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Observation of electromagnetically induced transparency in two-photon transitions of 39K2
Chemical Physics Letters 403 (2005) 262–267 www.elsevier.com/locate/cplett
Observation of electromagnetically induced transparency in two-photon transitions of 39K2 Li Li a
a,*
, P. Qi b, A. Lazoudis b, E. Ahmed b, A.M. Lyyra
b
Department of Physics and Key Laboratory of Atomic and Molecular Nanosciences, Tsinghua University, Beijing 100084, China b Department of Physics, Temple University, Philadelphia, PA 19122, USA Received 4 December 2004; in final form 4 January 2005 Available online 20 January 2005
Abstract Electromagnetically induced transparency has been observed in 39K2 two-photon transitions by fluorescence detection. The two1 þ 3 photon absorptions correspond to 23 Pg X1 Rþ g transitions through A Ru b Pu mixed intermediate enhancing levels, which are coincidentally on resonance with the excitation laser frequency. Laser intensity dependence of this effect has been studied and different detection schemes have been applied. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Coherence effects such as electromagnetically induced transparency (EIT) [1] are well known in various threelevel atomic systems [2,3]. These effects have been more difficult to observe in molecular systems since molecular transitions have smaller oscillator strengths and as a result any single molecular transition contributes very little to absorption. In spite of these complexities EIT studies have been extended from closed atomic systems to more complicated open molecular systems [4]. Recently, there has been a surge of interest in studying quantum interference effects in complicated multilevel systems with different energy level arrangements [5–8]. In addition to EIT many investigations involve Autler–Townes (A–T) splitting [4,9,10], which, for large laser Rabi frequencies, considerably modifies the observed spectra. Few earlier experimental studies have reported spectral manifestations of coherence effects such as dark resonances in molecular systems [11,12]. In our previous studies EIT and A–T splitting have been observed and
*
Corresponding author. Fax: +86 10 6278 1598. E-mail address: [email protected] (L. Li).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.01.016
analyzed theoretically in gas phase Li2 and Na2 molecular systems [4,10,13]. In these experiments, two or three single mode continuous wave (CW) lasers were used. For example in the case of the experiment described in [4] one intense pump (coupling) laser was set on reso0 0 nance with a G1 Pg v; J ¼ J 0 ; J 0 1 A1 R þ u v ; J transition of Li2 and a weak probe laser was scanned through the Doppler broadened line of the 0 00 0 0 00 A1 R þ X1 Rþ uv ;J g v ; J ¼ J 1 transition. EIT was observed at the center frequency of the Doppler broad0 00 0 0 0 ened line of both the A1 Rþ X1 Rþ uv ;J g v ;J ¼ J þ 1 1 þ 00 0 00 0 1 þ 0 and the A Ru v ; J X Rg v ; J ¼ J 1 transitions (Figs. 1 and 2 of [4]). We report in this Letter our observation of EIT in a 39 K2 two-photon transition system.
2. Experimental Potassium vapor was generated in a five-arm heatpipe oven. 1 torr Ar was used as buffer gas. The potassium vapor pressure and temperature were controlled with the buffer gas pressure. Under the heatpipe operating condition, 1 torr Ar (as well as potassium vapor) corresponds to about 300 °C.
L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
A CR 899-29 Ti:Sapphire laser was used to excite K2 two-photon transitions. The absolute laser frequency was calibrated by optogalvanic spectroscopy using a uranium hollow cathode lamp. Two laser beam configurations were used in our experiment: reflecting the forward beam back on itself and splitting the beam into two counter-propagating beams as shown in Fig. 1. In the reflected beam set-up, the laser beam was focused at the center of the heatpipe by a lens (L1). The laser output was 600–700 mW and reduced to about 60% by mirrors and lenses before entering the heatpipe window. The beam diameter was 0.46 mm at the heatpipe center. A mechanical chopper was used to modulate the laser beam at 1100 Hz. When a two-photon transition is excited by two photons from the laser beam in the same direction (for example, in Fig. 1 the laser beam is not reflected back by mirror M3 but blocked with a beam stop after passing through the heatpipe), the two-photon line shape is Doppler-limited. When the Ti:Sapphire laser frequency was scanned, two-photon excitation was detected by monitoring yellow-green fluorescence with a photomultiplier tube (PMT), whose output was sent to a lock-in amplifier (or a current pre-
263
amplifier). A set of color glass filters was used to transmit the yellow-green fluorescence from the two-photon 3 3 þ excited 3 Rþ g and Pg states to the a Ru state and eliminate the scattered IR laser light as well as the strong 1 þ one-laser induced A1 Rþ u ! X Rg IR fluorescence. The signals were recorded with a computer, which also controlled the laser frequency scan. When a two-photon transition was detected, fluorescence from the twophoton populated upper level was dispersed by a Spex 1404 monochromator. When a two-photon transition is excited by absorbing two photons, one from each counter-propagating laser beams, the two-photon absorption line is Doppler-free. In order to conduct the Doppler-free two-photon excitation experiment, after passing through the heatpipe, the laser beam was reflected by a mirror and the backward beam was focused to the center of the heatpipe with another Lens (L2). The backward reflected beam overlapped with the forward traveling beam at the center (with a very small angle in order to avoid an effect on the laser stability by the retro-reflected beam). At the heatpipe center, the diameter of the backward beam was 0.3 mm. The laser power of the backward reflected beam was 40% of the laser output before re-entering the heatpipe. The Doppler-free two-photon transitions were detected in the same way as the Doppler-limited twophoton transitions. Another experimental setup, in which the laser beam was split into two components, is shown in Fig. 1 by dashed lines. In this case a 60% reflecting and 40% transmitting beam splitter (BS) was used to split the laser beam into a stronger pump beam and a weaker probe beam. The two beams were counter-propagating, focused, and overlapped at the center of the heatpipe with a small angle. The pump and probe laser powers in front of the heatpipe windows were 180 and 80 mW, respectively. The diameters of the pump and probe beams at the heatpipe center were kept roughly the same as in the case of the reflected beam set-up. The mechanical chopper modulated either the pump or the probe beam or both. Two-photon transitions were detected as in the back-reflected beam set-up.
3. Observations 3.1. With back reflected laser beam set-up
Fig. 1. Experimental set-up. The back-reflected beam geometry did not involve beamsplitter (BS), mirrors M1, and M2, and the forward beam was reflected back on itself by the mirror M3. In the split beam geometry, the laser beam was split into a stronger pump (dashed line) and a weaker probe (solid line) beams with beam splitter (BS).
We scanned the frequency range of 11 000– 11 700 cm1 with only the forward beam (the beam was blocked after passing through the heatpipe) by detecting the yellow-green fluorescence. The laser frequency corresponds to the K2 A1 Rþ X1 Rþ u g transitions. Due to the large density of rovibrational levels in this case, tens of peaks appeared in the spectra in every wavenumber. Since the A ! X fluorescence is in
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the IR region, the yellow-green fluorescence must be from higher electronic states. These highly excited electronic states can be populated by direct two-photon transitions or by collisional energy transfer. It has been 3 observed in Na2 that whenever an A1 Rþ u or b Pu level was excited, violet fluorescence with a maximum at 436 nm could be detected [14]. This violet band originates from the Na2 23 Pg ! a3 Rþ u transition [15]. The 23Pg levels were populated by collisional energy pooling 3 of two excited molecules in the A1 Rþ u or b Pu state. The diffuse band in potassium vapor which peaks at 573 nm has also been observed and tentatively assigned to the K2 23 Pg ! a3 Rþ u transition [16]. Recently we confirmed this assignment [17]. In order to distinguish the direct two-photon signals from the collision-induced signals in our Doppler-limited excitation spectra, Dopplerfree two-photon excitation has been carried out. Fig. 2 gives a portion of the excitation spectrum in the 11667.0–11669.6 cm1 frequency range with both the forward and the backward traveling beams. From the spectrum we can see that some peaks have very narrow Doppler-free two-photon lines on top of the Doppler-limited lines. In this case the broad Doppler-limited background corresponds to two-photon (from same direction beam) absorption of molecules moving in different directions with different velocities and the narrow peaks correspond to Doppler-free twophoton (one photon from the forward beam and another photon from the backward beam) absorption of molecules moving in all directions with different velocities [18]. In principle, the Doppler-free peaks can be much more intense than the Doppler-limited background if the forward and backward laser beams match in intensity and geometry. In this experiment, no special efforts have been made to match the beams traveling in the opposite directions. The Doppler-limited peaks
without Doppler-free lines on top in Fig. 2 are collision-induced signals, not two-photon absorption. Instead of a Doppler-free narrow increase of intensity on top of the Doppler background as in most two-photon excitation cases, we saw intensity dips on the Doppler lines. In Fig. 2, the lines at 11667.71 and 11668.93 cm1 exhibit such dips. The enlargements of the two peaks are given on top of the lines. We observed a very strong two-photon transition at laser frequency 11540.089 cm1. The yellow-green fluorescence was so strong such that the whole heatpipe became very bright when the laser frequency was tuned to this frequency without the backward reflected beam. With the backward reflected beam, however, the yellow-green fluorescence became darker when the laser frequency passed the center frequency of the Doppler line. Fig. 3a gives the excitation line shape by detecting yellow-green fluorescence with a filtered PMT and a Lock-in amplifier without the backward reflected beam. The excitation line has a normal Doppler broadened line shape. Fig. 3b shows the line shape with the backward reflected beam. Instead of a Doppler-free narrow peak at the center of the Doppler line, a dip appears at the center. Several weak Doppler-free lines also appear in the 3.5 GHz scan. When the laser beams were not modulated and a current preamplifier replaced the lock-in amplifier, the excitation line shape was the same as Fig. 3b, confirming that the dip was due to the weakness of the two-photon absorption. The depth of the dip was laser intensity dependent: the stronger the laser intensity the deeper the dip. In order to assign this two-photon transition, resolved fluorescence from the 11540.089 cm1 photon excited upper level in the wavelength range 520–830 nm has been carried out without the backward reflected beam. The fluorescence contains three parts:
Intensity (Arbitrary Unit)
4000
11667.71 cm
-1
11668.93 cm
-1
3000
2000
1000
0
11667.0
11667.5
11668.0
11668.5
cm
11669.0
11669.5
-1
Fig. 2. A portion of the excitation spectrum. Enlargement of the peaks with dips at 11667.71 and 11668.93 cm1 are given above the lines.
L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
Intensity (arbitraryunit)
(a) 3000 2500 2000 1500 1000 500 0 11540.00
11540.05
11540.10
11540.15
cm-1
Intensity (arbitrary unit)
(b) 4000 3500 3000 2500 2000 1500 1000 500 0 11540.00
11540.05
11540.10
11540.15
cm-1
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(c) 1200
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8; J 0 ¼ 30, which mixes with the b3P0u v 0 = 20, J 0 = 31 level and has 18% 3P0u character [19–21]. This 0 0 A1 Rþ u v ¼ 8; J ¼ 30 level has been observed by all-optical triple resonance spectroscopy [19,20]. The observed 0 0 term value of the A1 Rþ level is u v ¼ 8; J ¼ 30 1 11733.286 cm [20], the calculated term value from the new molecular constants is 11733.287 cm1 [21]. The energy of the virtual level of the two-photon transi00 00 tion (the term value of the X1 Rþ g v ¼ 1; J ¼ 31 level [22] plus the laser frequency, 11540.089 cm1), is 11733.290 cm1, leading to the conclusion that the inter0 0 mediate enhancing A1 Rþ u v ¼ 8; J ¼ 30 level coincidently has the same energy as the virtual level and this two-photon transition actually becomes an IR–IR double resonance transition. Fig. 3c gives the excitation line shape by monitoring the 23P0g v 33, J = 31 fluorescence to the b3P0u v 0 = 0, J 0 = 30 level (752.86 nm) with the monochromator. In Fig. 3c the line looks more symmetric and other weak Doppler-free transitions were not detected when only selectively monitoring the fluorescence from the 23P0g v 33, J = 31 level.
1000
3.2. With split laser beam set-up
800 600 400 200 0 11540.00
11540.05
11540.10
11540.15
cm-1
Fig. 3. The line shapes of the two-photon transition at 11540.089 cm1 by monitoring yellow-green fluorescence with filters and PMT without the backward beam (a) and with the backward beam (b) and by monitoring the 23P0g v, J = 31 ! b3P0u v 0 = 0, J 0 = 30 fluorescence (752.86 nm) with a monochromator (c).
(1) Bound–bound fluorescence into the bound levels of the a3 Rþ u state and bound-free fluorescence into the repulsive continuum of the a3 Rþ u state with an oscillation (reflection) structure and a strong peak at 573 nm (Fig. 4a). (2) Fluorescence into the b3Pu levels (Fig. 4b). 1 þ (3) At longer wavelength, A1 Rþ u ! X Rg fluorescence. Since the upper electronic state can radiate to the 3 3 þ a3 Rþ u state, it must be a Rg or a Pg state. From the rotational patterns and vibrational spacings into the lev3 els of the a3 Rþ u and b Pu states, we have assigned this 3 upper state to the 2 Pg state. The 23Pg state has been observed recently by infrared–infrared double resonance and two-photon transitions [17]. Ref. [17] has given the 00 00 assignment procedure of the K2 23Pg v, J X1 Rþ g v ;J two-photon transitions. This two-photon transition excited by two 11540.089 cm1 photons has been assigned 00 00 as 23 P0g v 33; J ¼ 31 X1 Rþ g v ¼ 1; J ¼ 31 transi0 tion with an intermediate enhancing level of A1 Rþ uv ¼
In order to study intensity dependence of the forward and backward beams independently, a 60% reflection and 40% transmission beam splitter was used to obtain a pump beam with 60% and a probe beam with 40% of the initial laser power. The two beams counter-propagated and were overlapped at the center of the heatpipe. Figs. 5a–c give the line shapes at different probe intensities when the pump laser power was 180 mW and the probe beam was modulated. In the spectra, the relative intensities of the weak Doppler-free sharp lines become much stronger than in Fig. 3b, because the pump laser beam was not modulated (the strong Doppler background by the strong pump laser contribution was not detected) and the weak lines could be recorded at a more sensitive scale. It can be seen that the weaker the probe beam the deeper the dip. When the probe laser power was 1 mW, its absorption was near zero at the center of the Doppler line and EIT occurred. Several other Doppler-free two-photon transitions with dips have also been studied and the results are similar to this 11540.089 cm1 signal.
4. Discussion 4.1. Are the dips in the two-photon excitation spectra Lamb dips? The experimental set-up for studying a Lamb dip is similar to Fig. 1 [18]. When the laser frequency is tuned through a resonance transition, at the Doppler line
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L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
(a) 25 0 00 3
2 Πg
+
3
a Σ u transition
Intensity (arbitrary unit)
20 0 00
15 0 00
10 0 00
5 0 00
B ound-bound transition
0 52 0
54 0
56 0
5 80
6 00
nm (b)
3000 3
3
2 Πg b Πu fluorescence
v'=0
Intensity (arbitriry unit)
2500
2000 2
4p P3/2 4s
1500
2
4p P1/2
v'=1 1000
4s v'=5
v'=3 v'=2
500
0 750
755
760
765
770
775
780
nm 3 0 Fig. 4. Resolved fluorescence spectra from the two 11540.089 cm1 photon excited upper level: (a) to the a3 Rþ u state, (b) to the b Pu v = 0–5 levels. 1 þ 1 þ The unassigned doublets could be A Ru ! X Rg fluorescence and are not assigned.
center the forward and backward beams both excite the molecules with zero velocity projection on the laser propagation directions. The total absorption coefficient decreases at the line center and a Lamb dip appears. If an intermediate enhancing level is exactly on resonance, the Lamb dip of the transition between the ground level and intermediate enhancing level will appear at the same frequency as the Doppler-free two-photon line. But the increase by Doppler-free two-photon absorption of molecules with all velocities will be much stronger than the absorption based decrease of molecules with zero velocity projection only. In their Na2 experiment, Morgan et al. [23] and Xia et al. [24] simultaneously monitored both Doppler-free two-photon signals and Lamb dips of transitions between the ground X1 Rþ g and the enhancing A1 Rþ states. When their Doppler-free two-photon u
signals increased, the depths of the Lamb dips remained negligible in their spectra. Most Doppler-free two-photon signals in our K2 spectra were narrow peaks, a few showed dips. Clearly these dips are not Lamb dips, but manifestations of EIT due to Autler–Townes splitting (ac Stark effect) by a strong coupling laser field [10–12]. In Fig. 5c when the probe laser power was decreased to 1 mW, the absorption of the probe beam at the 11540.089 cm1 is near zero and transparency occurs. 4.2. Why EIT dips in two-photon transitions were relatively rare for other molecules? It is well known that two-photon transitions require enhancing intermediate level(s). In atoms or in mole-
L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
Acknowledgements
Intensity
(a) 3000 2500 2000 1500 1000 500 0 11540.04
11540.06
11540.08
11540.10
11540.12
(b) 2000 Intensity
267
1500 1000
The experiment was carried out at Temple University. Support from the NSF (PHY 0245311) in the US and from the NNSF (20173029 and 20473042) and NKBRSF in China is gratefully acknowledged. We thank Profs. L.M. Narducci and Frank Spano for helpful discussions and suggestions, Prof. T. Bergeman for 3 calculating the term values of the A1 Rþ u and b Pu states. Li Li acknowledges the Lagerqvist Research Fund of Temple University for support during her visit and Prof. B. Kim for his hospitality during her visit to KAIST, where she analyzed the data.
500 0 11540.02
11540.04
11540.06
11540.08
11540.10
11540.12
(c) 1000 Intensity
800 600 400 200 0 11540.02
11540.04
11540.06
11540.08
11540.10
11540.12
Fig. 5. Probe laser intensity dependence in the split beam geometry. The pump laser power was 180 mW, and the probe beam in (a), (b) and (c) were 40, 20, and 1 mW, respectively. The sensitivity settings of the Lock-in amplifier in cases (a), (b) and (c) were the same and the relative intensities of the signals are thus comparable.
cules with pulsed lasers, the enhancing level(s) can be far away from the virtual intermediate level. In molecular excitation with CW lasers, however, the enhancing levels have to be closer; otherwise the two-photon transition cross-section will be very small. If an intermediate enhancing level is close to resonance, a two-photon Doppler background can also be observed. Dips will appear if a strong pump laser induces EIT. K2 is a relatively heavy molecule and the density of the rovibronic levels is high. The spin–orbit interaction, which mixes the A1 Rþ u and b3Pu states, is strong for K2. A mixed intermediate enhancing level can be coincidentally resonant to give rise to EIT in K2 two-photon transitions into triplet states. Line shapes of Doppler-free two-photon transitions have been studied in atoms and lighter molecules, such as Na2 and Li2. Since their energy level densities are lower, no EIT has been observed in the Doppler-free two-photon excitation spectra. It is likely that this kind of EIT will be observed in heavier molecules such as Rb2 and Cs2 due to their high energy level density. Theoretical analysis of our results is in progress. The current theoretical model only applies when the coupling field frequency is kept fixed on resonance and the probe laser is detuned.
References [1] S.E. Harris, Phys. Today 50 (1997) 36. [2] J. Gea-Banacloche, Y. Li, S. Jin, M. Xiao, Phys. Rev. A 51 (1995) 576. [3] D.J. Fulton, S. Shepherd, R.R. Moseley, B.D. Sinclair, M.H. Dunn, Phys. Rev. A 52 (1995) 2302. [4] J. Qi, F.C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L.M. Narducci, R.W. Field, A.M. Lyyra, Phys. Rev. Lett. 88 (2002) 173003. [5] D. McGloin, D.J. Fulton, M.H. Dunn, Opt. Commun. 190 (2001) 221. [6] J.H. Xu, G.C. La Rocca, F. Bassani, D. Wang, J.Y. Gao, Opt. Commun. 216 (2003) 157. [7] D.J. McGloin, J. Phys. B 36 (2003) 2861. [8] A. Joshi, M. Xiao, Phys. Lett. A 317 (2003) 370. [9] M. Yan, G. Rickey, Y. Zhu, Phys. Rev. A 64 (2001) 43807. [10] J. Qi, G. Lazarov, X. Wang, L. Li, L.M. Narducci, A.M. Lyyra, F.C. Spano, Phys. Rev. Lett. 83 (1999) 288. [11] R. Sussmann, R. Neuhauser, H.J. Neusser, J. Chem. Phys. 103 (1995) 3315. [12] T. Halfmann, K. Bergmann, J. Chem. Phys. 104 (1996) 7068. [13] P. Qi, A. Hansson, Li Li, T. Kirova, A. Lazoudis, E. Ahmed, J. Qi, A.M. Lyyra (to be submitted). [14] Li Li, G. Lazarov, J. Huenneckens, A.M. Lyyra, unpublished. [15] G. Pichler, J.T. Bahns, K. Sando, W.C. Stwalley, D.D. Konowalow, Li Li, R.W. Field, W. Muller, Chem. Phys. Lett. 129 (1986) 425. [16] W.T. Luh, J.T. Bahns, A.M. Lyyra, K.M. Sando, P. Kleiber, W.C. Stwalley, J. Chem. Phys. 88 (1988) 2235; W.T. Luh, K.M. Sando, A.M. Lyyra, W.C. Stwalley, Chem. Phys. Lett. 144 (1988) 221. [17] Y. Chu, F. Xie, D. Li, Li Li, V.B. Sovkov, V.S. Ivanov, A.M. Lyyra, J. Chem. Phys. 122 (2005). [18] W. Demtro¨der, Laser Spectroscopy, Springer-Verlag, Heidelberg, New York, 2003, p. 450. [19] G. Jong, Li Li, T.-J. Whang, W.C. Stwalley, J. Coxon, M. Li, A.M. Lyyra, J. Mol. Spectrosc. 155 (1992) 115. [20] G. Jong, Ph.D. Thesis, University of Iowa, 1991. [21] M.R. Manaa, A.J. Ross, F. Martin, P. Crozet, A.M. Lyyra, Li Li, C. Amiot, T. Bergeman, J. Chem. Phys. 117 (2002) 11208. [22] J. Heinze, U. Schuhle, F. Engelke, C.D. Caldwell, J. Chem. Phys. 87 (1987) 43. [23] G.P. Morgan, H.R. Xia, A.L. Schawlow, J. Opt. Soc. Am. 72 (1982) 315. [24] H.R. Xia, G.-Y. Yan, A.L. Schawlow, Opt. Commun. 39 (1981) 153.
Observation of electromagnetically induced transparency in two-photon transitions of 39K2 Li Li a
a,*
, P. Qi b, A. Lazoudis b, E. Ahmed b, A.M. Lyyra
b
Department of Physics and Key Laboratory of Atomic and Molecular Nanosciences, Tsinghua University, Beijing 100084, China b Department of Physics, Temple University, Philadelphia, PA 19122, USA Received 4 December 2004; in final form 4 January 2005 Available online 20 January 2005
Abstract Electromagnetically induced transparency has been observed in 39K2 two-photon transitions by fluorescence detection. The two1 þ 3 photon absorptions correspond to 23 Pg X1 Rþ g transitions through A Ru b Pu mixed intermediate enhancing levels, which are coincidentally on resonance with the excitation laser frequency. Laser intensity dependence of this effect has been studied and different detection schemes have been applied. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Coherence effects such as electromagnetically induced transparency (EIT) [1] are well known in various threelevel atomic systems [2,3]. These effects have been more difficult to observe in molecular systems since molecular transitions have smaller oscillator strengths and as a result any single molecular transition contributes very little to absorption. In spite of these complexities EIT studies have been extended from closed atomic systems to more complicated open molecular systems [4]. Recently, there has been a surge of interest in studying quantum interference effects in complicated multilevel systems with different energy level arrangements [5–8]. In addition to EIT many investigations involve Autler–Townes (A–T) splitting [4,9,10], which, for large laser Rabi frequencies, considerably modifies the observed spectra. Few earlier experimental studies have reported spectral manifestations of coherence effects such as dark resonances in molecular systems [11,12]. In our previous studies EIT and A–T splitting have been observed and
*
Corresponding author. Fax: +86 10 6278 1598. E-mail address: [email protected] (L. Li).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.01.016
analyzed theoretically in gas phase Li2 and Na2 molecular systems [4,10,13]. In these experiments, two or three single mode continuous wave (CW) lasers were used. For example in the case of the experiment described in [4] one intense pump (coupling) laser was set on reso0 0 nance with a G1 Pg v; J ¼ J 0 ; J 0 1 A1 R þ u v ; J transition of Li2 and a weak probe laser was scanned through the Doppler broadened line of the 0 00 0 0 00 A1 R þ X1 Rþ uv ;J g v ; J ¼ J 1 transition. EIT was observed at the center frequency of the Doppler broad0 00 0 0 0 ened line of both the A1 Rþ X1 Rþ uv ;J g v ;J ¼ J þ 1 1 þ 00 0 00 0 1 þ 0 and the A Ru v ; J X Rg v ; J ¼ J 1 transitions (Figs. 1 and 2 of [4]). We report in this Letter our observation of EIT in a 39 K2 two-photon transition system.
2. Experimental Potassium vapor was generated in a five-arm heatpipe oven. 1 torr Ar was used as buffer gas. The potassium vapor pressure and temperature were controlled with the buffer gas pressure. Under the heatpipe operating condition, 1 torr Ar (as well as potassium vapor) corresponds to about 300 °C.
L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
A CR 899-29 Ti:Sapphire laser was used to excite K2 two-photon transitions. The absolute laser frequency was calibrated by optogalvanic spectroscopy using a uranium hollow cathode lamp. Two laser beam configurations were used in our experiment: reflecting the forward beam back on itself and splitting the beam into two counter-propagating beams as shown in Fig. 1. In the reflected beam set-up, the laser beam was focused at the center of the heatpipe by a lens (L1). The laser output was 600–700 mW and reduced to about 60% by mirrors and lenses before entering the heatpipe window. The beam diameter was 0.46 mm at the heatpipe center. A mechanical chopper was used to modulate the laser beam at 1100 Hz. When a two-photon transition is excited by two photons from the laser beam in the same direction (for example, in Fig. 1 the laser beam is not reflected back by mirror M3 but blocked with a beam stop after passing through the heatpipe), the two-photon line shape is Doppler-limited. When the Ti:Sapphire laser frequency was scanned, two-photon excitation was detected by monitoring yellow-green fluorescence with a photomultiplier tube (PMT), whose output was sent to a lock-in amplifier (or a current pre-
263
amplifier). A set of color glass filters was used to transmit the yellow-green fluorescence from the two-photon 3 3 þ excited 3 Rþ g and Pg states to the a Ru state and eliminate the scattered IR laser light as well as the strong 1 þ one-laser induced A1 Rþ u ! X Rg IR fluorescence. The signals were recorded with a computer, which also controlled the laser frequency scan. When a two-photon transition was detected, fluorescence from the twophoton populated upper level was dispersed by a Spex 1404 monochromator. When a two-photon transition is excited by absorbing two photons, one from each counter-propagating laser beams, the two-photon absorption line is Doppler-free. In order to conduct the Doppler-free two-photon excitation experiment, after passing through the heatpipe, the laser beam was reflected by a mirror and the backward beam was focused to the center of the heatpipe with another Lens (L2). The backward reflected beam overlapped with the forward traveling beam at the center (with a very small angle in order to avoid an effect on the laser stability by the retro-reflected beam). At the heatpipe center, the diameter of the backward beam was 0.3 mm. The laser power of the backward reflected beam was 40% of the laser output before re-entering the heatpipe. The Doppler-free two-photon transitions were detected in the same way as the Doppler-limited twophoton transitions. Another experimental setup, in which the laser beam was split into two components, is shown in Fig. 1 by dashed lines. In this case a 60% reflecting and 40% transmitting beam splitter (BS) was used to split the laser beam into a stronger pump beam and a weaker probe beam. The two beams were counter-propagating, focused, and overlapped at the center of the heatpipe with a small angle. The pump and probe laser powers in front of the heatpipe windows were 180 and 80 mW, respectively. The diameters of the pump and probe beams at the heatpipe center were kept roughly the same as in the case of the reflected beam set-up. The mechanical chopper modulated either the pump or the probe beam or both. Two-photon transitions were detected as in the back-reflected beam set-up.
3. Observations 3.1. With back reflected laser beam set-up
Fig. 1. Experimental set-up. The back-reflected beam geometry did not involve beamsplitter (BS), mirrors M1, and M2, and the forward beam was reflected back on itself by the mirror M3. In the split beam geometry, the laser beam was split into a stronger pump (dashed line) and a weaker probe (solid line) beams with beam splitter (BS).
We scanned the frequency range of 11 000– 11 700 cm1 with only the forward beam (the beam was blocked after passing through the heatpipe) by detecting the yellow-green fluorescence. The laser frequency corresponds to the K2 A1 Rþ X1 Rþ u g transitions. Due to the large density of rovibrational levels in this case, tens of peaks appeared in the spectra in every wavenumber. Since the A ! X fluorescence is in
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the IR region, the yellow-green fluorescence must be from higher electronic states. These highly excited electronic states can be populated by direct two-photon transitions or by collisional energy transfer. It has been 3 observed in Na2 that whenever an A1 Rþ u or b Pu level was excited, violet fluorescence with a maximum at 436 nm could be detected [14]. This violet band originates from the Na2 23 Pg ! a3 Rþ u transition [15]. The 23Pg levels were populated by collisional energy pooling 3 of two excited molecules in the A1 Rþ u or b Pu state. The diffuse band in potassium vapor which peaks at 573 nm has also been observed and tentatively assigned to the K2 23 Pg ! a3 Rþ u transition [16]. Recently we confirmed this assignment [17]. In order to distinguish the direct two-photon signals from the collision-induced signals in our Doppler-limited excitation spectra, Dopplerfree two-photon excitation has been carried out. Fig. 2 gives a portion of the excitation spectrum in the 11667.0–11669.6 cm1 frequency range with both the forward and the backward traveling beams. From the spectrum we can see that some peaks have very narrow Doppler-free two-photon lines on top of the Doppler-limited lines. In this case the broad Doppler-limited background corresponds to two-photon (from same direction beam) absorption of molecules moving in different directions with different velocities and the narrow peaks correspond to Doppler-free twophoton (one photon from the forward beam and another photon from the backward beam) absorption of molecules moving in all directions with different velocities [18]. In principle, the Doppler-free peaks can be much more intense than the Doppler-limited background if the forward and backward laser beams match in intensity and geometry. In this experiment, no special efforts have been made to match the beams traveling in the opposite directions. The Doppler-limited peaks
without Doppler-free lines on top in Fig. 2 are collision-induced signals, not two-photon absorption. Instead of a Doppler-free narrow increase of intensity on top of the Doppler background as in most two-photon excitation cases, we saw intensity dips on the Doppler lines. In Fig. 2, the lines at 11667.71 and 11668.93 cm1 exhibit such dips. The enlargements of the two peaks are given on top of the lines. We observed a very strong two-photon transition at laser frequency 11540.089 cm1. The yellow-green fluorescence was so strong such that the whole heatpipe became very bright when the laser frequency was tuned to this frequency without the backward reflected beam. With the backward reflected beam, however, the yellow-green fluorescence became darker when the laser frequency passed the center frequency of the Doppler line. Fig. 3a gives the excitation line shape by detecting yellow-green fluorescence with a filtered PMT and a Lock-in amplifier without the backward reflected beam. The excitation line has a normal Doppler broadened line shape. Fig. 3b shows the line shape with the backward reflected beam. Instead of a Doppler-free narrow peak at the center of the Doppler line, a dip appears at the center. Several weak Doppler-free lines also appear in the 3.5 GHz scan. When the laser beams were not modulated and a current preamplifier replaced the lock-in amplifier, the excitation line shape was the same as Fig. 3b, confirming that the dip was due to the weakness of the two-photon absorption. The depth of the dip was laser intensity dependent: the stronger the laser intensity the deeper the dip. In order to assign this two-photon transition, resolved fluorescence from the 11540.089 cm1 photon excited upper level in the wavelength range 520–830 nm has been carried out without the backward reflected beam. The fluorescence contains three parts:
Intensity (Arbitrary Unit)
4000
11667.71 cm
-1
11668.93 cm
-1
3000
2000
1000
0
11667.0
11667.5
11668.0
11668.5
cm
11669.0
11669.5
-1
Fig. 2. A portion of the excitation spectrum. Enlargement of the peaks with dips at 11667.71 and 11668.93 cm1 are given above the lines.
L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
Intensity (arbitraryunit)
(a) 3000 2500 2000 1500 1000 500 0 11540.00
11540.05
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11540.15
cm-1
Intensity (arbitrary unit)
(b) 4000 3500 3000 2500 2000 1500 1000 500 0 11540.00
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11540.15
cm-1
Intensity (Arbitrary Unit)
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265
8; J 0 ¼ 30, which mixes with the b3P0u v 0 = 20, J 0 = 31 level and has 18% 3P0u character [19–21]. This 0 0 A1 Rþ u v ¼ 8; J ¼ 30 level has been observed by all-optical triple resonance spectroscopy [19,20]. The observed 0 0 term value of the A1 Rþ level is u v ¼ 8; J ¼ 30 1 11733.286 cm [20], the calculated term value from the new molecular constants is 11733.287 cm1 [21]. The energy of the virtual level of the two-photon transi00 00 tion (the term value of the X1 Rþ g v ¼ 1; J ¼ 31 level [22] plus the laser frequency, 11540.089 cm1), is 11733.290 cm1, leading to the conclusion that the inter0 0 mediate enhancing A1 Rþ u v ¼ 8; J ¼ 30 level coincidently has the same energy as the virtual level and this two-photon transition actually becomes an IR–IR double resonance transition. Fig. 3c gives the excitation line shape by monitoring the 23P0g v 33, J = 31 fluorescence to the b3P0u v 0 = 0, J 0 = 30 level (752.86 nm) with the monochromator. In Fig. 3c the line looks more symmetric and other weak Doppler-free transitions were not detected when only selectively monitoring the fluorescence from the 23P0g v 33, J = 31 level.
1000
3.2. With split laser beam set-up
800 600 400 200 0 11540.00
11540.05
11540.10
11540.15
cm-1
Fig. 3. The line shapes of the two-photon transition at 11540.089 cm1 by monitoring yellow-green fluorescence with filters and PMT without the backward beam (a) and with the backward beam (b) and by monitoring the 23P0g v, J = 31 ! b3P0u v 0 = 0, J 0 = 30 fluorescence (752.86 nm) with a monochromator (c).
(1) Bound–bound fluorescence into the bound levels of the a3 Rþ u state and bound-free fluorescence into the repulsive continuum of the a3 Rþ u state with an oscillation (reflection) structure and a strong peak at 573 nm (Fig. 4a). (2) Fluorescence into the b3Pu levels (Fig. 4b). 1 þ (3) At longer wavelength, A1 Rþ u ! X Rg fluorescence. Since the upper electronic state can radiate to the 3 3 þ a3 Rþ u state, it must be a Rg or a Pg state. From the rotational patterns and vibrational spacings into the lev3 els of the a3 Rþ u and b Pu states, we have assigned this 3 upper state to the 2 Pg state. The 23Pg state has been observed recently by infrared–infrared double resonance and two-photon transitions [17]. Ref. [17] has given the 00 00 assignment procedure of the K2 23Pg v, J X1 Rþ g v ;J two-photon transitions. This two-photon transition excited by two 11540.089 cm1 photons has been assigned 00 00 as 23 P0g v 33; J ¼ 31 X1 Rþ g v ¼ 1; J ¼ 31 transi0 tion with an intermediate enhancing level of A1 Rþ uv ¼
In order to study intensity dependence of the forward and backward beams independently, a 60% reflection and 40% transmission beam splitter was used to obtain a pump beam with 60% and a probe beam with 40% of the initial laser power. The two beams counter-propagated and were overlapped at the center of the heatpipe. Figs. 5a–c give the line shapes at different probe intensities when the pump laser power was 180 mW and the probe beam was modulated. In the spectra, the relative intensities of the weak Doppler-free sharp lines become much stronger than in Fig. 3b, because the pump laser beam was not modulated (the strong Doppler background by the strong pump laser contribution was not detected) and the weak lines could be recorded at a more sensitive scale. It can be seen that the weaker the probe beam the deeper the dip. When the probe laser power was 1 mW, its absorption was near zero at the center of the Doppler line and EIT occurred. Several other Doppler-free two-photon transitions with dips have also been studied and the results are similar to this 11540.089 cm1 signal.
4. Discussion 4.1. Are the dips in the two-photon excitation spectra Lamb dips? The experimental set-up for studying a Lamb dip is similar to Fig. 1 [18]. When the laser frequency is tuned through a resonance transition, at the Doppler line
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(a) 25 0 00 3
2 Πg
+
3
a Σ u transition
Intensity (arbitrary unit)
20 0 00
15 0 00
10 0 00
5 0 00
B ound-bound transition
0 52 0
54 0
56 0
5 80
6 00
nm (b)
3000 3
3
2 Πg b Πu fluorescence
v'=0
Intensity (arbitriry unit)
2500
2000 2
4p P3/2 4s
1500
2
4p P1/2
v'=1 1000
4s v'=5
v'=3 v'=2
500
0 750
755
760
765
770
775
780
nm 3 0 Fig. 4. Resolved fluorescence spectra from the two 11540.089 cm1 photon excited upper level: (a) to the a3 Rþ u state, (b) to the b Pu v = 0–5 levels. 1 þ 1 þ The unassigned doublets could be A Ru ! X Rg fluorescence and are not assigned.
center the forward and backward beams both excite the molecules with zero velocity projection on the laser propagation directions. The total absorption coefficient decreases at the line center and a Lamb dip appears. If an intermediate enhancing level is exactly on resonance, the Lamb dip of the transition between the ground level and intermediate enhancing level will appear at the same frequency as the Doppler-free two-photon line. But the increase by Doppler-free two-photon absorption of molecules with all velocities will be much stronger than the absorption based decrease of molecules with zero velocity projection only. In their Na2 experiment, Morgan et al. [23] and Xia et al. [24] simultaneously monitored both Doppler-free two-photon signals and Lamb dips of transitions between the ground X1 Rþ g and the enhancing A1 Rþ states. When their Doppler-free two-photon u
signals increased, the depths of the Lamb dips remained negligible in their spectra. Most Doppler-free two-photon signals in our K2 spectra were narrow peaks, a few showed dips. Clearly these dips are not Lamb dips, but manifestations of EIT due to Autler–Townes splitting (ac Stark effect) by a strong coupling laser field [10–12]. In Fig. 5c when the probe laser power was decreased to 1 mW, the absorption of the probe beam at the 11540.089 cm1 is near zero and transparency occurs. 4.2. Why EIT dips in two-photon transitions were relatively rare for other molecules? It is well known that two-photon transitions require enhancing intermediate level(s). In atoms or in mole-
L. Li et al. / Chemical Physics Letters 403 (2005) 262–267
Acknowledgements
Intensity
(a) 3000 2500 2000 1500 1000 500 0 11540.04
11540.06
11540.08
11540.10
11540.12
(b) 2000 Intensity
267
1500 1000
The experiment was carried out at Temple University. Support from the NSF (PHY 0245311) in the US and from the NNSF (20173029 and 20473042) and NKBRSF in China is gratefully acknowledged. We thank Profs. L.M. Narducci and Frank Spano for helpful discussions and suggestions, Prof. T. Bergeman for 3 calculating the term values of the A1 Rþ u and b Pu states. Li Li acknowledges the Lagerqvist Research Fund of Temple University for support during her visit and Prof. B. Kim for his hospitality during her visit to KAIST, where she analyzed the data.
500 0 11540.02
11540.04
11540.06
11540.08
11540.10
11540.12
(c) 1000 Intensity
800 600 400 200 0 11540.02
11540.04
11540.06
11540.08
11540.10
11540.12
Fig. 5. Probe laser intensity dependence in the split beam geometry. The pump laser power was 180 mW, and the probe beam in (a), (b) and (c) were 40, 20, and 1 mW, respectively. The sensitivity settings of the Lock-in amplifier in cases (a), (b) and (c) were the same and the relative intensities of the signals are thus comparable.
cules with pulsed lasers, the enhancing level(s) can be far away from the virtual intermediate level. In molecular excitation with CW lasers, however, the enhancing levels have to be closer; otherwise the two-photon transition cross-section will be very small. If an intermediate enhancing level is close to resonance, a two-photon Doppler background can also be observed. Dips will appear if a strong pump laser induces EIT. K2 is a relatively heavy molecule and the density of the rovibronic levels is high. The spin–orbit interaction, which mixes the A1 Rþ u and b3Pu states, is strong for K2. A mixed intermediate enhancing level can be coincidentally resonant to give rise to EIT in K2 two-photon transitions into triplet states. Line shapes of Doppler-free two-photon transitions have been studied in atoms and lighter molecules, such as Na2 and Li2. Since their energy level densities are lower, no EIT has been observed in the Doppler-free two-photon excitation spectra. It is likely that this kind of EIT will be observed in heavier molecules such as Rb2 and Cs2 due to their high energy level density. Theoretical analysis of our results is in progress. The current theoretical model only applies when the coupling field frequency is kept fixed on resonance and the probe laser is detuned.
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