Nonadiabatic rotational excitation of benzene by nonresonant intense femtosecond laser fields

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Chemical Physics Letters 454 (2008) 148–152 www.elsevier.com/locate/cplett

Nonadiabatic rotational excitation of benzene by nonresonant intense femtosecond laser fields Hirokazu Hasegawa, Yasuhiro Ohshima * Institute for Molecular Science, National Institutes of Natural Sciences, Myodaiji, Okazaki 444-8585, Japan SOKENDAI, The Graduate University for Advanced Studies, Okazaki 444-8585, Japan Received 19 December 2007; in final form 31 January 2008 Available online 7 February 2008

Abstract We investigated the nonadiabatic rotational excitation of the oblate symmetric-top molecule, benzene, induced by nonresonant intense ultrashort laser fields. By employing a quantum-state resolved probe using ns laser pulses, rotational excitation up to J = 10 was observed for the irradiation of a molecular ensemble, initially cooled to 0.5 K in an adiabatic expansion, by the femtosecond laser pulse with the intensity of 2.2 TW/cm2. The observed excitation was analyzed by the aid of quantum mechanical calculations. These calculations show the systematic change in the excitation pathways for different K, which is characteristic of nonadiabatic rotational excitation in symmetric-top molecules. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Nonadiabatic molecular alignment (NAMA), or nonadiabatic rotational excitation (NAREX), induced by nonresonant intense ultrashort laser fields has been extensively investigated [1] since the initial proposal [2–4] and the first observation of the revival structure in the transient birefringence [5] and in the Coulomb explosion [6]. In addition to the basic researches of them, NAMA/NAREX has been utilized in many applications [7–12]. However, most of these experimental researches are restricted to diatomic and linear molecules, except for a small number of studies of symmetric- [13,14] and asymmetric-top [15,16] molecules. Recently, details of the NAREX process pertinent to the NO molecule have been studied experimentally [17,18] by introducing a quantum-state resolved probe on rotational distribution after the NAREX. As Meijer et al. pointed *

Corresponding author. Address: Institute for Molecular Science, National Institutes of Natural Sciences, Myodaiji, Okazaki 444-8585, Japan. Fax: +81 564 54 2254. E-mail address: [email protected] (Y. Ohshima). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.01.087

out [18], it may be possible to control a rotational-state distribution using the NAREX process when multiple-pulse excitation or pulse shaping is employed. Since NAREX/ NAMA is a universal phenomena induced by a nonresonant light, it can be applicable to any type of molecules except for spherical tops having no anisotropic polarizability. However, experimental studies of NAREX processes on the basis of quantum-state resolved measurements have been limited to only the diatomic molecule, NO. In this Letter, the rotational-state distribution of an adiabatically cooled molecular ensemble of benzene after the irradiation by a nonresonant intense femtosecond laser pulse is investigated experimentally, together with the theoretical consideration by quantum mechanical calculations, in order to clarify the NAREX process for a symmetric-top molecule. 2. Experiment The schematic of our experimental setup is shown in Fig. 1. A pulsed molecular beam containing a trace amount of benzene vapor (80 Torr) diluted in a He buffer gas was produced in a differentially pumped vacuum chamber. The

H. Hasegawa, Y. Ohshima / Chemical Physics Letters 454 (2008) 148–152

XeCl Excimer

Dye laser

SHG crystal L pr

p

Probe pulse

P K (J)

5

1 0

5

10 = J r

2.2 TW/cm

E pr

149

2

Q

TOF-MS S

PV

f

Obs.

e

Calc.

d

Obs.

c

R (0) R 1 (1) r P 1 (1) 0 R 2 (2) p P 2 (2) r Q p R 3 (3) P 3 (3) r R 0 (1) 0.5 K Calc.

b

D

(40 Hz)

E pu L pu Digital delay/pulse generator

Calc.

MB

Ti:Sapphire fs laser

Pump pulse

Fig. 1. Experimental setup. PV: pulsed valve, S: skimmer, MB: molecular beam, Lpr: lens for probe pulses, Lpu: lens for pump pulses, and D: MCP detector. Epu and Epr are the polarization directions of the pump and probe pulses, respectively.

Benzene ion yield (a.u.)

C 6 H 6 /He 90 atm

R K (J)

1.2 TW/cm

2

r

r

p

rotational temperature of a molecular ensemble in the beam was adiabatically cooled to less than 1 K by the aid of a high-pressure Even–Lavie valve [19] operating at a stagnation pressure of 90 atm. The molecular beam was then sequentially exposed to two laser fields: the fundamental from a fs Ti:Sapphire laser (820 nm, 2.5 mJ, 35 fs, 1 kHz) and the doubled output from a ns dye laser (258 nm, an energy resolution of 0.05 cm1, 650 lJ, 10 ns, 40 Hz) pumped by a XeCl excimer laser. Here, we refer to the former fs pulse as the pump and the latter ns pulse as the probe, respectively. The pump and probe delay is set to 100 ns. A plano-convex lens of f = 200 mm was used for focusing the probe pulse onto the molecular beam. The S1–S0 610 band of benzene was recorded by (1 + 1) resonance-enhanced multiphoton ionization (REMPI) by scanning the probe laser frequency. The pump pulse was focused by a plano-convex lens of f = 300 mm. Its focal point was slightly shifted from the interaction region by 10 mm to maximize the laser-beam overlap. The pump pulse was chirped to 700 fs by changing the position of the compressor grating in order to avoid ionization of benzene. The pulse width was measured by a single-shot autocorrelator. Benzene cations thus generated by REMPI were detected by a linear TOF mass spectrometer. Both polarizations of the fs pump and the ns probe were set parallel to the ion-extraction field. 3. Results and discussion Fig. 2a shows the (1 + 1) REMPI excitation spectrum measured without pump pulses. The spectrum is predominated by transitions only from the lower rotational states of JK = 00, 10, 11, 22, and 33. The weak peaks 3 cm1 above the origin are assigned to the S1–S0 610 transition of the benzene–He cluster [20], from which benzene cations were generated after ionization followed by dissociation. The rotational temperature is estimated to be 0.5 K by

0 TW/cm

-4

r

2

-2

0

R 4 (4) p R 3 (3) 2

Obs.

a

4 -1

Relative energy (cm ) Fig. 2. The excitation spectra of benzene. Observed (a) without the pump pulse (c) with the pump pulse of 1.25 mJ and (e) 2.40 mJ. Calculated with the laser intensities of (b) 0 TW/cm2, (d) 1.2 TW/cm2, and (f) 2.2 TW/cm2.

comparing the simulated spectrum as shown in Fig. 2b. Due to the D6h symmetry of the benzene molecule, rotational levels with K = 6n, 6n ± 1, 6n ± 2, and 6n ± 3 (where n is an integer) are associated to nuclear spin wavefunctions with B1 + B2, E2, E1, and A1 + A2 symmetries, respectively. For K = 0, even and odd J levels are assigned to B1 and B2, respectively. As Beck et al. pointed out [20], nuclear spin conversion during collisions is much inefficient so that molecules with different nuclear spin symmetries can be regarded as different molecular species, i.e., ‘nuclear spin isomers’. The JK = 00, 10, 11, 22, and 33 states are the lowest rotational states for the five nuclear spin isomers with B1, B2, E2, E1, and A1 + A2 symmetries. The excitation spectra change drastically when the pump pulses of 1.25 mJ and 2.4 mJ are applied as shown in Fig. 2c and e, respectively. Transitions from states with the maximum J up to 6 and 10 appear in Fig. 2c and e, respectively. Although the probe laser bandwidth of 0.05 cm1 is not narrow enough to resolve each rotational transition completely, we can recognize a series of triplet lines in the pP-branch, in particular in Fig. 2c. These characteristic triplet lines are assigned to transitions from JK states with K = 1, 2, and 3 in S0 to J  1K  1 states in S1.

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This is the consequence of the initial distribution restricted to K = 0 (8%), K = 1 (37%), K = 2 (30%), and K = 3 (24%) with small contributions from K P 4 (1%), and the conservation of K in the NAREX process due to the interaction term described below, having the symmetry around the axis perpendicular to the benzene plane (i.e., the c-axis). In order to ensure that the observed rotational excitation is induced by the NAREX process, a quantum dynamical calculation is performed to compare the observed spectra with calculated ones on the basis of the population determined by solving a time-dependent Schro¨dinger equation (TDSE). The calculation is quite similar to that adopted in our previous study on NO [17]. The interaction of a molecular anisotropic polarizability with a linearly polarized nonresonant laser field can be represented by 1 2 Vb ðtÞ ¼  ½EðtÞ ðDa cos2 h þ a? Þ; 2

ð1Þ

where E(t) is the electric field of the laser pulse, Da ¼ ak  a? , with static polarizabilities parallel and perpendicular to the molecular c-axis, ak and a\, respectively, and h is the angle between the molecular c-axis and the laser polarization [13,21]. We use a Gaussian temporal profile with a linear chirp as the laser electric field,     2 ln 2 2pc EðtÞ ¼ E0 exp  2 t2 cos t þ bt2 ; ð2Þ k0 C where C (=700 fs) the pulse width, k0 (=820 nm) the center wavelength of the carrier wave. From the Fourier-transform-limited pulse width of 35 fs, the group-delay-dispersion (GDD) is calculated to be 8.83 103 ps2. The b value is derived to be 56.5 ps2 from the FT-limited pulse width and the GDD. Because the chirped pulse is employed in the present experiment, we use the electric field with the carrier wave denoted in Eq. (2), for the calculations. Then, we have found that one-cycle averaged calculation over the carrier wave gives the same results. That is, time evolutions of wave packets and the resultant rotational-state distribution are predominately determined by the envelope of the pulse and independent of the carrier wave and the chirp of it. The rotational wave packet, j WðtÞJ i K i M i i, generated from the initial j J i K i M i i state by the interaction of the pump pulse is expanded by an oblate symmetric-top basis set, fj JKMig, as follows: X C JJ i K i M i ðtÞ expðixJK i tÞ j JK i M i i: ð3Þ j WðtÞJ i K i M i i ¼ J

Here C JJ i K i M i ðtÞ is the complex amplitude for j JK i M i i in the rotational wave packet, and xJK ¼ 2pcfBJ ðJ þ 1Þþ ðC  BÞK 2 g is the eigen energy for levels with J and K. We use rotational constants B = 0.18977 cm1 and C = 0.094885 cm1 from Ref. [22] and polarizabilities of ˚ 3 and a\ = 12.4 A ˚ 3 from Ref. [23]. Centrifuak = 6.67 A gal-distortion terms are not included due to their negligible contributions in energy for the range of J herein considered.

The matrix element can be explicitly expressed as follows [24]: hJ 0 K 0 M 0 j cos2 h j J 00 K 00 M 00 i  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J 0 2 J0 2 M 0 K 0 0 00 ð2J þ 1Þð2J þ 1Þ ¼ ð1Þ 3 K 0 0 K 00  0 00  J 2 J 1  ð4Þ þ dJ 0 ;J 00 dK 0 ;K 00 dM 0 ;M 00 : 0 00 3 M 0 M Selection rules, DJ = 0, ±2 for K = 0 and/or M = 0, DJ = 0, ±1, ±2 for K 6¼ 0 and M 6¼ 0, DK = 0, and DM = 0 are derived from the non-vanishing matrix elements. We determine j C JJ i K i M i ðt ¼ 1Þj2 , after NAREX by solving the TDSE numerically and take an average for the initial rotational-state distribution at 0.5 K. Fig. 2d and f shows the calculated spectra for which the pump intensities of 1.2 TW/cm2 and 2.2 TW/cm2 are used. The good agreement between the observed spectra and the calculated ones ensures that the observed rotational excitations are induced by NAREX. On the basis of the observed spot size of 5.5  104 cm2, the pump intensities are evaluated to be 3.2 TW/cm2 and 6.2 TW/cm2 for the pulse energies of 1.25 mJ and 2.40 mJ, respectively, with the 700 fs pulse duration. The agreement between the observed and the calculated intensities is reasonably good, though not perfect. The discrepancy of factor of 3 may be ascribed to an inhomogeneous intensity distribution in the finite interaction region because our calculation does not include the spatial distribution of the laser pulse. In order to investigate the NAREX process in more 2 details, time-dependent populations, j C JJ i K i M i ðtÞj , are calculated for the initial states of Ji = 0, 1, Ki = 0, 1, and Mi = 0, 1 when the intensity of 1.2 TW/cm2 and the pulse width of 700 fs are applied. Fig. 3a–c shows the calculated time-dependent populations for the J i K i ¼ 00 ; 10 ; and 11 states with Mi = 0, respectively. Excitation pathways for the states are rather simple because of the DJ = 0, ±2 selection rule for M = 0. The state populations are transferred from the J i K i initial state to higher rotational states by DJ = 2 in a stepwise manner. These NAREX dynamics are essentially identical to those in N2 [25]. Fig. 3d shows the time evolution of rotational populations when the initial state is J i K i ¼ 10 with Mi = 1. It is noted that this time evolution is identical to that for J i K i ¼ 11 and Mi = 0, shown in Fig. 3c. This identity is the result of the symmetry in the matrix elements given in Eq. (4) against the exchange of K and M. The NAREX dynamics for the initial state of J i K i ¼ 11 and M i ¼ 1 is much more complex than those for K i ¼ 0 and/or M i ¼ 0, because of the additional DJ ¼ 1 transitions. A detailed examination of Fig. 3e reveals that pairs of adjacent states, {J = 2, 3}, {4, 5}, and {6, 7}, show almost the same time dependence, and populations of J = 2, 4, and 6 are more than twice as large as those of J = 3, 5, and 7, respectively. These facts are explained as follows: because DJ ¼ 1 and 2 transitions are allowed, the initial population of J i K i ¼ 11 is transferred to states

H. Hasegawa, Y. Ohshima / Chemical Physics Letters 454 (2008) 148–152

1.0

JK =41 JK =51 J K = 61 J K = 71

JK = 11 0.5

J K = 21 J K = 31

b

0.30

e

151

NO M = 0.5, Ω = 0.5

0.25

M=1

0.20

ΔJ = 2 ΔJ = 1

0.15 0.10

Matrix elements of cos2θ

0.0 1.0

d

JK = 10

M=1 0.5

J K = 30

J K = 50 JK = 7 0

Population

0.0 1.0

0.05 0.00 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5

a

0.30

Benzene M = 1, K = 1

0.25 0.20

c

JK = 1 1

ΔJ = 2 ΔJ = 1

0.15

M=0

0.10

0.5 0.05

JK = 31

JK = 5 1

0.00

JK = 71

0.0 1.0

0

b

JK = 3 0

JK = 10

JK = 5 0

JK = 70 Laser intensity

JK = 0 0

a

J K = 20

M =0

JK = 4 0

0.5

J K = 60 0.0 -1

0

1

2

2

3

4

5

6

7

8

9

Fig. 4. The J-dependence of the matrix elements of cos2 h, hJ 0 KðXÞM j cos2 h j J 00 KðXÞMi, for (a) rotational-state of benzene with K = 1 and M = 1 and (b) NO with X = 0.5 and M = 0.5, where X means the component of the electronic angular momentum parallel to a molecular axis and DJ ¼ J 0  J 00 .

M=0

0.5

0.0 1.0

1

Rotational angular momentum J

3

Time (ps) Fig. 3. Time evolution of the rotational-state distributions calculated at the pump intensity of 1.2 TW/cm2 and the pulse width of 700 fs. The initial states are (a) JK = 00 (M = 0), (b) 10 (M = 0), (c) 11 (M = 0), (d) 10 (M = 1), and (e) 11 (M = 1).

with J = 2 and 3 almost simultaneously in the first excitation step. Here the J i K i ¼ 11 state is excited to the 21 state more efficiently than to the 31 state, since the DJ ¼ 1 coupling is larger than DJ ¼ 2 for J ¼ 1 as shown in Fig. 4a. However, the coupling strengths for DJ ¼ 2 quickly dominate over those for DJ ¼ 1 as J increases. As a result, the state population is transferred via two separate excitation pathways, starting from the common initial state, J ¼ 1 ! 2 ! 4 ! 6 !    and J ¼ 1 ! 3 ! 5 ! 7 !   . The similar bifurcated NAREX pathways have been already identified for NO molecules in the initial state of J = 0.5, X = 0.5, and M = 0.5 in the X 2 P1=2 (v = 0) mani-

fold [17,18]. However, the NAREX processes in the two molecules have a substantial difference. In the case of NO, the coupling strengths of DJ ¼ 2 are larger than those of DJ ¼ 1 for all J as shown in Fig. 4b. Therefore, the major excitation pathway is: J ¼ 0:5 ! 2:5 ! 4:5 !   , where all the excitations are driven by the DJ ¼ 2 transitions. The minor excitation pathway is: J ¼ 0:5 ! 1:5 ! 3:5 !   , where the initial step is driven by the DJ ¼ 1 transition. On the other hand, the major pathway in benzene starting from J K ¼ 11 with M ¼ 1 is the DJ ¼ 1 excitation in the first step, followed by the DJ ¼ 2 excitations, while the minor pathway results exclusively from the DJ ¼ 2 excitations. The aforementioned NAREX pathways in the symmetric-top molecule, revealed theoretically in the present study, can be experimentally examined by the measurement of rotational-state distribution by employing a doublepulse excitation, as Meijer et al. demonstrated for NO molecule [18]. Such an investigation on benzene is now under way in this laboratory. We finally point out that the NAREX from the J i K i ¼ 00 state results in the populations of states with K ¼ 0 and even J concentrated into the single M ¼ 0 sublevel because of the selection rules of DK ¼ 0 and DM ¼ 0. Similarly, since the excitations from 11 with M ¼ 0 into even J states are forbidden, populations for K ¼ 1 with even J come solely from the initial 11 state with j M j¼ 1 and thus yield

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to the single sublevel occupation (besides the ± sign). Such highly polarized rotational states will be utilized for various studies on reaction dynamics, for instance, rotational-state-selective measurements of alignment dependence on photo-ionization or photo-dissociation. 4. Conclusion We succeeded in observing the nonadiabatic rotational excitation of an oblate symmetric-top molecule, benzene, induced by nonresonant intense femtosecond laser fields. In this study, a jet-cooled molecular ensemble was irradiated by an intense 820-nm laser pulse with 700 fs duration. The rotational-state distributions after the nonadiabatic rotational excitation were measured by (1 + 1) REMPI detection employing a ns laser probe. The observed state distributions were well reproduced by the quantum mechanical calculations based on the time-dependent Schro¨dinger equation. The theoretical analysis was further employed for the systematic examination on the excitation processes starting from rotational states with different K and M values. Acknowledgements This work was partly supported by Grants-in-Aid from MEXT Japan (15035206, 16032206, 18244120, and 18750020), and the RIKEN-IMS joint program on ‘Extreme Photonics’. Additional financial supports from the Research Foundation for Opto-Science and Technology and the Mitsubishi Foundation are also appreciated. References [1] H. Stapelfeldt, T. Seideman, Rev. Mod. Phys. 75 (2003) 543.

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