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Zero-point energy of a trapped ultracold Fermi gas at unitarity: squeezing the Heisenberg uncertainty principle and suppressing the Pauli principle to produce a superfluid state

D. K. Watson

Abstract

The zero-point energy of a trapped ultracold Fermi gas at unitarity is investigated in relation to the combined effects of the Heisenberg uncertainty principle and the Pauli principle. This lowest allowed quantum state is a superfluid state which has been studied extensively both experimentally and theoretically. The method used for the current investigation is based on a recent series of papers that proposed microscopic dynamics based on normal modes to describe superfluidity instead of real-space Cooper pairs. This approach yielded excellent agreement with experimental data for multiple properties and allowed the microscopic behavior underlying these results as well as the basis of universal behavior to be analyzed in detail using the group theoretic basis of this general N-body approach. This microscopic picture is now used to illucidate the roles played by the uncertainty principle and the Pauli principle in determining the energy and character of the lowest allowed quantum state including the squeezed character of this superfluid state and the suppression of the Pauli principle.

Zero-point energy of a trapped ultracold Fermi gas at unitarity: squeezing the Heisenberg uncertainty principle and suppressing the Pauli principle to produce a superfluid state

Abstract

The zero-point energy of a trapped ultracold Fermi gas at unitarity is investigated in relation to the combined effects of the Heisenberg uncertainty principle and the Pauli principle. This lowest allowed quantum state is a superfluid state which has been studied extensively both experimentally and theoretically. The method used for the current investigation is based on a recent series of papers that proposed microscopic dynamics based on normal modes to describe superfluidity instead of real-space Cooper pairs. This approach yielded excellent agreement with experimental data for multiple properties and allowed the microscopic behavior underlying these results as well as the basis of universal behavior to be analyzed in detail using the group theoretic basis of this general N-body approach. This microscopic picture is now used to illucidate the roles played by the uncertainty principle and the Pauli principle in determining the energy and character of the lowest allowed quantum state including the squeezed character of this superfluid state and the suppression of the Pauli principle.
Paper Structure (7 sections, 13 equations, 10 figures)

This paper contains 7 sections, 13 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Symmetry-Invariant Perturbation Theory: a group theoretic and graphical approach to the general N-body problem
  4. Zero-point energy considerations
  5. Discussion
  6. Conclusions
  7. The ground state of an ultracold Fermi gas.

Figures (10)

  • Figure 1: Comparison of the SPT zero-point/ground state energies for the independent particle case and the unitarity regime as a function of $N$ in units of $\hbar\omega_{ho}$.
  • Figure 2: The independent particle ground state/zero-point energies with the separate contributions from the Pauli principle and the non-Pauli terms as a function of $N$ in units of $\hbar\omega_{ho}$.
  • Figure 3: The SPT ground state/zero-point energies at unitarity with the contributions from the Pauli and the non-Pauli terms as a function of $N$ in units of $\hbar\omega_{ho}$.
  • Figure 4: Comparison of the SPT zero-point energies per particle for the independent particle case and the unitarity regime as a function of $N$ for large values of $N$ in units of $\hbar\omega_{ho}$.
  • Figure 5: The independent particle ground state/zero-point energies per particle with the contributions from the Pauli principle and the non-Pauli terms as a function of $N$ in units of $\hbar\omega_{ho}$.
  • ...and 5 more figures