Matter-wave clocks

Summary form only given. It is a key principle of quantum mechanics that plane matter waves are proportional to exp(-ip_μx^μ/ħ)=exp(-iω₀τ), where p_μ and x^μ are respectively 4-momentum and position, and τ is the proper time measured along the particle´s tra-jectory. 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/ħ travelling along the particle´s trajectory. This equality, if it is not just an artifact of the theory, 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 (ω₀/2π=3×10²⁵ 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 selfreference a Ramsey-Bordé atom interferometer and synchronize an oscillator at a subharmonic of ω0 (Fig. 1) [1]. The clock has an accuracy and stability of 4×10-9 (Fig. 2). It highlights the intimate connection between frequency and mass: The Compton frequency can serve as a frequency reference directly, without requiring the particle to beannihilated - an explicit illustration of a key principle of quantum mechanics. It allows measurement of microscopic masses with 4×10-9 accuracy in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms. We will su- vey other applications, such as testing relativity [2,3] and verifying the gravitational Aharonov-Bohm effect [4].