Coherently refreshed acoustic phonons for extended light storage
Birgit Stiller, Moritz Merklein, Christian Wolff, Khu Vu, Pan Ma, Stephen J. Madden, Benjamin J. Eggleton
CCoherently refreshed acoustic phonons for extended light storage
Birgit Stiller , , , ∗ , † , Moritz Merklein , , ∗ , Christian Wolff , KhuVu , Pan Ma , Stephen J. Madden and Benjamin J. Eggleton , blanc Institute of Photonics and Optical Science (IPOS), School of Physics, University of Sydney, Sydney, NSW, 2006 Australia. The University of Sydney Nano Institute (Sydney Nano), University of Sydney, Sydney, NSW, 2006 Australia. Max-Planck-Institute for the Science of Light, Staudtstr. 2, 91058 Erlangen, Germany. Center for Nano Optics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Laser Physics Centre, RSPE, Australian National University, Canberra, ACT 0200, Australia. ∗ These authors contributed equally to this work. † [email protected] waves can serve as memory for optical information, however, acoustic phonons in the GHzregime decay on the nanosecond timescale. Usually this is dominated by intrinsic acoustic loss dueto inelastic scattering of the acoustic waves and thermal phonons. Here we show a way to counteractthe intrinsic acoustic decay of the phonons in a waveguide by resonantly reinforcing the acousticwave via synchronized optical pulses. This scheme overcomes the previous constraints of phonon-based optical signal processing for light storage and memory. We experimentally demonstrate on-chip storage up to 40 ns, four times the intrinsic acoustic lifetime in the waveguide. We confirmthe coherence of the scheme by detecting the phase of the delayed optical signal after 40 ns usinghomodyne detection. Through theoretical considerations we anticipate that this concept allowsfor storage times up to microseconds within realistic experimental limitations while maintaining aGHz bandwidth of the optical signal. The refreshed phonon-based light storage removes the usualbandwidth-delay product limitations of e.g. slow-light schemes. Coupling optical and mechanical waves in cavities,waveguides and nanostructures offers great potential foroptical signal processing [1–8], in particular for delaylines and storage schemes [9–19]. One particular optome-chanic interaction with GHz acoustic phonons is Brillouinscattering, which describes the interaction between opti-cal and traveling acoustic waves [20, 21]. While sponta-neous scattering is initiated by noise [22, 23], and henceis not coherent, stimulated Brillouin scattering (SBS) in-volves a coherent excitation of acoustic phonons withGHz frequency solely by optically forces. It was shownrecently that one can use these acoustic phonons to storeand delay optical signals [9, 17, 19]. The optical infor-mation is resonantly transferred to a coherent acousticphonon and is then transferred back to the optical do-main by a delayed optical retrieval pulse completely pre-serving the phase and amplitude [17] and the wavelengthof the signal [19]. However, these high-frequency acous-tic phonons decay exponentially with a lifetime of a fewnanoseconds determined by the material properties atroom temperature. This inherent decay is due to thedamping of the acoustic waves while propagating throughthe material. Therefore, the optical information storedin the acoustic waves is lost and a way of preserving thecoherent acoustic vibration is needed.Here, we introduce and demonstrate a concept to coun-teract the intrinsic acoustic decay of the phonon in awaveguide by resonantly reinforcing the coherent acous-tic phonons via synchronized optical pulses. Instead ofconverting the acoustic waves back to the optical do-main, refresh pulses at the wavelength of the original datapulses transfer energy to the acoustic wave and counter-act the decay. We experimentally demonstrate that in- formation can be stored and retrieved for 40 ns - a timemuch longer than the intrinsic acoustic lifetime of 10 ns- and we confirm that the coherence is preserved in thisprocess by measuring the optical phase after 40 ns via ho-modyne detection. We also experimentally demonstratean increase in readout efficiency for storage times shorterthan the acoustic lifetime. We theoretically explore thelimits of the scheme and demonstrate that within prac-tical limits even storage times up to micro seconds arewithin reach while maintaining a broad GHz bandwidthof the stored optical pulses. This scheme allows the ex-tension of the lifetime of the coherent acoustic phononsand the efficiency of optoacoustic memory, removing pre-vious constraints of phonon-based optical signal process-ing schemes. Most importantly, it decouples the possi-ble delay time from the bandwidth of the stored pulses,which typically limits slow light schemes based on non-linear effects, atomic vapours and cold atoms.The storage concept is based on the coupling of two op-tical waves with a traveling acoustic wave via the effect ofstimulated Brillouin scattering. The acousto-optic cou-pling depends on the overlap of the optical and acousticwaves and the intrinsic photo-elastic material response.The addressed acoustic wave is at Ω =7.8 GHz and thenonlinear gain is in the order of G b =500 W − m − forthe used photonic waveguide made out of As S with across-section of 2.2 µ by 800 nm. Figure 1 shows schemat-ically the principle of storing, coherently refreshing theacoustic phonons and retrieving the delayed optical in-formation. The information of the optical data pulse isinitially transferred to the acoustic phonons by a counter-propagating optical write pulse, offset in frequency by theacoustic resonance frequency of the waveguide ω acoustic = a r X i v : . [ phy s i c s . op ti c s ] A p r a d refreshedacoustic waveoptical data streamwith information optical refreshpulses without informationopticalwritepulse opticalreadpulse optical datanot detectable b e acoustic wave c acoustic wave decayedacoustic wave delayedoptical datastreamopticalreadpulse~ 10 nsup to µstt|A|a|A|a ω Data ω Data ω Refresh ω write ω read ω read ΩΩ ΩΩ
FIG. 1. Concept of the refreshed acoustic memory. a) An optical write pulse converts the information of an optical data streamto an acoustic wave; b) The acoustic wave propagates at a 5 orders of magnitude lower speed in the waveguide and decayswith the acoustic lifetime; c) in normal operation the acoustic wave dissipates and the read pulse cannot sufficiently interactwith the acoustic wave; therefore the information of the optical data is lost; d) to counteract the acoustic decay, optical refreshpulses at ω refresh = ω data transfer energy to the acoustic phonons; e) an optical read pulse converts the information back to theoptical domain and the delayed optical information exits the waveguide. ω write - ω data =7.8 GHz (Fig. 1a and b). The acousticresonance frequency relates to the acoustic velocity V A ,the effective refractive index n eff and the pump wave-length λ Pump as Ω = n eff V A λ Pump . The acousto-optic couplingnot only requires energy conservation but also phase-matching as k acoustic = k write - k data . An efficiency ofup to 30 % can be reached depending on the bandwidthof the optical pulse [17]. This initial storage process isa Anti-Stokes process because the data wave looses en-ergy to the acoustic wave. Without further action, theacoustic phonons decay after several nanoseconds (Fig.1b) due to the intrinsic dissipation of the material. Aread pulse at ω read = ω write cannot efficiently couple tothe acoustic grating and the information is lost (Fig.1c). To reinforce the acoustic vibration, we use opti-cal refresh pulses (Fig. 1d) with the same frequency andpropagation direction as the data pulse, ω refresh = ω data .Herewith, the refresh pulses are scattered by the exist-ing acoustic phonons - with two consequences: a portionof energy is transferred to the acoustic phonons, whichrefreshes the memory, and pulses with less energy at fre-quency ω write = ω refresh - ω acoustic are backscattered. Thiscan be related to a Stokes process originating from therefresh pulses and the coherent acoustic wave. In order toretrieve the original data, a counter-propagating opticalread pulse at ω read = ω write finally converts the informa-tion stored in the acoustic phonons back to the opticaldomain (Fig. 1e).The refresh process can also be understood in the con-text of coherent heating [24] as the existing acousticphonons are coherently amplified by the refresh pulseswhich satisfy the energy and momentum requirementsfor a Stokes process. It can also be seen as a classi-cal SBS backscattering process, however not initiated bythermal phonons but initiated by a deterministic local-ized seed created through the previous storage process.The refresh pulses do not contain any information butare coherent and synchronized with the data pulse. Thenumber of refresh pulses depends on how long the stor-age is needed and in principle can extend the memory by several orders of magnitudes, fully countervailing theintrinsic exponential decay of the acoustic wave. How-ever, in practice the signal-to-noise ratio (SNR) of theoptical pulses, the dissipation of the material at roomtemperature and the broadening of the acoustic dynamicgrating due to the convolution with finite control pulseslimit the time after which the delayed optical signal canstill be detected.The refreshed optoacoustic memory is implementedin a highly nonlinear As S chip with 2.2 µ m-large ribwaveguides. A simplified experimental setup is shownin Fig. 2. A continuous wave diode laser at 1550 nm isseparated into two branches: one for the write and readpulses and the other one for the data stream and refreshpulses. The write and read pulses with 500 ps duration data stream(amplitudeand phase)write and readpulses Ω AWGSSBIM chalcogenidechip IM da t a L O oscilloscopehomodyne detection PDPD d a t a CW laser1550 nm BP lensed fibresdirect detection . . . data streamto detection OS refresh pulses FIG. 2. Experimental setup for the refreshed optoacousticmemory. SSB single-sideband modulator, IM intensity mod-ulator, AWG arbitrary waveform generator, BP bandpass fil-ter, OS optical switch, LO local oscillator, PD photo diode. -2 0 2 4 6 8 10 1200.020.040.060.08 Original pulse0 refresh pulses4 refresh pulses7 refresh pulses time [ns] i n t en s i t y [ a r b . u .] FIG. 3. Experimental results for the refreshed Brillouin-basedmemory with a read-out after 8 ns (within the acoustic life-time): comparison of the efficiency while using 0, 4 and 7refresh pulses showing a three and five times enhancement,respectively. are carved in by an electro-optic modulator driven byan arbitrary waveform generator. The time distance be-tween them can be adjusted arbitrarily and defines thestorage time in the memory. They are amplified to about20 W peak power and coupled into the chip from one sideby lensed fibers. The other optical branch is firstly up-shifted in frequency by the corresponding Brillouin fre-quency shift, here 7.8 GHz. The frequency shift is im-plemented by a single-sideband modulator. Then a datastream in amplitude and phase is encoded by a secondelectro-optic modulator and a second channel of the ar-bitrary waveform generator. The data pulses are 500 pslong and are amplified to a peak power of about 100 mWand inserted from the opposite site as the write and readpulses into the photonic chip. In order to reinforce theacoustic wave, coherent refresh pulses are sent into thephotonic waveguide, following the data stream. Here, weexperimentally implement the refresh pulses by the samemodulator as the data stream. The pulses are 300 pslong and the peak power is varied to match the appropri-ate pulse area [9, 25], here about 200 mW. The length,peak power and number of the refresh pulses have to beadjusted carefully in order to minimize distortion due tospontaneous Brillouin scattering and interaction with theoptical background of the write and read pulses. Afterpassing through the photonic chip, the data stream is fil-tered by a 3 GHz broad filter to prevent from detectingbackreflections of the write and read pulses at anotherwavelength. Then an optical switch filters out residualrefresh pulses. This optical switch can be made superflu-ous when using the opposite polarization for refreshingthe memory. The detection is done either directly bya photodiode (amplitude) or using homodyne detection(phase). In the latter case, the data is interfered witha local oscillator at the same wavelength and the differ- time [ns] i n t en s i t y [ a r b . u .] -2 0 2 -38 40 42 i n t en s i t y [ a r b . u .] -0.100.1 time [ns] i n t en s i t y [ a r b . u .] -38 40 42-2 0 2 -0.0300.03-0.100.1 a)b) FIG. 4. Refreshed memory for read-out after 40 ns: a) directdetection and b) coherent phase retrieval. ent phases are seen as positive or negative signal on theoscilloscope.As a first experimental proof, we show that the effi-ciency of the Brillouin-based storage increases when theacoustic wave is refreshed (Fig. 2). Therefore, we com-pare the amplitude of the retrieved data at a given stor-age time of 8 ns. Without refresh pulses, the retrievalefficiency is about 4 %. With 4 or 7 refresh pulses, theefficiency can be increased to 10 % and 20 %, respectively.The 7 refresh pulses were sent in with a time delay of 1 nsafter the data pulse with 1 ns time spacing, the 4 refreshpulses at times 1, 3, 5 and 7 ns after the data pulse. Weuse an optical switch to remove residual refresh pulses.However, as an alternative, the refresh pulses could alsobe inserted at orthogonal polarization, such that an op-tical switch is not necessary.The increase of the efficiency allows for a far more im-portant feature which is extending the storage time be-yond the intrinsic acoustic lifetime, which so far limitedthe storage time of the memory to a few nanoseconds.As a proof of principle, we show in Fig. 3 that refreshingthe acoustic phonons enables a storage time far beyondthe acoustic lifetime of about 10 ns in As S , in this case40 ns. In Fig. 3a, an original data pulse (black solidline) is transferred to an acoustic phonon. The latteris refreshed by 39 consecutive refresh pulses which aresub-sequentially filtered out by an optical switch beforedetection. 40 ns after the initial data pulse, a read pulseconverts the information back to the optical domain andwe retrieve our delayed optical pulse (red dashed line).In a second measurement we use homodyne detection toshow that this process is coherent by storing and retriev-ing the optical phase. In this experiment, two opticalpulses with opposite optical phase “0” and “ π ” are sentinto the chip and stored via a counter propagating writepulse. The phase is detected via homodyne detection.After refreshing the memory with 39 pulses, we can de-tect the phase information after 40 ns (Fig. 3b).In order to illustrate the transfer of energy of the re-fresh pulses to the acoustic wave, we show the transmit-ted refresh pulses without the optical switch (Fig. 4). InFig. 4a, the original data pulse and the refresh pulses aredepicted (black solid trace). When switching on the writeand read process(red dashed trace), one can see, thatthe original data is depleted and that the refresh pulsesloose energy which is transferred to the coherent acous-tic phonons and backscattered pulses at frequency ω write = ω refresh - ω acoustic . In Fig. 4b, the refresh pulses havebeen suppressed by an optical switch. As mentioned, thismethod can be improved by using the orthogonal polar-ization, which was not possible in our case, due to highpolarization-depended loss of the photonic chips.Our experimental setup appeared to be limited by thefollowing pre-dominant factors: first, the extinction ra-tio of the optical modulators leads to a non-zero back-ground between the optical pulses, which acts as a seedfor acoustic phonons that do not hold information. Thisultimately limits the detection of the relevant stored in-formation. Second, spontaneous Brillouin scattering canbuild up, initiated by room temperature phonons andamplified by the refresh pulses. A third limitation is theSNR of the retrieved optical pulse in the photodetectionprocess, limited by the electronic noise of the detectorand the oscilloscope. At last, the acoustic dynamic grat-ing broadens with each refresh process due to the convo-lution with refresh pulse with a finite width, which limitsthe detectable signal at the photodiode.While the experimental results demonstrate that thelimits of an unrefreshed Brillouin-based memory can bebeaten, the question arises how long the storage timecan be extended. In other words, how does the SNRevolve over time such that we can still recover the infor-mation. To answer this, we performed a simple analy-sis of the noise accumulation assuming a train of Dirac-shaped refresh pulses (spaced by some time τ ) chosensuch that the acoustic amplitude is kept constant on av-erage. We decompose the acoustic field into the non-fluctuating excitation (the stored pulse including accu-mulated noise) and a fluctuating field caused by thermalexcitations. Both seek to exponentially approach ther-mal equilibrium with the acoustic decay constant α . Arefresh pulse amplifies both fields, adding a snapshot ofthe fluctuating field to the stored pulse. This effectively“resets” the fluctuation field, which is exponentially re- R ead ou t O r i g i na l pu l s e O r i g i na l pu l s e R ead ou t {{ a)b) time [ns] i n t en s i t y [ a r b . u .] i n t en s i t y [ a r b . u .] FIG. 5. Refreshed memory for storage time of 20 ns: a) Orig-inal data pulse with 19 refresh pulses (black solid line); de-pleted and retrieved data (red dashed line) with refresh pulsestransferring energy to the acoustic phonon; b) Original data(black solid line) and retrieved data (red dashed line) withsuppressed refresh pulses by an optical switch. populated ∼ [1 − exp( − αt )]. As a result, the SNR ratioafter n loss-compensating refresh pulses isSNR refreshed ( nτ ) ≈ SNR initial n [1 − exp( − ατ )] . (1)This means that the exponential decay SNR (cid:39) exp( − αt )of the unrefreshed is transformed into a first order alge-braic decay SNR (cid:39) t − . This means that refreshing dra-matically extends the visibility of stored information. Forexample, doubling the initial SNR doubles the practicalread-out time with refreshing, while it only leads to a con-stant extension ln(2) /α without refresh. In reality, therefresh pulses have a finite width and each refresh opera-tion applies a convolution to the stored data [26]. In ourcase, this effectively leads to a dispersion-like broadeningof the dynamic grating without imparing the coherenceor bandwidth of the signal. Assuming that this convolu-tion effect can be reverted (e.g. using chirped pulses [27])and assuming loss-compensating ideal refresh pulses, weestimate that it should be possible to maintained data inour system for at least 350 ns. This is based on the ap-parent SNR of the experiment, which includes significantdetector noise in addition to the thermal acoustic noiseand a constant background due to the finite extinctionratio of the modulator. Therefore, storage times into themicrosecond range are within reach.We demonstrated a way to compensate for the intrin-sic acoustic decay of a coherent acoustic phonon in achip-integrated waveguide. This leads to an increase inefficiency of the Brillouin-based memory and importantlyallows to overcome the limitation in storage time set bythe acoustic lifetime. The acoustic phonons are coher-ently refreshed allowing the storage and retrieval of theoptical phase. This demonstration overcomes the usualconstraint of the bandwidth-delay product and paves theway for long phonon-based light storage. Conservativeestimation promises storage times into the microsecondregime while conserving the large GHz-bandwidth of theoptical pulses. The resulting bandwidth-delay productcan therefore exceed the regime of electromagneticallyinduced transparency (EIT) systems [28, 29] while be-ing fully integrated on a photonic chip. Refreshing theacoustic waves and therefore increasing the efficiency andextending the storage time is relevant for a number ofapplications such as telecommunication networks, opti-cal interconnects and ultimately may be interesting forquantum communication systems. METHODS
Experimental setup.
The laser source, a narrow-linewidth distributed feedback laser at 1550 nm, is splitinto the data/refresh and the control (write, read) pulsearm. The data arm is frequency up-shifted by the Bril-louin frequency shift via a single-sideband modulator.The data, refresh and control pulses are imprinted by twointensity modulators connected to an arbitrary waveformgenerator. The control pulses are amplified by an erbium-doped fibre amplifier (EDFA). The amplified write andread pulses pass through a nonlinear fibre loop whichefficiently suppresses any noise or coherent backgroundpresent from the laser or amplifier, respectively. It also has the effect that it changes the pulse area to ensureefficient coupling between the data and control pulses.After the loop a second EDFA amplifies the pulses again.Bandpass filters (bandwidth 0.5 nm) in both arms min-imise the amplified spontaneous emission from the ED-FAs. The refresh pulses are encoded by the same modu-lator as used for the data pulses. The data/refresh pathleads to one side of the photonic chip, the control pulsepath to the opposite side. Before detection a tunablenarrowband filter ( ≈ Direct detection.
For measuring the amplitude, theoriginal and retrieved data are observed by a 12 GHz pho-todiode at the oscilloscope.
Homodyne detection.
For measuring the opticalphase, the data pulses are interfered with a local oscil-lator (CW) at the same wavelength. The beat signalis sent to a polarisation beam splitter which sends thepaths with different polarization to the two inputs of abalanced photodetector. The polarisation of the localoscillator and the data pulses are controlled such thatthe difference signal of both photodiodes of the balancedphotodetector is maximised.
ACKNOWLEDGEMENTS
This work was sponsored by the Australian ResearchCouncil (ARC) Laureate Fellowship (FL120100029)and the Centre of Excellence program (CUDOSCE110001010). We acknowledge the support of theANFF ACT. C.W. acknowledges funding from a MULTI-PLY fellowship under the Marie Skaodowska-Curie CO-FUND Action (grant agreement No. 713694). [1] Safavi-Naeini, A. H. and Painter, O., “Proposal for an op-tomechanical traveling wave phonon-photon translator,”New J. Phys. , 013017 (2011).[2] Pant, R. et al., “On-chip stimulated Brillouin scattering,”Opt. Express , 82858290 (2011).[3] Shin, H., et al., “Tailorable stimulated Brillouin scatter-ing in nanoscale silicon waveguides,” Nat. Comm. , 536587(2013).[5] Beugnot, J.-C., Lebrun, S., Pauliat, G., Maillotte, H.,Laude, V. and Sylvestre, T., “Brillouin light scatteringfrom surface acoustic waves in a subwavelength-diameteroptical fibre,” Nat. Comm. , 5242 (2014).[6] Van Laer, R., Bazin, A., Kuyken, B., Baets, R., VanThourhout, D., “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. , 346–352 (2016).[8] Li, H., Tadesse, S. A., Liu, Q. and Li, M., “Nanophotoniccavity optomechanics with propagating acoustic waves atfrequencies up to 12 GHz,” Optica , 826–831 (2015).[9] Zhu, Z., Gauthier, D. J., and Boyd, R. W., “Stored lightin an optical fiber via stimulated Brillouin scattering,”Science , 174850 (2007).[10] Chang, D. E., Safavi-Naeini, A. H., Hafezi, M. andPainter, O., “Slowing and stopping light using an op-tomechanical crystal array,” New J. Phys. , 023003(2011).[11] Safavi-Naeini, A. H. et al., “Electromagnetically inducedtransparency and slow light with optomechanics,” Nature , 69–73 (2011).[12] Fiore, V., Yang, Y., Kuzyk, M.-C., Barbour, R., andWang, H., “Storing optical information as a mechanicalexcitation in a silica optomechanical resonator,” Phys.Rev. Lett. , 15 (2011).[13] Jamshidi, K., Preuler, S., Wiatrek, A., and Schneider, T.,“A review to the all-optical quasi-light storage,” IEEEJournal on Selected Topics in Quantum Electronics ,884–890 (2012).[14] Fiore, V., Dong, C., Kuzyk, M. C. and Wang, H., “Op-tomechanical light storage in a silica microresonator,”Phys. Rev. A , 1–6 (2013).[15] Galland, C., Sangouard, N., Piro, N., Gisin, N., andKippenberg, T. J., “Heralded single-phonon preparation,storage, and readout in cavity optomechanics,” Phys.Rev. Lett. , 1–6 (2014).[16] Dong, C.-H., Shen, Z., Zou, C.-L., Zhang, Y.-L.,Fu, W. and Guo, G.-C., “Brillouin-scattering-inducedtransparency and non-reciprocal light storage,” NatureComm. , 6193, doi:10.1038/ncomms7193 (2015).[17] Merklein, M., Stiller, B., Vu, K., Madden, S. J.and Eggleton, B. J., “A chip-integrated coherentphotonic-phononic memory,” Nature Comm. , 574,doi:10.1038/s41467-017-00717-y (2017).[18] Merklein, M., Stiller, B., and Eggleton, B. J., “Brillouinbased light storage and delay techniques,” Journal of Op-tics , 083003 (2018).[19] Stiller, B., Merklein, M., Poulton, C. G., Vu, K., Ma,P., Madden, S. J., and Eggleton, B. J., “Crosstalk-freemulti-wavelength coherent light storage via Brillouin in-teraction,” APL Photonics , 040802 (2019). [20] Brillouin, L., “Diffusion de la lumi`ere par un corps trans-parent homog`ene,” Annals of Physics , 5514 (1990).[23] Gaeta, A. L., and Boyd, R. W., “Stochastic dynamics ofstimulated Brillouin scattering in an optical fiber,” Phys.Rev. A, , 3205 (1991).[24] Garmire, E., Pandarese, F. and Townes, C. H., “Coher-ently driven molecular vibrations and light modulation,”Phys. Rev. Lett. , 160 (1963).[25] Dong, M., and Winful, H. G., “Area dependence ofchirped-pulse stimulated Brillouin scattering: implica-tions for stored light and dynamic gratings,” Journal ofthe Optical Society of America B , 2514 (2015).[26] Santagiustina, M., Chin, S., Primerov, N., Ursini,L., and Th´evenaz, L., “All-optical signal process-ing using dynamic Brillouin gratings,” Sci. Rep. ,doi:10.1038/srep01594 (2013).[27] Winful, H., “Chirped Brillouin dynamic gratings for stor-ing and compressing light,” Opt. Express , 10039–10047 (2013).[28] Longdell, J. J., Fraval, E., Sellars, M. J., and Manson, N.B., “Stopped Light with Storage Times Greater than OneSecond Using Electromagnetically Induced Transparencyin a Solid,” Phys. Rev. Lett. , 063601 (2005).[29] Heinze, G., Hubrich, C., and Halfmann,T., “StoppedLight and Image Storage by Electromagnetically InducedTransparency up to the Regime of One Minute,” Phys.Rev. Lett.111