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Physical Review Letters

Matter-Wave–Optical-Wave Mixing-Induced Transparency and a Nonhyperbolic Matter-Wave Quasisoliton in Quantum Gases

Yan Li, Chengjie Zhu, W. R. Garrett, E. W. Hagley, L. Deng

Published Jan 5, 2017• 2 citations
Publisher

Abstract

The realization of atomic quantum gases has brought out surprising effects that have no correspondence in nonlinear optics with thermal gases, presenting intriguing and exciting challenges to the research discipline of nonlinear optics which has matured since the invention of the laser. Here, we show an unexpected optical wave-mixing gain cancellation effect in a quantum gas that restricts an, otherwise, strongly enhanced backward-propagating light-matter wave-mixing process. This results in a wave-mixing induced transparency and a nonhyperbolic quasi-matter-wave soliton that opens new research opportunities in hydrodynamic fluid research of degenerate quantum gases, such as phonon scattering in a two-dimensional sonic black hole horizon.

DOI
10.1103/physrevlett.118.013901

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The realization of atomic quantum gases has brought out surprising effects that have no correspondence in nonlinear optics with thermal gases, presenting intriguing and exciting challenges to the research discipline of nonlinear optics which has matured since the invention of the laser. Here, we show an unexpected optical wave-mixing gain cancellation effect in a quantum gas that restricts an, otherwise, strongly enhanced backward-propagating light-matter wave-mixing process. This results in a wave-mixing induced transparency and a nonhyperbolic quasi-matter-wave soliton that opens new research opportunities in hydrodynamic fluid research of degenerate quantum gases, such as phonon scattering in a two-dimensional sonic black hole horizon.
We discuss nonlinear optical processes in the presence of quantum gases. We show that, in contrast to a normal gas, where the medium ``passively'' participates in nonlinear optical processes, quantum gases ``actively'' interact with the wave mixing process by enforcing the properties arising from condensed matter physics on the generation and propagation of new light fields. This manifestation of condensed matter physics leads to intriguing suppression and enhancement effects in directional wave generation and propagation processes that have no counterpart in a normal gas. This opens a new chapter on light-matter-wave mixing and scattering: nonlinear optics with quantum gases.
Highly efficient, optical-degenerate wave-mixing involving bosonic quantum gas is studied using a crossed-beam geometry. We show a very large enhancement due to nonlinear gain from a matter-optical wave-mixing process involving four photons and two matter-wave excitations. Under suitable conditions with a red-detuned pump field this optically degenerate, four-photon process can be stronger than the traditional two-photon inelastic light-scattering mechanism, leading to strong nonlinear growth of the observed matter-wave scattering. This optically degenerate four-wave mixing is independent of other enhancements arising from bosonic stimulations. More importantly, this highly efficient, backward degenerate wave generation and growth process does not have a correspondence in thermal gases in nonlinear optics.
We show that optical processes originating from elementary excitations with dominant collective atomic recoil motion in a quantum gas can profoundly change many nonlinear optical processes routinely observed in a normal gas. Not only multi-photon wave mixing processes all become stimulated Raman or hyper-Raman in nature but the usual forward wave-mixing process, which is the most efficient process in normal gases, is strongly reduced by the condensate structure factor. On the other hand, in the backward direction the Bogoliubov dispersion automatically compensates the optical-wave phase mismatch, resulting in efficient backward light field generation that usually is not supported in normal gases.
We show that optical processes originating from elementary excitations with dominant collective atomic recoil motion in a quantum gas can profoundly change many nonlinear optical processes routinely observed in a normal gas. Not only multi-photon wave mixing processes all become stimulated Raman or hyper-Raman in nature but the usual forward wave-mixing process, which is the most efficient process in normal gases, is strongly reduced by the condensate structure factor. On the other hand, in the backward direction the Bogoliubov dispersion automatically compensates the optical- wave phase mismatch, resulting in efficient backward light field generation that usually is not supported in normal gases.
We present a semi-classical theoretical framework on light-wave mixing and scattering in single-component quantum gases. We show that these optical processes originating from elementary excitations with dominant collective atomic recoil motion are stimulated Raman or hyper-Raman in nature. In the forward direction, the wave-mixing process, which is the most efficient process in normal gas, is strongly reduced by the condensate structure factor even though the Bogoliubov dispersion relation perfectly compensates the optical-wave phase mismatch. In the backward direction, however, the free-particle-like condensate structure factor and Bogoliubov dispersion result in highly efficient light-wave mixing and collective atomic recoil motion that are enhanced by a stimulated hyper-Raman gain and a very narrow two-photon motional state resonance.
We demonstrate the possibility of drastically reducing the velocity of phonons in quasi-one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark soliton ``gas'' that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of qutrits (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter-wave phononics, in analogy with the electromagnetically induced transparency effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to \ensuremath{\sim}5 $\ensuremath{\mu}\mathrm{m}$/s, \ensuremath{\sim}103{10}^{3}103 times lower than the condensate sound speed. This is a value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of ``stopped-sound''-based quantum information protocols.