Interference of atomic matter waves has been used to measure acceleration and rotation, constants such as Newton's gravitational constant and the fine structure constant, and to test fundamental laws of physics, such as general relativity. Our atom interferometers reach high sensitivity by a combination of large momentum transfer, long free evolution of the matter waves, and techniques to counter perturbations such as Coriolis compensation.

I will discuss tests of general relativity that yield the most sensitive current bounds on parameters describing equivalence principle violations in the Standard Model Extension. These tests are based on probing the isotropy of the gravitational force and the gravitational redshift for matter waves. The bounds can be further sharpened by taking into account the composition of nuclear matter and the kinetic energy of protons and neutrons in nuclei.

We have also used atom interferometers to demonstrate a key principle of quantum mechanics, that plane matter waves are proportional to exp(-iω0τ), where 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/ℏ travelling along the particle’s trajectory. This implies that a single particle can be a reference for a clock. We have built such a clock by combining a Ramsey-Borde atom interferometer employing 2n-photon Bragg diffraction with a femtosecond optical frequency comb to self-reference the interferometer by locking the laser to the Nth multiple of the measured recoil frequency. The clock’s frequency ωm=ω0/(2nN2) is then fully determined by ω0. The clock has an accuracy and stability of 4×10-9. It allows measurement of microscopic

masses in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms.

We have meanwhile reduced systematic effects by another factor of about 10 and are working towards a new measurement of the fine structure constant. We will survey other applications of matter waves as

clocks, such as testing relativity and verifying the gravitational Aharonov-Bohm effect.