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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum noise in energy-efficient slow light structures for optical computing: sqeezed light from slow light

Ryan Hamerly, Kambiz Jamshidi, Hideo Mabuchi

Published Apr 29, 2016• 0 citations
Publisher

Abstract

Due to their strong light confinement, waveguides with optical nonlinearities may be a promising platform for energy-efficient optical computing. Slow light can enhance a waveguide’s effective nonlinearity, which could result in devices that operate in low-power regimes where quantum fluctuations are important, and may also have quantum applications including squeezing and entanglement generation. In this manuscript, slow-light structures based on the Kerr (χ(3)) nonlinearity are analyzed using a semi-classical model to account for the quantum noise. We develop a hybrid split-step / Runge-Kutta numerical model to compute the mean field and squeezing spectrum for pulses propagating down a waveguide, and use this model to study squeezing produced in optical waveguides. Scaling relations are explored, and the benefits and limitations of slow light are discussed in the context of squeezing.

DOI
10.1117/12.2227308

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Due to their strong light confinement, waveguides with optical nonlinearities may be a promising platform for energy-efficient optical computing. Slow light can enhance a waveguide’s effective nonlinearity, which could result in devices that operate in low-power regimes where quantum fluctuations are important, and may also have quantum applications including squeezing and entanglement generation. In this manuscript, slow-light structures based on the Kerr (χ(3)) nonlinearity are analyzed using a semi-classical model to account for the quantum noise. We develop a hybrid split-step / Runge-Kutta numerical model to compute the mean field and squeezing spectrum for pulses propagating down a waveguide, and use this model to study squeezing produced in optical waveguides. Scaling relations are explored, and the benefits and limitations of slow light are discussed in the context of squeezing.
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
Squeezed states of light enable enhanced measurement precision by reducing noise below the standard quantum limit. A key application of squeezed light is nonlinear microscopy, where state-of-the-art performance is limited by photodamage and quantum-limited noise. Such microscopes require bright, pulsed light for optimal operation, yet generating and detecting bright pulsed squeezing at high levels remains challenging. In this work, we present an efficient technique to generate high levels of bright picosecond pulsed squeezed light using a χ2χ^2χ2 optical parametric amplification process in a waveguide. We measure −3.2 dB-3.2~\mathrm{dB}−3.2 dB of bright squeezing with optical power compatible with nonlinear microscopy, as well as −3.6 dB-3.6~\mathrm{dB}−3.6 dB of vacuum squeezing. Corrected for losses, these squeezing levels correspond to −15.4−8.7+2.7 dB-15.4^{+2.7}_{-8.7}~\mathrm{dB}−15.4−8.7+2.7​ dB of squeezing generated in the waveguide. The measured level of bright amplitude pulsed squeezing is to our knowledge the highest reported to date, and will contribute to the broader adoption of quantum-enhanced nonlinear microscopy in biological studies.
The propagation of ultrafast pulses in dispersion-engineered waveguides, exhibiting strong field confinement in both space and time, is a promising avenue towards single-photon nonlinearities in an all-optical platform. However, quantum engineering in such systems requires new numerical tools and physical insights to harness their complicated multimode and nonlinear quantum dynamics. In this work, we use a self-consistent, multimode Gaussian-state model to capture the nonlinear dynamics of broadband quantum fluctuations and correlations, including entanglement. Notably, despite its parametrization by Gaussian states, our model exhibits nonlinear dynamics in both the mean field and the quantum correlations, giving it a marked advantage over conventional linearized treatments of quantum noise, especially for systems exhibiting gain saturation and strong nonlinearities. Numerically, our approach takes the form of a Gaussian split-step Fourier (GSSF) method, naturally generalizing highly efficient SSF methods used in classical ultrafast nonlinear optics; the equations for GSSF evaluate in O(M2log⁡M)O(M^2\log M)O(M2logM) time for an MMM-mode system with O(M2)O(M^2)O(M2) quantum correlations. To demonstrate the broad applicability of GSSF, we numerically study quantum noise dynamics and multimode entanglement in several ultrafast systems, from canonical soliton propagation in third-order (χ(3)χ^{(3)}χ(3)) waveguides to saturated χ(2)χ^{(2)}χ(2) broadband parametric generation and supercontinuum generation, e.g., as recently demonstrated in thin-film lithium niobate nanophotonics.
The signal to noise ratio of optical systems is ultimately limited by the shot noise due to the Poissonian statistics of the light field. In recent years there has been a considerable effort to find ways to overcome this limitation by generating non-classical light with sub-shot noise statistics. Several groups have demonstrated non-classical light generation in diode lasers or light emitting diodes, and the amplitude fluctuations have been reduced substantially below the shot noise level [1,2]. However, for phase-sensitive measurements it is necessary to generate the more general quadrature squeezed states. Such quadrature squeezed light can be generated either by second-order or third-order nonlinear processes provided the nonlinear material has very low losses at the optical wavelength. To date, the successful generation schemes for quadrature squeezed light have been restricted to atomic vapours, optical fibres, or second-order nonlinear crystals [3]. The possibility of using the large χ(3) nonlinearities of semiconductors at frequencies below the band gap where the optical absorption is small has been discussed in the literature, but so far there have been no successful experiments [4-6]. In this paper we report measurements on GaAs/Al0.3Ga0.7As multiple quantum well waveguides and bulk ZnS in the wavelength range 750 - 890nm. Although we measure much larger nonlinearities in the quantum wells, the strong two-photon absorption is detrimental for squeezed light generation. However, in the ZnS where the laser frequency is below the two- photon absorption edge, we have succeeded in generating quadrature squeezed light in a semiconductor for the first time. On the basis of our results, we would expect that squeezed light could be generated in many other semiconductor systems provided the photon energy is less than half the band-gap energy.
Squeezed light—nonclassical multiphoton states with fluctuations in one of the quadrature field components below the vacuum level—has found applications in quantum light spectroscopy, quantum telecommunications, quantum computing, precision quantum metrology, detecting gravitational waves, and biological measurements. At present, quantum noise squeezing with optical fiber systems operating in the range near 1.5 μm has been mastered relatively well, but there are no fiber sources of nonclassical squeezed light beyond this range. Silica fibers are not suitable for strong noise suppression for 2 µm continuous-wave (CW) light since their losses dramatically deteriorate the squeezed state of required lengths longer than 100 m. We propose the generation multiphoton states of 2-micron 10-W class CW light with squeezed quantum fluctuations stronger than −15 dB in chalcogenide and tellurite soft glass fibers with large Kerr nonlinearities. Using a realistic theoretical model, we numerically study squeezing for 2-micron light in step-index soft glass fibers by taking into account Kerr nonlinearity, distributed losses, and inelastic light scattering processes. Quantum noise squeezing stronger than −20 dB is numerically attained for a customized As2Se3 fibers with realistic parameters for the optimal fiber lengths shorter than 1 m. For commercial As2S3 and customized tellurite glass fibers, the expected squeezing in the −20–−15 dB range can be reached for fiber lengths of the order of 1 m.