Analytical approach to higher-order correlation functions in U(1) symmetric systems

Abstract

We derive a compact analytical solution of the $n$th-order equal-time correlation functions by using scattering matrix ($S$ matrix) under a weak coherent state input. Our solution applies to any dissipative quantum system that respects the U(1) symmetry. We further extend our analytical solution into two categories depending on whether the input and output channels are identical. The first category provides a different path for studying cross-correlation and multiple-drive cases, while the second category is instrumental in studying waveguide quantum electrodynamics systems. Our analytical solution allows for easy investigation of the statistical properties of multiple photons even in complex systems. Furthermore, we have developed a user-friendly open-source library in Python known as the quantum correlation solver, and this tool provides a convenient means to study various dissipative quantum systems that satisfy the above-mentioned criteria. Our study enables using $S$ matrix to study the photonic correlation and advance the possibilities for exploring complex systems.

arXiv comment22 pages, 8 figures, the QCS open-source library is available at http://github.com/ZhiGuangLu/qcs/

References in corpus (64)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Interfacing single photons and single quantum dots with photonic nanostructures
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum trajectories and open many-body quantum systems
• Natural and artificial atoms for quantum computation
• Resonance Fluorescence of a Single Artificial Atom
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Nonreciprocal Photon Blockade
• Strongly Correlated Two-Photon Transport in One-Dimensional Waveguide Coupled to A Two-Level System
• Single photons from coupled quantum modes
• The Single-Photon Router
• Strongly interacting photons in one-dimensional continuum
• Observation of Resonant Photon Blockade at Microwave Frequencies using Correlation Function Measurements
• Quantum Optics of Chiral Spin Networks
• Scalable integrated single-photon source
• Two-Photon Blockade in an Atom-Driven Cavity QED System
• Input-Output Formalism For Few-Photon Transport in One-Dimensional Nanophotonic Waveguides Coupled to a Qubit
• Single photons and unconventional photon blockade in quantum dot cavity-QED
• The Unconventional Photon Blockade
• Observation of Dicke Superradiance for Two Artificial Atoms in a Cavity with High Decay Rate
• Waveguide QED: Many-Body Bound State Effects on Coherent and Fock State Scattering from a Two-Level System
• Loss-enabled sub-Poissonian light generation in a bimodal nanocavity
• Open quantum systems
• Few-photon transport in low-dimensional systems: Interaction-induced radiation trapping
• Emitters of $N$-photon bundles
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Nonreciprocal microwave signal processing with a Field-Programmable Josephson Amplifier
• Multi-photon Scattering Theory and Generalized Master Equations
• Quantum dynamics of propagating photons with strong interactions: a generalized input-output formalism
• Theory of Subradiant States of a One-Dimensional Two-Level Atom Chain
• Two-Photon Transport in a Waveguide Coupled to a Cavity with a Two-level System
• Photon-photon interactions in cavity electromagnetically induced transparency
• Lehmann-Symanzik-Zimmermann Reduction Approach to Multi-Photon Scattering in Coupled-Resonator Arrays
• A Waveguide-Coupled On-Chip Single Photon Source
• Demonstration of efficient nonreciprocity in a microwave optomechanical circuit
• Subradiant states of quantum bits coupled to a one-dimensional waveguide
• Dynamics of many-body photon bound states in chiral waveguide QED
• Input-Output Formalism for Few-Photon Transport: A Systematic Treatment Beyond Two Photons
• Conventional and unconventional photon statistics
• Interacting Qubit-Photon Bound States with Superconducting Circuits
• Driven-dissipative quantum Kerr resonators: new exact solutions, photon blockade and quantum bistability
• Photon blockade in weakly-driven cavity QED systems with many emitters
• Manipulating the flow of thermal noise in quantum devices
• Closed form solution of Lindblad master equations without gain
• Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system
• Highly nonlocal optical nonlinearities in atoms trapped near a waveguide
• Experimental reconstruction of the few-photon nonlinear scattering matrix from a single quantum dot in a nanophotonic waveguide
• Dynamical blockade in a single mode bosonic system
• Simulating quantum light propagation through atomic ensembles using matrix product states
• Deterministic Generation of Photon Pairs within the Bad Cavity Limit
• Two-photon transport through a waveguide coupling to a whispering gallery resonator containing an atom and photon-blockade effect
• Few-photon scattering and emission from open quantum systems
• Cross-correlation between photons and phonons in quadratically coupled optomechanical systems
• Equivalence of matrix product ensembles of trajectories in open quantum systems
• Long-distance dissipation-assisted transport of entangled states via a chiral waveguide
• Quantum theory of light scattering in a one-dimensional channel: Interaction effect on photon statistics and entanglement entropy
• Single photon transmission in strong three-mode optomechanical circulatory system
• Exact Analysis of the Response of Quantum Systems to Two Photons Using a QSDE Approach
• General structure of two-photon S matrix in waveguide quantum electrodynamics systems containing a local quantum system with multiple ground states
• Quantum correlations among optical and vibrational quanta

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