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Physical Review A

Laser-induced coherence in ultrafast multiphoton excitation of individual molecules

Constantin Maïnos

Published May 15, 2000• 3 citations
Publisher

Abstract

The transfer of the intrinsic coherence of short pulses to molecular systems is investigated and an explicit derivation of the excitation probability of the ultrafast multiphoton process is presented. We show that for ultrafast excitation the angular cross section splits into two distinct factors: the ``frozen orientation weight,'' which involves the space configuration and nonlinear dependence, and the ``laser-induced coherence,'' which reflects the coherent superposition of the ground- and excited-state orientations. Quantum interferences give rise to a ``coherent polarizability'' and provide evidence for a sharp confinement of the excited electron motion. The confinement is inversely proportional to the number of coherently excited rotational states.

DOI
10.1103/physreva.61.063410

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 1, 1991•0 citations
The transfer of the intrinsic coherence of short pulses to molecular systems is investigated and an explicit derivation of the excitation probability of the ultrafast multiphoton process is presented. We show that for ultrafast excitation the angular cross section splits into two distinct factors: the frozen orientation weight,'' which involves the space configuration and nonlinear dependence, and the laser-induced coherence,'' which reflects the coherent superposition of the ground- and excited-state orientations. Quantum interferences give rise to a ``coherent polarizability'' and provide evidence for a sharp confinement of the excited electron motion. The confinement is inversely proportional to the number of coherently excited rotational states.
Multiphoton orientational wave packets induced by short resonant polarized laser pulses in a rotationally-frozen interacting molecule contain relevant information. The entanglement of the orbital, rotational and orientational degrees of freedom shows a strong dependence on the polarization state of the absorbed photons and the space orientation of the interacting molecule and enables one to assign the orbital state of the excited molecular electron, to measure the space orientation of the interacting molecule from the orientational recurrences, to relate the measured temporal widths to the angular momentum photon state and the coherence of the laser pulse, to obtain information on the ground rotational state, or to measure the effective temperature of an isotropic molecular assembly. The space orientation of a small number of independent molecules can be distinguished from their distinct orientational dependence in the formation of the individual orientational wave packets.
We present an experimental and theoretical investigation of the quantum control of ground-state rotational coherence in a linear molecule. A sequence of two temporally separated laser pulses creates a rotational superposition state in CO2{\mathrm{CO}}_{2}CO2​ whose evolution is monitored through a polarization technique. We study the influence of the phase difference between the two pulses. We show that the overlapping of the two wave packets, produced by each pulse, gives rise to quantum interference that affects the orientational anisotropy of the sample. Because of the large number of coherently excited levels, the interference produces well-separated temporal structures, whose magnitude can be controlled through the relative delay of the two pulses.
We introduce a theoretical framework to describe the interaction of an electromagnetic radiation field and a molecular system, such as a single molecule or a molecular crystal. By knowing in advance which electronic transitions are in resonance with the frequencies of the incident radiation, we propose a procedure to reduce the full problem to a description in terms of an effective Hamiltonian that fully takes into account the vibrational (nuclear) degrees of freedom, but that explicitly involves only those electronic states that meet the resonance condition. The influence of the rest of the electronic states appears as the polarizability of the system. We keep only those terms that give rise to Raman scattering but the scheme allows for a systematic inclusion of higher-order multiphoton processes. The resulting effective Hamiltonian is used to study the interaction of ultrashort laser pulses with a single molecule and with a molecular crystal. As applications, we study the interaction of a single ultrashort nonresonant pulse, and a train of such pulses, with a single molecule; we show that via Raman scattering the pulse impulsively transfers momentum to the molecule leaving it in a vibrational coherent state. We also study the interaction of two crossed laser pulses with a molecular crystal and show that a diffraction grating of lattice vibrations is impulsively created.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
A review is given of experimental and theoretical achievements in studies of multiphoton spontaneous scattering processes in atomic and molecular media. An analysis is made of integral multiphoton scattering, particularly of scattering in statistically inhomogeneous media with short-range quasiorder. A study of the intensity of the noncoherent multiphoton scattering component provides direct information on the nonlinear polarizability of atoms and molecules whilst the coherent component is associated with various atomic and molecular correlation mechanisms. An analysis of the spectra of elastic and inelastic multiphoton scattering processes yields information on the translational and rotational motion of the molecules. In particular, it is possible to measure the higher-order rotational relaxation times and to verify the adequacy of the various stochastic models of molecular motion. Observations of the spectral lines of three- or more-photon scattering, which obeys new selection rules, yield detail on the fine structure of the molecules and their linear and nonlinear vibrations. Examples are given of the most interesting spectra of three- or more-photon scattering in gases, liquids, and crystals obtained in singleand multichannel systems. The stochastic theory of multiphoton scattering in liquids is discussed, using the spherical tensor concept. The derived general expression reduces to known results for certain cases.
Using a semiclassical, effective-state approach to laser pulse propagation in a dilute gas of polyatomic molecules, a numerical model of multiphoton excitation which includes quasi- continuum transitions is used to calculate the effects of coherent propagation on multi-photon absorption. The initial laser field is assumed to be a quasimonochromatic Gaussian envelope which is nearly resonant with a portion of the lower vibrational states of the molecule. The molecular model consists of a single ground state and several bands of discrete states which are successively connected via electric dipole transitions. This model correctly mimics some of the major characteristics of multiphoton absorption, such as power threshold, fluence dependent absorption, and complete population inversion at high fluences. The model also allows for the calculation of the polarization induced in the medium by the electric field, and the subsequent influence that the polarization has on the field. As the pulse propagates, the Rabi oscillations induced in the lower level states become encoded onto the pulse, creating a series of peaks and troughs similar to the behavior of pulse propagation in two-level systems. Another coherent propagation effect which can change the excitation process is coherent sideband generation. The temporal distortions and the generation of new frequencies results in changes in the population distribution among the states, as well as changes in the total population transferred to the quasi-continuum. The pulse reshaping occurs while the total fluence of the pulse is decreasing due to energy loss to the quasi-continuum. The effective increase in total population transfer due to propagation effects is offset by the decrease in fluence. The resulting transfer of energy from the pulse to the molecule depends strongly on the initial characteristic of the pulse. These processes play an important role in any system where the efficient transfer of laser energy to the medium is required, such as laser-induced chemistry and laser isotope separation.