File:Directly detecting a geometric phase through wavepacket interference.png

English: "a, A motional wavepacket is initially displaced to the minimum of the potential energy surface, after which it begins to encircle the conical intersection, denoted CI. b, Initial wavepacket density in 2D (left), and integrated over Q1 (right). c, After sufficient time evolution, the two components of the wavepacket destructively interfere due to geometric phase, giving a nodal line along Q2 = 0 (dotted line). d, Motional wavepacket density at the maximum interference time T . e, If the geometric phase were neglected, the two wavepacket components would interfere constructively. f, Density at t = T with geometric phase neglected. Contours in b, d, and f correspond to the potential energy surface E−. g, The Jahn-Teller Hamiltonian HJT is engineered in an ion-trap quantum simulator with a single 171Yb+ ion. The ion (white sphere) is confined in a Paul trap and HJT is realised using two simultaneous laser-induced interactions (purple and pink, corresponding to colour-coded terms in HJT)."

"The effects of geometric phase on dynamics around a conical intersection can be directly observed from the motional probability density, fig. 1a–d."

"As the initial wave-packet, we choose the ground state of the non-interacting vibrational Hamiltonian, H0 = ω(a†1a1 +a† 2a2), displaced to the potential-energy minimum at Q1 = −κ/ω, Q2 = 0 (fig. 1a–b). During the time evolution, the wavepacket splits into two components evolving in opposite directions around the conical intersection. The two components overlap at Q1 > 0, causing destructive interference at the nodal line Q2 = 0, where their equal and opposite geometric phases lead to a vanishing density (fig. 1c–d).

By contrast, if geometric phase were disregarded, the two wavepacket fragments would interfere constructively, reaching maximum amplitude at Q2 = 0 (fig. 1e–f)."