is very low and approximately given by the ratio of homogeneous to inhomogeneous broadening ${\mathrm{\Gamma }_h}/{\mathrm{\Gamma }_{inh}}$. However, it is possible that perfectly resonant or near-perfectly resonant ions are still relatively close to each other in sub-domains of the crystal. In contrast, for resonant energy transfer between ions for which the homogeneous line shape just partially overlaps and for phonon-assisted non-resonant energy transfer to ions within the 7.65 GHz inhomogeneous distribution with no direct overlap of the electronic line shape (and hence need phonon assistance for the transfer), the hole depth will decrease with the transfer and the former leads to broadening as well. From the hole decay a lower limit for the average excitation energy transfer rate of k_ET = 872 s⁻¹ was deduced.

 

Fig. 3. Spectral hole-burning with E||c in the ⁷F₀→⁵D₀ transition of BaFCl:Sm²⁺ at 2 K. In a) the timescale for the burn and the readout pulses is shown for the transient hole-burning experiment. The timing of the laser frequency (blue dashed trace) and the pulse gating (black dashed line) are schematically indicated. The AOM amplitude, and consequently the light intensity, during the amplitude of the readout pulse was reduced by about a factor of 20 compared to the burn pulse. The red trace shows the transmitted light intensity after the sample. In b) the hole is shown in absorbance (as calculated from the transmission spectrum) and c) compares the hole-depth decay (blue solid squares fitted by a single exponential) with the excited state decay (red data points plus exponential fit).

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We note that no persistent (or longer timescale) hole-burning was observed despite the presence of the hyperfine splitting of the ⁷F₀ ground state for the ¹⁴⁷Sm and ¹⁴⁹Sm isotopes that would allow for the redistribution of ground state population. This is likely because the excitation laser light was polarized linearly parallel to the c-axis i.e., not carrying, and hence not transferring, any angular momentum.

In Fig. 4 some 2-pulse photon echo (2PE) and stimulated photo echo (SPE) experiments are illustrated. We note here that the shown pulse sequence for the SPE is not ideal as it should be a $\pi /2$, $\pi /2$, $\pi /2$ sequence. Nevertheless, the used pulse sequence still afforded a strong SPE signal and at the same time still gave the 2PE signal so that the echo decay could be directly compared in the same experiment. In fact, inspection of Fig. 4(a) reveals that the FID-stretched excitation pulse profiles partially merge with the echo pulses, which is indicative of early stages of formation of a McCall-Hahn soliton [22]. We have also conducted SPE experiments with a more ideal pulse sequence and the 2PE still occurred. It is evident that the optically dense medium facilitates a very high echo efficiency in agreement with earlier observations in other systems [23–25]. As can be seen in Fig. 4, after the first pulse FID is discernible and all three pulses show spectral hole-burning during their short durations on the low microsecond timescale. Interestingly, secondary, and tertiary i.e., multiple echoes, are observed for both the 2PE and SPE. For example, in Fig. 4(a) the secondary and tertiary echo for the 2PE were observed at ∼51 and ∼68 $\mu s$ i.e. at ∼2${\times} $ and ∼3${\times} $ ${\tau _{1 - 2}}$. The dependence of the echo decay in the stimulated photon echo (SPE) as a function of three delays $\tau $_2-3 is shown in Fig. 4(b) and in Fig. 4(c) the echo decay time as a function of the delay $\tau $_2-3 is shown. A fit to the simple exponential function given in Eq. (6) was used to obtain these decay times, where T₂ is the transversal relaxation time, which is approximately equal to the pure dephasing time T₂’ since the excited state lifetime is substantially longer.

From T₂ we can then also calculate the homogenous linewidth of the transition. At short delay times a width of ∼16 kHz was observed, and this width broadens to ∼26 kHz after 600 $\mu $s. This broadening is possibly due to the flipping of fluorine 1/2 and chlorine 3/2 nuclear spins in the environment of the Sm²⁺ ions. The amplitude I_echo(0) of the SPE decays quite rapidly with the separation of pulse 2 and 3 and the decay can be described with a bi-exponential function with rate constants of 1/ 169 and 1/1000 $\mu $s⁻¹ and relative amplitudes of approximately 2.7 and 1, respectively. This is again most likely due to energy transfer as is discussed for the hole decay above. The periodic population grating that is generated by the second pulse and causes the SPE upon the third pulse decays faster than the excited state lifetime if there is excitation energy transfer. It can be expected that the energy transfer is dispersive because of the distribution of the donor-acceptor pairs within the crystal lattice. It is possible that the initial fast decay of the SPE amplitude is due to energy transfer between perfectly (or near perfectly) resonant ions in sub-domains of the crystal which leads to a decay of the periodic population grating whereas it does not affect the hole-depth as discussed above. It is possible that there are some other mechanisms that lead to the relatively fast decay of the SPE amplitude. Importantly, the decay of the 2PE and SPE after the second and third pulse are on the shorter timescale that reflects the homogeneous linewidth of the ensemble of ions that produce the echoes.

 

Fig. 4. (a) Two-pulse photon echo (2PE) and stimulated photon echo (SPE) in the ⁷F₀-⁵D₀ transition of BaFCl:Sm²⁺ (0.5%). (b) SPE decay as a function of the separation between pulses 1 and 2, $\tau $_1-2, for three delays of pulse 3 $\tau $_2-3. (c) Dependence of T₂ (black data points) and corresponding homogeneous linewidth Γ_h (blue data points) on pulse separation time $\tau $_2-3.

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Results showing slow light generated by spectral hole-burning are summarized in Fig. 5. Figure 5(a) shows the 1.25 $\mu $s delay of a 2.08 $\mu $s Gaussian pulse by a ${\Delta} $A∼1.6 spectral hole that showed a directly measured hole width of 690 kHz. The latter was affected by the laser line width/jitter of about 200 kHz and time-dependent hole broadening (since the hole could only be measured with a 147 $\mu $s delay), so the effective hole width was most likely in the vicinity of 480 kHz. A calculation by the linear filter theory indicated a width of 470 kHz in accord with this estimate. The 1.25 $\mu $s delay corresponds to a group velocity v_G of ∼4000 m/s (v_G ∼5 mm/1.25 $\mu $s). In Fig. 5(b) the delayed pulse is shown for five different probe pulse timings (probe pulse delay after burn pulse). Since the hole decays, the pulse delay can be expected to decrease as well. The dependence on the probe pulse timing is summarized for more data points in Fig. 5(c) together with a linear filter calculation that assumes a constant hole width and the measured hole depth decay (as discussed above) with $\tau $_hole = 0.77 ms. It is obvious that the calculation underestimates the dependence somewhat and this is most likely due to the broadening of the spectral hole by near-resonant energy transfer to ions with slightly shifted transition energies so that the homogenous linewidth still overlaps. Table 1 displays calculated valued based on the linear filter theory and estimates of the hole width with increasing time are shown in the last column.

 

Fig. 5. Slow light and slow light delay dependence. a) Pulse delay with an initial OD change of ${\Delta} A$=1.6 and a probe pulse timing of 15 $\mu $s after the burn pulse. Input pulse width 2.08 $\mu $s; output pulse width 2.8 $\mu $s; delay is 1.25 $\mu $s (25 $\mu $s burn pulse) b) Probe pulse delay for a few different probe pulse timings c) Summary of probe pulse timing dependence of pulse delay.

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Table 1. Observed and calculated pulse delays as a function of probe pulse timing (delay of reference pulse with respect to burn pulse).^a

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4. Conclusions

At this point it may be of interest to discuss the spectroscopic parameters of Sm²⁺ in view of applications for optical quantum memories and quantum repeaters [26]. Preserving quantum correlations carried by the stored/retrieved photons hinges on maximising the ratio between the observed decoherence time versus the largest physically achievable decoherence time in the same electronic transition i.e. a first figure of merit FOM₁ = T₂/(2$\tau $_rad). Another useful figure of merit is the maximum number of parallel frequency- or time-domain bins, defined as the ratio between the inhomogeneous line width and the short-time homogeneous line width, FOM₂ = $\mathrm{\Gamma }$_inh/$\mathrm{\Gamma }$_hom, where $\mathrm{\Gamma }$_hom∼1/$\pi $T₂. At the same time, to facilitate interaction with freely propagating light beams, the same resonantly absorbing material should also offer sufficiently large optical depth, $\alpha L$. The photon echo-based storage schemes typically require moderate optical depths, in the range, $\alpha L$ ∼ 1–3, while techniques based on the formation of solitons require substantially larger values, $\alpha L$ > 5.

Ideally, one would strive towards maximizing the FOM₁, while, simultaneously, adjusting the FOM₂ and $\alpha L$ to suitable values, e.g. by tuning the host crystal composition and/or concentration of the ions. The latter would imply, however, that any potential contribution to the pure dephasing rate from the electron-phonon interactions and from the ion-ion interactions remain negligibly small. Even though ion-ion interactions may be alleviated in some cases by applying an external magnetic field, in reality, the above three requirements appear poorly compatible. Eu³⁺ ions doped in Y₂SiO₅ are known to possesses f-f transitions with exceptionally slow decoherence, FOM₁ ∼ 0.04.²⁶ On the other hand, because f-f transitions have relatively small oscillator strength compared to that of the d-d transition in, for example, ruby, reaching high $\alpha L$ values often requires considerably higher ion concentrations and/or much longer optical path lengths. It is noted though that d-d transitions are in general subject to larger inhomogeneous broadening as d-electron levels interact more strongly with the environment compared to f-electron levels, impacting on the peak absorption cross section. However, this is not the case, for example, with the R-lines in Czochralski grown rubies where the inhomogeneous broadening of 1.2 GHz is comparable to the one of rare earth ion doped systems. For example, observation of self-induced transparency (SIT) in an erbium-doped medium requires optical wave guides with long interaction length, L > 1 m [27], while in a ruby crystal this regime is readily achieved with L < 1 cm. Furthermore, propagation of guided waves could be adversely affected the nonlinear Kerr effect and also because of random orientation of the ions’ transition dipoles in an amorphous host such as glass. In such context, Sm²⁺, being isoelectronic to Eu²⁺, could potentially offer exceptional advantages. Firstly, due to vanishing magnetic moments of the involved levels (J = 0), the decoherence processes in Sm²⁺-doped crystals are relatively insensitive to high ion concentrations. Secondly, Eu³⁺ displays a significant electric quadrupole splitting of the ⁷F₀ ground state, which, upon repeated optical excitation, results in long-lived non-equilibrium population distribution between the ground state hyperfine levels. In contrast, such accumulative effects are much less prominent in the BaFCl:Sm²⁺, thus allowing the current system to behave as a long coherence time and high optical depth two-level absorber.

The present work yielded FOM₁ and FOM₂ values of ∼0.005 and ∼5${\times} $10⁵ for the ⁷F₀-⁵D₀ transition in BaFCl. In comparison, a FOM₁ value of ∼0.04 (see above) and a FOM₂ value of ∼5${\times} $10⁶ were reported for the same transition for the Y₂SiO₅:Eu³⁺ system [26]. Although the values for BaFCl:Sm²⁺ are approximately 1 order of magnitude lower compared to the Y₂SiO₅:Eu³⁺, there is much scope to improve these figures with modifying or changing the host material and/or using samples enriched with nuclear spin free isotopes.

In conclusion, we have demonstrated spectral hole-burning based slow light effects and, for the first time for the Sm²⁺ ion in the solid state, 2PE and SPE measurements. Broadening by spin-flipping and excitation energy transfer is observed. Importantly, the echo efficiencies are very high pointing to potential applications of the present material, or similar materials doped with Sm²⁺, in data storage applications.