Square-Wave Phase Modulation in Ramsey-Type Molecular Beam Resonance Experiments

Square-wave phase modulation of the microwave signal which induces transitions allows one to measure velocity-dependent frequency shifts in Ramsey resonance experiments. The output signal from the molecular beam apparatus is demodulated by a synchronous detector operating in phase with the modulation. This output is proportional to the derivative of the transition probability and provides the usual resonance signal which is used in a servo loop to keep a harmonic of a voltage tunable crystal oscillator on the central peak of the resonance. A quadrature synchronous detector operating 90° out of phase with the modulating signal provides a measure of any velocity-dependent frequency shifts. Such shifts arise when there is a phase difference between the oscillating fields or when an electric field applied to a magnetic system produces a v×ε shift. We have theoretically and experimentally demonstrated that this quadrature signal is proportional to the phase difference between the microwave cavities of a Ramsey apparatus with the in-phase signal constrained at zero. We have also shown that the sensitivity of the quadrature system depends on the width of the available velocity distribution.