Stochastic correction to the Maxwell-Bloch equations via the positive $P$ representation

• URL: http://arxiv.org/abs/2404.00402v2
• Date: Wed, 10 Jul 2024 07:35:39 GMT
• Title: Stochastic correction to the Maxwell-Bloch equations via the positive $P$ representation
• Authors: Johannes Stowasser, Felix Hitzelhammer, Michael A. Schreiber, Ulrich Hohenester, Gabriela Slavcheva, Michael Haider, Christian Jirauschek,
• Abstract summary: We find an advantageous degree of freedom in the choice of the involved nonorthogonal fermionic basis states. This approach explores the connection between semiclassical and field-quantized treatments of light-matter interaction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Focusing on two-level atoms, we apply the positive $P$ representation to a full-wave mixed bosonic and fermionic system of Jaynes-Cummings type and identify an advantageous degree of freedom in the choice of the involved nonorthogonal fermionic basis states. On this basis, we propose a stochastic correction to the Maxwell-Bloch equations by relating them to a stochastic differential equation on a nonclassical phase space, which captures the full second quantization dynamics of the system. This approach explores the connection between semiclassical and field-quantized treatments of light-matter interaction and can potentially be used for the simulation of nonclassical light sources while retaining the main advantages of a semiclassical model.

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