Quantum Noise Theory of Exceptional Point Sensors

Abstract

Distinct from closed quantum systems, non-Hermitian system can have exceptional points (EPs) where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of detected signal. Meanwhile, the noise might also be amplified at EPs and it is not obvious whether exceptional points will still improve the performance of sensors when both signal and noise are amplified. We develop quantum noise theory to systematically calculate the signal and noise associated with the EP sensors. We then compute quantum Fisher information to extract a lower bound of the sensitivity of EP sensors. Finally, we explicitly construct an EP sensing scheme based on heterodyne detection to achieve the same scaling of the ultimate sensitivity with enhanced performance. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.

arXiv comment5 pages, 2 figures

References in corpus (22)

• Quantum sensing
• Gaussian Quantum Information
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Topological energy transfer in an optomechanical system with exceptional points
• Spawning rings of exceptional points out of Dirac cones
• Quantum Metrology in Non-Markovian Environments
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Repulsion of Resonance States and Exceptional Points
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• No exceptional precision of exceptional point sensors
• Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound
• Phases of Wave Functions and Level Repulsion
• Quantum Fisher information for states in exponential form
• The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
• Quantum metrology with open dynamical systems
• Experimental demonstration of shaken lattice interferometry
• Quantum metrology with mixed states: When recovering lost information is better than never losing it
• Optimal Matterwave Gravimetry
• Phase Estimation of Coherent States with a Noiseless Linear Amplifier

Cited by in corpus (132)

• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Enhanced sensitivity operation of an optical gyroscope near an exceptional point
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
• Petermann-factor limited sensing near an exceptional point
• Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Quantum Non-Hermitian Topological Sensors
• Theory of reflectionless scattering modes
• Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
• Non-Hermitian dynamics without dissipation in quantum systems
• Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit
• Hierarchical construction of higher-order exceptional points
• Quantum sensing with a single-qubit pseudo-Hermitian system
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Quantum squeezing and sensing with pseudo anti-parity-time symmetry
• Observation of Exceptional Points in Thermal Atomic Ensembles
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Magnetic suppression of non-Hermitian skin effects
• Exceptional-point Sensors Offer No Fundamental Signal-to-Noise Ratio Enhancement
• High-order exceptional points in supersymmetric arrays
• Fundamental Sensitivity Limits for non-Hermitian Quantum Sensors
• Fundamental limits for reciprocal and non-reciprocal non-Hermitian quantum sensing
• Non-Hermitian Photonic Lattices: tutorial
• Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
• Emergence of PT-symmetry breaking in open quantum systems
• Exceptional precision of a nonlinear optical sensor at a square-root singularity
• Non-Dissipative Non-Hermitian Dynamics and Exceptional Points in Coupled Optical Parametric Oscillators
• Delayed sudden death of entanglement at exceptional points
• Linear response theory of open systems with exceptional points
• Zoology of non-Hermitian spectra and their graph topology
• Exceptional entanglement phenomena: non-Hermiticity meeting non-classicality
• Detection sensitivity enhancement of magnon Kerr nonlinearity in cavity magnonics induced by coherent perfect absorption
• Generating high-order quantum exceptional points in synthetic dimensions
• Non-Hermitian sensing in the absence of exceptional points
• Local master equations bypass the secular approximation
• Photon blockade in non-Hermitian optomechanical systems with nonreciprocal couplings
• Noise Constraints for Nonlinear Exceptional Point Sensing
• Stable Atomic Magnetometer in Parity-Time Symmetry Broken Phase
• Emergent $\mathcal{P}\mathcal{T}$ symmetry in a double-quantum-dot circuit QED set-up
• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
• Optimized Steering: Quantum State Engineering and Exceptional Points
• Quantum correlations in $\mathcal{P}\mathcal{T}$-symmetric systems
• Experimental Demonstration of Exceptional Points of Degeneracy in Linear Time Periodic Systems and Exceptional Sensitivity
• Manipulating non-Hermitian skin effect via electric fields
• Multiparameter estimation perspective on non-Hermitian singularity-enhanced sensing
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
• Dynamic magnetization in non-Hermitian quantum spin system
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Quantum statistical signature of $\mathcal{P}\mathcal{T}$ symmetry breaking
• Encircling the Liouvillian exceptional points: a brief review
• Chiral Bell-state transfer via dissipative Liouvillian dynamics
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Exceptional points for resonant states on parallel circular dielectric cylinders
• $\mathcal{P}\mathcal{T}$-symmetry-breaking enhanced cavity optomechanical magnetometry
• Excitation of absorbing exceptional points in the time domain
• Chiral state transfer under dephasing
• Near-unit efficiency of chiral state conversion via hybrid-Liouvillian dynamics
• Quantum parameter estimation of non-Hermitian systems with optimal measurements
• Critical non-Hermitian topology induced quantum sensing
• Exceptional points as signatures of dynamical magnetic phase transitions
• Exponential sensitivity revival of noisy non-Hermitian quantum sensing with two-photon drives
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• High-order spectral singularity
• Signature of exceptional point phase transition in Hermitian systems
• Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit
• Dynamic gain and frequency comb formation in exceptional-point lasers
• Observation of non-local impedance response in a passive electrical circuit
• Boosting the sensitivity of high frequency gravitational wave detectors by PT-symmetry
• Quantum theory of non-Hermitian optical binding between nanoparticles
• Subthreshold phonon generation in an optomechanical system with an exceptional point
• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Two-level system as topological actuator for nanomechanical modes
• Anomalous spontaneous emission dynamics at chiral exceptional points
• Transition from degeneracy to coalescence: theorem and applications
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Quantum Metrology with Higher-order Exceptional Points in Atom-cavity Magnonics
• Exceptional Point-enhanced Rydberg Atomic Electrometers
• Quantum correlations in dissipative gain-loss systems across exceptional points
• Overcoming the diffraction limit on the size of dielectric resonators using an amplifying medium
• Quantum metrology with quantum Wheatstone bridge composed of Bose systems
• Exceptional point enhanced optical gyroscope in mechanical PT-symmetric system
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Quantum Sensing with Driven-Dissipative Su-Schrieffer-Heeger Lattices
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Enhanced quantum sensing in time-modulated non-Hermitian systems
• Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• Enhanced quantum sensing with hybrid exceptional-diabolic singularities
• Space-time symmetry and nonreciprocal parametric resonance in mechanical systems
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• High-Order Perfect Absorption in the Absence of Exceptional Point
• Exceptional points in perturbed dielectric spheres: A resonant-state expansion study
• Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations
• Lindblad dynamics of open multi-mode bosonic systems: Algebra of bilinear superoperators, exceptional points and speed of evolution
• Strong coupling diagnostics for multi-mode open systems
• Recent advances in the combination of nonlinearity and exceptional points
• Acute entanglement and Photon/Phonons statistics in a balanced/unbalanced PT-symmetry systems
• Non-Hermitian physics and engineering in silicon photonics
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering
• Simulation of exceptional-point systems on quantum computers for quantum sensing
• Quantum Measurement Encoding for Quantum Metrology
• Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops
• Exceptionally deficient topological square-root insulators
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Exceptional points in SSH-like models with hopping amplitude gradient
• Beyond the Petermann limit: can exceptional points increase sensor precision?
• Squeezing enhanced sensing at an exceptional point
• Enhancement of sensitivity near exceptional points in dissipative qubit-resonator systems
• Non-Hermitian Aharonov-Bohm Cage
• Phase-controlled improvement of photon lifetime in coupled superconducting cavities
• Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss
• Emergent non-Hermitian conservation laws at exceptional points
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT-symmetric dynamics and unidirectional coupling
• Exceptional point in self-consistent Markovian master equations
• Properties and Application of Gaussian Quantum Processes
• Characteristic influence of exceptional points in quantum dynamics
• Stability via symmetry breaking in interacting driven systems
• The Role of Exceptional Points and Transmission Peak Degeneracies in Non-Hermitian Sensing
• A hybrid quantum interferometer bridging Hong-Ou-Mandel and N00N-state interference
• Impact of noise on nonlinear-exceptional-point-based sensors
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• Enhancement of quantum sensing in a dissipatively coupled two-mode system