Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model

Abstract

We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the Effective Hamiltonian together with a new decoherence term which should in general be included, and whose vanishing provides the criteria for validity of the Effective Hamiltonian approach. Finally, we apply the theory to examples of the AC Stark Shift and Three- Level Raman Transitions, recovering a new decoherence effect in the latter.

7 pages, 2 figures

References in corpus (3)

• Effective Hamiltonian Theory and Its Applications in Quantum Information
• Effective spin systems in coupled micro-cavities
• Analysis of quantum semigroups with GKS--Lindblad generators II. General

Cited by in corpus (59)

• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Building a fault-tolerant quantum computer using concatenated cat codes
• Effective operator formalism for open quantum systems
• Exponentially-Enhanced Light-Matter Interaction, Cooperativities, and Steady-State Entanglement Using Parametric Amplification
• Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism
• Mechanism of decoherence-free coupling between giant atoms
• Error-transparent operations on a logical qubit protected by quantum error correction
• Generating Large Cats with Nine Lives: Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles
• Emission of photon pairs by mechanical stimulation of the squeezed vacuum
• Quantum resources for hybrid communication via qubit-oscillator states
• Interaction of Mechanical Oscillators Mediated by the Exchange of Virtual Photon Pairs
• Generalized James' effective Hamiltonian method
• A proposal for a scalable universal bosonic simulator using individually trapped ions
• Quantum properties and dynamics of X states
• Strong Spin Squeezing Induced by Weak Squeezing of Light inside a Cavity
• Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay
• Proposal to Test Quantum Wave-Particle Superposition on Massive Mechanical Resonators
• One bound to rule them all: from Adiabatic to Zeno
• Dipole-dipole interaction driven antiblockade of two Rydberg atoms
• Signatures of the $A^2$ term in ultrastrongly-coupled oscillators
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops
• Slicing the Fock space for state production and protection
• Steady Fock states via atomic reservoir
• Reconstructing the quantum state of oscillator networks with a single qubit
• Coherently opening a high-Q cavity
• Exponentially Improved Dispersive Qubit Readout with Squeezed Light
• Steady entanglements in bosonic dissipative networks
• Enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect
• Atom-mediated effective interactions between modes of a bimodal cavity
• Input-output Gaussian channels: theory and application
• Quantum phase transition of light in a 1-D photon-hopping-controllable resonator array
• Squeezing of mechanical motion via qubit-assisted control
• Affecting Non-Markovian behaviour by changing bath structures
• Analysis of spin-squeezing generation in cavity-coupled atomic ensembles with continuous measurements
• Logical measurement-based quantum computation in circuit-QED
• Quantum sensing of the phase space displacement parameters using a single trapped ion
• Geometric entangling gates for coupled cavity system in decoherence-free subspaces
• Distributing entangled state using quantum repeater protocol: Trapped atomic ions in optomechanical cavities
• Quantum repeater protocol using an arrangement of QED-optomechanical hybrid systems
• Upper-bounded and sliced Jaynes- and anti-Jaynes-Cummings Hamiltonians and Liouvillians in cavity quantum electrodynamics
• Linear Mode-Mixing of Phonons with Trapped Ions
• Theory of double Cooper-pair tunneling and light emission mediated by a resonator
• Scalable nuclear-spin entanglement mediated by a mechanical oscillator
• Effective Formalism for Open Quantum System Dynamics: Time-coarse-graining Approach
• The superconducting circuit companion -- an introduction with worked examples
• Proposal of ensemble qubits with two-atom decay
• A Squeezed Vacuum State Laser with Zero Diffusion
• Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model
• Entanglement between uncoupled modes with time-dependent complex frequencies
• GPU-accelerated Effective Hamiltonian Calculator
• Dissipative qutrit-mediated stable charging
• Comment on "Generalized James' Effective Hamiltonian Method"
• Distributed entangled state production by using quantum repeater protocol
• Model Order Reduction for Open Quantum Systems Based on Measurement-adapted Time-coarse Graining
• Unconventional mechanism of virtual-state population through dissipation
• Dissipative cooling induced by pulse perturbations
• Multichromatic Floquet engineering of quantum dissipation
• Characterizing the transition from topology to chaos in a kicked quantum system
• Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout