Enhancing light-atom interactions via atomic bunching

Abstract

There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.

Spontaneous emergence of free-space optical and atomic patterns

“…This indicates that the atoms are cooled substantially and tightly bunched in the applied 1D optical lattice, as depicted in figure 1(b), in order to generate the instability that gives rise to pattern formation. We also note that we only observe pattern formation for D < 0 because D > 0 gives rise to reduced light-atom interaction strengths in the tight-bunching regime [6].…”

“…By increasing h  1 for D < 0, the light-atom coupling strength is enhanced because atoms bunch tightly at the intensity maxima of the lattice. As can be seen from equation (4), atomic bunching provides a new mechanism to achieve enhanced nonlinear light-atom interactions even for I I 1 sat  by using small D | |, which increases the dipole potential well depth, and by using small T z (e.g., via Sisyphus cooling) [6]. This bunching-induced nonlinearity is the primary mechanism that gives rise to pattern formation in our system, in contrast to others where the saturable nonlinearity dominates [20].…”

“…Early experiments exploring this regime used single-mode optical cavities to enhance the light-atom coupling strength [4,5]. Alternatively, we have shown theoretically that strong lightatom coupling can be achieved in free space by allowing many sub-Doppler-cooled atoms to spatially organize in the intensity maxima of an optical lattice [6]. Free-space systems are advantageous for many reasons, including experimental simplicity and access to an intrinsically multimode system [7,8].…”

Two-Photon Collective Atomic Recoil Lasing

“…Since the initial theoretical studies of CARL [1,2], numerous theoretical and experimental studies have been performed on related phenomena involving optical forces and cold atoms, e.g., instabilities involving self-organisation , collective cooling [24][25][26], optomechanical transverse pattern formation [27][28][29][30][31][32] and quantum simulation [33][34][35]. Experiments have involved a variety of atomic media, e.g., both thermal [8][9][10][11] and degenerate gases [3,7,12,17,20,23,[33][34][35], and a diverse range of configurations, including optical cavities consisting of multiple mirrors [8,9,11,20,23,[33][34][35][36], single mirror feedback [31] and mirrorless configurations [3,7,10,12,18,19].…”

“…It has been proposed and demonstrated that CARL-like induced bunching of atoms could play a role in providing this nonlinearity enhancement [18,19]. It is therefore timely to consider nonlinear optical interactions that combine quantum electronic nonlinearities associated with internal atomic excitation and optomechanical CARL-like behaviour.…”