Amplitudes and Transition Amplitudes

Man Mohan, R. K. Thareja

Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of $N$, where $N$ is the number of intense photons absorbed or emitted during the transition. For larger values of $N$ the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.

Elliot Leader

Haifeng Lang, Yi-Xin Chen, Qiantan Hong +1 more

Based on a kinematic approach in defining a geometric phase for a density matrix, we define the generalized Loschmidt overlap amplitude (GLOA) for an open system for arbitrary quantum evolution. The GLOA reduces to the Loschmidt overlap amplitude (LOA) with a modified dynamic phase for unitary evolution of a pure state, with the argument of the GLOA well defined by the geometric phase, thus possessing a similar physical interpretation to that of the LOA. The rate function for the GLOA exhibits nonanalyticity at a critical time, which corresponds to the dynamical quantum phase transition. We observe that the dynamical quantum phase transition related to GLOA is not destroyed under a finite temperature and weak enough dissipation. In particular, we find that an alternate type of dynamical quantum phase transition emerges in a dissipation system. The proposed GLOA provides a powerful tool in the investigation of a dynamical quantum phase transition in an arbitrary quantum system, which not only can characterize the robustness of the dynamical quantum phase transition but also can be used to search for new transitions.

H. Muirhead

P.V. Landshoff

Amir Erez, Yigal Meir

The Berezinskii-Kosterlitz-Thouless (BKT) transition is a generic transition describing the loss of coherence in two-dimensional systems and has been invoked, for example, to describe the superconductor-insulator transition in thin films. However, recent experiments have shown that the BKT transition, driven by phase fluctuations, is not sufficient to describe the loss of superconducting order, and amplitude fluctuations must also be taken into account. The standard models that are extensively used to model two-dimensional superconductors are the Hubbard and $\mathit{XY}$ models. Whereas the $\mathit{XY}$ model allows only phase fluctuations, the Hubbard model has an extra degree of freedom: amplitude fluctuations. In this paper we compare two Hubbard models with the same critical temperature but with different interactions and deduce the role of the amplitude fluctuations in the superconducting transition. For this purpose, a novel approximation is presented and used. We derive an effective phase-only ($\mathit{XY}$) Hamiltonian, incorporating amplitude fluctuations in an explicit temperature dependence of the phase rigidity. We study the relation between amplitude fluctuations and coupling strength. Our results support existing claims about the suppression of phase rigidity due to amplitude fluctuations not present in the $\mathit{XY}$ model.