Abstract

The gravitational force on antimatter has never been directly measured, largely because electromagnetic forces are too strong compared to gravitational forces and no form of low-energy neutral antimatter has been available. However, the technology now exists to make low-energy antihydrogen. We are working on a project to develop an atomic hydrogen interferometer that can determine the force of gravity on hydrogen and antihydrogen by measuring the phase shift caused by gravity. The initial stage of the project is a demonstration experiment that will measure the gravitational force on hydrogen. A precise difference measurement between hydrogen and antihydrogen would be capable of detecting a new force that couples differently to matter and antimatter.

Project Description

Motivation for the Antimatter Gravity Experiment

The gravitational force on antimatter has never been directly measured. According to the standard interpretation of General Relativity (GR), antimatter on the earth should feel exactly the same force as matter. However, GR is known to be incompatible with quantum mechanics, and string theories which attempt to unify gravity with the other known forces generally include deviations from classical GR which violate the principle that requires matter and antimatter to be gravitationally identical. Furthermore, it is possible even within the context of of GR to find repulsive solutions to some of the equations which are generally ignored, but which could be identified with antimatter[1]. Repulsive gravity between antimatter and matter could potentially solve some major cosmological puzzles, such as the apparent absence of antimatter in the universe and the cosmological constant.

Even if antimatter is found to respond to gravity just a matter does, the measurement will still be valuable for a number of reasons. As a new test of a fundamental physical law, the result will be an important constraint on theories that include gravity. Furthermore, by making a simultaneous measurement on hydrogen and antihydrogen in the interferometer, it will be possible to look for very small differences which would indicate a very weak force that couples differently to matter and antimatter. The interferometer should be ideal for making this precision difference measurement.

While the motivation for making a hydrogen interferometer is primarily to demonstrate the feasibility of the antimatter experiment, the hydrogen interferometer itself should be very interesting. Because hydrogen is so much lighter than other elements used in atomic interferometers it has a much longer wavelength, which leads to a much larger beam separation in the interferometer. This is important for experiments that measure phase shifts from conditions applied to one of the split beams before they are brought back together to form the interference pattern. In addition, theoretical calculations for hydrogen are much simpler than for other elements, so comparing experimental results with theory should be very productive with a hydrogen interferometer.

Technical Approach for the Antimatter Gravity Experiment

The antimatter gravity experiment has two technical challenges: making the antihydrogen and then measuring the force of gravity on it with an atomic interferometer. Making slow-moving antihydrogen appropriate for a gravity experiment requires trapping antiprotons and positrons in Penning traps, feats which have already been accomplished by other research groups[2], [3],[4]. The Athena and ATRAP collaborations at CERN are developing the technology for making antihydrogen, although their goal of trapping the antihydrogen in a neutral trap is considerably more challenging than making a beam that could be used in this experiment.

The best way to make cold antihydrogen appears to be with the three-body reaction \overline p + 2 e^+ -> \overline H + e^+. With the constituents in traps at 4.2° K and positron densities greater than 10^{7}/cm^3 the probability of for any single antiproton to pick up a positron becomes quite high[5]. An antihydrogen beam could be made by keeping the antiprotons and the positrons in separate electrostatic potential wells in the same solenoidal magnetic field[6]. The antiprotons would be released from their well, accelerated with a small voltage and made to pass through the positron plasma. Any antihydrogen made by collisions with the positrons would be neutral and would exit the trap. The velocity of the antihydrogen could be controlled by adjusting the voltage accelerating the antiprotons. Antiprotons that do not make antihydrogen will remain in the trap where they can be used for another pulse. Because of the large probability for making antihydrogen from any given antiproton, it should be possible to demonstrate this mechanism with protons and electrons. While it may be difficult to detect the hydrogen created because of background hydrogen in the vacuum, the disappearance of protons from the trap could easily be measured.

Making a beam of hydrogen atoms is much simpler than antihydrogen. Hydrogen gas is dissociated in a pyrex tube with an RF field, and the dissociated hydrogen passes into a vacuum chamber through an accomodator to cool it[7]. A skimmer and a collimator form a beam from this supersonic gas jet[8].

Detecting a beam of antihydrogen can be done by looking for the pions and photons produced when the antihydrogen annihilates on contact with matter. A hydrogen beam is more difficult to detect because there is a considerable amount of background hydrogen in the vacuum system. We will tag the hydrogen in the beam before it enters the interferometer by exciting some of it to the metastable 2s state with a pulsed electron gun. The 2s hydrogen will be detected after the interferometer by quenching it with an electric field and observing the Lyman-&alpha photon.

The pulsed nature of both the hydrogen 2s and the antihydrogen beams allows for the velocity of individual atoms to be determined from their time of flight. This is important because the gravitational phase shift will be a function of velocity. Without the time-of-flight measurement a large velocity spread would wash out the interference pattern.

The gravitational force on the hydrogen beam will be measured with an atomic interferometer. The interferometer design is based upon an atomic interferomer at MIT that uses a sodium beam[9],[10]. It consists of three transmission gratings placed in the beam about a meter apart. The gratings have a regular array of lines and slots with sub-micron dimensions which act just like an optical diffraction grating with light. The first two gratings set up an interference pattern that shapes part of the beam into a series of intensity peaks and valleys that have the same period as the gratings. The third grating is moved back and forth (transverse to the beam) to analyze the phase position of this interference pattern; the transmitted intensity depends upon whether the interference peaks fall on the lines or on the slots. The phase of this interference pattern will change when the atoms in the beam experience a force while traversing the interferometer. Essentially, the interference pattern will fall'' by the same distance as the atoms fall in transit. When the grating lines are vertical, the atoms will fall parallel to the lines and the interference pattern will not change. When the interferometer is rotated so the lines are horizontal, the interference pattern will shift and this will give a measurement of the force of gravity. The very fine structure of the gratings will permit measurements of the small gravitational deflection of the beam.

The accuracy of the measurement of g will be determined by the uncertainty in the physical dimensions of the interferometer. The initial goal will be to do better than 1%, which should be achieved using blue-print specifications. There are quite a few handles that can be used to improve upon this. For example, the grating spacing can be measured by shining a laser through the grating and measuring the diffraction angles. The length of the interferometer can be changed, and because the gratings will be mounted inside a pipe, it should be possible to get a very accurate measurement of the distance between mounts by measuring the RF resonant frequency of the cavity formed by the mounts and the pipe. The velocity of atoms traversing the interferometer will be determined by time-of-flight, and this measurement can be calibrated by changing the path length by well-known amounts. In the end, however, the most accurate measurement will be the difference measurement between matter and antimatter. Any measurement beyond a part in 10^5 or 10^6 will begin to probe for new forces that would have been too weak to have been seen by other experiments[11]. It is not immediately clear what the ultimate precision will be, and it is one of the goals of the prototype to determine what will be the leading systematic uncertainties.

The vacuum transmission gratings for the atom interferometer are made by using lithography on gold or low-stress silicon nitride membranes. While the technology is fairly well understood, it is still somewhat expensive. The gratings for the hydrogen interferometer could be made with existing techniques, but the larger-area gratings that would be needed to make efficient use of the broader antihydrogen beam would require some development effort. The MIT NanoStructures Lab has agreed to do this using techniques they have applied to making large x-ray diffraction gratings, but we will need to fund this development work. The most important requirement for the gratings is that they must be phase-coherent over their entire surface so that the interference pattern falls coherently on the third grating's pattern. Without this phase coherence we would need to image the transmission through the third grating, which could be done with microchannel plates at the cost of considerable complexity.

Summary

We currently have a window of opportunity for measuring the gravitational force on antimatter at a very reasonable cost because the accelerator required for making and collecting antiprotons has already been built for other purposes. This window of opportunity will close in a decade when antiprotons are no longer needed for high-energy colliders. If we fail to make the measurement now and we come up with a theory in few years that antimatter really is a hole in a negative-energy sea that should have negative gravitational mass (just as a random example[12]), then it may require funding on the scale of LIGO or Gravity Probe B to make the measurement. Measuring the force of gravity on antimatter will be an important test of our understanding of gravity.

References

Thomas J. Phillips -- phillips@phy.duke.edu