Equivalence Principle

Atom Interferometric Test of the Equivalence Principle (AITEP)

Atom interferometry uses the coherent splitting and recombination of atoms to make precision measurements of environmental parameters such as gravity, acceleration, or magnetic field. This apparatus has been designed to test Einstein’s Equivalence Principle to a precision of 10-15g by simultaneously launching ultracold atoms of different mass (specifically 85Rb and 87Rb) and accurately observing their free-fall motion. With such sensitivity, this apparatus can test General Relativity in a laboratory environment and can provide a testbed for future experiments to measure gravitational waves.

Read on for an introduction to our experiment, or take a look at our publications related to measuring the Equivalence Principle and gravitational waves.

You can also check out a recent semi-popular summary of our work at 2Physics.com.

Outline

Introduction
Atom Interferometry
The AITEP Interferometer
Sensitivity
The Experimental Procedure
Future Work

 

Introduction

Galileo

Galileo performing an early test of the Equivalence Principle using spheres of different mass

Apollo EP Test

Dave Scott of Apollo 15 dropping a feather and a hammer on the moon

In this modern version of Galileo’s apocryphal Leaning Tower of Pisa experiments, we simultaneously launch two isotopes of rubidium (87Rb and 85Rb) in a 10-meter tower. With lasers as rulers, we measure their position as they move through the trajectories determined by gravity. The sensitivity of such a large atom interferometer allows us to measure the differential gravitational acceleration on the two isotopes to an accuracy of 10-15 g.

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Atom Interferometry

Trajectory of the atom interferometer. At time t = 0, the π/2 beamsplitter pulse splits the atomic wave packet into two. The dashed state receives a momentum kick because of its interaction with the laser photons. The π mirror pulse at time T reverses the momentum kick. At time 2T, another beamsplitter pulse recombines and interferes the wavepackets.

Atom interferometry is very similar to optical interferometry, where analogs of beamsplitters and mirrors are created by pulses of light.

Sweeping a parameter of the laser pulses — e.g. the frequency or phase — traces out an interference pattern as the difference in phase accumulated over the upper and lower paths changes.

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The AITEP Interferometer

Features of the AITEP Interferometer include:

  • Standard pulse sequence: Bragg, π/2 – π – π/2
  • Long, magnetically shielded interferometer length: 8.2 meters
  • Large separation of wavepackets: 1 – 10 cm
  • Long interferometer time T (see figure above): 1.3 seconds

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Sensitivity

How sensitive will this apparatus be to differences in gravitational acceleration of the two rubidium isotopes? The accumulated phase of a single interferometer due to differing lengths of upper and lower paths is dominated by the phase of the laser at the three interrogation times:

Δφ = φ(0) – 2φ(T) + φ(2T) = keff g T2 ≈ 3 x 108 rad

Where ℏkeff is the momentum difference imparted to the atoms by the lasers. Meanwhile, the smallest measurable phase shift is (after 1 month of integration with 107 atoms per interferometer):

δφ ~ 1/N1/2 ~ 3 x 10-7 rad

These lead to a sensitivity to the differential acceleration between 87Rb and 85Rb of

(g87 – g85)/g ~ δφ/Δφ ~ 10-15

To use a physical comparison, this corresponds to detecting the gravitational attraction of a can of soda about 1 meter away.

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The Experimental Procedure

The procedure to create, launch and detect atoms is as follows

  • A 2D Magneto-Optical Trap (MOT) loads a 3D MOT with cold atoms
  • Atoms are further cooled to ~50 nK in two stages (evaporation followed by expansion)
  • Atoms are launched into a 10-meter vacuum tube, surrounded by a bias solenoid and 3 layers of magnetic shielding
  • Atoms are interrogated by an interferometer pulse sequence
  • Images of the atoms are used to measure the resulting phase
  • Experiment is repeated with a different interferometer phase to sweep a fringe pattern
Apparatus

Model of the AITEP apparatus

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Future work

Testing General Relativity

Einstein’s Equivalence Principle is the launching pad from which he developed his theory of General Relativity. Tests of the validity of GR have included measurements of the orbits of Mercury and the moon and the observation of the lensing of light by gravity. But because of the precision required to measure deviations from Newton’s gravitational laws, these tests typically require an astronomical body. With the sensitivity of our apparatus, we will be able to see effects of GR in a controlled environment.

Consider, for example, Einstein’s mass-energy equation E = mc2. Through this relationship, the kinetic energy of the atoms in motion is equivalent to a little bit extra mass. This extra mass slightly changes the rate at which the phase of the atoms evolve. For parameters based on the current apparatus, the size of the phase change is at the level of a part in 10-14, which is within our design sensitivity.

Measuring Gravitational Waves

Gravity waves are produced by large masses that oscillate rapidly in space. Sources of such waves include binary systems involving combinations of white dwarfs, neutron starts, and black holes—many of which are difficult to observe electromagnetically. Moreover, as gravitational waves are not limited by the surface of last scattering that limits the earliest time accessible by the electromagnetic spectrum, they can provide a unique picture of the early universe.

Artistic model of a proposed atomic gravitational wave sensor

Atom interferometers measure the local acceleration due to gravity. Two spatially separated atoms will feel different, time-varying accelerations due to gravity waves. Using two atom interferometers separated by a large distance, we can measure this difference in acceleration to detect the gravity wave.

Just how sensitive the pair is depends on the distance between the interferometers L, and the area of the interferometer, as determined by the momentum splitting keff, and the interrogation time T. In general, the longer T of each interferometer, the lower the frequencies that can be detected.

For a terrestrial detector, the distance between the two interferometers could be several kilometers. The interferometers at each end would be 10 meters in length, just like our current apparatus. In space, it becomes not only easier to create 100-meter interferometers, but it is also possible to separate the interferometers by thousands of kilometers, thereby increasing the sensitivity. In both situations, we would be able to take advantage of advanced atom optics, such as large momentum beamsplitters, which would increase keff.

With sensitivities complementary to LISA and LIGO, atom interferometer detectors are an exciting addition to the instruments measuring gravity waves.

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