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Journal of Physics B Atomic Molecular and Optical Physics

Correlation effect on the roton minimum of the rotating dipolar Fermi gas

Jing-Nuo Wu, Y. L. Chiang, Hsin-Chien Huang, Szu-Cheng Cheng

Published Nov 30, 2011• 1 citation

Abstract

[[abstract]]The collective-excitation spectrum from a filled Landau level in a rotating dipolar Fermi gas is investigated through the equation of motion method. The predicted excitation spectrum exhibits a roton structure which is affected by the strength of dipolar interactions and trapping potential. The correlation effect on the roton minimum is observed by varying the dipolar interaction strength. An increase of the dipolar interaction strength leads to a deeper roton minimum. The roton minimum can even become zero, where the system exhibits instability, as the dipolar strength approaches a critical value. As the dynamical stability of the system is studied through the roton structure, we find that this zero-value roton minimum is a precursor of the occurrence of a bubble crystal.

DOI: 10.1088/0953-4075/44/24/245301

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[[abstract]]The collective-excitation spectrum from a filled Landau level in a rotating dipolar Fermi gas is investigated through the equation of motion method. The predicted excitation spectrum exhibits a roton structure which is affected by the strength of dipolar interactions and trapping potential. The correlation effect on the roton minimum is observed by varying the dipolar interaction strength. An increase of the dipolar interaction strength leads to a deeper roton minimum. The roton minimum can even become zero, where the system exhibits instability, as the dipolar strength approaches a critical value. As the dynamical stability of the system is studied through the roton structure, we find that this zero-value roton minimum is a precursor of the occurrence of a bubble crystal.

We apply the equation-of-motion method to study the collective excitation spectrum from a filled Landau level in rotating dipolar Fermi gases. The predicted excitation spectrum of rotating dipolar Fermi gases can exhibit a roton-minimum character. This roton character is tunable by varying the dipole interaction strength and confining potential. An increase of the dipole interaction strength makes the roton minimum becoming zero, and the system becomes unstable. We also obtain a condition for the dynamical stability of rotating dipolar Fermi gases.

We point out that the Wigner crystal (WC) state of rotating dipolar fermions in the lowest Landau level is strongly correlated. From intra-Landau-level excitations of the fractional quantum Hall effect (FQHE) liquid, we find that the roton minimum of the excitation spectrum at $\ensuremath{\nu}=1/7$ becomes negative, indicating an absence of the FQHE state, which is supposed to be the ground state of the system. Therefore, we show that the Hartree-Fock theory of the WC does not predict the correct ground-state energy in the lowest Landau level. There exists a strong correlation effect on the Wigner crystallization of rotating dipolar gases.

We apply the magneto-roton theory of the fractional quantum Hall effect to study the collective excitation spectrum of rotating dipolar Fermi gases. The predicted spectrum has a finite energy gap in the long wavelength limit and a roton minimum at finite wave vector. The roton minimum being deepened from filling factor 1/3 to filling factor 1/5 is a signature of incipient crystallization near filling factor 1/7. We also demonstrate that there are no low-lying single-particle excitations below the roton mode. The fractional-quantum-Hall fluid rotating dipolar fermions behaves as an incompressible superfluid at low temperature.

We measure the excitation spectrum of a stable dipolar Bose-Einstein condensate over a wide momentum range via Bragg spectroscopy. We precisely control the relative strength ε_{dd} of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing ε_{dd}. Reaching the dipolar-dominated regime ε_{dd}>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with ε_{dd}. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.

We study the pair correlations and excitations of a dipolar Bose gas layer. The anisotropy of the dipole-dipole interaction allows us to tune the strength of pair correlations from strong to weak perpendicular and weak to strong parallel to the layer by increasing the perpendicular trap frequency. This change is accompanied by a roton-roton crossover in the spectrum of collective excitations, from a roton caused by the head-to-tail attraction of dipoles to a roton caused by the side-by-side repulsion, while there is no roton excitation for intermediate trap frequencies. We discuss the nature of these two kinds of rotons and the relation to instabilities of dipolar Bose gases. In both regimes of trap frequencies where rotons occur, we observe strong damping of collective excitations by decay into two rotons.