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PHYSICAL REVIEW A 77, 011401 R 2008

Laser-assisted control of molecular orientation at high temperatures
Dmitry V. Zhdanov* and Victor N. Zadkov
International Laser Center and Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119992, Russia Received 11 October 2007; published 18 January 2008 A method of laser-assisted field-free dynamic molecular orientation employing a short, moderately intense three-color phase-locked laser pulse is proposed. Numerical simulations show that it provides an exceedingly effective control of orientation in molecular gases even at room temperatures. The underlying mechanism is based on the specific laser-induced orientation-dependent selective excitation of molecules and subsequent self-transformation of the induced geometrical orientation into a dynamical one. It is shown that this mechanism is significantly more powerful than the widely investigated kick mechanism. DOI: 10.1103/PhysRevA.77.011401 PACS number s : 37.10.Vz, 42.50.Hz, 33.80. b

Laser-assisted molecular alignment and orientation are among the intriguing and rapidly developing areas of modern laser physics. In a simple one-dimensional case, molecular alignment means the confinement of one of the moleculefixed axes in the direction collinear with the laboratoryfixed z axis. As a result, the ensemble-averaged expectation ^ value cos2 , where = , z , is raised in values to unity, by contrast with its isotropic value of 1 / 3. Recent striking progress in the development of laser alignment strategies gives us powerful methods for molecular alignment both in one and in three dimensions see reviews 1­ 4 . Molecular orientation is a more complex and much more difficult problem. It implies alignment with the codirectional confinement between the molecular and spatially fixed axes. Mathematically it means the breakdown of both equilibrium the latter serves as the convenvalues cos2 and cos tional orientation measure . There is no straightforward way to adopt molecular alignment schemes for orientation because in most cases the effective field-molecule interaction is averaged over fast oscillations of the electric field and thus does not have necessary forward-backward asymmetry with respect to the directions of the molecular axes. One can avoid this obstacle by using one of the following strategies. First, it is possible to use a combined action of the laser field with an additional nonlaser asymmetric interaction for instance, with an electrostatic field 5­7 . Second, there are numerous proposals to achieve orientation with the help of a tailored laser pulse or sequences of such pulses 8 ­13 . Finally, the orientational effect can originate from an appropriate phase locking between the components of the multicolor laser pulses 14 ­17 . Although the last strategy looks most advantageous both because of its applicability to nonpolar molecules and because it avoids the need for intricate pulse shaping, it has not been confirmed experimentally to our knowledge so far. Nevertheless, both theory and a few experiments prove that at least the so-called geometric orientation which by contrast with the dynamic orientation means the orientationdependent accessing of the molecules, e.g., ionization, without affecting their isotropic distribution is attainable in this way 18 ­20 .

*zhdanov@phys.msu.ru
1050-2947/2008/77 1 /011401 4

This work has been spurred by the fact that even a very small about a few kelvins initial temperature of the molecules typically crushes almost completely the efficacy of the existing methods of laser control of molecular orientation. In this paper, we propose a scenario of field-free orientation employing the multicolor laser pulse strategy, which eliminates this restriction. The idea of our scenario is related to the recent investigations of isotope selective molecular alignment, in which it has been shown that a tiny mismatch in the moments of inertia of molecular isotopes can be efficiently utilized for separate manipulations on their rotational dynamics 21 . Our scenario rests on ideologically similar technique based on utilization of the tiny differences in molecular geometry of the ground and excited vibronic states. Specifically, we will show that macroscopic orientation in an ensemble of initially randomly oriented molecules can be produced by a sudden with respect to the molecular rotations excitation of a portion of molecules with well-defined orientation into a properly chosen vibronic state. Such molecular excitation is, in fact, a specific case of the geometrical orientation called the orientation-dependent selection ODS of molecules 22,23 . To show how the ODS can result in orientation, let us clarify it on the example of BF molecules. For this particular molecule, we define the unit vector directed from the boron to the fluorine atom as the controlled molecular direction see the definition in the introductory part of the paper . Suppose also that the ODS happens at the time t = 0, so that the portion n of the molecules with angles t=0 close to zero is suddenly transferred from the ground vibronic state 0 to the excited state 1 . Denoting the degrees of orientation of the molecules in the ground and excited vibronic states as cos 0 and cos 1, respectively, we can write cos = 1 - n cos 0 + n cos 1, where cos t=0 = 0 in the sudden impact limit. However, in accordance with the definition of 0 and cos 0 t=0 =- n / 1- n the ODS, cos 1 t=0 = 0. The general features of the field-free rotational dynamics of molecules, which follows the ODS, spring from an approximate commensurability of the rotation energies of the rotational sublevels of each vibronic level. Let us briefly recall that for a free linear rigid rotor with the rotational constant B the rotation energies are given by the expression
©2008 The American Physical Society

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FIG. 1. Color online a Scheme of laser-induced transitions employed in the ODS process. b Degree of orientation cos as the function of time. The corresponding frequencies and the peak intensities Ik of the laser pulse components are as follows: 0 = 2.577 1015 Hz 116.3 nm 24 , I0 = 4.67 1011 W / cm2; 1 = 5.384 1014 Hz 556.8 nm , I1 = 1.82 1011 W / cm2, 2 = 1.076 1015 Hz 278.4 nm , I2 = 1.64 1012 W / cm2. The components E1 and E2 are phase matched, so that 2 =2 1 + 2.9. The molecules initially had the temperature of 300 K. We also neglect the relaxation for simplicity.

an extremely effective tool for controlling molecular orientation, because of the strong orientational dependence of the effective energies of this sort of dressed state. In our scheme, we utilize the dependence of both the structure and energy of one of the dressed states on the orientation to produce orientation-dependent frequency detunings and absolute values of the transition dipole moment for nonadiabatic excitation induced by the component E0, which is tuned in the vicinity of the resonance with the transition 0 2 . With this, the appropriate choice of phase relationships between the components E1 and E2 determines the preferable molecular orientation with respect to the z axis of the laboratory frame for the selection process. Hereafter, we will assume that the states under consideration are linked by parallel transitions only. Then, for each particular molecular orientation, the corresponding effective interaction Hamiltonian of the ODS in the rotating wave approximation can be written in the basis of time-independent eigenstates 0 , 1 , 2 , 3 as
0

Erot = BJ J +1 with J being the total angular momentum quantum number, i.e., they are divisible by 2B. As a result, an initial oriented state of such rotors at t = 0 will be precisely reconstructed at the revival time instants m rev m =1,2, ... , where rev = h / 2B. At the interval between successive revivals the components of the rotation wave packet are essentially out of phase, so that the degree of orientation is perfectly close to zero anywhere except in narrow areas around the revival time instants, resulting in the well-known rotational revival pattern. Returning to the analysis of the post-ODS dynamics, we can conclude that the rotational wave packets for molecules in the ground and excited vibronic states should revive differently due to the small differences between the corresponding rotational constants B0 and B1 and, consequently, between the revival time instants rev,0 and rev,1. As a result, cos 1 t=m rev,1 , whereas cos 0 t=m rev,1 0 and, similarly, cos 0 t=l rev,0 - , whereas cos 1 t=l rev,0 0, except for cases where l rev,0 m rev,1 m and l are the arbitrary natural numbers . The overall effect is that the degree of orientation cos behaves in a revival-like manner, demonstrating positive spikes with amplitude close to n near t = m rev,1 and negative ones with almost the same amplitude near t = m rev,0. For realization of the sudden ODS we will employ a degenerate variant of the scheme introduced in Ref. 23 see Fig. 1 a . In this scheme, the ODS is induced by the electrodipole interaction with a three-color femtosecond linearly 2 2 polarized laser pulse E t = k=0Ek =2ez k=0Akcos kt + k , where Ak, k, and k are the envelopes, carrier frequencies, and phases of the corresponding components. The pulse should be short enough to view the molecules as rotationally frozen during the laser impact. The purpose of the phaselocked components E1 and E2 with the frequencies 2 =2 1 is to perform resonant adiabatic passage RAP in a subspace of three initially unpopulated near-equidistant excited vibronic states 1 , 2 , and 3 . During the pulse propagation each of these three states is adiabatically transformed into a dressed one. It has been shown recently 17 that the RAP is

0
1* 1,2 2* 2,3

^ H t,

0 =
0* 0,2

0 0,2 1 1,2

0
2 1,3 1 2,3

,

1

0

1* 2,3

-

^ ^ where i,kj t , = i d j Ak t cos ei k and d is the dipole moment operator. We define the RAP dressed states as eigen~ vectors of the form m = l3=1Cm,l t , l of 1 , in which 0 is artificially set to zero and Cm,l 0 for l m in the 0,2 zero-field limit. The population transfer efficacy from the ground state 0 into each of these dressed states induced by E0 can be controlled by i the value of the detuning ~ m = ~ m t , / - 0, where ~ m is the effective dressed energy, E E ^ ~ and ii the value of the transition dipole moment 0 d m , which is proportional to the expansion coefficient Cm,2. For the ODS, one needs to enhance the population transfer to the excited state 1 , if the angle is close to zero, and suppress it otherwise. For this, first of all, only the dressed state ~ should be accessed for population, so that it should 1 be energetically well separated from any other state. Second, the coefficient C1,2 should achieve its maximum near the value = 0 and fall to zero both at = 0 and in the absence of dressing i.e., when both E1 = 0 and E2 =0 . Third, the detuning ~ m should approach zero near = 0 and be as large as possible otherwise. The conditions listed above allow us to determine the optimal parameters of laser impact. For the BF molecule we suppose that all the components of the laser pulse have similar shapes: Ak t = Ak exp -t2 / 2 2 , with = 70 fs. Using the above conditions we found the optimal frequencies, intensities, and relative phases k of the components at the peak of the laser pulse. These results were then used as a starting point for further numerical optimization. In the simulations, we restrict the peak intensity to the value of 1012 W / cm2 to be confident of the absence of tunneling

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ionization. We choose as the states 1 , 2 , and 3 the lowest vibrational levels of the second, third, and fourth excited electronic levels of 1 symmetry their ab initio calculated energies with respect to the ground vibronic state are equal to 68 300.3, 87 111.9, and 104 415.0 cm-1, respectively . Numerical simulation of the laser-induced dynamics was carried out using the short-pulse approximation SPA 25 . To quantify the contribution of the off-resonant interaction, we explicitly included in the calculations 11 electronic terms with the different symmetries. Also, the effect of centrifugal distortion via the first-order corrections was taken into account. Figure 1 b shows the calculated degree of orientation, induced by one of the optimal laser pulses in the molecules at the room temperature. The parameters of interaction are such that just after the laser impact at t = 0 nearly 97% of the population resides on the vibronic levels 1 88.7 % and 0 8.3 % , and only 3% is transferred to the levels 2 and 3 , while population of other levels is negligibly small. This confirms the fact that the adiabatic regime of dressing during the ODS holds rather well. Therefore, the observed revival pattern is mainly composed of a sum of two series of rotational revivals of the molecules in the vibronic states 1 with the revival time rev,1 = 10.1 ps and 0 rev,0 = 10.8 ps . However, the molecular nonrigidity becomes an essential factor, especially at high temperatures, so that, in contrast to the rigid rotor model any subsequent revival in each series is not the exact clone of the former one and is essentially less pronounced and more smeared. The most striking feature in Fig. 1 b is that the degree of orientation reaches extremely high values of up to 0.0706. To our knowledge, there is no other alternative method of molecular orientation that gives similar efficiency for field-free orientation at room temperatures. However, the complementary effect of geometrical orientation is even more impressive. For example, at the time of the first rotational revival, the degree of orientation cos 1 of the excited molecules achieves its peak value equal to 0.704. Note that it is a record even for experiments with rotationally cold molecules. Moreover, the vibronic state sensitivity of the revival pattern in combination with the high efficiency of the geometrical orientation open an intriguing prospect for employing methods, similar to those recently suggested for the isotope and nuclear spin-selective control of molecular alignment 21 , to the coherent vibronic state-selective control of molecular orientation. Analysis of Fig. 1 b leads to the conclusion that the suggested ODS-based mechanism of molecular orientation is significantly more effective than the widely discussed kick mechanism. The latter is based on a laser-induced torque, which changes the molecular angular momenta in a way that forces molecular reorientation. In this case, therefore, strong orientation is inevitably accompanied by a significant increase of the rotational temperature. The largest degree of orientation typically occurs slightly after the laser pulse. In our case, the kick contribution to the overall orientation effect dominates only at the early time of the postpulse fieldfree evolution, emerging in small spikes just after the laser pulse. One can see, however, that the amplitudes of these

spikes are negligibly small compared to the amplitudes of the spikes arising near t = 10 ps. Thus, the kick-based orientational effect, even resonantly enhanced, is more than an order of magnitude smaller than the ODS-based one. Furthermore, the ODS-produced orientation of molecules in the ground state 0 corresponds to less than 0.6 K change in its rotational temperature. The average rotational energy of the vibronically excited molecules is 348 K, so that it is not significantly higher than the initial temperature too. Substantial differences between the ODS- and the kickbased mechanisms of orientation are also revealed in the distinct degree cos2 of induced molecular alignment. When the kick mechanism is employed, the laser pulse produces significant anisotropy in the spatial angular momentum distribution, so that besides the transient alignment of the molecules there is a permanent alignment prior to and after any transient revival 26 . However, no permanent alignment occurs when the orientation is induced via the ODS. In our between simulations, we found that the value of cos2 revivals at early times between 10-12 s and 4 10-12 s is almost equal with an accuracy of about 3 10-4 to its value 1 3 in the isotropic case. At later times, the deviations become more pronounced thanks to the spreading of revivals caused by the Coriolis distortions. We verified numerically that the efficiency of the orientation is fairly robust with respect to variations of the peak intensities of the components of the multicomponent laser pulse. We found, for example, that a two times lowering of the amplitudes of the revivals occurs only when the peak intensities of the pulse components are approximately two times different from the optimum values. However, the thorough tuning of the phase-locking parameter = 2 -2 1 describing the phase matching between the components E1 and E2 is also crucial to make our scenario feasible. In addition, there exists an exact relation

FIG. 2. Time dependence of the degree of orientation vicinity of the first rotational revival as a function of the locking parameter . Only the interval 0 is plotted into account relation 2 . The frequencies and amplitudes pulse components are the same as in Fig. 1 b .

in the phasetaking of the

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cos

=0

= - cos

= 0+

2

valid for any 0, from which it directly follows that the averaging over leads to the complete loss of orientational effect. Figure 2 shows the calculated dependence of the orientational dynamics on in the neighborhood of the first revival. It is interesting to note that the orientational effect appears unfor any value of . However, the amplitude of cos dergoes more than an order of magnitude change with vary/ 2 and maxima near ing , reaching minima near = =0, . In conclusion, we have shown that the RAP and ODS techniques can be efficiently employed for the laser-assisted orientation of molecules at high temperatures, up to room temperature, and we believe that this scenario can be experimentally feasible. Numerical simulations confirm that the method also allows production of ensembles of excited molecules with well-defined vibronic states with very high up to

0.7 degree of orientation. This may be an interesting alternative to the conventional molecular orientation in many applications, such as tomographic imaging of molecular orbitals, applications in quantum physics, control of chemical reactions, ionization, dissociation processes, and other stereochemical problems where the dynamics is essentially state dependent. In particular, in our forthcoming presentation we discuss the possibility of employing such a strategy for realization of laser-assisted laser asymmetric synthesis 23 . The described molecular orientation technique can be applied to other linear or symmetric-top molecules. For small molecules, one can also expect that the typical laser intensities and the pulse durations will be of the same order of magnitude as those considered in the paper. The wavelengths could be taken from a more widely available range of experimental wavelengths. However, this would require, in general, the replacement of a single E1 component with two components with different wavelengths and phase matching between three instead of two field components.

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