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We propose a multilevel scheme to coherently transfer the population of a diatomic molecule from a rovibrational level to a target rovibrational level of the same electronic state or another. It involves a linear chain of N rovibrational levels alternating between the initial electronic state and a second electronic state, conveniently selected according to the dipole couplings between consecutive levels. A set of N - 1 simultaneous weak laser $\pi$ pulses, with simple analytical shapes, each in resonance between two neighbors of the chain, transfers the population from the initial rovibronic state gradually and consecutively through the chain, until at the end of the process it resides in the target rovibronic state, as in a kind of ping-pong game between the two electronic states. Using the partial-wave expansion of the molecular wave function, vibrational bases within the J manifolds of each electronic state, and the rotating-wave approximation (RWA), we map the radial Hamiltonian to the one of a spin s = (N - 1)/2 under a static magnetic field, providing an analytical formula for the populations of the linked states. As an illustration, we apply the scheme to the stabilization into the absolute ground state of a KRb molecule initially in the high-lying $\upsilon$ = 75, J = 6 level of the ground electronic state $X^{1}\Sigma^{+}$. With a chain of seven rovibronic states, three of them belonging to the excited $A^{1}\Sigma^{+}$ electronic state, and pulses of 0.4 ns of duration, the population is fully transferred into the target state in about 1 ns.

We propose an optical control scheme for driving a polar molecule from a high-lying vibrational level to a target low-lying one, within the same electronic state. The scheme utilizes an infrared chirped laser pulse with an analytical shape, whose parameters are optimized by means of a heuristic formulation of quantum optimal control based on a genetic algorithm. We illustrate this methodology computationally for a KRb Feshbach molecule in the lowest triplet electronic state.

We present an alternative, univocal characterization of the continuous transition from atomic to molecular shape in the Coulomb system constituted by two identical particles and a third particle with the opposite charge, as the mass ratio of the particles varies. Applying a marginal-conditional exact factorization to a variationally optimized wavefunction, we construct a nonadiabatic potential energy surface for the relative motion between the single particle and each of the identical particles in the ground state. The transition is revealed through the evolution with the mass ratio of the topography of such surface and of the shapes of the associated marginal and conditional distributions. Our approach unifies and extends to the nonadiabatic regime the Born-Oppenheimer and charge-distribution pictures of molecular shape., Comment: 14 pages, 6 figures

We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of suitably chosen internal clock variables, thereby unifying the conditional probability interpretation (CPI) and the semiclassical approach for the problem of time in quantum theory. Our formalism stems from an exact factorization of the Hamiltonian eigenfunction of the clock plus system composite, where the clock and system factors play the role of marginal and conditional probability amplitudes, respectively. Application of the Variation Principle leads to a pair of exact coupled pseudoeigenvalue equations for these amplitudes, whose solution requires an iterative self-consistent procedure. The equation for the conditional amplitude constitutes an effective "equation of motion" for the quantum state of the system with respect to the clock variables. These coupled equations also provide a convenient framework for treating the back-reaction of the system on the clock at various levels of approximation. At the lowest level, when the WKB approximation for the marginal amplitude is appropriate, in the classical limit of the clock variables the TDSE for the system emerges as a matter of course from the conditional equation. In this connection, we provide a discussion of the characteristics required by physical systems to serve as good clocks. This development is seen to be advantageous over the original CPI and semiclassical approach since it maintains the essence of the conventional formalism of quantum mechanics, admits a transparent interpretation, avoids the use of the Born-Oppenheimer approximation, and resolves various objections raised about them., Comment: 10 pages. Typographical errors corrected

A strategy for the systematic design of polymeric superlattices with tailor-made mini-bandgaps and carrier mini-effective masses is described and computationally implemented by means of an envelope crystalline-orbital method, which is a straightforward adaptation for molecules of the envelope-function approximation widely used in solid-state physics. Such strategy relies on the construction of pi-conjugated periodic block copolymers from well-characterized parent polymers, in such a way that the above-mentioned electronic parameters can be predicted from the lengths of the blocks. Illustrative calculations for prototypical (PPP_x-PDA_y)_n superlattices demonstrate the plausibility of the strategy and the advantages of the computational implementation employed., Comment: To appear in Int. J. Quant. Chem. (2010)

A conceptually appealing and computationally economical course-grained molecular-orbital (MO) theory for extended quasi-linear molecular heterostructures is presented. The formalism, which is based on a straightforward adaptation, by including explicitly the vacuum, of the envelope-function approximation widely employed in solid-state physics, leads to a mapping of the three-dimensional single-particle eigenvalue equations into simple one-dimensional hole and electron Schr\"odinger-like equations with piecewise-constant effective potentials and masses. The eigenfunctions of these equations are envelope MO's in which the short-wavelength oscillations present in the full MO's, associated with the atomistic details of the molecular potential, are smoothed out automatically. The approach is illustrated by calculating the envelope MO's of high-lying occupied and low-lying virtual $\pi$ states in prototypical nanometric heterostructures constituted by oligomers of polyacetylene and polydiacetylene. Comparison with atomistic electronic-structure calculations reveals that the envelope-MO energies agree very well with the energies of the $\pi$ MO's and that the envelope MO's describe precisely the long-wavelength variations of the $\pi$ MO's. This envelope MO theory, which is generalizable to extended systems of any dimensionality, is seen to provide a useful tool for the qualitative interpretation and quantitative prediction of the single-particle quantum states in mesoscopic molecular structures and the design of nanometric molecular devices with tailored energy levels and wavefunctions., Comment: 14 pages, 6 figures

We propose a molecular setup for the physical implementation of a barrier global quantum computation scheme based on the electron-doped pi-conjugated copolymer architecture of nine blocks PPP-PDA-PPP-PA-(CCH-acene)-PA-PPP-PDA-PPP (where each block is an oligomer). The physical carriers of information are electrons coupled through the Coulomb interaction, and the building block of the computing architecture is composed by three adjacent qubit systems in a quasi-linear arrangement, each of them allowing qubit storage, but with the central qubit exhibiting a third accessible state of electronic energy far away from that of the qubits' transition energy. The third state is reached from one of the computational states by means of an on-resonance coherent laser field, and acts as a barrier mechanism for the direct control of qubit entanglement. Initial estimations of the spontaneous emission decay rates associated to the energy level structure allow us to compute a damping rate of order 10^{-7} s, which suggest a not so strong coupling to the environment. Our results offer an all-optical, scalable, proposal for global quantum computing based on semiconducting pi-conjugated polymers., Comment: To appear in J. Phys.: Conf. Series (2009)