[Paper Review] Quantum optomechanics of a two-dimensional atomic array

Ephraim Shahmoon, Mikhail D. Lukin+1 more|arXiv (Cornell University)|Oct 2, 2018

Mechanical and Optical Resonators4 citations

TL;DR

This paper proposes a two-dimensional atomic array as a novel platform for quantum optomechanics, leveraging its nearly perfect reflectivity and ultralight mechanical mass to enable strong optomechanical coupling without cavities. Under continuous-wave laser illumination, collective atomic motion generates multiple sidebands in the scattered light spectrum and induces large spatio-temporal quantum noise squeezing, demonstrating a cavity-free route to nonlinear quantum optomechanics with high mechanical susceptibility.

ABSTRACT

We demonstrate that a two-dimensional (2D) atomic array can be used as a novel platform for quantum optomechanics. Such arrays feature both nearly-perfect reflectivity and ultra-light mass, leading to significantly-enhanced optomechanical phenomena. Considering the collective atom-array motion under continuous laser illumination, we study the nonlinear optical response of the array. We find that the spectrum of light scattered by the array develops multiple sidebands, corresponding to collective mechanical resonances, and exhibits nearly perfect quantum-noise squeezing. Possible extensions and applications for quantum nonlinear optomechanics are discussed.

Motivation & Objective

• To explore quantum optomechanics in a cavity-free system using a 2D array of trapped atoms.
• To address the challenge of achieving strong optomechanical coupling in macroscopic systems with minimal mechanical zero-point motion.
• To demonstrate that collective atomic motion in a 2D array can lead to nonlinear optical responses and quantum correlations in scattered light.
• To establish a mapping between the 2D atomic array and standard cavity optomechanics in the bad-cavity, unresolved sideband regime.
• To investigate the potential for generating large spatio-temporal squeezing in the output light, enabling new regimes of few-photon quantum optomechanics.

Proposed method

• Model the 2D atomic array as a system of two-level atoms in a 2D lattice with fixed transverse positions and longitudinal motion around equilibrium.
• Use a quantum-mechanical treatment to describe light-induced collective atomic motion via dipole-dipole interactions and radiation pressure.
• Map the system to a standard cavity optomechanical model in the bad-cavity, unresolved sideband regime using effective optomechanical coupling constants.
• Derive the scattered light spectrum using input-output theory, accounting for nonlinear optomechanical response and collective mechanical modes.
• Analyze quantum noise and correlation properties of the output field using Bogoliubov transformations and commutation relations for the output field operators.
• Demonstrate that balanced, two-sided illumination can achieve optimal squeezing even without perfect reflection, by canceling vacuum noise from input ports.

Experimental results

Research questions

• RQ1 Can a 2D array of trapped atoms serve as a cavity-free platform for strong quantum optomechanics?
• RQ2 How does collective atomic motion under continuous-wave laser illumination lead to nonlinear optical sidebands in the scattered light spectrum?
• RQ3 What is the degree of quantum noise squeezing achievable in the scattered light from such a system, and how does it depend on mechanical resonance?
• RQ4 Can optimal squeezing be achieved without relying on nearly perfect reflection, by using a balanced two-sided illumination scheme?
• RQ5 How does the system's behavior map onto standard cavity optomechanics, and what are the implications for nonlinear and few-photon quantum optomechanics?

Key findings

• The 2D atomic array exhibits nearly perfect reflectivity at the cooperative resonance frequency, enabling strong light-matter interaction with minimal transmission.
• Collective mechanical modes emerge due to dipole-dipole interactions, leading to multiple sidebands in the scattered light spectrum that correspond to these resonances.
• The output light displays large spatio-temporal quantum noise squeezing, with squeezing levels approaching near-perfect quantum noise suppression.
• The system maps effectively to the bad-cavity, unresolved sideband regime of standard cavity optomechanics, validating its use as a benchmark platform.
• Even without perfect reflection, a balanced two-sided illumination scheme can achieve the same optimal squeezing by canceling vacuum noise from input ports.
• The squeezing remains robust and well-defined at mechanical resonance, despite formal breakdowns in the adiabatic-elimination approximation near resonance, due to the narrow width of the problematic region.