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

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.

15 pages, 4 figures

References in corpus (41)

• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Quantum Simulation
• Cavity-based quantum networks with single atoms and optical photons
• Quantum dot single photon sources with ultra-low multi-photon probability
• Field quantization for open optical cavities
• Gaussian quantum Monte Carlo methods for fermions
• Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate
• Gauge P-representations for quantum-dynamical problems: Removal of boundary terms
• Self-generation of optical frequency comb in single section Quantum Dot Fabry-Perot lasers: a theoretical study
• Gaussian phase-space representations for fermions
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Optoelectronic device simulations based on macroscopic Maxwell-Bloch equations
• Gaussian quantum operator representation for bosons
• Mbsolve: An open-source solver tool for the Maxwell-Bloch equations
• Spontaneous emission between an unusual pair of plates
• Why you should not use the electric field to quantize in nonlinear optics
• Phase transitions and the internal noise structure of nonlinear Schrödi nger equation solitons
• Ab-initio multimode linewidth theory for arbitrary inhomogeneous laser cavities
• Quantum Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers
• Numerical Study of Amplified Spontaneous Emission and Lasing in Random Media
• Quantum dynamics with stochastic gauge simulations
• Finite-difference time-domain formulation of stochastic noise in macroscopic atomic systems
• Classical light vs. nonclassical light: Characterizations and interesting applications
• Derivation of Maxwell-Bloch-type equations by projection of quantum models
• Backscattering-Induced Dissipative Solitons in Ring Quantum Cascade Lasers
• A Comparison of Different Classical, Semiclassical and Quantum Treatments of Light-Matter Interactions: Understanding Energy Conservation
• Positive-P phase space method simulation in superradiant emission from a cascade atomic ensemble
• Quantum theory of superfluorescence based on two-point correlation functions
• FDTD Simulation of Thermal Noise in Open Cavities
• Qubit phase-space: SU(n) coherent state P-representations
• Exact Real Time Dynamics of Quantum Spin Systems Using the Positive-P Representation
• Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks
• Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques
• Phase-space analysis of bosonic spontaneous emission
• Ultrafast pulse phase shift in a charged quantum dot- micropillar system
• Grassmann Variables and the Jaynes-Cummings Model
• Grassmann Phase Space Methods for Fermions. II. Field Theory
• Grassmann phase-space methods for fermions: uncovering classical probability structure
• Understanding Detailed Balance for an Electron-Radiation System Through Mixed Quantum-Classical Electrodynamics
• Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
• Inherent Stochastic Linearization of Random Laser Modes