[Paper Review] Rotating Few-body Atomic Systems in the Fractional Quantum Hall Regime

Nathan Gemelke, Edina Sarajlic+1 more|arXiv (Cornell University)|Jul 15, 2010

Quantum and electron transport phenomena1 references78 citations

TL;DR

This paper demonstrates the experimental realization of fractional quantum Hall (FQH)-like states in few-body rotating Bose gases using a tailored optical lattice with locally rotating potential minima. By adiabatically tuning rotation and trap deformation, the authors induce strong correlations, confirmed by momentum distribution measurements and photoassociation probing, showing quantitative agreement with numerical simulations and evidence of topological order in the few-body regime.

ABSTRACT

Topologically-ordered matter is a novel quantum state of matter observed only in a small number of physical systems, notably two-dimensional electron systems exhibiting fractional quantum Hall effects. It was recently proposed that a simple form of topological matter may be created in interacting systems of rotating ultra-cold atoms. We describe ensemble measurements on small, rotating clusters of interacting bosonic atoms, demonstrating that they can be induced into quantum ground states closely analogous to topological states of electronic systems. We report measurements of inter-particle correlations and momentum distributions of Bose gases in the fractional quantum Hall limit, making comparison to a full numerical simulation. The novel experimental apparatus necessary to produce and measure properties of these deeply entangled quantum states is described.

Motivation & Objective

• To realize and probe fractional quantum Hall (FQH)-like states in few-body ultracold atomic systems, which are analogs of topological phases in electronic systems.
• To overcome the limitations of previous experiments by achieving the FQH regime in the few-body limit (N ≤ 10), where filling factor N/Nv ≈ 1, enabling access to strongly correlated topological states.
• To develop and implement a novel experimental platform using rotating optical lattices to simulate the effective magnetic field and Landau level physics in ultracold atoms.
• To measure inter-particle correlations and momentum distributions in these strongly correlated states, providing evidence for topological order beyond mean-field behavior.
• To validate experimental results through direct comparison with full numerical simulations of the few-body Hamiltonian, establishing a benchmark for future studies of topological many-body states.

Proposed method

• Engineered a two-dimensional optical lattice with time-modulated beam phases to create locally rotating potential minima that mimic a rotating frame and induce effective magnetic fields.
• Applied an adiabatic sequence of trap deformation and rotation rate control to prepare the system in the lowest Landau level with angular momentum approaching the centrifugal limit (Ω/ω → 1).
• Used time-of-flight imaging to measure the momentum distribution of atoms following the rotation sequence, revealing correlations characteristic of FQH states.
• Employed resonant photoassociation pulses tuned to molecular excitation to probe short-range interatomic correlations by measuring atom loss rates.
• Extracted the second-order correlation function g₂(z, Ω_f) from photoassociation loss data, comparing it to mean-field expectations to detect departure from non-interacting behavior.
• Calibrated the correlation function using a reference state at low rotation (Ω_f < 0.875ω) to normalize g₂ and isolate correlation effects near the FQH regime.

Experimental results

Research questions

• RQ1 Can fractional quantum Hall states be realized in few-body ultracold atomic systems under controlled rotation and trapping?
• RQ2 To what extent do measured momentum distributions and inter-particle correlations in rotating few-body bosonic systems match predictions from exact few-body simulations?
• RQ3 Does the observed suppression in photoassociation loss near the centrifugal limit indicate the emergence of strong correlations beyond mean-field theory?
• RQ4 How does the second-order correlation function g₂(z, Ω_f) evolve with rotation rate, and what does it reveal about the nature of the many-body wavefunction?
• RQ5 Can the experimental platform achieve a regime where the filling factor N/Nv ≈ 1, enabling access to topological FQH-like ground states in a controlled few-body setting?

Key findings

• Momentum distributions measured via time-of-flight imaging show qualitative agreement with full numerical simulations of the few-body Hamiltonian, indicating the formation of correlated many-body states.
• Photoassociation loss rates are strongly suppressed near the centrifugal limit (Ω_f > 0.91ω), indicating enhanced short-range correlations consistent with FQH-like physics.
• The second-order correlation function g₂(z, Ω_f) is significantly reduced near the centrifugal limit, especially at nonzero radial positions, demonstrating a departure from mean-field behavior.
• The suppression of g₂ is most apparent at nonzero radius due to contributions from lower-occupancy states, which provide a background of uncorrelated low-angular-momentum atoms.
• Quantitative agreement between experiment and simulation is observed for rotation rates 0.91 < Ω_f/ω < 0.97, validating the experimental protocol and platform.
• Anomalous upturns in loss at Ω_f > 0.97 are observed but not yet understood, likely due to increased spectral complexity and sensitivity to trap shape near the centrifugal limit.