Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice

Abstract

The decay rate of an interstitial two-level spin impurity, located in the center of a unit cell of an anisotropic ferromagnetic lattice subjected to an external magnetic field is derived. The impurity is coupled to nearest-neighbor spins through Heisenberg $XY$ interaction. By mapping the lattice spin operators using the Holstein-Primakoff transformation, we establish the similarity with the Fano-Anderson model at low temperatures, and we calculate the retarded Green's function in one and two dimensions analytically for arbitrary coupling strength. It is shown that the reduced density matrix of the impurity satisfies an exact master equation in Lindblad form, from which the decay rate and the Lamb shift are deduced. The evolution in time of the latter together with the excited state occupation probability is investigated and its dependence on the applied magnetic field is discussed. It is found that there exists a critical resonance-like value of the magnetic field around which the behavior of the decay rate and the density matrix changes drastically. The Markovian decay law, as given by the Fermi golden rule, does not hold in the weak-coupling regime unless the magnetic field is weak, typically less than the critical value. The weak-coupling regime is further treated perturbatively up to second order, and the obtained results are compared with the exact solution. We also discuss the Zeno regime of the dynamics, where it is shown that at short times, the effective decay rate is twice as small as the exact decay rate, and that when the impurity energy lies outside the lattice continuum, the measurement speeds up the decay of the survival probability.

arXiv comment18 pages, close to the published version

References in corpus (44)

• Quantum Computation with Quantum Dots
• Decoherence, einselection, and the quantum origins of the classical
• Coupled quantum dots as quantum gates
• Conditional Quantum Dynamics and Logic Gates
• Electron spin decoherence in quantum dots due to interaction with nuclei
• Implementation of a Quantum Search Algorithm on a Nuclear Magnetic Resonance Quantum Computer
• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Observation of the Quantum Zeno and Anti-Zeno effects in an unstable system
• Quantum Zeno dynamics: mathematical and physical aspects
• Open system dynamics with non-Markovian quantum trajectories
• General non-Markovian dynamics of open quantum systems
• From the quantum Zeno to the inverse quantum Zeno effect
• Non-Markovian quantum jumps
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Quantum electrodynamics near a photonic band-gap
• Temporal behavior of quantum mechanical systems
• Universal many-body response of heavy impurities coupled to a Fermi sea
• Continuous and Pulsed Quantum Zeno Effect
• Quantum Computers and Quantum Coherence
• Quantum Zeno and Anti-Zeno Effect without Rotating Wave Approximation
• Open system dynamics with non-Markovian quantum jumps
• Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect
• Bound states in boson impurity models
• Zeno effect for quantum computation and control
• Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Two qubits entanglement dynamics in a symmetry-broken environment
• Quantum spin dynamics of individual neutral impurities coupled to a Bose-Einstein condensate
• Nonanalytic enhancement of the charge transfer from adatom to one-dimensional semiconductor superlattice and optical absorption spectrum
• Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium
• Quantum Zeno and anti-Zeno effects in quantum dissipative systems
• Fermi golden rule beyond the Zeno regime
• Zeno and anti-Zeno dynamics in spin-bath models
• Criterion for quantum Zeno and anti-Zeno effects
• Strongly Coupled Matter-Field and Non-Analytic Decay Rate of Dipole Molecules in a Waveguide
• Entanglement dynamics of one-dimensional driven spin systems in time-varying magnetic fields
• Exactly solvable model for the dynamics of two spin-1/2 particles embedded in separate spin star environments
• Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction
• Dissipative dynamics and cooling rates of trapped impurity atoms immersed in a reservoir gas
• Bosonic Josephson effect in the Fano-Anderson model
• On the partial trace over collective spin-degrees of freedom
• Impurity coupled to a lattice with disorder
• A nontrivial bosonic representation of large spin systems at high temperatures
• Non-Hermitian interaction of a discrete state with a continuum