Atom Interferometry in a 10 Meter Atomic Fountain

[From left to right] Mark Kasevich; the 10 m fountain team in 2013: Alex Sugarbaker, Tim Kovachy, Jason Hogan, Susannah Dickerson, Sheng-wey Chiow; and Dave Johnson

Authors: Alex Sugarbaker, Susannah M. Dickerson, Jason M. Hogan, David M. S. Johnson, and Mark A. Kasevich

Affiliation: Department of Physics, Stanford University, USA

Link to Kasevich Group Website >>

The equivalence principle states that all objects fall with the same acceleration under the influence of gravity. It is the conceptual foundation of Einstein’s general relativity, but is it true exactly? If not, there are profound implications for our understanding of gravity and the nature of the universe. It is therefore important to continue to test the equivalence principle as precisely as we can.

Galileo reportedly tested it by dropping spheres from the Leaning Tower of Pisa. Apollo astronauts tested it by dropping a hammer and a feather on the moon. More recent measurements have shown that the accelerations of two falling objects differ by no more than one part in 10¹³ [1, 2]. We aim to test the equivalence principle to one part in 10¹⁵ by dropping atoms of two different isotopes of rubidium in a 10 meter tower.

We will precisely measure acceleration differences between the two isotopes using atom interferometry. According to quantum mechanics, atoms are waves. Just as in optical interferometry, it is possible to split and recombine them to form an interference pattern [3, 4, 5]. In our interferometer, we send each atom along two different paths through space – each is in two places at once. When the atom waves are brought back together, the interference pattern depends on the phase difference between the two paths taken.

This phase difference in turn depends sensitively on the forces that act differently on the two parts of the atom while they are separated. This sensitivity to forces is what makes atom interferometry so useful. Compact atom interferometers have been made that can precisely measure rotation and acceleration, which can aid in navigation, mineral exploration, and geophysics. Atom interferometers have also measured the gravitational and fine-structure constants [6, 7]. They could also be used to search for gravitational waves [8].

The sensitivity of an atom interferometer increases with longer interferometer durations. Therefore, as recently described in Physical Review Letters [9, 10, 11], we have built an atom interferometer in which ⁸⁷Rb atoms are separated for 2.3 seconds before being recombined and interfered (Fig. 1). Three times longer than previous records [12], this multiple-second duration is well into the range of macroscopic, human-perceivable timescales. Furthermore, the two halves of each atom are separated by 1.4 centimeters before recombination – that's enough for you to swing your hand between them!

Fig. 1 Photograph of the 10 meter atomic fountain in a pit in the basement of the physics building at Stanford University.

How do we make a long-duration atom interferometer? We prepare a cloud of atoms at the bottom of a 10 meter vacuum tower and then launch them to the top. The interferometry is performed while the atoms rise up and fall back down to the bottom of the tower. The atoms are in free-fall, isolated from the noisy environment.

The cloud of atoms used must be very cold – a few billionths of a degree above absolute zero. At room temperature, the atoms in a gas move at speeds of hundreds of meters per second. Room-temperature rubidium atoms would collide with the walls of our vacuum chamber long before they fell back to the bottom. We therefore cool a few million rubidium atoms to a few nanokelvin before launching them into the tower. (The cooling process builds upon the same techniques used to generate Bose-Einstein condensates [13].)

Even at a few nanokelvin, individual atoms follow slightly different trajectories through the interferometer (like the droplets in a fountain of water), experiencing different position- and velocity-dependent forces. This yields a spatially-dependent phase, which in turn yields a spatial variation in the output atom density distribution that we can observe directly with a CCD camera (Fig. 2). This might at first appear undesirable, but it actually reveals rich details about the forces that generate the spatial interference pattern. Similar spatial fringe patterns have been used to great benefit in optical interferometers for centuries, but it is only recently that the effect has been leveraged in atom interferometry.

Fig. 2 Atomic interference patterns observed at the output of the interferometer. The images are sorted by phase, which can be measured for each experimental shot.

The long drift time of our interferometer enables it to have an acceleration sensitivity of 7 X 10^-12 g for each experimental shot, a hundredfold improvement over previous limits [14]. This is roughly the same as the gravitational attraction you would feel towards a person 10 meters away from you. We have used the sensitive interferometer and the spatial fringe patterns mentioned above to make precise measurements of Earth's rotation [9, 10].

The high sensitivity of the interferometer also holds great promise for our design goal – testing the equivalence principle (as mentioned above). By averaging more measurements or implementing advanced interferometry techniques, we can achieve the desired 10^-15 g sensitivity. Adding a simultaneous ⁸⁵Rb interferometer and comparing the results for the two isotopes will then enable us to make a new precision test of the equivalence principle. This will probe the fundamental assumptions of our current theory of gravity.

References:
[1] S. Schlamminger, K.Y. Choi, T.A. Wagner, J.H. Gundlach, and E.G. Adelberger, “Test of the Equivalence Principle Using a Rotating Torsion Balance”, Physical Review Letters, 100, 041101 (2008). Abstract.
[2] James G. Williams, Slava G. Turyshev, Dale H. Boggs, “Progress in Lunar Laser Ranging Tests of Relativistic Gravity”, Physical Review Letters, 93, 261101 (2004). Abstract.
[3] Mark Kasevich and Steven Chu, “Atomic interferometry using stimulated Raman transitions”, Physical Review Letters, 67, 181 (1991). Abstract.
[4] Alexander D. Cronin, Jörg Schmiedmayer, David E. Pritchard, “Optics and interferometry with atoms and molecules”, Reviews of Modern Physics, 81, 1051 (2009). Abstract.
[5] We focus on light-pulse atom interferometry, where pulses of laser light are used to split, recombine, and interfere the atoms.
[6] G. Lamporesi, A. Bertoldi, L. Cacciapuoti, M. Prevedelli, and G.M. Tino, “Determination of the Newtonian Gravitational Constant Using Atom Interferometry”, Physical Review Letters, 100, 050801 (2008). Abstract.
[7] Rym Bouchendira, Pierre Cladé, Saïda Guellati-Khélifa, François Nez, and François Biraben, “New Determination of the Fine Structure Constant and Test of the Quantum Electrodynamics”, Physical Review Letters, 106, 080801 (2011). Abstract.
[8] Jason Hogan, “A new method for detecting gravitational waves”, SPIE Newsroom, 6 May (2013). Article.
[9] Susannah M. Dickerson, Jason M. Hogan, Alex Sugarbaker, David M. S. Johnson, Mark A. Kasevich, “Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry”, Physical Review Letters, 111, 083001 (2013).  Abstract.
[10] Alex Sugarbaker, Susannah M. Dickerson, Jason M. Hogan, David M. S. Johnson, Mark A. Kasevich, “Enhanced Atom Interferometer Readout through the Application of Phase Shear”, Physical Review Letters, 111, 113002 (2013). Abstract.
[11] P. Bouyer, “Viewpoint: A New Starting Point for Atom Interferometry”, Physics, 6, 92 (2013). Article.
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[13] “Bose-Einstein condensate”. Past 2Physics Article.
[14] Holger Müller, Sheng-wey Chiow, Sven Herrmann, Steven Chu, Keng-Yeow Chung, “Atom-Interferometry Tests of the Isotropy of Post-Newtonian Gravity”, Physical Review Letters, 100, 031101 (2008). Abstract.