Table Of ContentSlow light of an amplitude modulated Gaussian pulse in
electromagnetically induced transparency medium
Wenzhuo Tang, Bin Luo, Yu Liu, and Hong Guo∗
CREAM Group, State Key Laboratory of Advanced Optical Communication Systems and Networks (Peking University)
and Institute of Quantum Electronics, EECS, Peking University, Beijing 100871, China
∗
Corresponding author: [email protected]
CompiledJanuary20,2009
The slow light effects of an amplitude modulated Gaussian (AMG) pulse in a cesium atomic vapor are
9 presented. In asingle-Λ type electromagnetically induced transparency (EIT) medium, moresevere distortion
0 is observed for an AMG pulse than a Gaussian one. Using Fourier spectrum analysis, we find that the
0 distortion, as well as the loss, is dominantly caused by linear absorption than dispersion. Accordingly,
2 a compensation method is proposed to reshape the slow light pulse based on the transmission spectrum.
Inaddition,wefindanovelwaytoobtainsimultaneousslowandfastlight. (cid:13)c 2009 OpticalSocietyofAmerica
n
OCIS codes: 270.1670, 270.5530.
a
J
0
2 Recently, slow light has attracted tremendous attention Then,theoverlappedlaserscopropagatethroughthecell
for its potential applications in optical communication. in order to reduce the total Doppler width of the two-
] Group velocity of light pulse can be slowed down us- photonprocess[9].Thebeamsplitter(BS)infrontofthe
h
ing various effects, such as electromagnetically induced cellsplits anappropriateportionofthe probetoPD1as
p
- transparency (EIT) [1,2], double absorption line [3,4], reference,whoseintensityissettobeequaltothatofout-
t
n coherent population oscillations [5,6], stimulated Bril- put when the probe is detuned far off-resonance. Thus,
a louinscattering[7]andstimulatedRamanscattering[8], the background absorption is eliminated and the refer-
u
etc. Among these effects, EIT is the most popular can- ence can be treated as “input”. A 10 cm-long paraffin-
q
didate to experimentally realizeslow light for,e.g., non- coated cesium vapor cell without buffer gas is used at
[
modulated Gaussian pulse. However, in real communi- room temperature (∼25 ◦C) and is placed in the mag-
1 cation,pulse modulationis ofgreatimportance,but has netic shield (MS) to screenoutthe earthmagnetic field.
v
not been well studied in slow light system. The exitbeams areseparatedby PBS3,sothatonly the
7
In this Letter, we demonstrate the slow light effects slowed probe beam reaches PD2 as the output.
9
9 for amplitude modulated Gaussian(AMG) pulses in ex- Inexperiment,the opticalintensities I(t) of the input
2 periment, and analyze the significant distortion of the andoutputpulsesarerecordedona100 MHz digitalos-
1. AMG pulse. Further more, a compensation method is cilloscope triggered by an AWG. Thus, the amplitudes
0 proposed and a well-reshaped AMG pulse is obtained. of both the input and output (slowed)pulses canbe ob-
9 Our experimental setup is schematically illustrated in tained from the relation E(t) = I(t). The two probe
0
Fig. 1(a). A homemade narrowband (∼300 kHz) diode (input) pulses with nonnegative apmplitudes in time do-
:
v laseris stabilizedto the D transition(852nm) of133Cs main are chosen as
2
i atom: F = 3 → F′ = 2,4 crossover. By the combina-
X (ln2)t2
tion of λ/2 (half-wave plate) and PBS1, the laser light Gaussian pulse: I (t)=exp − ,
ar is divided into two beams with perpendicular polariza- 1 (cid:20) T02 (cid:21)
tions and adjustable proportion. Then, we can precisely AMG pulse: I (t)=I (t)[1+cos(2πδt)]2,
2 1
control the optical frequency and amplitude (thus in-
tensity) of the coupling and the probe lasers separately. where I (t) and I (t) are the intensities of two pulses,
1 2
Thecouplinglaserfrequencyisredshifted∼175 MHz by respectively; δ = 700 kHz is the modulation frequency;
AOM2, with power ∼2.35 mW and 1/e2 beam diame- T is the FWHM of the Gaussian pulse.
0
ter ∼2.0 mm. The probe pulse is generatedby passing a TheexperimentalresultsareshowninFig.2.Thetwo
weak (<10 µW) continuous-wave laser through AOM1, pulses experience quite different slow light effects. For
withthefrequencyredshifted∼175 MHzand1/e2 beam Gaussian pulse case [Fig. 2(a)], it is delayed ∼0.47 µs,
diameter∼2.0 mm.Inexperiment,theprobefieldampli- with relatively low loss and little distortion. Hence, we
tude E(t) (≥ 0) is proportional to the amplitude of the can compensate for the loss by directly amplifying the
drivingradio-frequencywavetoAOM1,whichisdirectly pulseintensity.However,forAMGpulsecase[Fig.2(b)],
controlled by an arbitrary waveform generator (AWG) the output undergoes relativelyhigh lossand significant
[see Fig. 1(a)]. After that, both the coupling (vertically distortion,while the delay time (∼0.14 µs) is decreased.
polarized) and the probe (horizontally polarized) light Thus,the directamplificationis not feasible to compen-
′
areonresonancewiththeD transitionF =3→F =2 sate for its loss and distortion [see the “rescaled” pulse
2
of133Csatom[seeFig.1(b)],andarecombinedatPBS2. in Fig. 2(b)].
1
Itisknownthatthepulsedistortioniscausedbyboth dispersions. By transforming each spectral component
absorptionanddispersion[10].Wefirstanalyzethe“ab- back to time domain separately, we obtain three Gaus-
sorptivedistortion”usingthetransmissionspectrum[see sian pulses with absolutely different time “delays”. For
Fig. 1(c)]. The intensity spectrums of input, output and the resonant component, we obtain a slow light of a
compensatedpulsearecalculated,usingdiscreteFourier Gaussianpulse withthe samedelaytime asinFig.4(a).
transform (DFT) and the transmission spectrum, and On the contrary, for each sideband component, we ob-
are illustrated in Fig. 3. It can be seen that the inten- tain a Gaussian pulse with a little advance [fast light,
sity spectrum of the Gaussian pulse keeps unchanged see the inset of Fig. 4(b)]. As a result, the time delay
with the bandwidth of ∼74.4 kHz; by contrast, that of forthe AMGpulse isdecreased.Thiseffect,knowasthe
theAMGpulsehasnotonly aresonantGaussiancompo- simultaneous slow and fast light [12], inevitably causes
nent,butalsotwonon-resonantGaussiansidebandswith distortion (“dispersive distortion”), but it is negligibly
±700 kHz detunings. This phenomenon can be qualita- small for a single-Λ type system [13,14].
tively analyzed from the Fourier intensity spectrums of In conclusion, the slow light of an amplitude modu-
two input pulses: lated pulse is studied, according to our knowledge, for
the first time experimentally. We demonstrate that the
(ln2)∆2
Gaussian: I (∆)=exp − , lossanddistortionoftheamplitudemodulatedpulseare
1 (cid:20) Ω2 (cid:21)
0 significant, which is not desirable in application. Using
1 spectrum analysis, we analyze the loss and distortion in
AMG: I (∆)=I (∆)+ [I (∆−δ)+I (∆+δ)],
2 1 1 1
4 frequency domain in a single-Λ type system, and point
where I (∆) and I (∆) are the intensities of two spec- out that the distortion is dominantly caused by differ-
1 2
trums, respectively; ∆ is the detuning from resonance; ent absorption rate for each spectral component. Ac-
Ω (determined by T ) is the FWHM of the Gaus- cordingly,wepresentacompensationmethodtoreshape
0 0
sian pulse spectrum. Suppose the system is linear and slowlightpulsewithhighfidelity.Further,thedispersion
E (∆) = A(∆)eiΦ(∆)E (∆), where A(∆) [Φ(∆)] is a effect is analyzed,which shows that though the “disper-
out in
realfunctionrelatedtotheabsorption(dispersion).Note sive distortion” is negligible, this effect reveals a novel
that each spectral component has a different transmis- way,differentfrom[12],torealizesimultaneousslowand
sion rate that depends on its detuning. For AMG pulse, fast light. The aforementioned results can be extended
thesidebandcomponentsundergomuchmoresevereab- to an arbitrary amplitude modulated pulse in a single-
sorption than the resonant one, and so cause more sig- Λ type system in EIT. These techniques of amplitude
nificant distortion. In this way, we can explain that it modulation and reshaping in slow light have potential
is the frequency dependent absorption that causes the applications in optical buffer and the low-distortion op-
lossanddistortion,ratherthan“thepulses‘forget’their tical delay lines.
initial temporal shapes”, as stated in [11]. This work is supported by the Key Projectofthe Na-
Therefore, for the linear absorption, we have tional Natural Science Foundation of China (Grant No.
I (∆)=|A(∆)|2I (∆),wherethephaseinformationis 60837004).
out in
eliminated, and |A(∆)|2 is the transmissionspectrum in
Fig. 1(c). A compensation method is thus proposed and References
appliedto reshapethe output pulse.As showninFig.3,
1. S. E. Harris, Phys.Today 50, 36 (1997).
we obtain the compensated spectrums by simply ampli-
2. M.Fleischhauer,A.Imamogˇlu,andJ.P.Marangos,Rev.
fying the output spectrums according to the transmis- Mod. Phys.77, 633 (2005).
sion rate as Icomp(∆) = Iout(∆)/|A(∆)|2measured. Since 3. R.M.Camacho,M.V.Pack,J.C.Howell,A.Schweins-
the compensated and the input shown in Fig. 3 are well berg, and R. W. Boyd, Phys. Rev. Lett. 98, 153601
overlapped,this methodcanrecover the pulsewithhigh (2007).
fidelity. To further confirm this, we transform the com- 4. R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J.
pensated spectrum back to time domain using inverse C. Howell, Phys.Rev.Lett. 98, 043902 (2007).
discrete Fourier transform (IDFT), and plot the input 5. S. W. Chang, S. L. Chuang, P. C. Ku, C. J. Chang-
and the reshaped pulses (Fig. 4). The reshaped pulses Hasnain, P. Palinginis, and H. Wang, Phys. Rev. B 70,
235333 (2004).
of Gaussian and AMG, with different time delays, are
6. P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe,
both in good agreement with their corresponding input
andC.J.Chang-Hasnain,Opt.Express13,9909(2005).
ones in shape and intensity. Even with the significant
7. Y.Okawachi, M. S.Bigelow, J. E. Sharping,Z.Zhu,A.
distortion, the output of AMG pulse has still been com-
Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L.
pensated well. Thus, only considering the frequency de-
Gaeta, Phys. Rev.Lett. 94, 153902 (2005).
pendent absorption is sufficient to compensate for the
8. J. E. Sharping, Y. Okawachi, and A. L. Gaeta, Opt.
distortion in a single-Λ type system.
Express 13, 6092 (2005).
Itshouldbenotedthatthedelaytimeofthereshaped
9. J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, Phys.
AMG pulse is less than that of the Gaussian one, as Rev.A 51, 576 (1995).
showninFig.4.Thisis becausethethree separatespec- 10. M. D. Stenner, M. A. Neifeld, Z. Zhu,A. M. C. Dawes,
tral components of the AMG pulse experience different and D.J. Gauthier, Opt.Express 13, 9995 (2005).
2
11. G. Nikoghosyan and G. Grigoryan, Phys. Rev. A 72,
043814 (2005).
12. J. Zhang,G. Hernandez,and Y.Zhu,Opt.Lett.31, 17
(2006).
13. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E.
Wilner, Phys.Rev. A 71, 023801 (2005).
14. R. M. Camacho, M. V. Pack, and J. C. Howell, Phys.
Rev.A 73, 063812 (2006).
3
List of Figures
1 (color online). (a) Experimental setup. λ/2, half-wave plate; PBS, polarizing beam splitter; AOM,
acousto-optic modulator; AWG, arbitrary waveform generator; MS, magnetic shield; APD, 1 GHz
avalanchephotodiode.(b)Asimplifiedsingle-Λtypesystemof133Csatomsinteractswiththecoupling
and the probe lasers. Two groundstates |xi and |yi representappropriate superpositions of magnetic
sublevels. (c) Probe transmission spectrum (an average of 16 measured results) versus detuning from
resonance, with the bandwidth of ∼350 kHz (FWHM) and the maximum of ∼61.5%. . . . . . . . . . . 5
2 (color online). Input (normalized) and output pulses versus time, each pulse is an average of 16
measured results; rescaled is the normalized output. (a) Gaussian: low loss and little distortion. (b)
AMG: high loss and significant distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 (color online). The intensity spectrums of input, output and compensated pulse, and transmission
spectrum. (a) Gaussian:the compensated spectrum overlaps with the input one. (b) AMG: The com-
pensatedcomponentsoverlapwiththecorrespondinginputones,exceptthatthesidebandshavesome
minor deviations due to experimental errors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 (coloronline).Inputandreshaped(calculatedfromthecompensatedspectruminFig.3)pulsesversus
time. (a) Gaussian. (b) AMG. The inset shows the fast light (obtained by IDFT) of the two sideband
components of the compensated spectrum in Fig. 3(b). The reshaped pulse (blue dotted) is advanced
by a little time relative to the corresponding input one (black solid). . . . . . . . . . . . . . . . . . . . 8
4
PD1 PD2
(a)
Dllaaiossdeerre λ/2PPBBSS11 AWG ReferencePPBS2 MS PBS3Probe
BS Mirror
AAOOMM11 CsCell Coupling
Mirror
(b)
(c)
AOM2
F=2,4 70
CCrroossssoovveerr 60
~175MHz )(% 50
n
FF ==22 sssio 40
mi 30
ns 20
CCoouupplliinngg PPrroobbee a
rTr 10
0
F=3 -10000 -500 0 500 1000
||x> ||y>> Detuning(kHz)
Fig. 1. (color online). (a) Experimental setup. λ/2, half-wave plate; PBS, polarizing beam splitter; AOM, acousto-
optic modulator; AWG, arbitrary waveform generator; MS, magnetic shield; APD, 1 GHz avalanche photo diode.
(b) A simplified single-Λ type system of 133Cs atoms interacts with the coupling and the probe lasers. Two ground
states |xi and |yi represent appropriate superpositions of magnetic sublevels. (c) Probe transmission spectrum (an
averageof16 measuredresults)versusdetuning fromresonance,with the bandwidth of∼350 kHz (FWHM) andthe
maximum of ∼61.5%.
5
(a)
(b)
Fig. 2. (color online). Input (normalized) and output pulses versus time, each pulse is an average of 16 measured
results; rescaled is the normalized output. (a) Gaussian: low loss and little distortion. (b) AMG: high loss and
significant distortion.
6
(a)
(b)
Fig.3.(coloronline).Theintensityspectrumsofinput,outputandcompensatedpulse,andtransmissionspectrum.(a)
Gaussian: the compensated spectrum overlaps with the input one. (b) AMG: The compensated components overlap
withthecorrespondinginputones,exceptthatthesidebandshavesomeminordeviationsduetoexperimentalerrors.
7
(a)
(b)
Fig. 4. (color online). Input and reshaped (calculated from the compensated spectrum in Fig. 3) pulses versus time.
(a) Gaussian. (b) AMG. The inset shows the fast light (obtained by IDFT) of the two sideband components of the
compensated spectrum in Fig. 3(b). The reshaped pulse (blue dotted) is advanced by a little time relative to the
corresponding input one (black solid).
8
