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arXiv:cond-mat/0404329 · Physical Review Letters

Fractional Quantum Hall States in Ultracold Rapidly Rotating Dipolar Fermi Gases

M. A. Baranov, Klaus Osterloh, Maciej Lewenstein

Published Feb 24, 2005• 131 citations
arXivHTMLPDF

Abstract

We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultracold two-dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction nu = 1/3 is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow us to realize these very interesting highly correlated states in future experiments.

DOI
10.1103/physrevlett.94.070404

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We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultracold two-dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction nu = 1/3 is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow us to realize these very interesting highly correlated states in future experiments.
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 study strongly correlated ground and excited states of rotating quasi-2D Fermi gases constituted of a small number of dipole-dipole interacting particles with dipole moments polarized perpendicular to the plane of motion. As the number of atoms grows, the system enters an intermediate regime, where ground states are subject to a competition between distinct bulk-edge configurations. This effect obscures their description in terms of composite fermions and leads to the appearance of novel quasihole ground states. In the presence of dipolar interactions, the principal Laughlin state at filling nu=1/3 exhibits a substantial energy gap for neutral (total angular momentum conserving) excitations and is well-described as an incompressible Fermi liquid. Instead, at lower fillings, the ground state structure favors crystalline order.
We study the quantum Hall states that appear in the dilute limit of rotating ultracold fermionic gases when a single hyperfine species is present. We show that the ppp-wave scattering translates into a pure hard-core interaction in the lowest Landau level. The Laughlin wave function is then the exact ground state at filling fraction $\ensuremath{\nu}=1∕3$. We give estimates of some of the gaps of the incompressible liquids for $\ensuremath{\nu}=p∕(2p\ifmmode\pm\else\textpm\fi{}1)$. We estimate the mass of the composite fermions at $\ensuremath{\nu}=1∕2$. The width of the quantum Hall plateaus is discussed by considering the equation of state of the system.
We study ultracold Rydberg-dressed Bose gases subject to artificial gauge fields in the fractional quantum Hall (FQH) regime. The characteristics of the Rydberg interaction gives rise to interesting many-body ground states different from standard FQH physics in the lowest Landau level (LLL). The non-local but rapidly decreasing interaction potential favors crystalline ground states for very dilute systems. While a simple Wigner crystal becomes energetically favorable compared to the Laughlin liquid for filling fractions ν<1/12\nu<1/12ν<1/12, a correlated crystal of composite particles emerges already for ν≤1/6\nu \leq 1/6ν≤1/6 with a large energy gap to the simple Wigner crystal. The presence of a new length scale, the Rydberg blockade radius aBa_BaB​, gives rise to a bubble crystal phase for ν≲1/4\nu\lesssim 1/4ν≲1/4 when the average particle distance becomes less than aBa_BaB​, which describes the region of saturated, almost constant interaction potential. For larger fillings indications for strongly correlated cluster liquids are found.
Ultracold atomic gases in rapidly rotating traps display a wealth of interesting physics. One of the most striking achievements in this field is the observation of th e Abrikosov lattice of vortices. When the rotation frequency is equal to the harmonic trap frequency, the atomic gases is similar to charged particles in a magnetic f ield. It has been predicted that for weak interactions and strong confinement along the rotation axis, this system will exhibit quantum phases equivalent to the one o f the fractional quantum Hall effect. The talk will be focused on bosonic atoms with only one hyperfine species (i.e spinless bosons). We will give numerical evidences of the fractional quantum Hall states in these systems. We will describe how they can be understood using the Laughlin wave function and the Jain's composite fermion theory. We will also discuss about more exotic quantum phases that have also been predicted in such regime. These quantum phases are described by the Read-Rezayi wave functions whose one of the most remarkable properties is that their excitations obey non-abelian statistics.
The long-term goal of our study is to perform a simulation on a rapidly rotating gas of ultracold bosonic atoms. When the rotation frequency is close to the harmonic trap frequency, the trapping force is compensated by the centrifugal force and only the Coriolis force remains, analogous to the Lorentz force. The quantum Hall effect regime is reached when the number of vortices is larger than the number of atoms. In this work, we demonstrate a variety of excitations of the fractional quantum Hall states of composite fermions and ultracold two-dimensional rapidly rotating bosonic atoms. Second, we can also check directly whether there is a relationship between these two phenomena by calculating the energy of N = 8 bosons in the ground state of the harmonic oscillator and a few-boson elementary excitations for the Bose–Laughlin state at the half filling factor.