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Journal of Modern Optics

The quantum noise of guided wave acoustic Brillouin scattering with applications to continuous-variable quantum key distribution

Zheshen Zhang, Xuan Quyen Dinh, Paul L. Voss

Published Jul 10, 2011• 2 citations
Publisher

Abstract

The spectra and optical quantum state of guided acoustic wave Brillouin scattering in optical fibers are measured. Spectra from 0.95 to 2 GHz are obtained with amplitude resolution as sensitive as 0.01 shot noise unit. Quantum homodyne tomography measurements confirm the thermal quantum statistics of guided acoustic wave Brillouin scattering, which is useful knowledge in the context of experimental continuous-variable quantum key distribution.

DOI
10.1080/09500340.2011.589915

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The spectra and optical quantum state of guided acoustic wave Brillouin scattering in optical fibers are measured. Spectra from 0.95 to 2 GHz are obtained with amplitude resolution as sensitive as 0.01 shot noise unit. Quantum homodyne tomography measurements confirm the thermal quantum statistics of guided acoustic wave Brillouin scattering, which is useful knowledge in the context of experimental continuous-variable quantum key distribution.
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In silica glass fibers, thermally excited acoustic phonons scatter light into the beam propagating in the forward direction. At acoustic frequencies up to several hundreds of megahertz, the wave vectors of the phonons interacting with the light propagate essentially transversally to the fiber axis. This effect is known as Guided Acoustic Wave Brillouin Scattering (GAWBS) and leads to phase and polarization noise in the guided light. For fiber-based quantum optics experiments, this excess noise is a major limitation. In Photonic Crystal Fibers (PCFs), light is guided by a microstructure simultaneously acting as a 2D transversal phononic crystal which modifies the acoustic noise spectrum. We demonstrate a GAWBS-noise reduction in commercially available PCFs. This gives rise to the prospect of fiber-based quantum optic devices exhibiting less excess noise, thus resulting in higher quantum state purity. Further improvement can be achieved by tailoring the photonic microstructure such that a reduction of phonon noise by design is achieved.
Thermally excited transverse phonons in glass fibers generate guided acoustic wave Brillouin scattering (GAWBS) which afflicts the propagating light with phase and polarization noise. This excess noise is a major limitation for fiber-based squeezing sources as well as for the transmission of quantum information through fibers. In order to achieve quantum states of high quality it is therefore important to reduce the harmful effect of GAWBS. The thermal nature of GAWBS naturally allows for a reduction by cooling the fiber. Alternatively, subtracting the correlated noise of two closely spaced pulses leads to a cancellation. These methods, however, are inconvenient for fiber-based squeezing sources and inapplicable in practical quantum information transmission systems.
We report a comprehensive experimental study of spontaneous Brillouin scattering in a few-mode optical fiber, resolving both forward and backward scattering processes for intra- and inter-modal interactions. Using heterodyne detection, Stokes and anti-Stokes components without external acoustic excitation are observed and quantitatively extracted Brillouin shifts, linewidths, and gain coefficients. Forward scattering is mediated by guided torsional-radial acoustic modes with frequencies ranging from MHz to GHz, while backward scattering involves longitudinal core-guided modes at frequencies of tens of GHz. These results provide calibrated benchmarks for Brillouin interactions in few-mode fibers, offering insights relevant to phonon-based quantum applications and mode-selective optomechanics.
We give a quantum theoretical analysis of squeezed light generation via nondegenerate four-wave mixing in an optical fiber. The medium is modeled by an ensemble of anharmonic oscillators and loss is included. We include the coupling to acoustic phonons which gives rise to guided acoustic wave Brillouin scattering (GAWBS). The GAWBS introduces random noise which destroys the squeezing at room temperatures. By cooling the fiber to temperatures ~2 K the GAWBS is substantially reduced and the observation of squeezing becomes possible. A comparison is made with the recent experimental results of Levenson et al.1, 2 A scheme to suppress the GAWBS at room temperatures using a two-frequency pump and difference detection is analyzed and the conditions in which good squeezing results are determined.