Interference of a thermal Tonks gas on a ring.pdfVIP

a r X i v : c o n d - m a t / 0 2 0 5 6 0 5 v 1 [ c o n d - m a t .s o f t ] 2 8 M a y 2 0 0 2 Interference of a thermal Tonks gas on a ring Kunal K. Das,? M.D. Girardeau,? and E.M. Wright? Optical Sciences Center and Department of Physics, University of Arizona, Tucson, AZ 85721 (Dated: February 1, 2008) A nonzero temperature generalization of the Fermi-Bose mapping theorem is used to study the exact quantum statistical dynamics of a one-dimensional gas of impenetrable bosons on a ring. We investigate the interference produced when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Nonzero temperature is shown not to be a limitation to obtaining high visibility fringes. PACS numbers: 03.75.Fi,03.75.-b,05.30.Jp A fundamental assumption at the heart of current proposals to realize integrated atom sensors is that the guided atom wavepackets will display interference phe- nomena when they are split, propagated, and recom- bined. On the other hand it is well known that the coherence properties of atomic gases are affected by di- mensionality, there being no true off-diagonal-long-range order in less than three dimensions, and this raises the issue of interference in restricted geometries. Motivated by recent theoretical arguments [1, 2] demonstrating that several stimulated processes for matter waves such as four-wave mixing, superradiance, and matter-wave am- plification can be achieved in degenerate fermion gases as well as in Bose-condensed gases, we have recently shown [3, 4] that a one-dimensional gas of hard-core bosons, or Tonks gas, at zero temperature can exhibit high visibil- ity interference fringes. These results suggest that the same mechanisms might be capable of overcoming the weakening of interference due to thermal excitation. The quantum Tonks gas is realized [5, 6] in a regime essen- tially opposite from that required for BEC, namely, the re