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Physical Review Letters

Time-Resolved Measurements of Thermodynamic Fluctuations of the Particle Number in a Nondegenerate Fermi Gas

Christopher M. Wilson, Luigi Frunzio, D. E. Prober

Published Jul 20, 2001• 57 citations
Publisher

Abstract

We report on time-resolved measurements of thermodynamic fluctuations in the number of particles in a nondegenerate Fermi gas. The gas is comprised of thermal quasiparticles, confined in a superconducting Al box by large-gap Ta leads. The average number of quasiparticles is about 10(5). This number fluctuates due to quasiparticle generation and recombination. The number is measured from the tunneling current through a barrier that bisects the box. The recombination time is independently measured by single-photon excitation and agrees with the frequency dependence of the fluctuations.

DOI
10.1103/physrevlett.87.067004

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We present a general theory of quasiparticle number fluctuations in superconductors. The theory uses the master equation formalism. First, we develop the theory for a single occupation variable. Although this simple system is insufficient to describe fluctuations in a physical superconductor, it is illustrative, allowing this discussion to serve as a self-contained introduction. We go on to develop a multivariate theory that allows for an arbitrary number of levels with transitions of arbitrary size between levels. We specialize the multivariate theory for two particular cases. First, we consider intrinsic quasiparticle fluctuations. In a previous Letter, these results were used to describe time-resolved measurements of thermodynamic fluctuations in a superconducting Al box [C.M. Wilson, L. Frunzio, and D.E. Prober, Phys. Rev. Lett. 87, 067004 (2001)]. Finally, we extend these results to include fluctuations due to extrinsic loss processes.
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We investigate an ultracold Fermi gas at unitarity confined in a periodic box V=L3V={L}^{3}V=L3 using renormalization group techniques. Within this approach we can quantitatively assess the long-range bosonic order parameter fluctuations, which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finite-size and particle-number effects present in Monte Carlo simulations of ultracold Fermi gases.
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The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.