Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes
arXiv:2201.00894 · doi:10.21468/SciPostPhysLectNotes.44
Abstract
These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to the theory of non-reciprocal quantum interactions and devices. The goal is connect various approaches and concepts, including Hamiltonians encoding synthetic gauge fields, scattering descriptions, quantum master equations, and non-Hermitian Hamiltonians. The importance of having both non-trivial synthetic gauge fields and dissipation for obtaining non-reciprocal interactions is stressed. Connections to broader topics such as quantum reservoir engineering and the quantum theory of continuous-measurement based feedforward are also discussed.
arXiv commentSubmitted to SciPost Lecture Notes. To appear in 'Quantum Information Machines; Lecture Notes of the Les Houches Summer School 2019,' eds. M. Devoret, B. Huard, and I. Pop
References in corpus (24)
- Edge states and topological invariants of non-Hermitian systems
- Introduction to Quantum Noise, Measurement and Amplification
- Symmetry and Topology in Non-Hermitian Physics
- Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
- Vortex Pinning and Non-Hermitian Quantum Mechanics
- A Straightforward Introduction to Continuous Quantum Measurement
- Non-reciprocal phase transitions
- Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering
- Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
- Quantum state tomography across the exceptional point in a single dissipative qubit
- Time-reversal symmetry breaking in circuit-QED based photon lattices
- Artificial gauge fields in materials and engineered systems
- Noiseless nonreciprocity in a parametric active device
- Tutorial on Electromagnetic Nonreciprocity and Its Origins
- Driven-dissipative preparation of entangled states in cascaded quantum-optical networks
- The reconfigurable Josephson circulator/directional amplifier
- Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
- Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
- Graph-based analysis of nonreciprocity in coupled-mode systems
- Non-equilibrium stationary states of quantum non-Hermitian lattice models
- Directional amplification with a Josephson circuit
- Non-reciprocal quantum interactions and devices via autonomous feed-forward
- Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer
- Distinguishing between quantum and classical Markovian dephasing dissipation
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- Many-Body Open Quantum Systems
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- Dynamical phase transitions in the nonreciprocal Ising model
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- Quantum Optical Binding of Nanoscale Particles
- Quantum theory of non-Hermitian optical binding between nanoparticles
- Parametrically controlled chiral interface for superconducting quantum devices
- Engineering synthetic gauge fields through the coupling phases in cavity magnonics
- Toolbox for nonreciprocal dispersive models in circuit QED
- Observing Parity Time Symmetry Breaking in a Josephson Parametric Amplifier
- Geometric correspondence of noisy quantum dynamics and universal robust quantum gates
- Level attraction from interference in two-tone driving
- Chiral excitation flows of a multinode network based on synthetic gauge fields
- Dissipative phase transition of interacting non-reciprocal fermions
- Quantum Measurement Encoding for Quantum Metrology
- Solving the Kinetic Ising Model with Non-Reciprocity
- Symmetry induced enhancement in finite-time thermodynamic trade-off relations
- The Role of Exceptional Points and Transmission Peak Degeneracies in Non-Hermitian Sensing