arXiv:cond-mat/0410593 v1 22 Oct 2004 Optical Coherent Control of Lattice Deformations in Organic Semiconductors M. V. Katkov and C. Piermarocchi Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 (Dated: October 26, 2004) We investigate theoretically a semiconducting polymer chain under the effect of an intense off- resonant laser field. The coherent polarization induced by the field couples to the lattice and causes local deformations. Due to the off-resonant nature of the excitation, the deformations are reversible and controllable by the intensity and frequency of the laser. We derive and solve numerically a nonlinear equation describing the distribution of the optical polarization in the chain. Localized solutions exhibit characteristic saturation features. We analyze the light-induced force acting on the lattice in the case of polydiacetylene. When an atomic system or a semiconductor is irradi- ated by a pump laser in the transparency spectral region, it responds to the field with its dynamic polarizability and gains a polarization energy [1]. In the case of semi- conductors, this dynamic Stark effect is well understood in terms of the creation of virtual electron-hole pairs (ex- citons) across the band gap by pump photons [2], and it explains the excitonic blue shift experimentally ob- served [3]. It has been recently pointed out that the dynamic polarization can be used as a quantum control tool in semiconductors. For instace, the virtual excitons created by an off-resonant pump field interact with spins localized by impurities or quantum dots and can create a local magnetic field [4], induce spin-spin coupling [5, 6], and paramagnetic to ferromagnetic transitions [7]. In this paper we will show that the dynamic optical polarization can be used to induce forces and control lat- tice deformations in a semiconducting chain. Virtual ex- citons created by the pump field interact strongly with phonons in the lattice and lead to nonlinear effects which, in turn, produce local forces on the ions. As in the case of the optical spin control, there is no absorption of energy since the pump photons are tuned in the transparency region: the effect is due to radiative (stimulated) cor- rections to the ground state of the system. The coherent nature of the effect makes it reversible and finely control- lable with lasers. We calculate this effect in polydiacety- lene [8] which has been heavily studied for its strong non- resonant optical nonlinearities [9] and exciton-phonon ef- fects. Phonon-mediated optical nonlinearities have been observed in this material [10, 11]. Recently developed experimental techniques can detect light-induced lattice displacement in molecules and semi- conductor systems. Examples include pump-probe elec- tron diffraction [12] and ultrafast x-ray absorption spec- troscopy [13]. These techniques can be extremely sensi- tive and measure laser-induced lattice dynamics within picosecond and milli- ˚ Angstr¨ om resolution [14]. Polydi- acetylene has been already identified as a good system where the vibrational dynamics after optical excitation could be observed [15], and the possibility of addressing optically a single polymer chain of this material has been recently demonstrated [16]. We are focussing here on the steady state regime of the polymer driven by a cw or nanosecond laser. This should be easier to address ex- perimentally, yet it contains rich and unexplored features related to light-matter interaction in strong coupling. The coherent many-body ground state of the chain in the presence of the light field can be parametrized as a BCS-like wavefunction that depends on variational pa- rameters. By a functional minimization of the ground state energy with respect to these variational parame- ters, we obtain a non-homogeneous nonlinear equation that describes the distribution of the optical polarization along the chain. The total polarization in the chain is not fixed, like in the case of a single excitonic polaron [17, 18], but is determined by the intensity and frequency of the laser field. The nonlinear equation is solved numerically to calculate the distribution of the polarization in the chain and therefore the forces acting on the ions. The model consists of a molecular crystal chain coupled to a single mode of the electromagnetic field. Molecular- like states localized at the unit cells of the chain (Frenkel excitons) can propagate along the chain by hopping. The ground state of the organic semiconductor in the pres- ence of the electromagnetic field can be investigated by adding the effect of the exciton-light coupling H XL to the SSH [19] Hamiltonian as H = H SSH + H XL , (1) where H SSH =  n p 2 n 2M +  n 1 2 C(u n+1 − u n ) 2 −  n t n+1,n (B † n+1 B n + B † n B n+1 ) (2) and H XL =  n Ω 2 (B † n +B n )+  n (E g +2t 0 −¯ hω L )B † n B n . (3) M , C, u n and p n are the mass, force constant, total dis- placement and momentum of the n-th unit cell in the chain. B + n , B n are operators of creation, annihilation of Frenkel excitons localized in the n-th cell in a singlet spin