Laser isotope separation schemes which require resonant photoexcitation of atoms or molecules with complex spectra will in general involve processes more complicated than a simple chain of transitions between successive pairs of energy levels. In the rotating-wave approximation these situations can be described by excitation graphs with side branches and cycles. For many cases a simple change of basis removes the time dependence of the interaction Hamiltonian and reduces the calculation of level populations and interlevel flows to an eigenvalue problem. By this method it is shown that a side branch with a large matrix element strongly inhibits the flow of population along the path to which it is attached. When several phase-locked lasers are employed, the populations and flows depend on certain linear combinations of the phases, one for each independent cycle in the excitation graph. In the simplest one-cycle example this phase dependence allows a continuous change from no population inversion to complete inversion.
Laser isotope separation schemes which require resonant photoexcitation of atoms or molecules with complex spectra will in general involve processes more complicated than a simple chain of transitions between successive pairs of energy levels. In the rotating-wave approximation these situations can be described by excitation graphs with side branches and cycles. For many cases a simple change of basis removes the time dependence of the interaction Hamiltonian and reduces the calculation of level populations and interlevel flows to an eigenvalue problem. By this method it is shown that a side branch with a large matrix element strongly inhibits the flow of population along the path to which it is attached. When several phase-locked lasers are employed, the populations and flows depend on certain linear combinations of the phases, one for each independent cycle in the excitation graph. In the simplest one-cycle example this phase dependence allows a continuous change from no population inversion to complete inversion.
I discuss the flow of excitation probability along a multistate chain of resonant excitations as driven by coherent photoexcitation, in particular the gated interruption of this probability flow caused by a strongly coupled side branch. If the side branch is itself a chain, not a single transition, then flow inhibition occurs if the number of branch transitions is odd, but no inhibition occurs if the number is even. The inhibition provides a limiting bound on the intensity of amplified stimulated emission.
The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.
An analytic solution is presented for the time development of an n-level atom in resonant interaction with n-1 lasers in a branch configuration, which is an alternative generalization of the three-level atom to the commonly studied cascade configuration. The same analytic approach is also applied to a four-laser resonant interaction with a four-level atom in a cyclic configuration, where it is found that a change of phase of any one of the lasers has a critical effect on the population dynamics and, with certain Rabi frequency and laser phase relationships, double-quantum transitions can be eliminated completely.
A strong laser field interacting with an atom or a molecule can induce a coherent process which includes a large number of energy levels. If we can find a transformation which eliminates the explicit time dependence of the interaction Hamiltonian (for example, the rotating-wave approximation), we can reduce the dynamic problem to the consideration of eigenvalues and eigenvectors of the Hamiltonian. However, the complexity of an arbitrary multilevel Hamiltonian usually forces us to use numerical methods, and, therefore, not much general understanding about multilevel systems can be achieved. We consider the multilevel problems in a more general setting. Our approach is based on the observation that an arbitrary Hamiltonian matrix can be transformed into a tridiagonal form by unitary transformation.1 A tridiagonal form represents a ladder-type multilevel system. From all W-level systems the ladder configuration is the simplest in the sense that the number of level connections is the smallest possible. This means that the most effective analysis of a given multilevel system can be achieved using the transformation to ladder configuration. The spectral analysis of ladders is facilitated by the connections to orthogonal polynomials and continued fractions. The investigations about the spectral properties of ladders are reported.
We propose a method of laser isotope separation based on the phenomenon of adiabatic inversion and illustrate the method in a multilevel system consisting of a single ground state and multiplet excited states. In this model, population may be transferred from the ground state to one of the excited manifolds with nearly 100% efficiency by using laser pulses, the envelope of which rises slowly and then decays rapidly on an internal time scale that can be precisely calculated. Adiabatic inversion in this model is strongly dependent on the laser frequency, thus permitting separation of isotopes by faking advantage of small shifts in molecular or atomic energy level spacings. The criterion that determines whether a laser pulse is adiabatic also depends strongly on the laser frequency and thereby enhances the separation. We demonstrate the effectiveness of the method with a solution of the time-dependent Schroedinger equation for a specific model of two isotopes.
The dynamics of populations of the vibrational states in a NO molecule (one-photon absorption) and of the electronic states in a 4,4'-bis(dimethylamino) stilbene molecule (two-photon absorption) is studied versus the frequency, intensity and shape of the laser pulse. We show that specially designed infrared laser pulses can build selective populations of certain vibrational states. A detuning of light frequency from the vibrational resonance qualitatively changes the dynamics of populations. It is found out that the populations of the nonresonant levels follow the pulse shape adiabatically if the detuning significantly exceeds the inverse characteristic time of the change of the pulse. Depopulation of the nonresonant vibrational states leads to a high population of the resonant state at the end of the pulse. Complete breakdown of the standard rotating wave approximation for a two-photon absorption process is observed even for a rather small intensity of the laser pulse. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation is obtained, and it is in close agreement with the strict numerical solution of the amplitude equations. Special attention is paid to the population dynamics of randomly oriented molecules. The orientational disorder as well as the vibrations limit the coherent population transfer. Calculations show the strong role of the anisotropy of photoexcitation in the coherent control of populations which can affect the anisotropy of photobleaching.