It is a key principle of quantum mechanics that plane matter waves are proportional to exp(-ip_μx^μ)=exp(-iω₀), where p_μ and x^μ are respectively 4-momentum and position, and τ is the proper time measured along the particle's trajectory. Thus, the quantum state of a free particle of mass m accumulates the same phase as a clock ticking at the particle's Compton frequency of ω₀=mc²/h-bar travelling along the particle's trajectory. This implies that a single particle can be a reference for a clock. In principle, such a clock could be built by annihilating particle-antiparticle pairs and counting the frequencies of the generated photons. This would provide a frequency reference with virtually infinite quality factor Q and unsurpassed stability against systematic influences. The frequency (3x10²⁵ Hz for a Cesium atom), however, is far beyond modern counting techniques. A method to divide it into a technically accessible range is thus required.

We demonstrate a "Compton clock," a clock referenced to ω₀, using an optical frequency comb to self-reference a Ramsey-Borde atom interferometer and synchronize an oscillator at a subharmonic of ω₀. The interferometer is based on n-photon Bragg diffraction. It is self-referenced by locking the laser to the Nth multiple of the measured recoil frequency. The clock's frequency is then fully determined by ω₀ and the known numerical factors. The clock has an accuracy and stability of 4x10^-9. It highlights the intimate connection between frequency and mass: The Compton frequency can serve as a frequency reference directly, without requiring the particle to be annihilated. It allows measurement of microscopic masses with 4x10^-9 accuracy in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms. We will survey other applications of matter waves as clocks, such as testing relativity and verifying the gravitational Aharonov-Bohm effect.

Argonne Physics Division Colloquium Schedule