We have experimentally studied the reflection of a weak probe beam from a
dense atomic potassium vapor in the presence of a strong laser field tuned to
the atomic resonance transition. We have observed an Autler-Townes doublet
under hitherto unexplored conditions, namely that the Rabi frequency induced by
the strong laser field is much smaller than the self-broadened width of the
resonance transition of the unexcited vapor. We attribute our observation to a
reduction of the atomic decoherence by the strong drive field. We present a
theoretical model of nonlinear processes in a dense atomic gas to explain the
observed results

A. Schabert

C. Cohen-Tannoudji

D. Meiser

D. Meschede

E. A. Oks

Eric R. Eliel

H. A. Lorentz

H. Li

I. I. Sobelman

M. D. Levenson

M. O. Scully

R. Friedberg

Robert W. Boyd

S. Svanberg

S. T. Cundiff

Vladimir A. Sautenkov

Yuri V. Rostovtsev

Physical Review A

English

arXiv

Sautenkov, Vladimir A.

Rostovtsev, Yuri V.

Eliel, Eric R.

OAKTrust Digital Repository (Texas A&M Univ)

arXiv:0804.4151v1  [quant-ph]  25 Apr 2008Observation of narrow Autler-Townes components in the resonant response of a denseatomic gasVladimir A. Sautenkov,1, 2 Yuri V. Rostovtsev,1 and Eric R. Eliel31 Department of Physics and Institute of Quantum Studies,Texas A&M University, College Station, Texas 77843-42422 P. N. Lebedev Institute of Physics, 119991 Moscow, Russia3 Huygens Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands(Dated: August 25, 2018)We have experimentally studied the reflection of a weak probe beam from a dense atomic potas-sium vapor in the presence of a strong laser field tuned to the atomic resonance transition. We haveobserved an Autler-Townes doublet under hitherto unexplored conditions, namely that the Rabifrequency induced by the strong laser field is much smaller than the self-broadened width of theresonance transition of the unexcited vapor. We attribute our observation to a reduction of theatomic decoherence by the strong drive field. We present a theoretical model of nonlinear processesin a dense atomic gas to explain the observed results.PACS numbers: PACS numbers: 32.70.-n, 42.50.Hz, 42.50.NnSpectral line broadening is a universal phenomenonand a multitude of techniques has been devised to reduceor eliminate it altogether, enabling the study of spectralfeatures that would, otherwise, remain hidden [1, 2, 3, 4].In particular this applies to atomic or molecular gaseswhere the collision rate can be made sufficiently smallby, for instance, rarefying the vapor. However, whenthe interest lies with the (strongly) interacting gas, linebroadening becomes the essence, and the study of thewidth of the fundamental resonance transitions in high-density atomic vapors is well-documented [5, 6].FIG. 1: (Color online) Energy-level scheme for potassium.The bare atomic states are shown in (A), where level a cor-responds to the 4p 2P1/2 excited state, level b to the 4s2S1/2ground state, and level c to the 4p 2P3/2 excited state. Thestrong drive field, with Rabi frequency Ω, couples states band c, while the probe laser beam, with Rabi frequency Ωp isscanned over the b−a transition. Frame (B) shows the probetransition in the dressed basis, the states being written as |+〉and |−〉, and (C) provides a sketch of the experimental setup.Although, in the general case, the broadening of theresonance line has many contributions [7], for dense ho-mogeneous gases, the major contribution is caused by theresonant dipole-dipole interaction between ground- andexcited-state atoms of the same species, and is knownas self- or resonance broadening [5, 6]. The interac-tion is long range, so that already at reasonably mod-est densities of order 1017 cm−3 one leaves the binary-collision regime and multi-perturber effects may comeinto play [6, 8]. It has, for instance, been shown thatthe Zeeman effect is modified at atomic densities of thisorder [9]. We note that multi-perturber effects were ob-served in high presure buffer gas [10, 11, 12] when theduration of collisions cannot be neglected.In a high-density vapor the atom responds not just tothe externally applied EM field but also to the field re-radiated by other atoms in the vapor, i.e. it responds tothe local field. As first shown by Lorentz, this causes theposition of the resonance to be shifted [13]. During thelast decade this local-field shift, named after Lorentz, hasbeen studied by both frequency [14, 15, 16, 17, 18, 19]and time-domain [20] techniques. It is proportional tothe atomic density, and of the same order of magnitudeas the line width [21].It has been predicted that the Lorentz local-field shiftdepends on the degree of (incoherent) excitation of thevapor [21, 22], a prediction that stimulated the study ofa variety of nonlinear optical phenomena in dense atomicvapors, such as piezophotonic switching and lasing with-out inversion [23]. The experimental demonstration ofthe excitation dependence of the Lorentz shift [17, 19]brought to light that the self-broadened width itself isalso excitation dependent, an effect that could be ex-plained in terms of a quasistatic (multi-perterber, quasi-molecular) collision model [6, 17]. Recently, it was shownby using a time-domain technique, that non-Markoviancollision dynamics can be observed in these high density2resonantly-broadened vapors, indicating that the dura-tion of a collision can no longer be neglected [24].FIG. 2: (Color online) Frequency-modulated reflectivity spec-tra of a potassium vapor at a density of 4.9 × 1017 cm−3, asmeasured on the D1 transition. Curves(a) and (b) display theFM reflection spectrum of the vapor when the pump laser isswitched off, and when it operates at a power of ≈ 0.5 W andis tuned far (130 GHz) above the D2 transition. When thedetuning of the pump laser is reduced to ≈ 3 GHz the spectralline in the FM spectrum becomes an Autler-Townes doublet(curve (c)). Curve (d) shows the Autler-Townes componentsat zero pump detuning.The experimental study of resonance broadening re-mains a topical issue in view of theoretical claims that,because of the long-range nature of the interaction,many-body effects play a role at all densities [6]. Here weshow that at a higher number density of 4.9× 1017 cm−3the atomic ensemble can be made to evolve coherentlyas if it is a two-level system with intensity dependentline width. We deduce this behavior from our measure-ments of the Autler-Townes splitting [25] of the potas-sium atomic ground state. Observation of the Autler-Townes splitting of optical transition in delute gaseswere previously reported in [26]. Essential to our ob-servation is the effect of collision-induced line narrow-ing [16, 17, 19].At the number density of our experiment, the self-broadened line width of both resonance lines of potas-sium is considerably larger than either their hyperfinestructure or their Doppler width. Under these condi-tions the level structure of potassium is well-representedby a three-level scheme, shown in Fig. 1. A strong driv-ing field (Rabi frequency Ω) couples levels b and c, whilea weak probe field, with Rabi frequency Ωp is scannedover the a↔ b transition.The experiment is performed in reflection (see Fig. 1C),using an experimental arrangement similar to that of Ref.[19]. The strong coupling field is produced by a CW Ti-sapphire laser tuned close to the D2-line (λ = 766 nm)of atomic potassium. The laser beam, having a maxi-mum power of ≈ 0.5 W, has its focus (the area of thebeam is 5 10−4 cm2) at the window of a vapor cell thatis constructed entirely out of sapphire. A weak probebeam from an external cavity diode laser is focussed tooverlap with the pump beam at the entrance window ofthe cell. The probe laser is scanned over the D1-line atλ = 770 nm, at a power level of ≈ 10−4 W, far below theonset of saturation (saturation parameter [3] is < 0.1).Both the pump and probe beams are linearly polarizedand are incident on the sapphire cell at near-normal inci-dence. While being scanned, the probe laser is frequencymodulated over a range of 100 MHz at a frequency of 400Hz. The reflected probe beam is captured by a photodi-ode whose signal output is fed to a lock-in amplifier. Ourexperiment runs at an atomic density of 4.9×1017 cm−3,yielding a self-broadened linewidth Γself/2π of 28.4 GHzfor the D1 line [9].Figure 2 shows the measured FM-modulated spec-tra. The zero on the frequency axis refers to the centerfrequency of the absorption spectrum of a low density(N ≃ 1011 cm−3) potassium vapor in a reference glasscell. Curve (a) displays the reflection spectrum whenthe pump beam is switched off, i.e. it shows the FMlinear reflectivity of the sapphire/high-density vapor in-terface. When the pump laser is switched on, operatesat an output level of 0.5 W, and is tuned 130 GHz abovethe D2 line, the FM spectrum of curve (b) is obtained.At this large detuning the pump-laser beam penetrates aconsiderable distance into the vapor cell. Due to radia-tion trapping the decay of the excited-state population isslowed down and, as a result of radiative transport, thevapor near the sapphire window becomes homogeneouslyand incoherently excited. In line with earlier observations([19]) one notices that the FM spectrum of the stronglyexcited vapor (curve (b)) is narrower than its unexcitedcounterpart (curve (a)), and that their centers do not co-incide. However, both spectra are described by the samespectral function, with adjusted values for the Lorentzlocal-field shift and self-broadened width [16, 17, 19].The spectral width Γself of the resonance line can beestimated from the interval ∆ωmm between the maximumand minimum of the reflection spectrum or, equivalently,from the zeros of the FM spectrum. For theD1 transitionone has Γself = 0.87∆ωmm [9, 19]. By this method, wedetermine the line width for the unexcited vapor as 31GHz (Fig. 2a), in reasonable agreement with the valueΓself/2π = 28.4 GHz, calculated using the known self-broadening coefficient and our estimate for the atomicdensity. Similarly, we estimate the line width for theincoherently excited vapor as just 11 GHz (Fig. 2b).Hereby we show that the excitation dependence of theself-broadened line width is a valid concept also at thevapor density of the present experiment.In order to observe coherent effects we tune the pump3laser close to the center of the atomic line. Curves (c)and (d) show the experimental FM reflectivity spectra fora pump detuning of 3 and 0 GHz, respectively. In bothcases one observes that the single resonance of curve (b) issplit into an Autler-Townes doublet [25, 26]. The asym-metry of the doublet in curve (c) reflects the fact that,for this curve, the pump laser is tuned slightly above theD2 resonance transition, while the near-perfect symmetryof curve (d) shows that the pump laser is, in that case,tuned on resonance. Note that, as a result of the variousline shifts, there is no easy method, beyond looking atthe symmetry of the Autler-Townes doublet, to establishwhether the pump laser is tuned exactly to resonance ornot.To obtain a good estimate for the width and separationof the the components of the Autler-Townes doublet wehave made a non-linear fit of the experimental data ofcurve (d) in Fig. 2, yielding a width of 8.5 GHz and asplitting of 7.6 GHz.It is well known that the separation between the twocomponents of the Autler-Townes doublet equals theRabi frequency induced by the pump laser [3, 27]. For theconditions of the present exeriment where hyperfine andZeeman substructure can be ignored, the Rabi frequencyΩ for the potassium D2 line can be expressed asΩ/2π = 8× 107√I[Wcm2]Hz, (1)where I = cE2/(8π) is the pump laser intensity (in unitsof W/cm2). Here the Rabi frequency is written asΩ = E℘x/h¯, (2)with E the optical electric field and ℘x the projectionof the atomic dipole moment ~℘ along that field. Thevalue of ℘x = ℘/3 has been obtained from experimentaldata for the spontaneous lifetime [28]. Using Eq. (1) wecalculate the Autler-Townes splitting to be 8 GHz at apump power of 0.5 W, in satisfying agreement with theexperimental value (7.6 GHz).We have recorded the Autler-Townes doublet for sev-eral values of the detuning ∆ and intensity of the pumplaser. When |∆| increases one of the components of thedoublet becomes stronger while the other fades away.When |∆/2π| > 6 GHz the weak component can nolonger be measured, and only a single resonance is ob-served. For this case, where the pump laser is de-tuned from exact resonance, the Autler-Townes splittingis given by the generalized Rabi frequency [27]Ω˜ =√Ω2 +∆2. (3)The measured values of the Autler-Townes splitting asa function of the generalized Rabi frequency Ω˜ are pre-sented in Fig. 3. The three points for Ω˜/2π ≤ 8 GHz havebeen measured at zero detuning and pump laser powersequal to 0.3, 0.4 and 0.5 W, respectively. The points atΩ˜/2π ≥ 8.5 GHz were measured by using a pump powerequal to 0.5 W and detunings of ∆/2π = ±3 GHz and ±6GHz, respectively. Also shown is a linear fit through thedata; its slope equals 0.92, in quite good agreement withthe expected value, equal to 1 (the error of slope is 2%and the difference between theoretical and experimentalcurves is about 6% due to systematic uncertanties).FIG. 3: The measured Autler-Townes splitting versus gener-alized Rabi frequency. The solid line shows the result of alinear fit.To explain our results we use the optical Bloch equa-tions for a V-type three-level atom, suitably modified forthe fact that the system under study is a dense ratherthan a dilute vapor. From these equations we evaluatethe susceptibility of the probe at frequency ωp as [29]χ(ωp) = i3λ2γ8π(na − nb) +Ω2ΓcbΓca(nc − nb)Γab +Ω2Γca. (4)Here the level populations na, nb and nc depend on theRabi frequency of the driving field Ω, γ is the radiativerate on the a → b transition, and the generalized coher-ence decay rates are Γcb = γ˜cb + iδcb, Γca = γ˜ca + iδca,Γab = γ˜ab+ iδ. The frequency of the pump is denoted asω¯, and its detuning is given by δcb = ωcb−ω¯+∆ωL+∆ωc,with ∆ωL the Lorentz local field shift, and ∆ωc the col-lisional frequency shift, which is independent of the levelof excitation [14, 15, 19]. The detuning of the probefrom resonance is δ = ωab − ωp + ∆ωL + ∆ωc, with ωpthe frequency of the probe laser. For the two photondetuning we write δca = ωca − ω¯ + ωp + ∆ωL + ∆ωc.For γ˜cb, γ˜ca and γ˜ab we write γ˜ab = γ/2 + Γself ≃ Γself ,γ˜cb = γ/2 + Γself ≃ Γself , and γ˜ca = γ + Γself ≃ Γself ,since the self-broadened line width is much larger thanthe natural width of the transitions.4For the self-broadened width we write [17, 19]Γself = knb, (5)with k the self-broadening coefficient [5]. The Lorentzlocal-field shift is given by [21, 22]∆ωL =k3(nb − na). (6)The reflectivity of the coherently driven dense vaporcan now be evaluated usingR(ω) =∣∣∣∣n(ω)− n0n(ω) + n0∣∣∣∣2, (7)with n(ω) =√1 + 4πχ(ω) and n0 the refractive indicesof the vapor and of the window material of the vapor cell,respectively. Using Eq. (7) and appropriate values for theexperimental parameters we calculate the FM reflectionspectra, as shown in Fig. 4, for a pump detuning of zeroand 3 GHz, respectively, and a pump Rabi frequency of12 GHz. Fully in line with the experimental result ourtheoretical model predicts a well-resolved Autler-Townesdoublet under circumstances that the Rabi frequency ismuch smaller than the unsaturated self-broadened linewidth.FIG. 4: Results of the theoretical model for the FM-reflectionspectrum of a vapor of coherently driven V-type three-levelatoms at high density, using Eqns. (4) and (7).It is worth to mention here that, even though the ex-periments and theoretical analysis have been done forconditions corresponding to hot dense gases, it will beinteresting to study discussed multy-perturber effects indense cold atomic and molecular gases, and possible in-fluence on coherent backscattering in cold atoms [30].In conclusion, we have observed the Autler-Townessplitting of the atomic ground state in the reflectionspectrum of a dense potassium vapor in a regime wherethe separation of the two Autler-Townes components, asgiven by the Rabi frequency, is much smaller than thenominal self-broadened width of the transition. We at-tribute our observation to the fact that the strong drivefield, in addition to inducing coherent evolution of theatomic levels, also causes a dramatic narrowing of thespectral line. Taking into account the excitation depen-dence of both the local-field shift and the resonance linewidth we obtain good agreement between our experimen-tal results and an effective three-level model based onmodified Bloch equations.We wish to acknowledge S.T. Cundiff, H. van Kam-pen, S. Mukamel, and J. P. Woerdman for useful discus-sions and beneficial help. This work was done, in part,while V.A.S. was a visitor at Leiden University as part ofthe research program of the ”Stichting voor Fundamen-tal Onderzoek der Materie”. V.A.S. and Yu.V.R. alsogratefully acknowledge the support from the NSF, theOffice of Naval Research, the Air Force Research Labora-tory (Rome, NY), Defense Advanced Research ProjectsAgency, and the Robert A. Welch Foundation (Grant#A-1261).[1] D. Meschede, Optics, Light and Lasers, (Wiley-VCH,Weinheim, Germany, 2004).[2] M. D. Levenson and S. S. Kano, Introduction to nonlinearlaser spectroscopy, (Academic Press, San Diego, 1988).[3] Robert W. Boyd, Nonlinear Optics (San Diego, CA : Aca-demic Press, 2003).[4] S. Svanberg, Atomic and Molecular Spectroscopy,(Springer, Berlin, 1992).[5] E. L. Lewis, Phys. Rep. 58, 1 (1980).[6] J. A. Leegwater and S. Mukamel, Phys. Rev. A 49, 146(1994).[7] I.I. Sobelman, L.A. Vainshtein, E.A. Yukov Excitation ofatoms and broadening of spectral lines (Berlin, New York,Springer-Verlag, 1981). Spectral line shapes : 18th Inter-national Conference on Spectral Line Shapes, Auburn,Alabama, 4-9 June 2006, Editors, Eugene Oks, MichaelPindzola (Melville, N.Y. : American Institute of Physics,2006). E.A. Oks, Plasma spectroscopy : the influence ofmicrowave and laser fields, (Berlin, New York, Springer-Verlag, 1995). Hans R. Griem, Spectral line broadeningby plasmas (New York, Academic Press, 1974).[8] W. P. West and A. Gallagher, Phys. Rev. A 17, 1431(1978).[9] H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P.5H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman,Phys. Rev. A 56, 310 (1997).[10] R. E. Walkup, A. Spielfiedel, and D. E. Pritchard, Phys.Rev. Lett. 45, 000986 (1980);[11] J.P. Woerdman, E.J. Blok, M. Kristensen, et al., Phys.Rev. A 53, 1183 (1996).[12] R.S. Trawinski, R. Ciurylo, J. Szudy, Phys. Rev. A74,022716 (2006).[13] H. A. Lorentz, Verh. Kon. Ned. Acad. Wet. 18, 1 (1879).[14] J. J. Maki, M. S. Malcuit, J. E. Sipe, R. W. Boyd. Phys.Rev. Lett. 67, 972 (1991).[15] J. J. Maki, W. V. Davis, R. W. Boyd, J. E. Sipe, Phys.Rev. A 46, 7155 (1992).[16] H.Li, T.S. Varzhapetyan, V.A. Sautenkov, Yu.V. Ros-tovtsev, H. Chen, D. Sarkisyan, and M.O. Scully, ac-cepted to be published in Appl.Phys. B (2008).[17] V. A. Sautenkov, H. van Kampen, E. R. Eliel, and J. P.Woerdman, Phys. Rev. Lett. 77, 3327 (1996).[18] P. Wang, A. Gallagher, and J. Cooper, Phys. Rev. A 56,1598 (1997).[19] H. van Kampen, V. A. Sautenkov, C. J. C. Smeets, E. R.Eliel and J.P. Woerdman, Phys. Rev. A 59, 271 (1999).[20] S. T. Cundiff, Laser Physics, 12, 1073 (2002).[21] R. Friedberg, S. R. Hartmann and J. T. Manassah, Phys.Rep. 7, 101 (1973); Phys. Rev. A 42, 5573 (1990).[22] J. T. Manassah, Phys. Rep. 101, 359 (1983).[23] A. S. Manka, J. P. Dowling, C. M. Bowden and M. Fleis-chhauer, Phys. Rev. Lett. 73, 1789, (1994).[24] V. O. Lorenz and S. T. Cundiff, Phys. Rev. Lett. 95,163601 (2005). V.O. Lorentz, S. Mukamel, W. Zhuangand S.T. Cundiff, Phys. Rev. Lett. 100, 013603 (2008).[25] S. H. Autler, and C. H. Townes, Phys. Rev. 100, 703(1955).[26] A. Schabert, R. Keil, P.E. Toschek, Opt. Commun. 13,265 (1975); A. Schabert, R. Keil, P.E. Toschek, Appl.Phys. 6, 181 (1975).[27] C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg,Atom-Photon Interactions: Basic Processes and Appli-cations (Wiley, New-York, 1992) Chap.VI.[28] I. I. Sobelman, Atomic Spectra and Radiative Transitions,(Springer, Berlin, 1992).[29] M. O. Scully and M. S. Zubairy, Quantum Optics (Cam-bridge University Press, Cambridge 1997).[30] D. Meiser, T. Miyakawa, H. Uys, P. Meystre, Advances inAtomic, Molecular, and Optical Physics 53, 151 (2006).G. Labeyrie, F. de Tomasi, J.C. Bernard, C.A. Muller,C. Miniatura, R. Kaiser, Phys. Rev. Lett. 83, 5266(1999). D.V. Kupriyanov, I.M. Sokolov, C.I. Sukenik,M.D. Havey, Laser Phys. Lett. 3, 223 (2006).

Observation of narrow Autler-Townes components in the resonant response of a dense atomic gas

Texas A&M University

Crossref

https://oaktrust.library.tamu.edu/bitstream/1969.1/183435/1/document-1.pdf

Observation of narrow Autler-Townes components in the resonant response
  of a dense atomic gas

Observation of narrow Autler-Townes components in the resonant response of a dense atomic gas

Abstract

Similar works

Full text

Available Versions

OAKTrust Digital Repository (Texas A&M Univ)

Texas A&M University

Crossref