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Bulletin of the American Physical Society

Particle Number Conserving Approach to the Collective States in a Small Fermi-System

Jennifer R. Glick, Vladimir Zelevinsky

Published Mar 6, 2014• 0 citations
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We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to be robust to introducing a finite temperature as long as it is much smaller than the interaction induced single particle gap in the final state of the sweep.
We investigate the phase sensitivity of a linear two-mode atom interferometer subject to environmental noise, modeled within the framework of open quantum systems with both number-conserving and non-conserving Lindblad operators. Considering several input states, we first study the cases N=1,2 (N number of particles) and perform numerical simulations for N>2. The sensitivity as a function of the holding time can display divergence points where phase estimation becomes impossible, to which we refer as insensitivity points. We characterize their behavior as the input state, particle number, and noise operator are varied, and we find that their positions are independent of the noise intensity. Moreover, while our fixed measurement scheme may favor number-conserving noise at small N (i.e., having better sensitivity), the Cramér-Rao bound reveals that particle non-conserving noise yields strictly lower achievable sensitivity for all particle numbers.
Anharmonic effects in the capillary branch of excitations of a Fermi-liquid drop are considered. The limiting transition to classical hydrodynamics is found. It exists when the orbital angular momenta L/sub i/ of the collective excitations are large. The situation of the classical conservation law for the volume of the system is analyzed in the quantum case. It is found that when the frequency of a collective oscillation is small compared with the characteristic single-particle frequencies, the results obtained on the basis of the phenomenological scheme with a phonon-phonon Hamiltonian are reproduced. It is shown that no new parameters are required to calculate the constants of this Hamiltonian in the theory of finite Fermi systems.