Quantum Many-Body Effects in Optical Kerr Media

Nonlinear quantum optics is emerging as one of the most important research directions in photonics. These include quantum solitons (QSs), and highly nonclassical supercontinuum generation (SCG). We need new strategies to design nonlinear optical devices operating at low photon numbers and theory to describe how they work.

Following Drummond et al. [1], we adopt a phase-space analysis to map the second quantized field theory of optical propagation in nonlinear dispersive media into a system of two coupled stochastic nonlinear Schrödinger equations (SNLSEs). This mapping allows numerical simulations of QSs, quantum dispersive shock waves (QDSWs) and quantum rogue waves (QRWs) generation by the nonlinear box problem [2] at low photon number.

As recently proved [3], quantum control furnishes new opportunities. By combining SNLSEs and CRAB optimization, we look for the best control function to limit effects as quantum spreading of QSs, to maximize the spectral generation of QDSWs, and to enhance the peak intensity of QRWs.

We believe that this approach unveils essential insights into the design of new quantum sources.

[1] P. D. Drummond et al., Nature 365 (1993).
[2] G. Marcucci et al., arXiv:1908.05212, accepted on Nat. Commun.
[3] P. Doria et al., PRL 106 (2011).