TY - JOUR
T1 - Strongly correlated states of trapped ultracold fermions in deformed Landau levels
AU - Burrello, M.
AU - Rizzi, M.
AU - Roncaglia, M.
AU - Trombettoni, A.
PY - 2015/3/9
Y1 - 2015/3/9
N2 - We analyze the strongly correlated regime of a two-component trapped
ultracold fermionic gas in a synthetic non-Abelian U (2 ) gauge
potential, that consists of both a magnetic field and a homogeneous
spin-orbit coupling. This gauge potential deforms the Landau levels
(LLs) with respect to the Abelian case and exchanges their ordering as a
function of the spin-orbit coupling. In view of experimental
realizations, we show that a harmonic potential combined with a Zeeman
term gives rise to an angular momentum term, which can be used to test
the stability of the correlated states obtained through interactions. We
derive the Haldane pseudopotentials (HPs) describing the interspecies
contact interaction within a lowest LL approximation. Unlike ordinary
fractional quantum Hall systems and ultracold bosons with short-range
interactions in the same gauge potential, the HPs for sufficiently
strong non-Abelian fields show an unconventional nonmonotonic behavior
in the relative angular momentum. Exploiting this property, we study the
occurrence of new incompressible ground states as a function of the
total angular momentum. In the first deformed Landau level (DLL) we
obtain Laughlin and Jain states. Instead, in the second DLL three
classes of stabilized states appear: Laughlin states, a series of
intermediate strongly correlated states, and finally vortices of the
integer quantum Hall state. Remarkably, in the intermediate regime, the
nonmonotonic HPs of the second DLL induce two-particle correlations
which are reminiscent of paired states such as the Haffnian state. Via
exact diagonalization in the disk geometry, we compute experimentally
relevant observables such as density profiles and correlations, and we
study the entanglement spectra as a further tool to characterize the
obtained strongly correlated states.
AB - We analyze the strongly correlated regime of a two-component trapped
ultracold fermionic gas in a synthetic non-Abelian U (2 ) gauge
potential, that consists of both a magnetic field and a homogeneous
spin-orbit coupling. This gauge potential deforms the Landau levels
(LLs) with respect to the Abelian case and exchanges their ordering as a
function of the spin-orbit coupling. In view of experimental
realizations, we show that a harmonic potential combined with a Zeeman
term gives rise to an angular momentum term, which can be used to test
the stability of the correlated states obtained through interactions. We
derive the Haldane pseudopotentials (HPs) describing the interspecies
contact interaction within a lowest LL approximation. Unlike ordinary
fractional quantum Hall systems and ultracold bosons with short-range
interactions in the same gauge potential, the HPs for sufficiently
strong non-Abelian fields show an unconventional nonmonotonic behavior
in the relative angular momentum. Exploiting this property, we study the
occurrence of new incompressible ground states as a function of the
total angular momentum. In the first deformed Landau level (DLL) we
obtain Laughlin and Jain states. Instead, in the second DLL three
classes of stabilized states appear: Laughlin states, a series of
intermediate strongly correlated states, and finally vortices of the
integer quantum Hall state. Remarkably, in the intermediate regime, the
nonmonotonic HPs of the second DLL induce two-particle correlations
which are reminiscent of paired states such as the Haffnian state. Via
exact diagonalization in the disk geometry, we compute experimentally
relevant observables such as density profiles and correlations, and we
study the entanglement spectra as a further tool to characterize the
obtained strongly correlated states.
KW - Quantum Hall effects
KW - Degenerate Fermi gases
U2 - 10.1103/PhysRevB.91.115117
DO - 10.1103/PhysRevB.91.115117
M3 - Journal article
SN - 1550-235X
SN - 2469-9969
VL - 91
JO - Physical Review B
JF - Physical Review B
IS - 11
M1 - 115117
ER -