Ultra-cold Interferometry

   We are interested in constructing ultra-cold matter-wave interferometers for inertial forces sensing applications and for precision measurements of fundamental forces. The interferometers will be based on ultra-cold Fermi degenerate 40K atoms sympathetically cooled by bosonic 87Rb atoms. Here are some quick links to our current research interests:

Interference fringes from a 87Rb BEC interferometer
(data courtesy of the Thywissen Lab, U. of Toronto).

Ultra-cold Fermions for Interferometry

   Ultra-cold atoms, and fermions in particular, have a number of advantages as the particle of choice for matter-wave interferometers. Their low temperature reduces the transverse momentum spread, so that they behave similar to single mode lasers, and their low velocity permits long integration times and local measurements. While the short deBroglie wavelength of atoms makes them attractive for interferometry, atoms also experience important inter-atom interactions. These interactions affect the internal energy of the atoms and hence the interferometric phase. Accurate interferometric measurements are consequently dependent on the atomic density, which is generally difficult to reproducibly control at the requisite level.

   Ultra-cold bosons, or BEC, are the matter-wave equivalent of photons in a laser. However, they suffer from large atom-atom interactions, though a careful choice of element, atomic state, and the use of Feschbach resonances can lower these appreciably. Ultra-cold boson interferometers will ultimately be limited by their atom-atom interactions.

   Atom-atom interactions between ultra-cold identical fermions are negligible. S-wave scattering, the dominant interaction at ultra-cold temperatures, is forbidden by the anti-symmetry of identical fermion wavefuntions. P-wave scattering is strongly suppressed by the ultra-cold momentum spread of the atoms. The lack of any significant interactions make ultra-cold degenerate fermions ideal candidates for precision matter-wave interferometry.
   This same lack of interaction between identical ultra-cold fermions also means that fermions require special care when cooling. The standard technique of evaporative cooling does not work because the fermionic atoms cannot rethermalize with themselves, after the "hot" atoms have been selectively removed. Instead, one must have at second type of non-identical particle around such as a second fermion spin state or another atomic species. In our apparatus, we use bosonic 87Rb to sympathetically cool the fermionic 40K.

Applied Physics Interferometers

   Ultra-cold atoms can be used to make precision measurements of time (atomic clock), magnetic and electric fields, and inertial forces, such as accelerations, rotations, and local gravity. Ultra-cold interferometer can made relatively compact, so that measurements can restricted to small regions.

Inertial forces
   A matter-wave Mach-Zender interferometer can be used to measure acceleration, gravity, and gavity gradients. A matter-wave Sagnac interferometer can used for rotation measurements.

Electric and magnetic fields
   Matter-wave interferometers are particularly attractive for measurements of magnetic and electric fields due to the magnetic and electric dipole moments of atoms and molecules.

      Conceptual sketch of an atom
      Mach-Zender interferometer.

Atomic Clocks
   Atomic clocks are currently limited by atom-atom interactions. The ground level hyperfine transitions of ultra-cold fermions can be used for atomic clock time-keeping with significantly reduced frequency shifts due to collisions.

Precision Measurements of Fundamental Forces

   The compactness and precision of ultra-cold atom interferometers can be exploited to study weak forces in the vicinity of surfaces. We are interested in measuring the surface-atom interaction called the Casmir-Pölder force and the gravitational force very close to a test mass. 

The Casimir-Polder force 
   The Casimir-Pölder interaction is the dominant electromagnetic force between a surface and an atom at distances between about 0.1 mm and 7 mm. The attractive force falls off like 1/d5 and is due to the quantum nature of the electromagnetic vacuum -- d is atom-surface distance. Below 0.1 mm, the interaction becomes the Van der Waal force, and above about 7 mm, the interaction acquires a temperature-dependence, and falls more slowly off as 1/d4.

Sub-millimeter Gravity
   Measuring the gravitational force at sub-millimeter distances is quite difficult and has only been undertaken in the last decade. An ultra-cold fermion interferometer can be used to probe the gravitational interaction and its 1/r2-dependence in the vicinity ( 10-100 mm) of a planar test mass. In the proposed planar configuration, a 1/r2-dependence would manifest itself as a 1/d-dependence with respect to the surface.

   At these distances the atom-surface force will be dominated by the thermal Casimir-Pölder interaction. The gravitational interaction can be distinguished from the Casimir-Pölder force by placing a thin membrane between the test mass and the interferometer, as shown in the figure on the right. This scheme clamps the Casimir-Pölder interaction, and the gravitational force can then be distinguished by moving the test mass and measuring the resulting change in the interferometric signal.

Conceptual sketch of an experiment to measure gravity at sub-millimeter distances.

Web page updated: January 16, 2007.