Quantum Tunneling of Magnetization in Small Ferromagnetic Particles

Chudnovsky, Eugene M.; Gunther, Leon

doi:10.1103/physrevlett.60.661

Cited by 588 publications

(357 citation statements)

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“…In the area of magnetic nano-particles, a notion of an effective temperature greater than the temperature of the environment was advocated in Ref. [74] and it would be interesting to explore the connection with effective temperature defined in this paper.…”

Section: Discussionmentioning

confidence: 99%

Real-time nonequilibrium dynamics of quantum glassy systems

1999

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We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the p spin-glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely aging, survives the quantum fluctuations. In the sub-critical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin-glasses and the relevance of the effective temperatures with respect to the understanding of the low temperature dynamics.

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Section: Discussionmentioning

confidence: 99%

Real-time nonequilibrium dynamics of quantum glassy systems

1999

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“…From the theoretical point of view, spin tunneling has been treated mainly by the use of a WKB method adapted to spin systems [9,10], by using Feyman's path integral treatment of quantum mechanics [11,12], and also by using su(2) coherent states [13] in order to establish a correspondence between the spectrum of the spin system with the energy levels of a particle moving in an effective potential [14].…”

Section: Introductionmentioning

confidence: 99%

Quantum description of spin tunneling in magnetic molecules

Galetti

2007

Physica A: Statistical Mechanics and its Applications

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Abstract.A new approach is used that allows to describe the magnetic molecules main properties in a direct and simple way. Results obtained for the F e 8 cluster show good agreement with the experimental data.PACS numbers: 03.65. Ca, 75.45+j, 75.60Jp Submitted to: J. Phys. C: Solid State Phys.In recent years, with the experimental advances in the measurement of magnetic molecular clusters properties, it has emerged a new frontier in this area. One of the interesting aspects that came out of these studies is the possibility of measuring spin tunneling in mesoscopic systems what corresponds, in a standard quantum description, to the tunneling of the collective degree of freedom corresponding to the magnetization direction through a potential barrier separating two minima of an effective potential associated with the spatial orientation [1,2,3,4,5,6,7,8].From the theoretical point of view, spin tunneling has been treated mainly by the use of a WKB method adapted to spin systems [9,10], by using Feyman's path integral treatment of quantum mechanics [11,12], and also by using su(2) coherent states [13] in order to establish a correspondence between the spectrum of the spin system with the energy levels of a particle moving in an effective potential [14].In the present letter we intend to show that still another approach may be used for describing spin tunneling -in angle representation -in such a way that analytic expressions for the characteristic parameters of the magnetic molecular clusters can be obtained; in particular, the results for the spectrum and energy barrier heights are directly obtained and the spin tunneling process can be easily interpreted.The starting point of the present approach is the introduction of a quantum phenomenological Hamiltonian describing the spin system, written in terms of angular momentum operators obeying the standard commutation relations, and that reflects

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“…Contrary to [20] the present algorithm simulates the quantum dynamics with mixed (chaotic/integrable) classical phase space and is optimal for the investigation of chaos-assisted tunneling in semiclassical regime. Indeed, while for MQT in molecular magnets [4,5,22] the effective Planck constanth is inversely proportional to the number of spins (h ∝ 1/n q ) in our algorithmh ∝ 2 −nq . Hence with only 10 qubits the algorithm allows to study MQT with the semiclassical parameter being larger by almost two orders of magnitude.…”

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confidence: 99%

Simulation of chaos-assisted tunneling in a semiclassical regime on existing quantum computers

Chepelianskii

Shepelyansky

2002

Phys. Rev. A

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We present a quantum algorithm which allows to simulate chaos-assisted tunneling in deep semiclassical regime on existing quantum computers. This opens new possibilities for investigation of macroscopic quantum tunneling and realization of semiclassical Schrödinger cat oscillations. Our numerical studies determine the decoherence rate induced by noisy gates for these oscillations and propose a suitable parameter regime for their experimental implementation.PACS numbers: 03.67. Lx, 05.45.Mt, 75.45.+j Since 1935 until recently, the metaphor of Schrödinger cat oscillations between life and death [1] was considered as a purely theoretical concept. However, during the last decade such oscillations in a quantum limit were observed for two states of a Rydberg atom in a quantum cavity [2] and an experimental evidence was presented for a quantum superposition of macroscopically distinct states in a superconducting quantum interference device (SQUID) [3]. Manifestations of macroscopic quantum tunneling (MQT) were also observed in magnetization experiments with spin-ten molecular magnets F e 8 and M n 12 [4,5]. In addition to their fundamental interest these experiments promise to provide important applications, e.g. for solid-state qubit realization [6] and information storage [7] based on the Grover algorithm [8].The regime discussed in [1] assumes that the quantum tunneling takes place for a semiclassical object with a regular dynamics in two symmetric regions of phase space. Recently, the investigations of quantum chaos led to an extension of this concept to the phenomenon of chaos-assisted tunneling between islands of regular integrable dynamics separated by a chaotic sea [9]. In this case, due to chaos the period T u of tunneling oscillations becomes very sensitive to the variation of system parameters and statistical description should be used to describe the average distribution of T u [9][10][11]. This unusual tunneling is strongly influenced by complex instanton orbits and scarring effects [10,11] and a chaos enhancement of tunneling rate by orders of magnitude may be reached by a small variation of parameters. The first direct experimental observations of the chaos-assisted tunneling have been realized recently with cold [12] and ultracold atoms from a Bose-Einstein condensate [13] thus opening new possibilities for investigation of this interesting process. However, quantum tunneling is a very sensitive phenomenon and experimental studies are complicated by the decoherence produced by the environment. Due to that theoretical investigations of decoherence effects on MQT were initiated from the very beginning [14,15] and are continued up to now [16,17].In this Letter, we show that quantum entanglement and quantum computer simulations [18] can be efficiently used to study quantum tunneling in deep semiclassical regime. We illustrate this on the example of a quantum symplectic map (double well map) which has a rich phase space structure with integrable islands surrounded by chaotic sea. Our algorithm has certain...

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Quantum Tunneling of Magnetization in Small Ferromagnetic Particles

Cited by 588 publications

References 13 publications

Real-time nonequilibrium dynamics of quantum glassy systems

Real-time nonequilibrium dynamics of quantum glassy systems

Quantum description of spin tunneling in magnetic molecules

Simulation of chaos-assisted tunneling in a semiclassical regime on existing quantum computers

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