RAPID COMMUNICATIONS PHYSICAL REVIEW A 83, 041403(R) (2011) Nonadiabatic molecular high-order harmonic generation from polar molecules: Spectral redshift Xue-Bin Bian and Andr´ e D. Bandrauk * D´ epartement de Chimie, Universit´ e de Sherbrooke, Sherbrooke, Queb´ ec, Canada J1K 2R1 (Received 8 February 2011; published 22 April 2011) Molecular high-order harmonic generation (MHOHG) from the polar diatomic molecule HeH 2+ in short intense laser fields is studied numerically. Due to the nonadiabatic response of the molecular dipole to the rapid change of laser intensity, a spectral redshift is predicted in high-intensity and ultrashort laser pulses, contrary to the blueshift observed in the harmonics generated from atoms in long laser pulses. The MHOHG temporal structures are investigated by a wavelet time-frequency analysis, which shows that the enhanced excitation of localized long lifetime excited states shifts the harmonic generation spectrum in the falling part of short laser pulses, due to the presence of a permanent dipole moment, and thus is unique to polar molecules. DOI: 10.1103/PhysRevA.83.041403 PACS number(s): 33.80.Rv, 42.65.Ky, 34.50.Gb High-order harmonic generation (HHG) has become an im- portant tool to generate coherent attosecond (1 as = 10 −18 s) laser pulses [1]. It provides us with an important coherent optical source to investigate ultrafast electronic dynamics [2–5]. Usually, HHG comes from the interaction between intense laser pulses and atoms [2,4], molecules [5], and plasmas [6]. The general feature of HHG spectra is a rapid decay of the lower-order harmonics, then a long plateau, and a short cutoff with photon energy around I p + 3.17U p (where I p is the ionization potential and U p = I/4ω 2 denotes the ponderomotive energy). Currently, a semiclassical three-step model is used to interpret the HHG mechanism for initial zero velocity ionized electrons [7] and nonzero velocity electrons [8]. In this model, when atoms and molecules are exposed to intense laser fields, the electron can be ionized by tunneling from the ground state. It is then accelerated by the laser field, and returns back to the original ion to recombine with the parent ion and emit HHG photons due to a phase change of the electric field. This model is successful in explaining the maximum cutoff energy I p + 3.17U p of HHG observed in atoms and molecules [5]. However, cutoff energies larger than I p + 3.17U p can be obtained in a laser-induced electron transfer (LIET) with the neighboring ions [9–12] in molecules and is called molecular high-order harmonic generation (MHOHG). Recent progress in ultrafast optics has allowed the gen- eration of ultraintense laser pulses comprising only a few field oscillation cycles [2]. The change of amplitude of the electric field during one optical cycle is not negligible. One of the central questions concerns this nonadiabatic response effect [13] of atoms and molecules to the short high-intensity laser fields. The temporal and spectral structures of HHG from atoms have been well studied previously [14–19]. Most of the theoretical [14,15] and experimental [16–18] results show spectral blueshift for atoms in intense laser pulses. The spectral blueshift mainly comes from two physical processes. One is predicted by the strong-field approximation (SFA) model [20,21]. The electron ionized on the rising part of the laser field will experience additional accelerations and acquire more energy, which will lead to a blueshift in the HHG spectra [22]. * Andre.Bandrauk@USherbrooke.ca The other process is one in which the ionized electron changes the refractive index of the ionized media [23]. This propagation effect leads to an additional blueshift in HHG [17–19]. A spectral redshift is observed in laser cluster interaction [24] and harmonics from the multiphoton ionization of atoms interacting with a long laser-pulse field (300 ps) [25]. However, this reported redshift is also explained by the propagation effect because of the change of the index of refraction. To our knowledge, except for the propagation effect, no redshift has been reported in either atomic or molecular HHG. In this Rapid Communication, we will show the spectral redshift in the MHOHG from polar molecules with short intense laser pulses. Due to the permanent dipole, polar molecules have received increasing attention recently [26–28]. The phenomena of enhanced excitation (EE) and enhanced ionization (EI) have been reported [26]. The Stark shift of the ionization potential leads to a higher cutoff energy of MHOHG [27]. The long lifetime of excited states leads to strong resonance and multichannel MHOHG in the harmonic spectrum [12]. In this Rapid Communication, we probe the nonadiabatic effects [29] in the temporal and spectral structures of MHOHG from the model asymmetric diatomic molecule HeH 2+ in short intense laser pulses. The MHOHG spectra of HeH 2+ are obtained by numerically solving the time-dependent Schr ¨ odinger equation (TDSE). For computational details, we refer to Refs. [30,31] for this one-electron system. The internuclear distance R is fixed at 4 a.u. (near the excited-state minimum R = 3.89 a.u.). The energies of the ground state 1sσ and the first excited state 2pσ are −2.25 and −1.03 a.u., respectively. The initial state for time evolution is the ground state 1sσ . The laser polarization is along the molecular axis. The electric field of the laser pulse is given by E(t ) = E 0 f (t ) cos(ωt ), t ∈ [−τ/2,τ/2], with the pulse shape f (t ) = cos 2 (πt/τ ), where τ is the total duration of the laser pulses. Thus the total electric-field area is zero. The power spectra of MHOHG is calculated by Fourier transformation of the dipole momentum in acceleration form d A (t ), as it is the most reliable numerical method for strong-field interactions [32], thus avoiding transient effects in very short pulses. A MHOHG spectrum of HeH 2+ in laser field at wavelength 400 nm and intensity I = 3.3 × 10 15 W/cm 2 with a 15 cycle duration is shown in Fig. 1. A typical difference from the 041403-1 1050-2947/2011/83(4)/041403(4) ©2011 American Physical Society