Dynamic phase shifts in nanoscale distance measurements by double electron electron resonance (DEER)

The off-resonant pump pulse used in double electron electron resonance (DEER) measurements produces dynamic phase shifts that are explained here by simple analytic and vector descriptions of the full range of signal behaviors observed during DEER measurements, including: large phase shifts in the signal; changes in the position and shape of the detected echo; and changes in the signal intensity. The dynamic phase shifts depend on the width, amplitude and offset frequency of the pump pulse. Isolated radicals as well as pairs or clusters of dipolar-coupled radicals have the same dynamic phase shift that is independent of pump pulse delay in a typical measurement. A method of calibrating both the pump pulse offset frequency and the pump pulse field strength is outlined. A vector model is presented that explains the dynamic phase shifts in terms of precessing magnetization that is either spin locked or precessing about the effective pump field during the pump pulse. Implications of the dynamic phase shifts are discussed as they relate to setting up, calibrating and interpreting the results of DEER measurements.