The University of Massachusetts Amherst

Research Interests

Our research is in theoretical studies of quantum liquids, solids, and gases. In the past we have treated equilibrium and transport in highly polarized Fermi systems, and such as 3He  in its various phases. More recently we have centered our attention on Bose-Einstein condensates.

Quantum Interference in Bose-Einstein Condensation: The discovery of Bose-Einstein condensation (BEC) in alkali gases held in magnetic and optical traps has caused great excitement among researchers in the area of quantum systems. In these gases particles avalanche into the lowest quantum state below a certain transition temperature, which can be as low as nanokelvin for a small number of particles.

Because of the coherence of these systems  quantum interference is possible. One of the most interesting early experiments in this system was the MIT interference experiment, in which two condensates are allowed to mix, causing an interference pattern of oscillations in the density. It is as if the two condensates had a relative phase before they met. Indeed the experiment can be explained by assuming a classical broken symmetry wave function for each having a given phase. But one can show that even starting with the condensates in number (Fock) states, that a relative phase will develop as particles are detected. Moreover Fock state allow the detection of quantum interference that goes beyond what is allowed by the classical broken symmetry wave function. We have theoretically shown quantum interference in detections by a simple beam splitter, have created interfering Schrödinger cats in an interferometer showing quantum interference between macroscopically distinct states, and also have shown that Fock states allow the violation of Bell’s theorem at arbitrary numbers of particles by varying either the phases in the arms of the interferometer or by varying the transmission coefficients of the beam splitters. We have also shown how one can use an interferometer to create NOON states, which can have important uses in measuring phases beyond the Heisenberg limit.  This work is done in collaboration with Franck Laloë  of École Normale Supérieure in Paris.

A curious effect occurs in the measurement of transverse spin with overlapping up- and down-spin condensates. After a number of measurements a net transverse polarization of all of the spins develops in a random direction, which seems to violate conservation of angular momentum in each such individual measurement. Conservation occurs only as an average over many such measurements. We are investigation the consequences of this odd effect and whether it might be seen experimentally.

Generalized Bose-Einstein Condensation: In association with Asaad Sakhel of Al-Balqa Applied University, Amman, Jordan, we are pursuing theoretical path integral Monte Carlo calculations on cigar-shaped condensates to study the quasi-condensate in this near one-dimensional finite system. Recently we published a review of “generalized Bose condensation,” which involves the condensation in the lowest band of states. Our study of this effect involved only ideal Bose gases and we are considering how this translates to an interacting gas.  Our hypothesis is that the quasi-condensate likely fits the description. Experimentally one studies the number fluctuations in the system to identify the transition to a quasi-condensate state. We will also consider the use of the so-called projection Gross-Pitaevskii method, in which several states are considered to have macroscopic occupation and therefore behave classically, a la the standard GPE method for the ground state.