Daniel Christensen and Dr. Dallin Durfee, Physics and Astronomy

Our research group is currently building a highly precise and stable atom interferometer/ atomic time standard. This is an atomic clock which, among other capabilities, will enable precision measurements of fundamental constants. Some of the long term goals of this project include time rate-of-change measurements of the fine structure constant, measurements of time dilation, and inertial force sensors.

An interferometer can be described as a precision measurement instrument relying on the interference of waves. In our experiment, we are interfering calcium atoms in different atomic states. The “timing mechanism” of the clock is generated by carefully measuring the energy states of the atoms after they interact with the lasers.

My research was divided between two separate projects connected by the similar element of atom interferometry. My first project involved the development of a thermal atomic beam source which will be utilized in the previously mentioned atomic time standard. While working on this project, some members of our group thought of a novel application of interferometers which would set a new lower limit on the mass of a photon. My second project was calculations which I performed to confirm the validity of this proposed table-top experimental apparatus.

For the atomic clock to operate properly, lasers need to interact with a high-flux, stable, columnated atomic beam. I designed a two-stage beam source system which first heats the element of interest and then columnates it. The first stage of the system is a cylindrical oven made of stainless steel and copper. Directly after the oven and perpendicular to the beam path are four windows which allow the atomic beam to be transversely laser cooled.

The second stage of the atomic beam system is a heated aperture which columnates the beam. Since the aperture is small (~5 micrometer) it needs to be heated (600+ degrees C) to avoid clogging. The aperture is not necessarily symmetric, so it also needed to be easily positioned. The aperture system consists of two parts, one heated aperture and one unheated aperture. Both parts are made of stainless steel and are cylindrical. They are positioned in series, with the leading one being wrapped in a heating wire. All components of both systems are designed to be vacuum compatible.

My second project confirmed the validity of a proposed ion interferometer which can set a new lower limit on the non-zero mass of a photon. We had two main concerns for error in the proposed experiment- that electric fringing fields leaking in from outside the system would negate its effectiveness, and that our preliminary “infinite cylinder” approximation would yield results comparable to empirical reality.

Using C++, I set up a worst-case scenario model of the system using realistic table-top dimensions and physical parameters. My model also included objects inside the system representing gratings and any other optical equipment which could be used in the actual experiment. I employed a successive-over-relaxation (SOR) iteration algorithm to compute values at every point in the grid. The equations actually used to calculate each grid point are modified Poisson equations. My calculations confirmed that our proposed experiment is empirically feasible and could possibly yield a lower bound on the rest mass of a photon over two orders of magnitude better than previous lab results obtained by other groups.

For further information regarding these projects, my senior thesis “Instrumentation and Calculations for Matter-Wave Interferometry Experiments” is available in the Physics Library of the Eyring Science Center. I also have two publications related to this research which may be consulted – D. Christensen, B. Neyenhuis, and D.S. Durfee, “Numerical calculation of classical and non-classical electrostatic potentials” submitted to Am. J. Phys. (2008) and B. Neyenhuis, D. Christensen, and D.S. Durfee, “Testing Nonclassical Theories of Electromagnetism with Ion Interferometry”, Phys. Rev. Lett. 99, 200401 (2007) .