Multimode approach to quantum optics for quantum information and quantum metrology

Light offers a vast potential in the development of modern quantum technologies due to its intrinsic resilience to decoherence effects and its capacity to convey a huge amount of information. The many modes of light, would they be spatial modes or spectral modes, are as many quantum harmonic oscillators, leading to a largely unexplored Hilbert space[1]. In this talk, we will specifically consider the continuous variable approach, where the observables of interest are the quadratures of the electric field. 

We will first review how modal decomposition can be used to improve measurement sensitivity,  and reach the fundamental limits impose by the vacuum fluctuations in simple problems, as for instance estimating the separation of incoherent sources[2].

But continuous variables have also proven their worth as a platform for creating huge entangled states (entangling up to one million optical modes). Additionally, this entanglement can be created in a deterministic fashion and easily manipulated with standard techniques in optics. We will demonstrate how this can be achieve using time/frequency modes[3]. 

Finally, to reach a quantum advantage, and perform a task that cannot be efficiently simulated with a classical device, we require more than just entanglement. The additional ingredient is non-Gaussian statistics in the outcomes of the quadrature measurements. We will demonstrate how photon subtraction, a well know non-gaussian operation, can be rendered mode-dependent and allow for the generation of non-Gaussian multimode state of lights, required for quantum information processing[4].

[1] C. Fabre and N. Treps, Modes and States in Quantum Optics, Rev. Mod. Phys. 92, 035005 (2020).

[2] P. Boucher, C. Fabre, G. Labroille, and N. Treps, Spatial Optical Mode Demultiplexing as a Practical Tool for Optimal Transverse Distance Estimation, Optica, 7, 1621 (2020).

[3] J. Roslund, R. M. de Araújo, S. Jiang, C. Fabre, and N. Treps, Wavelength-Multiplexed Quantum Networks with Ultrafast Frequency Combs, Nature Photonics 8, 109 (2014).

[4] Y.-S. Ra, A. Dufour, M. Walschaers, C. Jacquard, T. Michel, C. Fabre, and N. Treps, Non-Gaussian Quantum States of a Multimode Light Field, Nature Physics 11, 1 (2019).