Current laser technology is capable of generating laser fields from the IR to visible wavelength regions in the form of well-tailored sequences of pulses with controllable phase and envelopes (pulse shape) [1–2]. Such pulses can be used for the efficient preparation of ensembles of atoms or molecules in specific states. This is of considerable interest not only in spectroscopy but also in studies of chemical dynamics [2–4]. Furthermore short pulses allow one to attain electric field strengths e (V cm-1) or equivalently laser intensities I (W/cm2) = ce 2 /8π (c = velocity of light) which are comparable or greater than atomic fields. An important consequence of the progress in this area is that one can greatly enhance radiative transition rates and even ionize molecules. Clearly strong field science and short pulse science are two fields which will become increasingly intertwined. Efficient rapid excitation requires increasingly higher intensities as can be seen from the simple example of a resonantly driven two-level system [6–7].

Molecules in Laser Fields

The Maxwell–Schrodinger equations describing the ultrashort laser pulse propagation in multilevel molecular media are shown to be analytically solvable and to reduce to nonlinear multisine‐Gordon equations for certain models of the field–molecule system. Special cases of level schemes are shown to lead to soliton propagation. A numerical study is presented in order to examine the effect of nonresonant (virtual) transitions on pulse propagation and amplification in a three‐level molecular system as a function of intensity and detuning.The Maxwell–Schrodinger equations describing the ultrashort laser pulse propagation in multilevel molecular media are shown to be analytically solvable and to reduce to nonlinear multisine‐Gordon equations for certain models of the field–molecule system. Special cases of level schemes are shown to lead to soliton propagation. A numerical study is presented in order to examine the effect of nonresonant (virtual) transitions on pulse propagation and amplification in a three‐level molecular system as a function of intensity and detuning.

Coherent propagation of intense ultrashort laser pulses in a molecular multilevel medium

The total Schrodinger equation for an electromagnetic field interacting with a molecule is shown to lead to time independent or time dependent coupled differential equations. The time independent equations result from using a quantized representation, i.e., photon number states, of the electromagnetic field. The stationary states of such a quantized field-molecule system are called dressed states. Appropriate numerical methods are presented in order to treat radiative and non-radiative interactions simultaneously for any coupling strength, i.e. from the perturbative, Fermi-Golden rule limit, to the non-perturbative regime for both types of interactions. Both bound-bound, bound-continuum and continuum-continuum radiative and non-radiative transitions can be treated exactly in the present scheme. The relationship between the quantized time independent approach and the time dependent semiclassical field method is achieved through consideration of the coherent states of the quantized radiation field....

Molecular multiphoton transitions. Computational spectroscopy for perturbative and non-perturbative regimens

We derive the condition for a time dependent quantum system to exhibit an exact or higher order adiabatic time evolution. To this end, the concept of adiabaticity is first analyzed in terms of the transformation properties of the time‐dependent Schrodinger equation under a general unitary transformation U(t). The system will follow an adiabatic time evolution, if the transformed Hamiltonian, K(t)=U° HU−iℏU° U, is divisible into an effective Hamiltonian h(t), defining adiabatic quasistationary states, and an interaction term Ω(t), whose effect on the adiabatic states exactly cancels the nonadiabatic couplings arising from the adiabatic states’ parametric dependence on the time. This decoupling condition, which ensures adiabaticity in the system’s dynamics, can be expressed in a state independent manner, and governs the choice of the unitary operator U(t), as well as the construction of the effective Hamiltonian h(t). Using a restricted class of unitary transformations, the formalism is applied to the time evolution of an atomic or molecular system in interaction with a spatially uniform electromagnetic field, and gives an adiabatic approximation of higher order to the solutions of the semiclassical Schrodinger equation for this system. The adiabatic approximation so obtained exhibits two properties that make it suitable for the studies of intense field molecular dynamics: It is valid for any temporal profile of the field, and improves further as the field intensity increases, as reflected in the weakening of the associated residual nonadiabatic couplings with increasing field strength.

Adiabatic time evolution of atoms and molecules in intense radiation fields

A coupled equations method is used to examine nonadiabatic effects on two‐ and three‐photon transitions in diatomics. Using C12 as a test case, it is shown that nonadiabatic corrections are less important for virtual (nonresonant) transitions than in the case of resonant transitions. The contributions from virtual transitions diminish with the order of the multiphoton transition. Finally, the present method enables one to calculate transition amplitudes. The phase information in such amplitudes are shown to be useful to identify photon pathways in some multiphoton transitions especially at high intensities where the coupled equations approach enable us to go beyond perturbative methods.

Nonadiabatic effects in multiphoton transitions: A coupled equations study

The dressed molecular Hamiltonian for molecules in strong electromagnetic fields is derived in the Bloch–Nordsieck (BN) and electric field (EF) representations beyond the dipole approximation. Both representations, which are related by simple unitary transformations generate photon coherent states beyond the dipole approximation. It is shown that applying the dipole approximation to the complete molecule–field equations leaves recoil corrections of order (v/c) which are field dependent. This implies that in the BN representation all Coulomb potentials will be modified at high intensities. In particular, electron–electron repulsions are subject to field dependent photon recoil corrections, which for very intense fields necessitate relativistic corrections as well.

O. F. Kalman

Papers

Molecular dynamics in intense fields. IV. Beyond the dipole approximation