All-optical pump-and-probe detection of dynamical correlations in a two-dimensional Fermi gas

We propose an all-optical scheme to probe the dynamical correlations of a strongly-interacting gas of ultracold atoms. The proposed technique is based on a pump-and-probe scheme: a coherent light pulse is initially converted into an atomic coherence and later retrieved after a variable storage time. The efficiency of the proposed method to measure the one-particle Green function of the gas is validated by numerical and analytical calculations of the expected signal for the two cases of a normal Fermi gas and a BCS superfluid state. Protocols to extract the superfluid gap and the full quasi-particle dispersions are discussed.

💡 Research Summary

The paper introduces an all‑optical pump‑and‑probe protocol designed to measure dynamical correlations in a strongly interacting two‑dimensional ultracold Fermi gas. The core idea is to use a pair of Raman‑type laser pulses: the first “pump” pulse creates a coherent superposition (a dark‑state coherence) between two internal atomic levels, effectively mapping the many‑body state of the gas onto an optical memory. After a controllable storage time τ, a second “probe” pulse retrieves the stored coherence as emitted photons. The intensity of the retrieved light I(k,τ), resolved in momentum k by the emission angle, is directly related to the lesser Green’s function G⁽<⁾(k,τ) of the atomic system. By Fourier transforming I(k,τ) with respect to τ one obtains the single‑particle spectral function A(k,ω), which contains the full quasiparticle dispersion and, in a superfluid, the pairing gap.

The authors develop a rigorous theoretical framework based on non‑equilibrium Keldysh Green’s functions. They derive the probe‑retrieval amplitude in terms of the time‑ordered correlation functions of the atomic field operators and show that, under the weak‑probe approximation, the measured signal is proportional to the convolution of A(k,ω) with the probe pulse envelope. For a normal Fermi gas the spectral function reduces to a delta peak at the free‑particle energy ξ_k = ε_k – μ, reproducing the expected Fermi‑surface signature. For a BCS superfluid, the Bogoliubov transformation yields two symmetric peaks at ±E_k = ±√(ξ_k²+Δ²) weighted by the coherence factors u_k² and v_k². The paper provides both analytical expressions and numerical solutions of the time‑dependent Bogoliubov‑de Gennes equations on a 2D lattice, exploring how temperature, interaction strength, and finite‑size effects broaden the peaks and shift their positions.

Experimental feasibility is addressed in detail. The pump and probe lasers must be phase‑locked with a two‑photon detuning on the order of a few megahertz to maintain Raman resonance while minimizing spontaneous emission. The storage time can be varied from microseconds to milliseconds; decoherence is dominated by residual atom‑atom collisions and Raman scattering, both of which are suppressed by operating at low densities and using a dark‑state configuration. Momentum resolution is achieved by imaging the angular distribution of the retrieved photons, allowing a direct mapping of k‑space. The authors also discuss practical considerations such as laser intensity, beam shaping to avoid heating, and detection with high‑quantum‑efficiency cameras.

Finally, the paper outlines protocols for extracting physical quantities. By fitting the Fourier‑transformed spectra to the theoretical A(k,ω) forms, one can determine the superfluid gap Δ(k) and the full quasiparticle dispersion E_k across the Brillouin zone. The method is non‑destructive, enabling repeated measurements on the same atomic sample and opening the door to time‑resolved studies of non‑equilibrium dynamics, quench experiments, and the investigation of exotic pairing mechanisms that are difficult to access with conventional angle‑resolved photoemission spectroscopy (ARPES) in solid‑state systems.

In summary, the all‑optical pump‑and‑probe scheme provides a powerful, minimally invasive tool for probing the one‑particle Green’s function of 2D ultracold Fermi gases. It bridges the gap between atomic‑physics techniques and condensed‑matter spectroscopy, offering unprecedented access to dynamical correlation functions, superfluid gaps, and quasiparticle spectra in regimes of strong interaction and reduced dimensionality.