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The European Physical Journal B

Decoherence and entanglement in coherent quantum tunneling of magnetization with dissipation

Yi-Hang Nie, J.-Q. Liang, Yunlong Shi, J.-Q. Liang

Published Jan 1, 2005• 3 citations
Publisher
DOI
10.1140/epjb/e2005-00035-5

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Single molecule magnets are novel mesoscopic materials exhibiting both classical and quantum properties. Revealing the decoherence and entanglement mechanisms in these systems is crucial for the applications in quantum information technologies. In this thesis, quantum tunneling of magnetization is studied in single molecule magnet dimer [Mn4]2. Motivated by the recent experiments demanding the modification of the current theories, phonon mediated spin bath decoherence model is proposed. In the first part of the thesis, the magnetization of the [Mn4]2 dimer under external magnetic field is investigated. Alternative entangled spin states involved in quantum tunnelings are identified by means of the exact solution of the Schrödinger equation and the Landau-Zener-Stückelberg method. Later, a decoherence model is introduced in which the interaction between the single molecule magnet (central spin) and spin bath is mediated by phonons in a coherent state or thermal distribution. It is observed that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times for coherent states and low temperature thermal distribution. In the former case, if the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important role in decoherence with increasing temperature. Possible effects of the temperature on spin bath contribution to decoherence is discussed. Then, the effect of entangled environment on decoherence is analyzed. Entanglement within environment is shown to reduce the decoherence of central spin. Also, the entanglement dynamics of the central bipartite spin system is studied. Classification of the Bell states is examined for common spin bath, and separate spin baths. Last part of the thesis is the analysis of dephasing in entangled qutrits (three level quantum systems) under the classical noise, and quantum decoherence. Density matrix formalism is shown to give equivalent results for both cases. For common and separate baths, robust and fragile Bell-like qutrit states were determined, and Horodecki's bound entangled state is shown to be more robust to decoherence in the latter case.

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We analyze the effects of the environment on the spin tunneling process of paramagnetic and superparamagnetic particles and conclude that the “bare” macroscopic tunneling rate is hardly affected in such case, but other more effective processes come up to change the magnetization state of the particle. We measure the degree of coherence loss by the linear entropy which will account for all correlations present in the process. We conclude that for both paramagnetic and superparamagnetic particles, the decoherence time scale is extremely short (~10 -8 ... -16 s), indicating that coherent tunneling should be strongly suppressed in favor of incoherent tunneling, i.e., the population of higher levels with subsequent decay. Interestingly enough, the ground state tunneling rate is hardly affected by such dissipative mechanisms. However other processes immediately give rise to new (incoherent) possibilities of crossing the barrier.

arXiv:quant-ph/0304185•Physica Scripta•Jan 1, 2005•0 citations
Single molecule magnets are novel mesoscopic materials exhibiting both classical and quantum properties. Revealing the decoherence and entanglement mechanisms in these systems is crucial for the applications in quantum information technologies. In this thesis, quantum tunneling of magnetization is studied in single molecule magnet dimer [Mn4]2. Motivated by the recent experiments demanding the modification of the current theories, phonon mediated spin bath decoherence model is proposed. In the first part of the thesis, the magnetization of the [Mn4]2 dimer under external magnetic field is investigated. Alternative entangled spin states involved in quantum tunnelings are identified by means of the exact solution of the Schrödinger equation and the Landau-Zener-Stückelberg method. Later, a decoherence model is introduced in which the interaction between the single molecule magnet (central spin) and spin bath is mediated by phonons in a coherent state or thermal distribution. It is observed that the decoherence factor decays in a Gaussian fashion and it becomes independent of the phonon frequencies at short times for coherent states and low temperature thermal distribution. In the former case, if the phonon energies are much larger than spin-phonon coupling or bath spins are fully polarized, decoherence time becomes independent of the initial phonon state. For the thermal state case, phonons play more important role in decoherence with increasing temperature. Possible effects of the temperature on spin bath contribution to decoherence is discussed. Then, the effect of entangled environment on decoherence is analyzed. Entanglement within environment is shown to reduce the decoherence of central spin. Also, the entanglement dynamics of the central bipartite spin system is studied. Classification of the Bell states is examined for common spin bath, and separate spin baths. Last part of the thesis is the analysis of dephasing in entangled qutrits (three level quantum systems) under the classical noise, and quantum decoherence. Density matrix formalism is shown to give equivalent results for both cases. For common and separate baths, robust and fragile Bell-like qutrit states were determined, and Horodecki's bound entangled state is shown to be more robust to decoherence in the latter case.
A novel quantum dynamical model based on the dissipative quantum dynamics of open quantum systems is presented. It allows the treatment of both deep‐inelastic processes and quantum tunneling (fusion) within a fully quantum mechanical coupled‐channels approach. Model calculations show the transition from pure state (coherent) to mixed state (decoherent and dissipative) dynamics during a near‐barrier nuclear collision. Energy dissipation, due to irreversible decay of giant‐dipole excitations of the interacting nuclei, results in hindrance of quantum tunneling.
We analyze the effects of the environment on the spin tunneling process of paramagnetic and superparamagnetic particles and conclude that the “bare” macroscopic tunneling rate is hardly affected in such case, but other more effective processes come up to change the magnetization state of the particle. We measure the degree of coherence loss by the linear entropy which will account for all correlations present in the process. We conclude that for both paramagnetic and superparamagnetic particles, the decoherence time scale is extremely short (~10 -8 ... -16 s), indicating that coherent tunneling should be strongly suppressed in favor of incoherent tunneling, i.e., the population of higher levels with subsequent decay. Interestingly enough, the ground state tunneling rate is hardly affected by such dissipative mechanisms. However other processes immediately give rise to new (incoherent) possibilities of crossing the barrier.