Bonnie L. Schmittberger

Bunching-induced optical nonlinearity and instability in cold atoms [Invited]

We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(⁵) = 7.6 × 10⁻¹⁵ (m/V)⁴, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/10⁵), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.

Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers

The SU(1,1) interferometer can be thought of as a Mach-Zehnder interferometer with its linear beamsplitters replaced with parametric nonlinear optical processes. We consider the cases of bright and vacuum-seeded SU(1,1) interferometers using intensity or homodyne detectors. A simplified, truncated scheme with only one nonlinear interaction is introduced, which not only beats conventional intensity detection with a bright seed, but can saturate the phase sensitivity bound set by the quantum Fisher information. We also show that the truncated scheme achieves a sub-shot-noise phase sensitivity in the vacuum-seeded case, despite the phase-sensing optical beams having no well-defined phase.

Spontaneous emergence of free-space optical and atomic patterns

The spontaneous formation of patterns in dynamical systems is a rich phenomenon that transcends scientific boundaries. Here, we report our observation of coupled optical-atomic pattern formation, which results in the creation of self-organized, multimode structures in free-space laser-driven cold atoms. We show that this process gives rise to spontaneous three-dimensional Sisyphus cooling even at very low light intensities and the emergence of self-organized atomic structures on both sub- and super-wavelength scales.

Enhancing light-atom interactions via atomic bunching

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-resonant 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 atomic temperature regimes and simultaneously accounts for the back-action of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only a limited range of temperatures. 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.

Transverse optical and atomic pattern formation

The study of transverse optical pattern formation has been studied extensively in nonlinear optics, with a recent experimental interest in studying the phenomenon using cold atoms, which can undergo real-space self-organization. Here, we describe our experimental observation of pattern formation in cold atoms, which occurs using less than 1 μW of applied power. We show that the optical patterns and the self-organized atomic structures undergo continuous symmetry breaking, which is characteristic of nonequilibrium phenomena in a multimode system. To theoretically describe pattern formation in cold atoms, we present a self-consistent model that allows for tight atomic bunching in the applied optical lattice. We derive the nonlinear refractive index of a gas of multilevel atoms in an optical lattice, and we derive the threshold conditions under which pattern formation occurs. We show that by using small detunings and sub-Doppler temperatures, one achieves intensity thresholds for pattern formation that are reduced by two orders of magnitude compared to warm atoms.

Ultra-low-threshold optical pattern formation in a cold atomic vapor

The authors have developed a new model that accounts for Sisyphus cooling and accurately describes the obtained data. Due to yhe observed ultra-low threshold for pattern formation and the strong fifth-order nonlinear response, the system is a novel testing ground for a broad range of applications and studies of fundamental science.