We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum is obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level crossings, which correspond to two-fold energy degeneracy.

Based upon an over-one-month frequency comparison of two (40)Ca(+) optical clocks, the frequency difference between the two clocks is measured to be 3.2×10(-17) with a measurement uncertainty of 5.5×10(-17), considering both the statistic (1.9×10(-17)) and the systematic (5.1×10(-17)) uncertainties. This is the first performance of a (40)Ca(+) clock better than that of Cs fountains. A fractional stability of 7×10(-17) in 20,000 s of averaging time is achieved. The evaluation of the two clocks shows that the shift caused by the micromotion in one of the two clocks limits the uncertainty of the comparison. By carefully compensating the micromotion, the absolute frequency of the clock transition is measured to be 411 042 129 776 401.7(1.1) Hz.

The Einstein Gravity Explorer mission (EGE) is devoted to a precise measurement of the properties of space-time using atomic clocks. It tests one of the most fundamental predictions of Einstein's Theory of General Relativity, the gravitational redshift, and thereby searches for hints of quantum effects in gravity, exploring one of the most important and challenging frontiers in fundamental physics. The primary mission goal is the measurement of the gravitational redshift with an accuracy up to a factor 10 4 higher than the best current result. The mission is based on a satellite carrying cold atombased clocks. The payload includes a cesium microwave clock (PHARAO), an optical clock, a femtosecond frequency comb, as well as precise microwave time transfer systems between space and ground. The tick rates of the clocks are continuously compared with each other, and nearly continuously with clocks on earth, during the course of the 3-year mission. The highly elliptic orbit of the satellite is optimized for the scientific goals, providing a large variation in the gravitational potential between perigee and apogee. Besides the fundamental physics results, as secondary goals EGE will establish a global