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Frontiers in Optics

Achieving the gauge potential in a synthetic space using coherent Raman sideband generation

Luqi Yuan, Dawei Wang, Shanhui Fan

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We study nontrivial topological effect in the Raman sideband generation process, where probe field shows features of one-way transport and Landau levels. Our proposal provides a unique connection between topological photonics and nonlinear optics.
DOI
10.1364/fio.2017.fw5b.3

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Experimental results from the generation of Raman sidebands using optical vortices are presented. By generating two sets of sidebands originating from different locations in a Raman-active crystal, one set containing optical orbital angular momentum and the other serving as a reference, Young's double slit experiment was simultaneously realized for each sideband. The interference between the two sets of sidebands was used to determine the helicity and topological charge in each order. Topological charges in all orders were found to be discrete and follow selection rules predicted by a cascaded Raman process.
Abelian and non-Abelian gauge potentials and quantum gauge theories play central roles in our understanding of Nature. Gauge potentials are also of great significance in condensed matter physics. In fact, minimal coupling of electrons to an Abelian or non-Abelian gauge potential is the essential ingredient for the realization of topological states of matter. Due to the high controllability of ultracold atoms, they are commonly exploited to test fundamental theories of physics, simulate intractable systems, and realize exotic many-body states. Nonetheless, the charge neutrality of atoms places severe constraints on ultracold atomic systems, since neutral particles do not couple to gauge potentials the way charged particles do. That said, coupling a multi-component quantum gas to laser light can lead to the emergence of artificial Abelian and non-Abelian gauge potentials minimally coupled to the center-of-mass momenta of ultracold neutral atoms, paving the way for realizing topological states of matter and simulating gauge theories in quantum gases. All previous proposals for inducing gauge potentials have been developed in the semiclassical regime, where the radiation field is treated classically. I have developed a two-photon Raman scheme in the strong atom-photon coupling (i.e., quantum) regime, based on two counter-propagating modes of a ring cavity, to induce both synthetic magnetic field and spin-orbit coupling for a single neutral atom inside the cavity. The spin-orbit interaction is only weakly dependent on the occupation of the cavity modes, whereas the strength of the magnetic field is proportional to the square of the total number of photons in the cavity and can be made arbitrarily large, which is desirable for realizing the quantum Hall phase. I have then extended this single-atom cavity quantum-electrodynamics scheme to many bosons in the weak atom-photon coupling regime. In addition to inducing spin-orbit coupling for the individual atoms, the cavity fields also mediate infinite-ranged interactions between atoms, whose strengths and signs can readily be tuned experimentally. The interplay between these cavity-mediated interactions and the intrinsic two-body interactions determines the many-body ground state and its elementary excitations, with novel consequences such as the stabilization of an attractive Bose-Einstein condensate which otherwise is unstable.
We theoretically demonstrate nontrivial topological effects for a probe field in a Raman medium undergoing molecular modulation processes. The medium is driven by two noncollinear pump beams. We show that the angle between the pumps is related to an effective gauge potential and an effective magnetic field for the probe field in the synthetic space consisting of a synthetic frequency dimension and a spatial dimension. As a result of such an effective magnetic field, the probe field can exhibit a topologically protected one-way edge state in the synthetic space, as well as Landau levels which manifest as suppression of both diffraction and sideband generation. Our work identifies a previously unexplored route towards creating topological photonics effects and highlights an important connection between topological photonics and nonlinear optics.
It is quite important to enhance and control the optomechanically induced high-order sideband generation to achieve low-power optical comb and high-sensitivity sensing with an integrable structure. Here we present and analyze a proposal for enhancement and manipulation of optical nonlinearity and high-order sideband generation in a hybrid atom-cavity optomechanical system that is coherently driven by a bichromatic input field consisting of a control field and a probe field and that works beyond the perturbative regime. Our numerical analysis with experimentally achievable parameters confirms that robust high-order sideband generation and typical spectral structures with nonperturbative features can be created even under weak driven fields. The dependence of the high-order sideband generation on the atomic parameters are also discussed in detail, including the decay rate of the atoms and the coupling parameter between the atoms and the cavity field. We show that the cutoff order as well as the amplitude of the higher-order sidebands can be well tuned by the atomic coupling strength and the atomic decay rate. The proposed mechanism of enhancing optical nonlinearity is quite general and can be adopted to optomechanical systems with different types of cavity.