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Archives of Acoustics

Coherent states in brillouin light scattering

Tomasz Błachowicz

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The present article describes inelastic light scattering or the theory of photon acoustic- phonon interactions to which the coherent state formalism can be applied; it belongs partly to quantum acoustics. Such quantum calculations lead to the same results as the classical ones, and what is important, they are not in full agreement with the results of measurements. The article provides some formulae useful for comparison of the optical signals intensity in Brillouin light scattering experiments.

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The present article describes inelastic light scattering or the theory of photon acoustic- phonon interactions to which the coherent state formalism can be applied; it belongs partly to quantum acoustics. Such quantum calculations lead to the same results as the classical ones, and what is important, they are not in full agreement with the results of measurements. The article provides some formulae useful for comparison of the optical signals intensity in Brillouin light scattering experiments.
Recent experiments demonstrating storage of optical pulses in acoustic phonons via stimulated Brillouin scattering raise questions about the spectral and temporal capacities of such protocols and the limitations of the theoretical frameworks routinely used to describe them. We consider the dynamics of photon-phonon scattering induced by optical pulses with temporal widths comparable to the period of acoustic oscillations. We revisit the widely adopted classical formalism of coupled modes and demonstrate its breakdown. We use a simple extension to the formulation and find potentially measurable consequences in the dynamics of Brillouin experiments involving ultrashort pulses.
We analyze the quantum statistical properties of light scattered by an acousto-optic modulator. From the perspective of quantum mechanics, the acousto-optic effect arises from a nonlinear interaction between three bosonic fields: the laser light, the Brillouin-scattered light, and an acoustic wave. The Hamiltonian coincides with that of sum-frequency generation, where the sum-frequency mode is known to exhibit sub-Poissonian statistics. We calculate the free temporal evolution of the Fano factor for Brillouin backscattered light and determine that sub-Poissonian statistics are obtained when faint laser light is scattered by a counter-propagating coherent acoustic wave with low average phonon number. The use of sub-Poissonian light would lead to an increase of the security for quantum key distribution.
Brillouin–Mandelstam scattering is one of the most accessible nonlinear optical phenomena and has been widely studied since its theoretical discovery one hundred years ago. The scattering mechanism is a three-wave-mixing process between two optical fields and one acoustic field and has found a broad range of applications spanning microscopy to ultra-narrow-linewidth lasers. Building on the success of utilizing this nonlinearity at a classical level, a rich avenue is now being opened to explore Brillouin scattering within the paradigm of quantum optics. Here, we take a key step in this direction by employing quantum optical techniques yet to be utilized for Brillouin scattering to characterize the second-order coherence of Stokes scattering across the Brillouin lasing threshold. We use a silica microsphere resonator and single-photon counters to observe the expected transition from bunched statistics of thermal light below the lasing threshold to Poissonian statistics of coherent light above the threshold. Notably, at powers approaching the lasing threshold, we also observe super-thermal statistics, which arise due to instability and a “flickering” in and out of lasing as the pump field is transiently depleted. The statistics observed across the transition, including the “flickering,” are a result of the full nonlinear three-wave-mixing process and cannot be captured by a linearized model. These measurements are in good agreement with numerical solutions of the three-wave Langevin equations and are well demarcated by analytical expressions for the instability and the lasing thresholds. These results demonstrate that applying second-order-coherence and photon-counting measurements to Brillouin scattering provides new methods to advance our understanding of Brillouin scattering itself and progress toward quantum-state preparation and characterization of acoustic modes.
Brillouin optomechanics provides a way to coherently control traveling acoustic excitations in waveguides system, which enables the manipulation and processing of classical and quantum information. Although Brillouin optomechanics has been largely investigated in the steady-state regime using continuous waves [1]–[3], waveguide experiments are often realized by using optical pulses for example for Brillouin-based memory [4], [5]. This requires a dynamic framework treatment for the temporal domain including the noise dynamics.
Optical and acoustic waves can interact over the nonlinear effect of stimulated Brillouin scattering (SBS), which is a coherent process. By using traveling acoustic waves, we recently showed proof-of-principle experiments of Brillouin-based light storage. The particularity of Brillouin-based light storage is the strict phase-matching condition. This allows for different features: simultaneous storage at multiple wavelengths, cascaded storage at different spatial positions, and nonreciprocal storage with a GHz bandwidth. However, the delay time of this technique has so far been limited to the acoustic lifetime of about 10 ns. In this talk, I will discuss our recent results on coherent photon-phonon interaction. One focus will be on a proof-of-principle experiments on how to reinforce acoustic phonons. This enables us to overcome the obstacle of the limited acoustic lifetime by optically reinforcing the acoustic wave.
Brillouin-Mandelstam scattering offers several favourable properties to control sound with light at a quantum mechanical level. In particular, the high acoustic frequencies, acoustic mode selectivity, and low optical absorption provide a promising route towards this goal whilst also overcoming several current hindrances within optomechanics. Utilizing these properties, some of our main results in this direction include: the first observation of Brillouin optomechanical strong coupling, studying the second-order coherence across the Brillouin lasing threshold, and, we’ve performed heralded single-phonon addition and subtraction to a thermal state of the acoustic field observing the resulting non-Gaussianity with a precision that advanced the forefront of opticsbased mechanical state tomography. More recently, we’ve demonstrated that laser cooling may be enhanced via zero-photon detection, and we’ve characterized the Brillouin scattering response in optical fibre at millikelvin temperatures. This talk will cover these results, what they enable, and the broader direction of our lab including the prospects of this platform for quantum science and technology.