Quantum System Dynamics and the Quasistatic Approximation

Understanding the dynamics of quantum systems to time-varying perturbations is not only a question of basic physics, it is a question that can have life-critical relevance. Specifically, as GPS signals take on greater roles in autonomous navigation, means must be found to ensure the moment-by-moment integrity of those signals, and thereby the integrity of GPS atomic clock frequencies. The frequency of an electro-magnetic field, like the microwave field in a GPS atomic clock, is stabilized to a quantum system's energy structure by modulating the field's frequency and then demodulating the quantum system's response. The first harmonic (i.e., fundamental) demodulated signal provides the correction for field frequency, while the second harmonic is often taken as an instantaneous status-of-health indicator for the correction signal. The interpretative problem for the second harmonic is that the modulation frequency, the quantum system's dephasing rate, and the Rabi frequency are all approximately equal in these frequency stabilization systems, violating the textbook assumptions of quantum mechanics: the quasistatic approximation (QSA), the adiabatic approximation, and the sudden approximation. Here, we take a careful experimental and theoretical look at the QSA under realistic conditions for field stabilization (i.e., the approximation most often employed for the engineering interpretation of atomic dynamics behavior). Our results demonstrate that the second harmonic can be employed as a rapid-response herald of correction signal degradation, and that while the QSA is useful as a means for diagnosing causal effects through the second harmonic, a small-signal approximation (SSA) is better.