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arXiv:1610.03355 · Physical Review Letters

Quantum Nonlinear Optics in Optomechanical Nanoscale Waveguides

Hashem Zoubi, Klemens Hammerer

Published Sep 21, 2017• 19 citations
arXivHTMLPDF

Abstract

We show that strong nonlinearities at the few photon level can be achieved in optomechanical nanoscale waveguides. We consider the propagation of photons in cm-scale one-dimensional nanophotonic structures where stimulated Brillouin scattering (SBS) is strongly enhanced by radiation pressure coupling. We introduce a configuration that allows slowing down photons by several orders of magnitude via SBS from sound waves using two pump fields. Slowly propagating photons can then experience strong nonlinear interactions through virtual off-resonant exchange of dispersionless phonons. As a benchmark we identify requirements for achieving a large cross-phase modulation among two counterpropagating photons applicable for photonic quantum gates. Our results indicate that strongly nonlinear quantum optics is possible in continuum optomechanical systems realized in nanophotonic structures.

DOI
10.1103/physrevlett.119.123602

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We show that strong nonlinearities at the few photon level can be achieved in optomechanical nanoscale waveguides. We consider the propagation of photons in cm-scale one-dimensional nanophotonic structures where stimulated Brillouin scattering (SBS) is strongly enhanced by radiation pressure coupling. We introduce a configuration that allows slowing down photons by several orders of magnitude via SBS from sound waves using two pump fields. Slowly propagating photons can then experience strong nonlinear interactions through virtual off-resonant exchange of dispersionless phonons. As a benchmark we identify requirements for achieving a large cross-phase modulation among two counterpropagating photons applicable for photonic quantum gates. Our results indicate that strongly nonlinear quantum optics is possible in continuum optomechanical systems realized in nanophotonic structures.
This study investigates the possibility of achieving a slow signal field at the level of single photons inside nanofibers by exploiting stimulated Brillouin scattering, which involves a strong pump field and the vibrational modes of the waveguide. The slow signal is significantly amplified for a pump field, with a frequency higher than that of the signal and attenuated for a lower pump frequency. We introduce a configuration for obtaining a propagating slow signal without gain or loss and with a relatively wide bandwidth. This process involves two strong pump fields with frequencies both higher and lower than that of the signal where the effects of signal amplification and attenuation compensate each other. We account for thermal fluctuations due to the scattering of thermal phonons and identify conditions under which thermal contributions to the signal field are negligible. The slowing of light through Brillouin optomechanics may serve as a vital tool for optical quantum information processing and quantum communications within nanophotonic structures.
A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon-photon interactions mediated by mechanical motion may be within experimental reach.
We develop a systematic method for deriving a quantum optical multi-mode Hamiltonian for the interaction of photons and phonons in nanophotonic dielectric materials by applying perturbation theory to the electromagnetic Hamiltonian. The Hamiltonian covers radiation pressure and electrostrictive interactions on equal footing. As a paradigmatic example, we apply our method to a cylindrical nanoscale waveguide. We use the resulting multi-mode Hamiltonian to derive an effective phonon-mediated interaction between photons propagating in the material. We predict strong non-linear phase shifts even among two photons, comparable to what can be achieved in nonlinear atomic media (comprising cold Rydberg atoms).
In this paper we theoretically show that counterpart photonic Cooper pairs can be achieved in nanoscale waveguides with radiation pressure effect. We demonstrate that due to Brillouin scattering a Stokes photon and an anti-Stokes one can exchange virtual phonons, leading to an effective photon-photon interaction. The effective interaction Hamiltonian of the two photons is identical to that for electrons in the BCS theory, and the photonic counterpart of the superconducting energy gap can appear. Quite different from the conventional stimulated Brillouin scattering the number of photon pairs can be amplified. The result could be used as a photon-pair laser and might have a possible application in integrated optics and quantum information processing in the future.
The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities.
The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplification. Moreover, the amplified phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir, which ultimately leads to the realization of photon blockade in a weakly coupled OMS. The reached nonlinear quantum regime also allows us to engineer the nonclassical states (e.g., Schr\"odinger cat states) of the cavity field, which are robust against the phonon noise. This work offers an alternative approach to enhance the quantum nonlinearity of an OMS, which should expand the applications of cavity optomechanics in the quantum realm.