Non-Hermitian quantum dynamics of a two-level system and models of dissipative environments

Abstract

We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling two-level system. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various physical situations with different properties, such as dephasing, vanishing population difference and purification.

Updates: [v2] Added: mixed states and purification, connection between non-Hermitian and non-linear QM; [v3] Fixed found errors/typos; [v4] Updated references, some stylistic corrections; [v5] Final/published version

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Wave packet evolution in non-Hermitian quantum systems
• Scattering theory using smeared non-Hermitian potentials
• Physical Purification of Quantum States

Cited by in corpus (48)

• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Increase of entanglement by local PT -symmetric operations
• Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
• Time correlation functions for non-Hermitian quantum systems
• Quantum entropy of systems described by non-Hermitian Hamiltonians
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
• Photon blockade in non-Hermitian optomechanical systems with nonreciprocal couplings
• Non-Hermitian Hamiltonians and stability of pure states
• Non-hermitian operator modelling of basic cancer cell dynamics
• Exactly solvable time-dependent pseudo-Hermitian $su$(1,1) Hamiltonian models
• Exact dynamics of quantum systems driven by time-varying Hamiltonians: solution for the Bloch-Siegert Hamiltonian and applications to NMR
• Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
• Non-Hermitian Heisenberg representation
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Linear Quantum Entropy and Non-Hermitian Hamiltonians
• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla
• Chiral Bell-state transfer via dissipative Liouvillian dynamics
• Nonlinear extension of the quantum dynamical semigroup
• Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides
• Non-Hermitian Chiral Magnetic Effect in Equilibrium
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• Sustainability of environment-assisted energy transfer in quantum photobiological complexes
• Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators
• Simple but accurate estimation of light-matter coupling strength and optical loss for a molecular emitter coupled with photonic modes
• Embedding quantum systems with a non-conserved probability in classical environments
• Spin-chain-star systems: entangling multiple chains of spin qubits
• Unified entropies and quantum speed limits for nonunitary dynamics
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature
• Temporal correlation beyond quantum bounds in non-hermitian dynamics
• Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble
• Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
• Non-Hermitian Model for Asymmetrical Tunneling
• Expectation value dynamics within real Hilbert space quantum mechanics
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• A comparative study on different non-Hermitian approaches for modeling open quantum systems
• Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay
• Dynamics of mode entanglement in a system of cavities coupled with a chiral mirror
• Non-Markovian Light-Matter Dynamics in the Time Fractional Jaynes-Cummings Model with Modulated Coupling
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Clock frequency estimation under spontaneous emission
• Mixedness timescale in non-Hermitian quantum systems
• Density operator approach to turbulent flows in plasma and atmospheric fluids
• Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme
• Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
• Quantum Speed Limits Based on the Sharma-Mittal Entropy
• Environment-assisted squeezing in a coherently driven non-Hermitian degenerate parametric oscillator