Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials

Accurate diabatization based on combined-hyperbolic-inverse-power-representation: 1,2 2A' states of BeH2

A diabatic potential energy matrix (DPEM) for the two lowest states of BeH2+ has been constructed using the combined-hyperbolic-inverse-power-representation (CHIPR) method. By imposing symmetry constraints on the coefficients of polynomials, the complete nuclear permutation inversion symmetry is correctly preserved in the CHIPR functional form. The symmetrized CHIPR functional form is then used in the diabatization by ansatz procedure. The ab initio energies are reproduced with satisfactory accuracy. In addition, the CHIPR-based DPEM also reproduces the local topology of a conical intersection. Future work will focus on a complete four-state diabatic representation with emphasis on the long-range interactions and spin-orbit couplings, which will enable accurate quantum scattering calculations for the Be+(2P) + H2 → BeH+(X1Σ+) + H(2S) reaction.

The geometric phase controls ultracold chemistry

The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.

A scheme for a single molecule phase-shift gate in a solid matrix

We propose a feasible scheme to implement a phase-shift gate ((1 0) (0 eiγ)) based on a two-state single molecule in a solid matrix, where γ is a geometric phase controlled through a fast on-resonant laser field and a slow off-resonant radio-frequency field. In our scheme, a non-Hermitian quantum model is employed to characterize the single molecule in a solid matrix including the spontaneous decay effect. By the coupling between the radio-frequency field and the two-state permanent dipole difference resulting from the solid matrix, the spontaneous decay fatal to the preservation of geometric phase can be effectively suppressed for a considerably long waiting time.