A zero-width resonance (ZWR) is also called a bound state in a continuum. Such resonances occur when the Floquet method is applied to a diatomic molecule submitted to a continuous wave field. This circumstance requires particular choices of wavelength and electric field amplitude. The corresponding wave function can be factorised with a method devised for bound states. The result is a product of an electronic factor depending parametrically on the nuclear coordinate by a nuclear factor. The factorisation of the wave function is done through the introduction of a fictitious time-independent Hamiltonian yielding the same coupled equations as the Floquet algorithm applied to the time-dependent Hamiltonian. The potential which determines the nuclear factor is calculated and used to recover the real ZWR quasi-energy. Application is made to the molecule Na2 prepared by photoassociation in the metastable 3Σ+ u state. Photodissociation of this state by laser-coupling to the (1)3Π g state requires an intensity low enough to require the consideration of only two channels (one photon interaction) in the application of the Floquet method.
A zero-width resonance (ZWR) is also called a bound state in a continuum. Such resonances occur when the Floquet method is applied to a diatomic molecule submitted to a continuous wave field. This circumstance requires particular choices of wavelength and electric field amplitude. The corresponding wave function can be factorised with a method devised for bound states. The result is a product of an electronic factor depending parametrically on the nuclear coordinate by a nuclear factor. The factorisation of the wave function is done through the introduction of a fictitious time-independent Hamiltonian yielding the same coupled equations as the Floquet algorithm applied to the time-dependent Hamiltonian. The potential which determines the nuclear factor is calculated and used to recover the real ZWR quasi-energy. Application is made to the molecule Na2 prepared by photoassociation in the metastable 3Σ+ u state. Photodissociation of this state by laser-coupling to the (1)3Π g state requires an intensity low enough to require the consideration of only two channels (one photon interaction) in the application of the Floquet method.
In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected zero-width resonances (ZWRs) with, in principle, infinite lifetimes. Their potential to induce basic quenching mechanisms has recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A 87, 031403(R) (2013)]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelope-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage of its continuous transport on the corresponding ZWR all along the pulse duration. As compared with previous control scenarios that actually suffered from nonadiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps us to find and interpret a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, turns out to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, which has the potential to be transposed to other diatomics, is Na2 prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.
A semiclassical model supporting the destructive interference interpretation of zero-width resonances (ZWRs) is extended to wavelengths inducing ${c}^{\ensuremath{-}}$-type curve crossing situations in Na2 strong-field dissociation. This opens the possibility to get critical couples of wavelengths $\ensuremath{\lambda}$ and field intensities I to reach ZWRs associated with the ground vibrationless level v=0, that, contrary to other vibrational states (v>0), is not attainable for the commonly referred c+-type crossings. The morphology of such ZWRs in the laser $(I,\ensuremath{\lambda})$ parameter plane and their usefulness in filtration strategies aiming at molecular cooling down to the ground v=0 state are examined within the frame of an adiabatic transport scheme.
In this chapter,we shall analyze the particular case of an atom interacting with a laser pulse whose duration is sufficiently long, so that the evolution of the atom in the laser field is adiabatic. When this condition is fulfilled, the atom can be considered to interact with a monochromatic laser field. As a consequence, the Hamiltonian of the system is periodic in time, and the Floquet theory [1] can be used to solve the time-dependent Schrödinger equation (TDSE) non-perturbatively. We begin in Section 4.1 by considering the Hermitian Floquet theory. We first derive the Floquet theorem for a monochromatic, spatially homogeneous laser field and show that the solutions of the TDSE correspond to dressed states having real quasi-energies , which can be obtained by solving an infinite system of time-independent coupled equations. We then generalize the Floquet theory to multicolor laser fields and to “non-dipole” laser fields which are not spatially homogeneous. In Section 4.2, the Floquet theory is applied to study the dynamics of a model atom having M discrete levels interacting with a monochromatic laser field. In this case, the coupling between the bound and continuum atomic states is neglected.We analyze the relationship between the Floquet theory and the rotating wave approximation, and examine the perturbative limit of the Floquet theory. We also consider the population transfer between Floquet dressed states.
Resonances manifest as the sharp peaks observed in graphs of scattering cross section versus energy. Resonances in binary collisions are closely related to twobody bound or quasi-bound states, which are the discrete quantum states whose amplitudes fall off (usually exponentially) in space as the separation r → ∞. In the case of a single channel, a bound state is formed at a specific negative energy; that is, below the channel threshold. In the multichannel case, as mentioned in the preceding chapter, a bound state occurs when all the channels are closed; that is, below the threshold of the lowest channel. Under specific circumstances, a bound state may occur at zero energy; that is, right at the lowest threshold. Quasi-bound states are also discrete quantum states that are formed temporarily at a discrete positive energy (above the lowest threshold). Both resonant and bound states (including quasibound ones) can be described by a unified approach to cold collisions. The temporary binding of a quasi-bound state at a discrete energy enhances the scattering cross section at that energy. This occurs because the quasi-bound state eventually decays into the continuum of scattering states whose central energy equals the binding energy. The resonance width is determined by the coupling between the bound and continuum states.
A description of photoassociation by cw laser is formulated in the framework of grid methods. The Hamiltonian describing one or several bound states coupled to a multiple of continuum manifolds via a radiative field is written in the energy representation and diagonalized. The generality of the treatment allows us to compute accurately and efficiently physical properties such as nonlinear high-intensity energy shifts, line shapes, and photoassociation rates both for isolated and nonisolated resonances. Application is given to sodium photoassociation in the experimental conditions of McKenzie et al. [Phys. Rev. Lett. 88, 090403 (2002)]. Inverted regions for the dependency of the rate vs the intensity and nonsymmetric line shapes are predicted to occur above the saturation limit. Comparison with the model of Bohn and Julienne [Phys. Rev. A 60, 414 (1999)] is discussed.
The spectral and dynamic effects associated with a non-zero difference, d, between the permanent dipole moments of two molecular states involved in a transition, are investigated for a variety of electromagnetic field-molecule interactions. Both analytical and exact numerical techniques are used to solve the time-dependent Schrodinger equation and to obtain the temporal populations of the molecular states and the associated absorption spectra, for molecular interactions with a Gaussian pulsed, or one or two continuous wave (CW), laser(s).;Analytical rotating wave approximation results are derived for a single CW laser interacting with a two-level d {dollar}\\ne{dollar} 0 molecule with an excited state lifetime, and for a two-level d {dollar}\\ne{dollar} 0 molecule interacting with two CW lasers. A symmetry-adapted Riemann product integral method for exact calculations of pulsed laser-molecule interactions is developed and applied to specific problems. The Floquet technique for the treatment of periodic Hamiltonians is extended to accommodate the interaction of a molecule with two CW lasers.;The one-field RWA results are used to predict and interpret the effects of permanent dipoles on the temporal behaviour of the molecular states for a decaying two-level system interacting with a CW laser, and for a non-decaying two-level system interacting with a pulsed laser. It is shown that the excited state lifetime and the pulse duration can act as internal and external probes, respectively, of the temporal effects of permanent dipoles, relative to the often-studied d = 0 problem. The two-field analytical RWA solutions are used to help discuss and predict the effects of permanent dipole moments in two-laser multi-photon transitions. Several examples of multi-photon, two-colour, two-level resonance profiles, calculated in the RWA and by using exact Floquet techniques, are used to demonstrate how particular multi-photon transitions can be optimized, and to help quantify the conditions for the validity of the two-colour RWA. The effects of neighbouring energy levels on the transition of interest, for both probe and pump-probe laser-molecule interactions, are investigated using a series of three- to seven-level model molecular systems.