Eur. Phys. J. D (2013) 67: 78DOI: 10.1140/epjd/e2013-30653-1

Regular Article

THE EUROPEANPHYSICAL JOURNAL D

Optical switching in a Ξ system: A comparative studyon DROP and EIT

Ayan Ray, Md. Sabir Alia, and Alok Chakrabarti

Radioactive Ion Beam Facility Group Variable Energy Cyclotron Center, 1/AF, Bidhan Nagar, 700064 Kolkata, India

Received 25 October 2012 / Received in final form 11 February 2013Published online 30 April 2013 – c© EDP Sciences, Societa Italiana di Fisica, Springer-Verlag 2013

Abstract. In this experimental work we address the issue of optical switching through pump inducedatomic coherence in pump-probe spectroscopy of Doppler broadened medium of Rubidium atoms. Here acascade system 5S → 5P → 5D is chosen as the medium for optical switching. The merit of using this levelscheme for current study lies in the fact that two photon spectroscopy conducted in the above-mentionedmanifold results into a combination of double resonance optical pumping (DROP) and electromagneticallyinduced transparency (EIT) signals. Within an intensity modulation frequency range of 10 Hz → 10 MHz,DROP and EIT behave differently. This fact may be attributed to the distinctive difference in mechanismsgiving rise to DROP and EIT signals. Though both DROP and EIT stem from two photon spectroscopy,unlike DROP, which arises due to population transfer between dipole forbidden 5S → 5D levels, EIToriginates from destructive quantum interference mechanism. This subtle difference is well evidenced whenoptical switching is conducted through the coherently prepared alkali vapour sample. The EIT is found tobe more agile towards faster optical switching while DROP acts as an over damped medium for the same.A simple qualitative discussion is included to explain our results on optical switching.

1 Introduction

The subject of pump-probe spectroscopy in alkali vapourmedium provides an unique opportunity to study differentperspectives of coherence, manifested through results likecoherent population trapping (CPT), EIT, electromag-netically induced absorption (EIA) [1–3], etc. Importanttechnical applications of coherent photon-atom interac-tion encompasses key areas like slowing down the light [4],miniaturized atomic clock [5], ultra-sensitive magnetome-try [6] and frequency offset locking [7–9]. As a whole thisparticular topic of quantum optics has generated tremen-dous attention in the physics community.

It may be noted that the most common experimen-tal configuration of coherent pump-probe spectroscopyconsists of two independent lasers connecting atomic hy-perfine (Zeeman) levels (sublevels) in a fashion to sat-isfy the geometry of certain level coupling schemes: Λ,V, Ξ, N , etc. The coherence results into correlation be-tween pump and probe lasers, which are otherwise inde-pendent. This fascinating aspect of coherence has beenrevisited in connection with atomic frequency offset lock-ing [7–9]. A particular commonality among all these earlierpapers is related to use of a single external modulation ina Λ type system, which in turn makes its presence felton the power spectrum of the other laser due to coher-ence assisted transfer of frequency modulation. Recently

a e-mail: sabirbarc@gmail.com

Moon [10] demonstrated the same modulation transfertechnique in connection with frequency stabilization un-der the framework of Ξ scheme. Other than frequencymodulation one more important parameter, which canalso be transferred through coherence, is intensity mod-ulation [11]. The intensity modulation is related to thesubject of coherence assisted optical switching [11–15].Some of these reports [12,15] are focused on demonstrationof optical switching in Ξ system. However spectroscopyof Ξ system reveals hyperfine structure of the excitedstate in terms of double resonance optical pumping signal(DROP) [16–20] along with the EIT structure. Thoughboth DROP and EIT originate from two photon process,their difference is subtle. The DROP is a result of twophoton absorption while the EIT is a byproduct of twophoton coherence. Hence it is necessary to gain insightabout any possible difference in the roles of DROP andEIT under intensity modulation.

This experimental work reports about relative com-parison between DROP and EIT during coherence assistedoptical switching. We have modulated intensity of the cou-pling laser and found that the medium under dominantEIT condition shows prominent switching over a widefrequency region (10 Hz → 3 MHz). However the samemedium under prominent DROP condition favors switch-ing over a limit up to 100 kHz only. This fact rendersthe possibility of practical realization of variable switch-ing bandwidth based on manipulation of coupling laserparameters in a particular Ξ configuration. To explore

Page 2 of 9 Eur. Phys. J. D (2013) 67: 78

Fig. 1. Level scheme in 5S1/2 → 5P3/2 (D2) → 5D5/2 tran-sition of Rubidium atom (87Rb), where the levels relevantfor DROP and EIT experiments are denoted by |1〉, |2〉 and|3〉. The pump (probe) laser frequency, detuning and Rabifrequency are ωpu (ωpr), Δpu (Δpr) and Ωpu (Ωpr), respec-tively. Dephasing between ground state (|1〉) hyperfine com-ponents (F = 2, 1) is γg,1↔2. Spontaneous decay rate from|j〉 is Γj (dotted arrows). Here Γ3 = 2π × 0.97 MHz, Γ2 =2π× 6.066 MHz, Γ1 = 0 are the natural linewidths and γg, 1↔2

is governed by the transit time broadening (for a room temper-ature vapor cell without buffer gas). The coherent dephasing

rate between |j〉 and |i〉 is γji ≈ Γj+Γi

2. The two photon reso-

nance condition is Δpu + Δpr ≈ 0 where Δpu (Δpr) are sameas of reference [21].

the physical basis of the results obtained during intensitymodulation, a detailed experiment is conducted. The ef-fect of pump (probe) laser detuning and probe laser powervariation on the resultant DROP (EIT) spectrum is in-vestigated in details. A simple qualitative explanation isincluded herewith to further support our observation.

2 Experiment

The relevant level scheme used in this experiment is shownin Figure 1. The probe laser (Ωpr ∼ 2π × 9 MHz) is reso-nant (ωpr ∼ 780 nm) with the 5S1/2 (F = 2) → 5P3/2

(F ′ = 3, 2, 1) manifold whereas the pump laser is inresonance with 5P3/2 → 5D5/2 transition. Thus the 5S(|1〉) → 5P (|2〉) → 5D (|3〉) connection satisfies the con-dition of a Ξ system. Decay rates [21] entailed with thelevels are also shown in Figure 1. See caption of Figure 1for the list of nomenclature, which is used in the text. Theexperimental arrangement is shown in Figure 2 where twolasers ECDL1 (ECDL2) are used as pump (probe). Bothpump (probe) beams are linearly polarized. A small partof the probe beam is used in a saturation absorption spec-troscopy (SAS) setup to reveal the hyperfine structure of

5S1/2 (F = 2)→ 5P3/2 (F ′ = 3, 2, 1), which are extractedwith high S/N ratio (for F = 2→ F ′ = 3 hyperfine com-ponent FWHM ∼ 12 MHz). The SAS spectrum helps usduring calibration of the probe absorption spectrum andalso helps in direct frequency stabilization of the laser.

The pump laser (Ωpu ∼ 2π × 70 MHz), emittingωpu ∼ 776 nm, is used under counter propagating con-figuration (see Fig. 2) to the probe beam. This configu-ration helps in largely eliminating the first order Dopplerbroadening as ωpu ≈ ωpr. To calculate Rabi frequencies{Ωpu (Ωpr)} we used the overall transition dipole matrixelements (5S1/2 → 5P3/2, 5P3/2 → 5D5/2) data from stan-dard literature1 [22]. The pump laser frequency is directlymonitored by using a wavemeter and a scanning FabryPerot Interferometer. An Electro-Optic Amplitude Mod-ulator (Thorlabs EO-AM-NR-C1, broadband) is placed inthe pump laser beam path for intensity switching. Theexperiment is conducted in three parts: (i) exploring theprobe absorption spectra as a function of pump frequencydetuning; (ii) systematic investigation of coherence in-duced switching; and (iii) study of the effect of variationof probe laser power on the two photon spectra.

To conduct the first part we subsequently locked theprobe laser directly to the sides of 5S1/2 (F = 2) →5P3/2 (F ′ = 3), crossover transition between 5S1/2

(F = 2)→ 5P3/2 (F ′ = 1, 3) and crossover transition be-tween 5S1/2 (F = 2)→ 5P3/2 (F ′ = 1, 2). Frequency mod-ulation spectroscopy (FMS) is willfully avoided here forlocking purpose to avoid any modulation induced fluctua-tion of the laser frequency. The coupling laser is scannedaround 5P3/2 (F ′) → 5D5/2 (F ′′) manifold. The resultsobtained under probe absorption spectra prompted us toscrutinize the system specific two photon process in a moresubtle manner. For this purpose we monitored the probeabsorption as a function of probe detuning while the pumplaser is static on different frequency positions (tuned byshifting the piezo offset voltage). Note here that in thisparticular interrogation the pump laser remains free run-ning. Since the data recording time is limited to ∼1 s, therecoded spectrum is limited by the short term linewidth(Δνlaser ∼ 1 MHz) of the lasers only. The effect of longterm frequency drift is negligible.

In the second part of experiment we subsequentlylocked the probe frequency on two different positions:5S1/2 (F = 2) → 5P3/2 (F ′ = 3), crossover transition be-tween 5S1/2 (F = 2) → 5P3/2 (F ′ = 1, 3). The pumplaser is initially scanned to monitor the probe absorptionand the interferometer (FPI) fringe simultaneously on thescreen of oscilloscope. At this point the DC offset voltagecontrolling the FPI cavity dimension is varied to bring thefringe exactly at the desired position matching the twophoton absorption spectrum. At this condition the pumplaser is locked on the side of fringe directly. Afterwardsintensity modulation is introduced in the pump beamthrough EOAM. For this purpose a reference sinusoidalvoltage is applied to the high voltage driver (Thorlabs,HVA 200). While this is sufficient for a moderate band-width, the driver itself has a sharp cut-off at 1 MHz. As a

1 http://steck.us/alkalidata/rubidium87numbers.pdf

Eur. Phys. J. D (2013) 67: 78 Page 3 of 9

Fig. 2. Schematic of the experimental arrangement. ECDL: external cavity diode laser, M: mirror, BS: beam splitter, PCBS:polarizing cube beam splitter, OI: optical isolator, BD: beam dump, D: photodetector, λ/2: half waveplate, EOAM: electrooptic amplitude modulator, FPI: Fabry Perot Interferometer, WM: wavemeter, LO: local oscillator, GP: glass plate and SAS:saturation absorption setup. Preamp + Servo combo unit is used for direct locking of the laser. The readings from D1, D2and FPI are simultaneously monitored on oscilloscope. For intensity modulation the HVA 200 unit is used for 10 Hz → 1 MHzfrequency range. For >1 MHz intensity switching frequency ZHL-32A rf Power Amplifier is used as buffer.

remedy a ZHL-32-A (Minicircuits) amplifier is used for in-tensity modulation frequency beyond 1 MHz. At the exitof the pump beam from the Rb vapour cell, a photode-tector is placed to monitor the original intensity switch-ing. The two photon process induced transfer of intensityswitching of the probe beam is measured and normalizedw.r.t. the same of the pump.

The third and last part of the experiment is dedicatedto investigation of the dependence of two photon absorp-tion spectrum on the probe power. Here the probe laseris purposefully locked to the crossover transition between5S1/2 (F = 2) → 5P3/2 (F ′ = 1, 3). The probe absorp-tion is monitored w.r.t. the variation in probe power as afunction of pump detuning. This part of the experimentis conducted in search of any possible presence of demar-cation feature, which can distinguish the transition fromweak DROP+ prominent EIT effect to strong DROP ef-fect regime. Rather it is more convenient to state that thedemarcation will indicate how two different zones of var-ied optical switching speed can be achieved by varying theprobe power only.

3 Results and discussions

The result of part (i) of the experiment is depicted inFigures 3 and 4. Figure 3 reveals the probe absorptionspectrum as a function of pump detuning. It can be

seen from different plots in Figure 3 that the DROP andDROP + EIT signals are observed on a flat backgroundfor a frequency locked probe laser. As the probe laser fre-quency is locked at respective SAS signals (|1〉 → |2〉),the laser in principle addresses small velocity groups ofatoms (taking into consideration laser linewidth Δνlaser)resonant with laser frequency. These atoms are furtherreached to the upper state |3〉 by the pump laser itself.Due to this fact the resultant Doppler background, as ob-served under probe laser scanning condition (see Fig. 4,where the probe laser is addressing a larger velocity groupsof atoms during scan around 5S1/2 → 5P3/2 transition),is absent in Figure 3. It is seen in Figure 3c that thetwo photon absorption spectrum is composed of promi-nent DROP signal (extremely weak EIT feature seen onlywithin F ′ = 3 → F ′′ = 4 profile) when the probe laserconnects F = 2→ F ′ = 3 closed transition. On the otherhand when the probe laser is locked on the crossover tran-sitions between F = 2→ F ′ = 3, 1 and F = 2→ F ′ = 2,1hyperfine components, the effect of DROP is gradually re-duced (see Figs. 3b, 3a) and the EIT signals are clearlydiscernible.

The physical reason behind near absence of EIT evenunder strongest two photon resonance condition (Δpu ≈Δpr ≈ 0; probe is locked on F = 2 → F ′ = 3 com-ponent; same as plots designated (c) in Fig. 3) maybe explained as follows: the atoms participating in the

Page 4 of 9 Eur. Phys. J. D (2013) 67: 78

Fig. 3. Experimental data recording of probe absorption spec-trum as a function of pump frequency scan. Here the probelaser is side locked to amplified signals of (i) crossover transi-tion between 5S1/2 (F = 2) → 5P3/2 (F ′ = 2, 1) (see plot (a));(ii) crossover transition between 5S1/2 (F = 2) → 5P3/2 (F ′ =3, 1) (see plot (b)); and (iii) closed transition 5S1/2 (F = 2) →5P3/2 (F ′ = 3) (see plot (c)). Here Ωpu (Ωpr) is 2π × 70 MHz(2π × 9 MHz). Plot (a) shows (prominent EIT + reducedDROP) feature whereas (strong DROP + very weak EIT) isseen in plot (c). The inset shows simultaneous recording ofFPI fringes (F.S.R 1.5 GHz) with the probe absorption spec-trum. The spectrum is calibrated with the help of simultaneousrecording of FPI fringes.

transition 5S1/2 (F = 2) → 5P3/2 (F ′ = 3) can getpreferentially pumped to 5D5/2 (F ′′ = 4) level. Similarlythe decay route F = 2 ← F ′ = 3 (branching ratioη = 1)← F ′′ = 4 (η = 0.74 [23]) is also the preferred one,which forms almost a pseudo closed decay channel. As aresult relatively large number of atoms keeps on recyclingwithin these levels. The number of atoms leaked throughDROP mechanism to F = 1 level is relatively less forF = 2 ↔ F ′ = 3 ↔ F ′′ = 4 channel. On the other handthe origin of EIT is formally described under the dressed-atom picture. Here the bare atomic state |2〉 is consideredas a set of ‘coupled’ |C〉 and ‘non-coupled’ |NC〉 states [24].Both |C〉, |NC〉 are formed through a superposition of |1〉and |3〉 normalized to the respective Rabi frequencies oflasers. The nomenclature of |C〉, |NC〉 indicates transitionprobability w.r.t. bare atomic state |1〉. When atoms aretransferred to |NC〉 (so called ‘Dark State’), the absorbingmedium becomes transparent to the probe laser resultinginto Two Photon Coherence (EIT). Ideally this particularphysical mechanism demands no loss of atoms to F = 1state. But even in case of almost closed two photon tran-sition F = 2 → F ′ = 3 → F ′′ = 4, which is favorable forEIT, the DROP effect is sill so prominent that it almostsuppresses the EIT signature (cf. Fig. 3c). A very weaksignature of EIT in seen on the F ′ = 3 → F ′′ = 4 twophoton absorption feature.

Fig. 4. Recording of probe absorption spectra as a function ofprobe detuning. Here Ωpu (Ωpr) are kept same as of Figure 3(see caption). The pump laser is kept stationary at differentpositions. Initially the simultaneous recordings of probe ab-sorption and probe SAS spectra are monitored on oscilloscope.The piezo offset of the pump laser is adjusted to bring the twophoton spectrum exactly on the same position of closed tran-sition 5S1/2 (F = 2) → 5P3/2 (F ′ = 3). The pump laser is keptfree running but static. As the recording time is fast (1s), theshort-term linewidth of laser mainly limits the precision. Otherpositions (red/blue detuned w.r.t. F = 2 → F ′ = 3 transition)of the pump frequency is adjusted by monitoring the instanta-neous readout on the wavemeter (see plots. (a), (b), (d)–(g)). Itis seen in plot (g) that EIT signals appear within all DROP sig-nal components indicating strong influence of AT componentscontributed by different velocity groups of atoms. Inset showssimultaneous recording of probe SAS where 1,4,6 are transi-tions from 5S1/2 (F = 2) → 5P3/2 (F ′ = 3, 2, 1) and 2, 3, 5 arethe crossovers between F = 2 → F ′ = 3, 2, F = 2 → F ′ = 3, 1and F = 2 → F ′ = 2, 1. The spectrum is calibrated with thehelp of probe SAS (see inset).

For other F ′ → F ′′ components we may intu-itively conclude that they are less populated comparedto F ′ = 3→ F ′′ = 4 transition because of relatively lowertransition probabilities. For these channels relativelylarger number of atoms can leak through DROP mech-anism to F = 1 level, thus in principle DROP being thedominant mechanism helps in obscuring the signature ofEIT altogether from signatures of F ′ = 3 → F ′′ = 3, 2transitions. It is noteworthy that strength of DROP is pro-portional to two photon transition probability [17]; henceits maximum for F = 2 → F ′ = 3 → F ′′ case renderingfor the nomenclature ‘Strong DROP’. However the specificcase F = 2 → F ′ = 3 → F ′′ = 4 (i.e. Δpu ≈ Δpr ≈ 0) isalso the strong condition for manifestation of EIT. As a re-sult a very weak EIT feature is observed F ′ = 3→ F ′′ = 4while no EIT is seen on F ′ = 3 → F ′′ = 3, 2 peaks. Thisparticular situation of probe/pump transmission truly ac-counts for the ‘Strong DROP + Weak EIT’ window.

It may also be noted that other possible decay routesare also present to a small extent due to leakage of

Eur. Phys. J. D (2013) 67: 78 Page 5 of 9

atoms from the F = 2 ↔ F ′ = 3 ↔ F ′′ = 4absorption-emission cycle. These decay channels can pop-ulate 5S1/2 (F = 1) level, which is outside the pump-probecoupling scheme, thereby can reduce absorption. This ef-fect is very minimal for a closed transition as is evidentthrough Figures 3c and 4c.

In case of Figures 3b and 3a the presence of EIT sig-nal is clearly seen. Here the probe frequency is lockedsubsequently to the positions of ω23 − 212 MHz andω22 − 345 MHz. The detuning (Δpr) of probe laserprompts us to introduce ‘Generalized Rabi Frequency’Ωpr =

√Ω2

pr + Δ2pr [25], which takes into account the ve-

locity dependent character of F → F ′ transition. In effectthe probe laser addresses broader velocity group of atoms(less frequency selective compared to F = 2 → F ′ = 3case) and this helps in populating the overall F ′′ hyper-fine manifold through pump coupling. In the present case(consider Figs. 3a and 3b) average population in F ′′ = 2,3 levels increase considerably, as well as the probabilityof decay of atoms to F = 1 level, which is outside thelevel coupling scheme, also increases. However it is to bepointed out that this situation is unlike the earlier one (seeFig. 3c) where atoms are almost resonantly coupled to F ′′levels (taking into account ΔEF ′→F ′′ � ΔEF→F ′ ) result-ing into dominance of DROP. Though the mechanism ofDROP is still very effective, the overall supply of atoms toF ′′ levels decreases because the probe laser is largely off-resonant to F = 2 → F ′ = 3 transition while the pumpscans over ∼F ′ = 3 → F ′′ domain. More precisely wemay infer that for a weak but non-resonant probe laserthe DROP effect gets weaker, as evident in Figures 3aand 3b compared to the earlier one i.e. Figure 3c. Hencereduction of two photon absorption and consequent clarityin two photon coherence (EIT) becomes prominent. Thuswe are led to the nomenclature of ‘Weak DROP + StrongEIT’ window.

It may be noted that probe coupling (F = 2 → F ′)also favors ‘Single Resonance Optical Pumping’ (SROP)whereby atoms decay back to F = 1 level and effectivelyreducing the absorption. This effect also contributes toreduction of absorption when probe frequency is detunedfrom the closed transition. Once the atoms reach F = 1state, they can only be transferred from F = 1 → 2through dephasing (γg,1↔2). In our case a room temper-ature Rb vapour cell (without buffer gas) is used; henceγg,1↔2 is mainly governed by transit time effect. The dutycycle of this particular process is very slow (∼<50 kHz)compared to other relatively faster processes (e.g. opticalpumping and decay). Their effects on the atom-field sys-tem are averaged many times within the long duty cycleof γg,1↔2; thus setting the system into equilibrium.

We have revisited the effect of laser frequency detun-ing on DROP and DROP + EIT feature in Figure 4. Herethe probe laser is scanned over F = 2 → F ′ hyperfinelevels. The pump laser is kept stationary at a nominal fre-quency, ν0 ∼ 776 nm. The probe absorption spectra (seeFig. 4) clearly show the evolution of DROP + EIT featurewith changing frequency positions of pump laser as donethrough adjustment of piezo offset voltage. By observing

the signals from all photodetectors on the oscilloscope,the pump frequency is adjusted to match the position ofthe two photon features with the 5S1/2 (F = 2)→ 5P3/2

(F ′ = 3) hyperfine position on the probe SAS spectrum(see Fig. 4c). Apart from Doppler background arising dueto scanning of probe laser, Figure 4c is identical to thespectrum of Figure 3c. We adjusted the piezo offset toshift ωpu, which shifts the two photon feature at variouspositions (see caption of Fig. 4). It may be seen clearlythat the EIT feature becomes prominent with increasingdeparture of the pump frequency from the F = 2→ F ′ =3 → F ′′ = 4 condition (i.e. DROP mechanism weakens).The shapes of EIT signals on two photon absorption spec-tra F = 2 → F ′ = 3 → F ′′ = 4, 3, 2 clearly suggests thestrong influence of Autler-Townes (AT) splitting of differ-ent velocity groups of atoms [25] on the probe absorptionprofile.

The results of transfer of intensity switching underthe current Ξ level scheme are shown in Figures 5 and 6.The two photon process induced intensity switching of theprobe beam is normalized with the same (pk. to pk. excur-sion) of coupling beam at every step to eliminate system-atic contribution from any other factors (e.g. fluctuationof vapour pressure inside the Rb cell due to same in roomtemperature, etc.). The frequency of intensity switchingis varied from 10 Hz → 10 MHz. During this part of theexperiment the probe laser is subsequently side locked toF = 2→ F ′ = 3 closed transition and the crossover tran-sition between F = 2 → F ′ = 3, 1. The pump laser isinitially scanned to reproduce the spectra presented inFigures 3b and 3c. Simultaneously the FPI fringes arealso seen on the oscilloscope. By adjusting the DC off-set of the FPI cavity mirror we shifted one fringe match-ing with the position of the respective two photon featureand the coupling laser is side locked to the fringe. Notehere the FWHMfringe ∼ 5 MHz, which is considerablyless than the overall frequency spacing of the 5D5/2 F ′′ =4, 3, 2, 1 (δνF ′′ ∼ 50 MHz) and also less than linewidth ofthe DROP (FWHMDROP F ′=3→F ′=3 ∼ 6.5 MHz) signal.Hence the FPI fringe locking reference is sufficient to fixthe pump laser at the desired frequency for selection of twophoton events (DROP or EIT). Note here that in this casewe did not employ any active stabilization of cavity (onlypassive stabilization measures were followed e.g. isolationof cavity environment), which is unlike the schematic de-scribed in reference [26]. However it did not affect ourexperiment as the readings were taken within a period offew minutes. No visible shift in FPI fringe is observed dur-ing this period under a preliminary test run. The resultsare as follows: Figure 5a clearly shows the performanceof dominant DROP + weak EIT condition (ωpr ≈ ω23)under intensity switching for different frequency range.Figure 5b shows the same under reduced DROP + dom-inant EIT condition (ωpr ≈ ω23 − 212 MHz). The domi-nant DROP + weak EIT condition shows a sharp cutoffstarting from 100 kHz frequency of intensity modulationwhile the reduced DROP+ dominant EIT condition showsa cutoff at 3 MHz switching frequency. These results arecompiled in Figure 6 and it clearly shows the bimodal

Page 6 of 9 Eur. Phys. J. D (2013) 67: 78

χ(v)dv =4i�Ω2

pr/ε0

γ21 − iΔpr − iωpr

cv +

Ω2pu

4

[γ31 − i(Δpu + Δpu) − i(ωpr − ωpu) v

c

]−1N(v)dv (1)

(a)

(b)

Fig. 5. The examples of intensity switching under strongDROP (see plot (a)) and strong EIT (see plot (b)) conditions.In each case Trans. Dx indicates recoding of transmitted inten-sity from respective Xth photodetector (see caption of Fig. 2).In each case the probe transmission data (D2) is normalizedto the same of pump laser (D1). Plot (a) shows the modula-tion at 100 kHz (for strong DROP probe frequency is lockedto 5S1/2 (F = 2) → 5P3/2 (F ′ = 3) and plot (b) shows the sameat a switching frequency of 1 MHz under strong EIT condition.For each case the pump laser is locked to an FPI fringe coincid-ing with the two photon spectrum (see text for details). Thephase difference between the pump switching waveform andthe same of two photon condition induced probe modulationcan be noticed in the picture. This may be attributed to thefact that different physical mechanisms with varied time con-stants are involved in this process; thus introducing the phasedifference.

(slow and fast) operation of the all optical switchingscheme depending on the respective probe frequency posi-tion. The physical mechanisms, which may be responsiblebehind this bimodal behavior, are related to the processesof optical pumping and relaxation. Unlike the analysis ofEIT in case of an isolated Λ system, which by far is fullycharacterized with analytical expression of Optical Pump-ing (Ω2

pu/Γ ), the Optical Pumping process in a realistic Ξsystem is highly complex [27]. Intuitively we can conclude

Fig. 6. Relative comparison between conditions of (strongDROP + weak EIT) and (reduced DROP + dominant EIT)during transport of intensity switching are presented throughplots (a) (�) and (b) (©). The voltage variation as observed onD2 (cf. caption of Fig. 2) is weighted by the same of D1. TheDROP condition shows downfall of switching action startingfrom ∼100 kHz (see Fig. 5) while the same for EIT conditionis observed at ∼3 MHz.

that these pumping processes are faster enough to com-pensate for the decay mechanisms so that the two pho-ton effects (both absorption and coherence) are realized inpractice. Hence it may be inferred that the process of opti-cal pumping gets enslaved during each duty cycle of the in-dividual relaxation process (Γ3, Γ2 for DROP and γ31, γ21

for EIT). Under external perturbation the Dynamic Evo-lution of the system will be limited by the time constantof the slowest physical process. For DROP the main lim-iting factor is a combination of Γ3 (2π × 0.97 MHz), Γ2

(2π × 6.066 MHz) [17] and for EIT it is a combinationof coherent dephasing γ31 {(Γ3) /2 ≈ 2π × 0.5 MHz}, γ21

{(Γ2) /2 ≈ 2π × 3.0 MHz} [21]. In case of DROP, whichis a two photon absorption feature, the effect of inten-sity modulation directly competes with the rate of popu-lation transfer from |1〉 → |3〉. Hence relatively slower in-tensity modulation (∼100 kHz) can be accommodated inthe atom-field system without disturbing the equilibrium.

To discuss the case of EIT, we consider the genericequation of probe transmission [21]:

see equation (1) above.

Here N (v) is the Maxwell-Boltzmann velocity distribu-tion of the Doppler broadened (ΔωD) atomic systemand χ is the susceptibility of the medium. See captionof Figure 1 for other notations. For observation of EITΩ2

pu/4γ31γ21 1 [21] needs to be satisfied provided twophoton resonance condition (Δpu + Δpr ≈ 0) is simul-taneously fulfilled. Note here equation (1) describes the

Eur. Phys. J. D (2013) 67: 78 Page 7 of 9

steady state; hence effect of transient response of the EITmedium, which is of prime concern in case of switching, isnot immediately retrievable from it. The case of transientproperties of a Ξ type EIT system has been described ear-lier by Li and Xiao [28] with condition Ωpu γ21 γ31.Though we cannot immediately bring in the effect of tran-sient in equation (1), it is possible to demonstrate theintensity modulation in a simplistic manner by substitut-ing Ω2

pu → Ω20 [C1 + C2 cosωmt]. Here Ω0 is the nominal

pump Rabi frequency. The constants C1, C2 are so ad-justed that the bare minimum value of Ωpu i.e. ∼4γ21γ31

is maintained. If we solely consider the effect of AC Starkshift, Ωpu, min >∼ 4γ21γ31 is the threshold value requiredto just set the transparency into the system. A sinusoidalvariation of Ω2

pu (external perturbation) superimposedover Ω2

pu, min will bring in the effect of intensity modu-lation without violating the steady state assumptions (asthe threshold transparency is always retained). Figure 7shows the result of simulation where plot (a) providesa 2D view of transparency window vs. probe detuning.Figure 7b shows the Dynamic Evolution of the systemin the switching timescale, which is adjusted to ∼3γ−1

21 .The plot clearly shows the sinusoidal variation of the EITwindow, which is more clarified under contour plot of Fig-ure 7c. It is clearly evident that the effect of high speedintensity switching (tested with 1 MHz in simulation) actson the EIT window and this do not disturb the equilib-rium even in a short timescale of 3γ−1

21 (see Fig. 7). Here,in the simulation, timescale of the physical processes in-volved is in the order of (Ω2

pu/γ21)−1 < ω−1m < γ−1

31 . Sinceideal EIT condition requires limγ31→0, we consider the sit-uation where (Ω2

pu/γ21), ωm are getting enslaved withinrelatively slower duty cycle of γ31 and the system settlesinto equilibrium. In such a case the Dynamic Evolution ofthe system within a single period of γ−1

31 may be describedin the time scale of ω−1

m . It gives a phenomenological de-scription of the system under external perturbation.

Further insight into evolution of the medium under thetimescale of∼� γ21 requires the investigation of transientspercolating into the system. Here the decay γ21 is equiv-alent to ‘Damping Rate’ towards normalized probe ab-sorption [28]. Since the speed of transition of the mediumfrom opaque → transparent can be very fast (see Fig. 6),it may touchdown or surpass the time scale of decayprocess. Hence the highest speed of switching in a EITmedium is related to the timescale required for onset ofAC Stark shift. This subtle physical fact compels us toinfer that the upper limit of timescale of pulse propaga-tion in a Ξ type EIT medium is governed by Ωpu. Con-sidering the factor

(Ω2

pu/γ21

) γ31, which is analogousto (Ω2/Γ γdipole-forbidden) condition in a Λ system, itis expected that much faster modulation (∼�1 MHz) canbe successfully transported through Ξ system when EITcondition is predominant. In effect for an almost null co-herence dephasing (ideal EIT) the ‘Dark State’ |NC〉 needsto be prepared once to facilitate the switching process.

It is evident from the physical origin of two photon pro-cess that for a fixed pump laser power the bimodal char-acter of optical switching can be exhibited by adjusting

(a)

(b)

(c)

Fig. 7. Theoretical simulation of intensity switching in theEIT system of Figure 1 with Ω2

pu → Ω20 [C1 + C2 cos ωmt] sub-

stituted in equation (1): (a) Doppler averaged probe absorp-tion spectrum. (b) Doppler averaged probe absorption spec-trum under pump intensity modulation, showing sinusoidalswitching of EIT window. Switching is zero elsewhere in thespectrum. (c) Contour plot of optical switching time(s) versesprobe detuning (MHz). The transferred switching of 1 MHzonly at EIT window is directly seen. Here Ω0 ∼ 50 MHz,C1 = 1.04, C2 = 1.0 is used, which guarantees Ωpu, min ∼10 MHz ∼� 4γ31γ21 is maintained. This ensures bare mini-mum pump intensity required for onset of EIT, over which thesinusoidal intensity perturbation is superimposed. It is to benoted that γ31 in a Ξ system is equivalent to the dephasing be-tween dipole forbidden levels of a Λ system i.e. γdipole-forbidden.Here γ31 (=0.5 MHz)< γ21 (=3.0 MHz) is considered.

the probe laser frequency. However the boundary betweenDROP and EIT dominated switching zones is not very welldefined. It requires a proper demarcation feature to iden-tify the two different modes of operations of the same opti-cal switch. For this purpose we conducted the last part ofthe experiment i.e. to study the effect of variation of probepower on the DROP + EIT profile. Here the coupling

Page 8 of 9 Eur. Phys. J. D (2013) 67: 78

Fig. 8. Recording of the probe absorption spectra as a func-tion of pump frequency scanning. Here the probe is lockedto the crossover transition between 5S1/2 (F = 2) → 5P3/2

(F ′ = 3, 1). Here Ωpu is 2π× 70 MHz while Ωpr is varied from2π×(9, 13, 15, 18, 29, 37, 43) MHz for plots (a)–(g). The DROPspectra and the EIT window are getting gradually broadened.The plot (g) shows that the D2 detector is near saturationat high probe power. The onset of dominance of multi-photonprocess is demarcated through the 5D → 6P → 5S decay route.The blue line is the result of decay from 6P → 5S at 422 nm.

laser is scanned and probe laser is fixed on the crossovertransition between F = 2 → F ′ = 3, 1 hyperfine compo-nents (same condition as Fig. 3b). With the increase inprobe power it is found that the contrast of the EIT fea-ture deteriorates and ultimately nearly smeared out fromthe probe absorption spectrum (see Fig. 8). The eras-ing of EIT (i.e. complete dominance of DROP) is ear-marked by the appearance of a faint blue radiation lineappearing in the vapour cell (cf. inset of Fig. 8). The ap-pearance of blue line indicates onset of domination byother multi-photon processes (especially the decay rote5D5/2 → 6P3/2 → 5S1/2 is responsible for blue radia-tion). Wielandy and Gaeta [29] earlier showed that theanalytical expression of probe absorption spectrum for aΞ level scheme contains higher powers of Ωpr and Ωpu.These multi-photon processes starts interfering with theEIT condition; hence the EIT feature is almost obscuredfrom the probe spectrum (Fig. 8) though the two photonresonance condition is still met.

4 Conclusion

There remains always tremendous interest in exploring thepossible application of EIT in case of all optical switch-ing [11–15]. The main purpose behind this particular topicof research is to develop a rapid and practical opticalswitch for next generation communication system. Theprospective application of EIT based switch may find itswide application in routing, buffering, etc. in a commu-nication network. Though there exist recent reports onswitching application of EIT, only Lee et al. [14] pointed

out typical role of detuning in achieving optimum perfor-mance of switching under a particular atomic level cou-pling scheme. This may be due to the fact that there hasbeen always a competition between two photon coherenceand other single/multi- photon processes occurring in thesystem. Hence a systematic experimental investigation isrequired for optimization of switching performance.

In this work we explored the dual nature of a Ξ levelscheme during intensity switching process. We have foundthat two types of phenomena dominate the probe laserabsorption spectrum: the DROP and the EIT. The ef-fect of detuning of pump/probe laser on the DROP andEIT spectra is investigated in details. Under the applica-tion of external switching introduced through the pumplaser it is found that the system under EIT condition canexhibit rapid switching even at >1 MHz while the sameunder DROP condition shows a rapid fall in switchingperformance at a frequency of 100 kHz. This particulardifference in performance may be attributed to the factthat decoherence in EIT is due to fast coherent dephas-ing (γ31) while the DROP is limited by comparativelyslower spontaneous decay (Γ ) process. Lastly we have ex-perimentally studied the influence of probe laser intensity(∞Ω2

pr) on the DROP + EIT spectrum. It is experimen-tally found that the appearance of faint blue line (dueto decay route 5D → 6P → 5S at 422 nm) indicates to-tal almost obscurity of EIT signal from the absorptionspectrum indicating dominance of other multiphoton pro-cesses. However the DROP spectrum remains intact evenunder strong probe regime. This may be considered as thedemarcation feature for operating the Ξ scheme based op-tical switch in a bimodal way: slow speed switch based onDROP and high speed switch based on EIT. The currentstudy will be further helpful in optimizing the performanceof an all optical switch based on EIT.

The authors gratefully acknowledge support provided by Dr.Sumit Som and his group (RF Division, VECC) with rf elec-tronics in the experiment. One of the authors A. Ray per-sonally acknowledge valuable suggestions received from Dr.Q.V. Lawande, ThPD, BARC and Dr. B.N. Jagatap, AMPD,BARC.

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