We report a new determination of muonium 1S-2S transition frequency and its isotope shift with deuterium by recalibrating the iodine reference lines using an optical frequency comb. The reference lines for the muonium and deuterium 1S-2S transitions
are determined with a precision of 2.4*10^-10 and 1.7*10^-10 respectively. A new muonium-deuterium 1S-2S isotope-shift frequency is derived from these references to be 11 203 464.9(9.2)(4.0) MHz, in agreement with an updated bound-state quantum-electrodynamics prediction based on 2010 adjustments of Committee on Data for Science and Technology and 2.3 times better in the systematic uncertainty than the previous best determination.
We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy level struc
ture, fidelity, and adiabatical geometric phase, we confirm that the system exists a second-order phase transition from an atommolecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular we find that both the critical exponents and the behaviors of ground-state geometric phase change obviously in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to ?pi/3 at the critical point. This discontinuous behavior has been checked by numerical simulations and it can be used to identify the phase transition in the system.
We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by a
n intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.
