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Register a new userGeometric squeezing into the lowest Landau level
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The equivalence between neutral particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. In their quantum descriptions, translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. Here, we exploit the ability to squeeze non-commuting variables to dynamically create a Bose-Einstein condensate occupying a single Landau gauge wavefunction in the lowest Landau level. We directly resolve the extent of the zero-point cyclotron orbits, and demonstrate geometric squeezing of the orbits guiding centers by more than ${7}~$dB below the standard quantum limit. The condensate attains an angular momentum of more than ${1000},{hbar}$ per particle, and an interatomic distance comparable to the size of the cyclotron orbits. This offers a new route towards strongly correlated fluids and bosonic quantum Hall states.
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We study the thermodynamics of short-range interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.
We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved background. Using the symmetries of the microscopic electron theory in this massless limit we find a number of constraints on any low-energy effective theory. We find that any low-energy description must couple to a geometry which exhibits nontrivial curvature even on flat space-times. Any composite fermion must have an electric dipole moment proportional and orthogonal to the composite fermions wavevector. We construct the effective action for the composite Dirac fermion and calculate the physical stress tensor and current operators for this theory.
The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our work provides the first controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multi-vortex solutions.
We investigate the lowest scattering state of one-dimensional Bose gas with attractive interactions trapped in a hard wall trap. By solving the Bethe ansatz equation numerically we determine the full energy spectrum and the exact wave function for different attractive interaction parameters. The resultant density distribution, momentum distribution, reduced one body density matrix and two body correlation show that the decreased attractive interaction induces rich density profiles and specific correlation properties in the weakly attractive Bose gas.
We study the effect of electron-electron interaction and spin on electronic and transport properties of gated graphene nanoribbons (GNRs) in a perpendicular magnetic field in the regime of the lowest Landau level (LL). The electron-electron interaction is taken into account using the Hartree and Hubbard approximations, and the conductance of GNRs is calculated on the basis of the recursive Greens function technique within the Landauer formalism. We demonstrate that, in comparison to the one-electron picture, electron-electron interaction leads to the drastic changes in the dispersion relation and structure of propagating states in the regime of the lowest LL showing a formation of the compressible strip and opening of additional conductive channels in the middle of the ribbon. We show that the latter are very sensitive to disorder and get scattered even if the concentration of disorder is moderate. In contrast, the edge states transport is very robust and can not be suppressed even in the presence of a strong spin-flipping.
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