We report on the observation of slow light induced by transient spectral hole-burning in a solid, that is based on excited-state population storage. Experiments were conducted in the R1-line (2E←4A2 transition) of a 2.3 mm thick pink ruby (Al2O3:Cr(III) 130 ppm). Importantly, the pulse delay can be controlled by the application of a low external magnetic field B||c≤9 mT and delays of up to 11 ns with minimal pulse distortion are observed for ~55 ns Gaussian pulses. The delay corresponds to a group velocity value of ~c/1400. The experiment is very well modelled by linear spectral filter theory and the results indicate the possibility of using transient hole-burning based slow light experiments as a spectroscopic technique.
© 2012 Optical Society of America
The generation of slow light has attracted a great deal of attention over recent years [1–4]. Slow light is characterized by a low group velocity vg that is much smaller than the velocity of light in vacuum c. The group velocity of a light pulse propagating through a medium is given byEq. (2), a refractive index that changes rapidly as a function of frequency will lead to a significant enhancement of the group index and hence to a large change in the value of the group velocity vg. It is noted here that if dn/dω is negative, then the light propagation may become superluminal (fast light). One possibility to achieve vg«c is when the absorbance in a medium changes dramatically over a very narrow frequency range. For example, if one can induce a narrow transparency window at wavelength λ in a strongly absorbing medium, then ng will be vastly different from n at λ as predicted by the Kramers-Kronig relations. Such transparency windows can be obtained by different means as is discussed below. The growing interest in slow light stems from its many potential applications in variable optical delay lines, optical data storage, all-optical signal processing, high-precision spectroscopy and non-linear optics [1–6]. Specific applications include the enhancement of non-linear processes by factors of up to 10,000 by employing slow light waveguides, the improvement of the operation of optical switches, the storage of the quantum state of light for a sufficiently long time to enable quantum operations, quantum operations based on the extended interaction of two slow pulses with the same group velocity, and optical memories that temporarily store data in an all-optical router. It is of particular interest that suitable solid-state systems are identified for these applications.
Slow light experiments reported so far are mostly based on electromagnetically induced transparency (EIT) (see for example [7–9]) and coherent population oscillations (CPOs) [10,11], with the latter being critically discussed by some researchers [12,13]. Bigelow et al reported the observation of slow light in ruby based on coherent population oscillations at room temperature . However, Zapasskii and Kozlov  and Selden  have argued that the observed effects can well be accounted for by pulse distortion in a saturable absorber and that a reduction in group velocity may not need to be invoked. Importantly, Selden proposed a necessary condition for unambiguous demonstration of slow light, which consists in the requirement that pump and probe beams are independent, i.e. the beams do not interfere with each other.
There are also reports where persistent spectral hole-burning (PSHB) was employed [14–18]. Recently, it has been pointed out that PSHB may be advantageous for the generation of slow light [19–21]. Electronic transitions in the solid state suffer from inhomogeneous broadening due to imperfections in the crystal lattice. Because each optical centre has a (slightly) different environment, transition frequencies of a specific electronic origin are spread over a relatively large frequency range compared to the homogenous linewidth. Spectral hole-burning can overcome the inhomogeneous broadening. PSHB is a frequency selective bleaching technique that removes a subset of optical centres within the inhomogeneously broadened absorption line at the laser frequency for time periods longer than the excited state lifetime . This results in a dip due to depletion of the ground state at the laser frequency. PSHB can be classified as photochemical hole-burning where the photoexcited centre undergoes some photochemistry, and non-photochemical hole-burning that is based on slight rearrangements of host-guest interactions upon photoexcitation. Also, population redistribution within long-lived spin levels of the ground state, in particular in rare earth systems, are classified as PSHB by some researchers.
In the present work we demonstrate the generation of slow light in pink ruby (130 ppm) by transient spectral hole-burning based on excited state population storage where spectral hole decays within lifetime of excited state. Importantly, we apply indeed individual burn and probe pulses that are separated in time. Ruby (Al2O3:Cr(III)) has been an archetypal system in the development of optical spectroscopy of impurity ions in insulators over the last two centuries. In particular the so-called R-lines (2E←4A2 transitions) have been rigorously investigated (see  and references therein). Figure 1 shows a schematic energy level diagram and the transitions used for the present work.
The 4A2 ground state and the 2E lowest-excited state are split by the combined action of the trigonal ligand field component and spin-orbit coupling, resulting in splittings of 11.4 GHz and 29 cm−1 respectively. In a magnetic field parallel to the crystal c axis, B||c, the Kramers’ doublets are subject to a first-order linear Zeeman splitting. In the experiments described below a spectral hole was burnt into the R1( ± 3/2) transition at around 693.6 nm in zero field and in B||c. In high quality crystals the inhomogeneous width of the R1 transitions can be as narrow as ~2 GHz. Since only low magnetic fields were applied (<10 mT) the Zeeman splitting is much less than this width and hence the laser is in resonance with both the −3/2→-1/2 and the + 3/2→ + 1/2 transitions. Upon excitation into the lowest-excited state, the system radiatively decays back to the ground state with a lifetime of ~3.5 ms and a quantum efficiency of close to unity. In zero field, this decay occurs to both spin levels in the 4A2 ground state and hence could lead to a build up of population in the ± 1/2 level as the spin-lattice relaxation time at 2.5 K is ~200 ms. However, for rubies with a concentration of >10 ppm rapid cross-relaxation between the resonant and non-resonant ions prevents the build up of the ± 1/2 level for the resonant ions . In a magnetic field B||c, pseudo thermalization between the −1/2 and + 1/2 Zeeman levels in the excited state can occur via spin-lattice relaxation and cross-relaxation between the two levels. We note here that, again, at 2.5 K the former is relatively slow, occurring on a time scale of ~7 ms, but is subject to a very strong temperature dependence. Cross-relaxation depends on the level of excited state population and is more significant for concentrated rubies. The system then decays to the various split spin levels in the ground state on the 3.5 ms time scale and the depleted ground state spin level is rapidly replenished by spin lattice and cross-relaxation where the latter is slowed down by the application of an external magnetic field B||c.
Transient spectral hole-burning was first observed by Szabo in 1974 for the R lines in ruby . We note here that for very low concentration rubies holes can display a long lived component in magnetic fields due to population storage in ground state spin levels on a time scale of 200 ms (spin-lattice relaxation time at 2 K)  but for the present work a relatively concentrated crystal of 130 ppm chromium(III) was used where no build-up of spin level population in the ground state of the resonant ions can occur due to rapid cross-relaxation to non-resonant ions and hence holes decay with the excited state lifetime. This is clearly defined as transient spectral hole-burning.
In hole-burning experiments the hole width is given by twice the homogeneous linewidth, power broadening and the laser linewidth (~1 MHz for this work). In a 130 ppm ruby the homogenous line width mostly determines the hole width. The homogeneous linewidth of the R1 line in ruby is dominated by fast dephasing due to indirect Cr-Cr electron spin flipping even down to concentrations of 20 ppm . This dephasing source can be suppressed by the application of large magnetic fields B||c and experiments have shown that the hole width is non-linearly dependent on the magnetic field strength, varying from tens of MHz at zero field to ~20 KHz at 3.8 T for a 23 ppm ruby . At high fields, the homogeneous linewidth is mostly determined by Al nuclear spin flipping since most chromium(III) ions are in the 4A2(−3/2) level at temperatures below 2.5 K. The dependence on the magnetic field strength was already observed in the first report of a photon echo in ruby (50 ppm), in particular a field B||c of at least 5 mT had to be applied to observe an echo . This requirement is of course based on the narrowing of the homogeneous linewidth. More recent studies were reported in Ref . and the effect of Al spin flipping on the photon echo has been modeled in Ref .
At low fields the homogeneous linewidth is given by a complex interplay between the electronic and nuclear spin flipping . In a 20 ppm ruby the homogeneous linewidth is about 20 MHz in zero field and <1 MHz in B||c = 11 mT . In the 130 ppm ruby employed for the present work, dephasing due to electron spin-spin flipping is more pronounced due to the higher chromium(III) concentration and the hole width varies from 88 to 44 MHz from zero field to B||c = 9mT. Naturally, it is possible to obtain a significantly narrower hole width by increasing the magnetic field strength. However, this would require the adjustment of the laser wavelength as the transition then would shift significantly. For applications it may be advantageous to control the pulse delay by the application of an external magnetic field only without having to adjust the laser frequency.
The pink ruby crystal (130 ppm Cr(III) concentration) used in the experiments of the present work was grown by the horizontal directed crystallization method (also called Bagdasarov method) and was obtained from Morion Company Brighton, MA 02135, USA. The crystal was orientated by a Laue x-ray camera in backscattering geometry, cut perpendicular to the crystal c-axis to 2.3 mm thickness and then polished with different grades (down to 1/10 micron) of diamond paste.
The crystal was mounted on the cold finger of a closed-cycle refrigerator (Janis/Sumitomo SHI-4.5) by imbedding it with copper grease (Cry-con). The laser light propagated along the crystal c-axis (α-polarization) and the magnetic field supplied by two external Helmholtz coils was applied in the longitudinal direction, B||c. For high-resolution transmission spectroscopy and hole-burning experiments a free running diode laser (Hitachi/Opnext HL6738MG) mounted in a thermoelectric mount (Thorlabs TCLMD9) was used and the injection current was controlled by an ILX Lightwave LDX-3620 ultra-low noise current source. The laser frequency was modulated via the injection current by a triangular ramp at 2500 Hz, provided by an arbitrary waveform generator (Stanford Research Systems DS345) for these experiments. In case of hole-burning, typically a burn period of ~1 ms was followed by a rapid readout period of 400 μs. The slow light experiments were conducted by using an external cavity diode laser (Toptica DL110) locked to a 1.5 GHz Fabry-Perot interferometer (Thorlabs SA200-5B) by means of a digital laser controller unit (Toptica Digilock 110 Feedback Controlyzer). Some of the hole-burning experiments were also conducted using this latter laser system by direct modulation of the injection current at a rate of 500 Hz. For the pulse generation in the slow light experiments the laser beam was modulated by an acousto-optic modulator (AOM) Isomet 1205C-1 and its radiofrequency supply was gated by Tektronix AFG3102 arbitrary waveform generators. The setup for the slow light experiment is schematically illustrated in Fig. 2 . Burn pulses of 0.25 to 2 ms and probe pulses of ~50 ns were employed. The probe pulse was delayed in the range of 10 to 250 μs with respect to the falling edge of the burn pulse. To minimize further changes of ground and excited state populations a power of only 0.01 mW was used for the probe pulse; this corresponds to 3% of the power of the burn pulse (1.65 mW) and to ~0.007% of the energy of the burn pulse. In order to ensure that the system was fully thermalised, the pulse sequence was applied at a low repetition rate of 10 Hz. The laser light was tightly focused onto the 2.3 mm crystal in order to achieve a high level of excited state population (saturation).
In Ref . a theory was developed that describes how the shape of a probe pulse changes when it propagates in a hole-burning medium; in the present paper we apply this theory to slow light generated by transient hole-burning that is based on population storage in the excited-state, i.e. basically two-level saturation. In particular, a burn pulse creates a deep spectral hole in a strongly absorbing medium, and subsequently the delay is measured by employing a much weaker probe pulse well within the lifetime of the excited state, i.e. within the lifetime of the population storage. If the energy and amplitude of the probe pulse is low, such that the probing process does not cause significant changes in the population, then the interaction of the probe pulse with the hole-burning medium can be described within the framework of linear response.Eq. (6) :Eqs. (1) to (6) were implemented into a Matlab code, where the transmission spectrum, T(ω), with and without hole-burning is calculated using experimental parameters i.e. the inhomogeneous width, the experimentally determined hole-width, the initial absorbance at the burn wavelength and the hole-depth. The hole shape in these calculations is approximated by a Gaussian. Also, the incident probe pulse is well approximated by a Gaussian with an experimentally determined width and this information is used to calculate the shape of the probe pulse in the frequency domain. The complex frequency-domain amplitude response function is evaluated using the calculated transmission spectrum, T(ω) and together with Ep(ω) yields the frequency-domain amplitude of the probe pulse after the medium. Employing an inverse FFT we then obtain the calculated pulse shape in the time domain. We note here that the hole width in these calculations is an empirical input parameter and the model is not attempting to incorporate, in an ab initio, way the magnetic field dependence.
4. Results and discussion
Figure 3 displays the 2.4-K absorption (Absorbance = A = log10(I0/I)) spectrum in the region of the R1 lines (~693.6 nm) in α-polarization for a 2.3 mm thick Bagdasarov pink sapphire (Al2O3:Cr(III) 130 ppm) employed for the slow light experiments discussed below. The inhomogeneous width of this crystal is ~1.9 GHz, i.e. significantly narrower than for flame-fusion (Verneuil) grown crystals. The latter display inhomogeneous widths of ~10 GHz . It is noted here that macroscopic strain broadening plays an important part in ruby [32,33]. Since a high optical density is advantageous for the generation of slow light via hole-burning, it appears that the choice of the crystal growth method is very important. The low inhomogeneous width leads to the R1( ± 3/2) and R1( ± 1/2) lines of the stable isotopes being resolved; this has already been reported for Czochralski grown ruby by fluorescence-excitation spectroscopy .
Figure 4 shows transmission spectra of the crystal described in Fig. 3 with, Ib, and without, Inb hole-burning in the R1( ± 3/2) line at ~693.58 nm in α-polarization at 2.4 K (Ib and Inb denote transmitted intensity with and without burn pulse, respectively). Inb was measured in pseudo-steady-state “burst” mode, i.e. repetitively, a ~1 ms burn period is followed by a rapid 400 μs readout period i.e. well within the lifetime (3.5 ms) of the excited state . The hole-burning spectrum ΔA is calculated from the two transmission spectra by employing the relationship ΔA = log10(Inb/Ib). Burning a spectral hole into the R1( ± 3/2) line yields a narrow spectral side hole in the R1( ± 1/2) line. As observed in earlier work (see for example Refs [24,35].), burning of the R1( ± 3/2) hole leads to a decrease and increase of the entire inhomogeneously broadened R1( ± 3/2) and R1( ± 1/2) lines, respectively. This is caused by rapid cross-relaxation between the resonant and non-resonant ions. Interestingly, cross-relaxation also happens between the resonant 52Cr(III) ions and the non-resonant 50Cr(III), 53Cr(III) and 54Cr(III) isotopes. In particular, it is somewhat surprising to observe that there is cross-relaxation between 52Cr(III) and 53Cr(III) as the latter has a nuclear spin of 3/2 that leads to hyperfine splitting of the 4A2 and 2E levels .
In (low) magnetic fields B||c, the central hole burnt into R1( ± 3/2) is accompanied by side holes at ± (3g||gs-g||ex)μBB since the + 3/2→ + 1/2 and −3/2→-1/2 selection rule applies. The properties of these side holes has been previously evaluated and discussed in great detail . The occurrence of these side holes requires some thermalization (e.g. spin lattice relaxation and/or cross-relaxation) between the split excited state and ground state spin levels.
Slow light experiments are illustrated in Figs. 4 and 5 for the 2.3 mm pink Bagdasarov grown ruby (130 ppm). In these experiments a burn pulse of 0.75-1 ms was followed by a much weaker 55-57 ns probe pulse delayed by 10 to 250 μs after the falling edge of the former. Figure 5 shows the 10.8 ns experimental pulse delay after a burn pulse of 750 μs in B||c = 9 mT together with the pulse shape calculated according to Eq. (6), where the latter yields a delay of 10.7 ns For the simulation empirical parameters were used only (ΔA = −1.09; 57 ns Gaussian probe pulse width; initial absorbance A = 1.53; hole width = 44 MHz). The observed delay corresponds to a group velocity value of ~c/1400. It is noted here that, in general, Eqs. (3-6) also predict a change in the pulse shape but in the current experiments this effect was too little to notice any significant distortion within the experimental accuracy. The probe pulse as observed and calculated in the absence of a burn pulse is also shown in Fig. 5, serving as a reference. The inset of Fig. 5 displays typical hole-shapes obtained under similar conditions as used for the slow light experiments. The readouts of the hole are delayed by 280 μs since the laser frequency cannot be scanned above this rate. Due to the decay of the initially excited excited state by excited-state spin-lattice and cross-relaxation and deactivation to the ground state (3.5 ms), the hole depth in these spectra is lower than for the corresponding pulse delay experiments of Fig. 5, which were measured with a 10 μs delay only. It is important to note here that in the slow light experiment, ΔA is very well defined by the probe pulse height ratio with and without a burn pulse. It appears that the hole width is not much larger for deep holes compared to relatively shallow holes, confirming that fast spectral diffusion based on Cr-Cr electron-spin-electron-spin flip-flops in the environment of an excited centre is predominantly responsible for the observed hole-width in this relatively concentrated crystal. Figure 6 demonstrates the effect of a low magnetic field B||c on the pulse delay; since the hole width in ruby is strongly magnetic field dependent, as has been discussed above, a significantly larger delay is observed in a low magnetic field B||c compared to the zero field experiment. As a consequence, we can literally slow light down, i.e. control the delay of a light pulse, by the application of a weak external magnetic field. The calculated pulse shapes shown in the lower panel of Fig. 6 reproduce the observed delays within the experimental accuracy. We note here that the delay can be controlled by varying the flux of the magnetic field, B||c, because the hole width is a function of the field and changes from 88 MHz to 44 MHz from zero field to B||c = 9 mT (see above). It is noted here that this dependence is not linear. Naturally, in high fields the laser frequency would need to be tuned as the transition will shift more than the inhomogeneous width. The low magnetic field allows the control/switching of the light without having to change the carrier frequency of the laser. As follows from Figs. 5 and 6, very good signal-to-noise ratios were achieved and in the present experiment we could readily detect delays <0.5 ns.
The present work reports slow light generated by transient hole-burning in the solid state based on excited state population storage. Significant pulse delays are observed upon burning transient spectral holes in the R1( ± 3/2) line of 52Cr(III) in pink sapphire in zero field and low magnetic fields B||c. Since the hole-width in ruby is strongly magnetic field dependent, due to slowing down of electron-spin-electron-spin interactions, narrower spectral holes can be burnt in a field compared with zero field. This enables a significant increase in the pulse delay upon spectral hole-burning in a magnetic field (as is predicted by the Kramers-Kronig relations), i.e. light is slowed down by the application of an external magnetic field, as well as the fine tuning of the group velocity by changing the strength of an external magnetic field. In the present work we employed a relatively high concentration of chromium(III) of 130 ppm. Lower chromium(III) concentrations will facilitate much narrower hole-widths in magnetic fields and hence much larger delays. We are currently conducting such experiments on nominally chrome-free sapphire rods.
One parameter of particular importance for storage of the quantum state of light is the overall optical transmission loss. In our experiment the loss comprised residual absorption in the sample as well as reflection/scattering by the crystal, cryostat windows and some other optical elements. We estimate the minimum residual absorption loss to be ~40% of the input photons, whereas the corresponding minimum reflection/scattering loss was typically 5-10%. The absorption losses could be substantially lowered by burning deeper and higher contast spectral holes, which may be achieved e.g. by using higher laser fluence or by using waveguides or other side-way hole-burning geometry . Another potential advantage of our experiment relative to EIT is that in our case we can perform direct comparison to a simple quantitatively accurate theoretical model. Because the linear response theory does fully account for the propagation of the pulse in the hole-burning medium, our approach may be used to further optimize the maximum delay versus absorption losses, pulse shape distortions and other relevant parameters. One may also point out that related studies were performed in the past regarding persistent spectral hole-burning holography , including controlled pulse delays by scattering from spectral gratings . Also, the spectral modification and temporal reshaping of a narrow-band light pulse through a still narrower spectral hole was discussed in the past .
The present experiments also highlight the potential of slow light experiments as a spectroscopic technique and show quantitative correspondence between the linear response theory and the experiment within the experimental accuracy. The temporal shapes could potentially be used to determine spectral hole shapes more accurately than direct spectral measurements.
For example, spectral diffusion can easily be measured since the laser frequency does not have to be scanned rapidly; in practice this would mean that the probe pulse would be applied at several delays. Since the delay is a function of A, ΔA and the hole-width, and ΔA is very well defined by the probe pulse height ratio with and without a burn pulse, the hole-width as a function of delay is readily determined. In general, the pulse delay measurement is a much simpler way of determining hole-widths, e.g. a major advantage of the present technique in studying spectral diffusion is that a snapshot of the hole shape can be measured at a specific time.
For applications such as storage of quantum states of light, transient hole-burning may allow for a higher refresh rate (determined by the excited state life time) than persistent hole-burning (determined by ground electronic energy level life times).
Ivana Carceller thanks UNSW Canberra for a postgraduate research scholarship. Hans Riesen acknowledges the Australian Research Council for supporting his research program. Aleks Rebane thanks the AFOSR for financial support.
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