Laser Control of Vibrational Transfer Based on Exceptional Points

Characteristic footprints of an exceptional point in the dynamics of Li dimer under a laser field

Non-hermitian quantum mechanics is a formalism that excels in describing time-dependent states such as resonances. As one, it opens up a window to explore new and undiscovered phenomena. Under this formalism coalescence of two eigenstates and a deficient spectrum are a possible situation. These situations are unique and can occur solely in specific conditions known as Exceptional Points (EPs). An EP holds unique characteristics. One of which is a switch-like behavior: upon adiabatically changing the conditions in a closed loop around the EP, the population of one resonance can be transferred completely to another resonance. The phenomenon was not experimentally observed in an atomic or molecular system so far, although experiments involving nonlinear PT symmetry optics and microwave cavities have already indicated its existence. In this work, we demonstrate and confirm that the switch-like behavior exists in the spectrum of a lithium dimer taking into account both the rotations and the vibrations of the system. Moreover, a footprint of the EP is also shown to exist in the photo-association process of the lithium dimer. In this process, the EP's resonances serve as the mean to associate two free lithium atoms into a dimer. Based on this, we suggest a corresponding experiment to demonstrate for the first time the EP phenomenon in a molecular system.

Exceptional points and non-Hermitian degeneracy of resonances in a two-channel model

We study the mixing and degeneracy of two unbound energy eigenstates (resonances) in a two coupled channel model of scattering and reactions. We derive the necessary and sufficient conditions for existence of an exceptional point in the extended spectrum of bound and resonance energy eigenvalues in this model and show that these are not the same as in the single channel case. When these conditions are satisfied, in the complex energy plane, the two simple resonance poles of the scattering matrix merge into one double pole at the exceptional point. In parameter space, the surface of the eigenenergies has a branch point of square root type and branch cuts in its real and imaginary parts that start at the exceptional point and extend in opposite directions. The rich phenomenology of crossings and anticrossings of energies and widths of the doublet of unbound states, as well as the changes of identity of the poles of the scattering matrix observed when one control parameter is varied while the other is kept constant, is fully explained in terms of sections of the eigenenergy surfaces.

Proposal for a laser control of vibrational cooling in Na(2) using resonance coalescence

With a specific choice of laser parameters resulting in a so-called exceptional point (EP) in the wavelength-intensity parameter plane, it is possible to produce the coalescence of two Floquet resonances describing the photodissociation of the Na(2) molecule, which is one of the candidates for the formation of samples of translationally cold molecules. By appropriately tuning laser parameters along a contour encircling the exceptional point, the resonances exchange their quantum nature. Thus a laser-controlled transfer of the probability density from one field-free vibrational level to another is achieved through adiabatic transport involving these resonances. We propose an efficient scenario for vibrational cooling of Na(2) referring to cascade transfers involving multiple EPs and predicted to be robust up to a 78% rate against laser-induced dissociation.