Composite fermion basis for two-component Bose gases
arXiv:1701.04278 · doi:10.1103/PhysRevA.95.033633
Abstract
Despite its success, the composite fermion (CF) construction possesses some mathematical features that have, until recently, not been fully understood. In particular, it is known to produce wave functions that are not necessarily orthogonal, or even linearly independent, after projection to the lowest Landau level. While this is usually not a problem in practice in the quantum Hall regime, we have previously shown that it presents a technical challenge for rotating Bose gases with low angular momentum. These are systems where the CF approach yields surprisingly good approximations to the exact eigenstates of weak short-range interactions, and so solving the problem of linearly dependent wave functions is of interest. It can also be useful for studying higher bands of fermionic quantum Hall states. Here we present several ways of constructing a basis for the space of so-called "simple" CF states for two-component rotating Bose gases in the lowest Landau level, and prove that they all give sets of linearly independent wave functions that span the space. Using this basis, we study the structure of the lowest-lying state using so-called restricted wave functions. We also examine the scaling of the overlap between the exact and CF wave functions at the maximal possible angular momentum for simple states.
arXiv comment11 pages, 8 figures
References in corpus (28)
- Many-Body Physics with Ultracold Gases
- Artificial gauge potentials for neutral atoms
- Synthetic magnetic fields for ultracold neutral atoms
- The dynamics of component separation in a binary mixture of Bose-Einstein condensates
- Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
- Rapidly Rotating Atomic Gases
- Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level
- Do attractive bosons condense?
- Vortex phase diagram in rotating two-component Bose-Einstein condensates
- New Class of Non-Abelian Spin-Singlet Quantum Hall States
- Spin textures in rotating two-component Bose-Einstein condensates
- Band Structure of the Fractional Quantum Hall Effect
- A Composite Fermion Description of Rotating Bose-Einstein Condensates
- Quantum Hall physics in rotating Bose-Einstein condensates
- Vortices in quantum droplets: Analogies between boson and fermion systems
- Composite Fermions in Quantum Dots
- Bose condensates at high angular momenta
- Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings
- Vortex Clusters in Quantum Dots
- From Rotating Atomic Rings to Quantum Hall States
- State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
- Excitation Spectrum and Collective Modes of Composite Fermions
- Quantum Hall phases of two-component bosons
- Manipulating the rotational properties of a two-component Bose gas
- Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases
- Rotational properties of two-component Bose gases in the lowest Landau level
- Asymptotically exact trial wave functions for yrast states of rotating Bose gases
- Linear dependencies between Composite Fermion states