Photon counting statistics in Gaussian bosonic networks
arXiv:2407.20477 · doi:10.21468/SciPostPhys.18.4.116
Abstract
The statistics of transmitted photons in microwave cavities play a foundational role in microwave quantum optics and its technological applications. By utilizing quantum mechanical phase-space methods, we here develop a general theory of the photon counting statistics in Gaussian bosonic networks consisting of driven cavities with beamsplitter interactions and two-mode-squeezing. The dynamics of the network can be captured by a Lyapunov equation for the covariance matrix of the cavity fields, which generalizes to a Riccati equation, when counting fields are included. By solving the Riccati equation, we obtain the statistics of emitted and absorbed photons as well as the time-dependent correlations encoded in waiting time distributions and second-order coherence functions. To illustrate our theoretical framework, we first apply it to a simple linear network consisting of two coupled cavities, for which we evaluate the photon cross-correlations and discuss connections between the photon emission statistics and the entanglement between the cavities. We then consider a bosonic circulator consisting of three coupled cavities, for which we investigate how a synthetic flux may affect the direction of the photon flow, similarly to recent experiments. Our general framework paves the way for systematic investigations of the photon counting statistics in Gaussian bosonic networks.
37 pages, 7 figures
References in corpus (57)
- Quantum entanglement
- A computable measure of entanglement
- Gaussian Quantum Information
- Circuit Quantum Electrodynamics
- The large deviation approach to statistical mechanics
- Continuous-variable optical quantum state tomography
- Quantum Thermodynamics
- Continuous variable quantum information: Gaussian states and beyond
- The Kerr-Cat Qubit: Stabilization, Readout, and Gates
- Real-time quantum error correction beyond break-even
- Time-reversal symmetry breaking in circuit-QED based photon lattices
- Creation and control of multi-phonon Fock states in a bulk acoustic wave resonator
- Reconciliation of quantum local master equations with thermodynamics
- Fluctuation theorem in quantum heat conduction
- Testing the validity of the local and global GKLS master equations on an exactly solvable model
- Quantum limited amplification and entanglement in coupled nonlinear resonators
- All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
- Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor
- Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
- Quantum state preparation, tomography, and entanglement of mechanical oscillators
- Hybrid Microwave-Cavity Heat Engine
- Bolometer operating at the threshold for circuit quantum electrodynamics
- Quantum control of bosonic modes with superconducting circuits
- Detecting itinerant microwave photons with engineered non-linear dissipation
- Factorial cumulants reveal interactions in counting statistics
- Optomechanical realization of the bosonic Kitaev-Majorana chain
- Emission of non-classical radiation by inelastic Cooper pair tunneling
- Efficient and Continuous Microwave Photodetection in Hybrid Cavity-Semiconductor Nanowire Double Quantum Dot Diodes
- Universal control of a bosonic mode via drive-activated native cubic interactions
- Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium
- In-situ Tuning of the Electric Dipole Strength of a Double Dot Charge Qubit: Charge Noise Protection and Ultra Strong Coupling
- Waiting for rare entropic fluctuations
- Thermodynamic uncertainty relations for coherently driven open quantum systems
- Photon counting statistics of a microwave cavity
- High-Fidelity Measurement of a Superconducting Qubit using an On-Chip Microwave Photon Counter
- Microwave photon detection at parametric criticality
- Local master equations bypass the secular approximation
- Photon cross-correlations emitted by a Josephson junction in two microwave cavities
- Quantum Simulation of the Bosonic Kitaev Chain
- Quadrature nonreciprocity: unidirectional bosonic transmission without breaking time-reversal symmetry
- Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
- Quantum trajectory analysis of single microwave photon detection by nanocalorimetry
- Nanoscale Quantum Calorimetry with Electronic Temperature Fluctuations
- Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
- Full counting statistics of the photocurrent through a double quantum dot embedded in a driven microwave resonator
- Energetics of microwaves probed by double quantum dot absorption
- Effective temperature pulses in open quantum systems
- Integrability of a globally coupled complex Riccati array: quadratic integrate-and-fire neurons, phase oscillators and all in between
- Efficient Microwave Photon to Electron Conversion in a High Impedance Quantum Circuit
- Statistics of heat exchange between two resistors
- Generation and structuring of multipartite entanglement in Josephson parametric system
- Microwave photon-number amplification
- Photon emission statistics of a driven microwave cavity
- Continuous microwave photon counting by semiconductor-superconductor hybrids
- Intermediate Times Dilemma for Open Quantum System: Filtered Approximation to The Refined Weak Coupling Limit
- Quantum-correlated photons generated by nonlocal electron transport
- Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries