An introduction to atom interferometry

Atom interferometry is the technique that underlies most of our precision measurements. We exploit the fact that matter, like light, exhibits wave-like properties. Atoms, unlike light, are massive and bear gravitational signals in their interference patterns. To understand atom interferometry, we first must understand optical interferometry.

In optical interferometry, light waves are recombined after propagating along separate paths. Depending on the difference in the waves' phase accumulated along the two paths, the light may interfere constructively and appear bright or it may interfere destructively and appear dark.

In atom interferometry, we use atoms that are laser-cooled to millionths of a degree above absolute zero. With pulses of light, we drive each atom into a quantum superpositions of having been kicked with the momentum of photons and not having been kicked. The atoms, in two places at one time, are in a superposition of recoiling backwards or staying still. By manipulating the state of the atoms using one of two types of such light pulses, termed Bragg and Raman transitions (see Figures 2 and 3), we steer the matter waves' paths and recombine the matter waves at the end of the experiment. The atoms' trajectories are shown in Figure 1. We use clouds of millions of atoms to get better statistics on our measurement, and the interference signal manifests as a population difference between final momentum states.

  Figure 1 : Spacetime trajectories of matterwave interferometers where (A) is a Mach-Zender geometry and (B) is a pair of conjugate Ramsey Bordé interferometers. The vertical motion of atoms as a function of time (black) is manipulated by the effects of fast light pulses (blue). Figure reproduced from  arxiv:1312.6449

Figure 1: Spacetime trajectories of matterwave interferometers where (A) is a Mach-Zender geometry and (B) is a pair of conjugate Ramsey Bordé interferometers. The vertical motion of atoms as a function of time (black) is manipulated by the effects of fast light pulses (blue). Figure reproduced from arxiv:1312.6449

The energy and couplings along the atoms' path and their interaction the light pulses serve to determine the phase shift between matter waves at the output of the interferometer. Any effect that modifies the potential energy, internal energy, or kinetic energy across the two arms of the interferometer appears in the interferometer phase. Different atom interferometer geometries can be used to cancel certain phase terms while enhancing others. For example, in a Mach-Zehnder interferometer we are only sensitive to the phase of the laser at the time that photons are transferred, and all other phase terms cancel out. We therefore use the laser like a ruler to measure exactly how fast the atoms accelerate. As another example, a simultaneous conjugate Ramsey-Borde interferometer geometry cancels out all laser phase and also cancels out gravity to first order. The primary phase term that is left is from the kinetic energy of absorbing photons, and we use this recoil phase to measure the fine-structure constant.

Atom interferometers are used to measure gravitational acceleration, gravity gradients, accelerations, rotations, fundamental constants such as the gravitational constant and the fine structure constant, and can be used to measure or constrain new physics that couples to matter.

  Figure 2 : In a stimulated Raman transition, the atom is illuminated with counter-propagating laser beams. The atom absorbs a photon from one beam and emits a photon into a beam moving the opposite direction. The result is a net kick of 2 photon momenta. In this type of transition, the atom changes both its kinetic energy and its internal state.

Figure 2: In a stimulated Raman transition, the atom is illuminated with counter-propagating laser beams. The atom absorbs a photon from one beam and emits a photon into a beam moving the opposite direction. The result is a net kick of 2 photon momenta. In this type of transition, the atom changes both its kinetic energy and its internal state.

  Figure 3 : In a Bragg transition, two counter-propagating beams are detuned so that transferring a specific number of photon momenta is resonant. In this diagram, the atom absorbs the momentum of 8 photons, though a different detuning would transfer a different number of photon momenta. The atom remains in the ground electronic state, but gains kinetic energy. Our group helped invent and characterize this method for atom interferometry and remains a speciality of two of our interferometers.

Figure 3: In a Bragg transition, two counter-propagating beams are detuned so that transferring a specific number of photon momenta is resonant. In this diagram, the atom absorbs the momentum of 8 photons, though a different detuning would transfer a different number of photon momenta. The atom remains in the ground electronic state, but gains kinetic energy. Our group helped invent and characterize this method for atom interferometry and remains a speciality of two of our interferometers.