Optical Signatures of Antiferromagnetic Ordering of Fermionic Atoms in an Optical Lattice

Abstract

We show how off-resonant light scattering can provide quantitative information on antiferromagnetic ordering of a two-species fermionic atomic gas in a tightly-confined two-dimensional optical lattice. We analyze the emerging magnetic ordering of atoms in the mean-field and in random phase approximations and show how the many-body static and dynamic correlations, evaluated in the standard Feynman-Dyson perturbation series, can be detected in the scattered light signal. The staggered magnetization reveals itself in the magnetic Bragg peaks of the individual spin components. These magnetic peaks, however, can be considerably suppressed in the absence of a true long-range antiferromagnetic order. The light scattered outside the diffraction orders can be collected by a lens with highly improved signal-to-shot-noise ratio when the diffraction maxima are blocked. The collective and single-particle excitations are identified in the spectrum of the scattered light. We find that the spin-conserving and spin-exchanging atomic transitions convey information on density, longitudinal spin, and transverse spin correlations. The different correlations and scattering processes exhibit characteristic angular distribution profiles for the scattered light, and e.g., the diagnostic signal of transverse spin correlations could be separated from the optical response by the scattering direction, frequency, or polarization. We also analyze the detection accuracy by estimating the number of required measurements, constrained by the heating rate that is determined by inelastic light-scattering events. The imaging technique could be extended to the two-species fermionic states in other regions of the phase diagram where the ground-state properties are still not fully understood.

Stochastic electrodynamics simulations for collective atom response in optical cavities

“…Off-resonance spontaneous scattering in optical lattices has actively studied as a diagnostic tool for quantum and thermal states of atoms; see for instance Refs. [31,[96][97][98][99][100][101][102][103][104].…”

Cavity Quantum Electrodynamics of Continuously Monitored Bose-Condensed Atoms

“…More generally, light can act as a sensitive diagnostic tool of ultracold atoms in periodic lattice systems, see e.g. [60][61][62][63][64][65]. In addition, BEC-cavity systems have previously been considered, e.g., in weak force sensing applications [66,67].…”

Probing the dynamic structure factor of a neutral Fermi superfluid along the BCS-BEC crossover using atomic impurity qubits

“…Density fluctuations in homogeneous systems are characterized by the dynamic structure factor (DSF), denoted by S(q, ν), which plays a central role in the linear-response theory of many-body systems [23]. In a cold-atom setting, S(q, ν) can be measured via Bragg spectroscopy [24][25][26] or inelastic light scattering [27][28][29]. However, these methods have drawbacks, including their destructive nature and diffraction-limited spatial resolution.…”