Collective resonance displacement in strongly driven cold atoms

TL;DR

The paper investigates collective dynamics in strongly driven, optically thick clouds of cold two-level atoms using a semi-classical mean-field model of coupled dipoles. It predicts a dynamical collective resonance displacement, quantified by $oldsymbol{δ_c}$, that scales with optical depth and vanishes in the steady state, distinguishing it from linear-regime shifts. The displacement arises from long-range dipole–dipole interactions and persists with increasing drive up to a point, while attenuation and saturation modulate its magnitude. The findings offer insight into out-of-equilibrium many-body light–matter effects with potential relevance to metrology and optical clocks, and suggest directions for beyond-mean-field investigations and experimental observation in cold-atom platforms.

Abstract

Cold atoms are promising platforms for metrology and quantum computation, yet their many-body dynamics remains largely unexplored. We here investigate Rabi oscillations from optically-thick cold clouds, driven by high-intensity coherent light. A dynamical displacement from the atomic resonance is predicted, which can be detected through the collective Rabi oscillations of the atomic ensemble. Different from linear-optics shifts, this dynamical displacement grows quadratically with the optical depth, yet it reduces with increasing pump power as dipole-dipole interactions are less effective.

Figures (7)

• Figure 1: (a) Schematic of the three-dimensional cloud driven with a monochromatic coherent light starting from time $t=0$ ($I_\mathrm{laser}$ in the intensity graph), which makes the atoms undergo Rabi oscillations ($I_\mathrm{scat}$ in the same graph). The driving field is characterized by the driving strength $\Omega_\mathrm{L}$, detuning $\Delta$ and wavevector $\mathrm{k}_0$. (b) Collective dynamical resonance displacement $\delta_\mathrm{c}$ as a function of optical depth $b_0$, for different driving Rabi frequency $\Omega_\mathrm{L}$. The inset shows the same data in log-log scale, showing that the displacement scales quadratically with $b_0$, but decreases with increasing drive strength due to reduced atomic coherences and weakened dipole-dipole interactions.
• Figure 2: (a) Inelastically scattered intensity as a function of time for $\Omega_\mathrm{L}=25\Gamma$ and $\Delta=0$ shown for two different optical depths $b_0$, showing the shift in Rabi frequency for higher optical depth. (b) Corresponding Fourier transforms of the signals in (a), with the vertical dashed-dotted line indicating the peak oscillation frequency obtained from Lorentzian fits.
• Figure 3: Local amplitude of the total field in the cloud along the laser propagation direction (solid lines), compared to Beer–Lambert predictions (dashed lines) for different optical depths $b_0$ in the steady-state. The $y$-axis is normalized to the probe’s incident Rabi frequency. The intensity is computed at the center of the cloud ($x=y=0$), at resonance $\Delta = 0$ and with $\Omega_\mathrm{L} = 25\Gamma$.
• Figure 4: (a) Extracted oscillation frequency $\Omega^{(N)}_{\mathrm{G}}$ as a function of the detuning $\Delta$ for different $b_0$, with dashed lines showing fits to Eq. \ref{['eq:Omegacol']}. The two star markers correspond to the specific curves in Fig. \ref{['fig:intenfft']}. (d) Collective resonance displacement $\delta_\mathrm{c}$ extracted from the fits in (b), as a function of the optical depth and for different atom numbers. Despite minor deviations, the results confirm that optical depth is the relevant control parameter for the resonance displacement. The black dashed curve corresponds to a quadratic scaling.
• Figure 5: Collective resonance displacement $\delta_\mathrm{c}$ as a function of (a) optical depth $b_0 = 2N/(kR)^2$, (b) rescaled parameter $N/(kR)^{2.4}$, and (c) normalized atomic density $N/(kR)^3$. Each color represents a different atom number. The best data collapse occurs for $\alpha = 2.4$, suggesting that the collective displacement scales primarily with optical depth, with a minor correction related to spatial density.