Blurring time of a pair-condensed Fermi gas


About twenty years ago, cold atoms made it possible to produce atomic condensates in the laboratory. This new state of matter has remarkable coherence properties analogous to those of lasers for matter waves. Contrarily to their spatial coherence which is well understood and known to extend over macroscopic length scales, their temporal coherence and its decay mechanisms are presently the object of an intense research both experimentally and theoretically.

This problem was first studied in the bosonic case, in particular with Jean Dalibard at LKB in 1997. It was shown that one can use two equivalent approaches. The first one steams from the evidence that in an experiment one can only measure the relative phase between two systems; the question is then to know how an initially well defined relative phase between two condensates evolves. The second approach breaks the U(1) symmetry and focuses on the evolution of the order parameter in a finite size system. In both cases the blurring of the phase originates from the combined effect of interactions and of fluctuations of the condensate atom number, the conjugate variable of the phase.

The fermionic case was still open. It is of particular interest as it allows one to access the strongly interacting regime. From a theoretical point of view, it was also more challenging : it required to go beyond the BCS theory which predicts a gapped excitation spectrum with no low frequency mode. In 1958 Anderson put forward a more advanced theory to predict the existence of a phononic branch for the fermionic condensates. We have extended Anderson's approach to show that, besides the expected zero frequency mode resulting from U(1) symmetry breaking, there exists an anomalous mode leading to phase blurring. We moreover could generalize this prediction to the strongly interacting regime, and obtain the following expression of the blurring time:

ħ/tbr = (dμ/dN) Δ(Na-Nb)

where dμ/dN is the derivative of chemical potential with respect to the particle number in each condensate and Δ(Na-Nb) is the standard deviation of the atom number difference. We also propose an experimental scheme to prepare two gases of spin 1/2 fermions in an initial state with a well defined relative phase and to subsequently measure the phase evolution (see the figure).



Figure
Two pair-condensed Fermi gases are prepared in a state with a well defined relative phase after splitting by a potential barrier. They subsequently evolve independently under the influence of interactions. This dynamics combined with the initial fluctuations in the atom numbers causes their phases to blur.
 

figure

Publication

"Phase operators and blurring time of a pair-condensed Fermi gas", H. Kurkjian, Y. Castin and A. Sinatra, "Editor suggestion" of Physical Review A (2013).

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