Resonant Quantum Tunneling Research Articles

Local field dynamics in a resonant quantum tunneling system of magnetic molecules

We observed non-exponential relaxation for a quantum tunneling molecular magnetic system at very low temperatures and argue that it results from evolving intermolecular dipole fields. At the very beginning of the relaxation, the magnetization follows a square-root time dependence. A simple model is developed for the intermediate time range that is in good agreement with the data over 4 decades in time. Detailed numerical calculations as well as measurements are presented which indicate unusual correlation effects in these systems.

Quantum hysteresis and resonant tunneling in bistable systems

The decay rates of damped bistable quantum systems show at low temperatures multi-resonant behavior as a function of an external bias. These resonances are connected with steps in the response of the double well system to strong external forcing and to steps in the hysteresis loop when the strong forcing is periodic. Both of these phenomena have been observed in different experiments. We provide a unified theoretical scheme and a streamlined computational analysis for their explanation.

The principle of detailed balance and the Lindblad dissipative quantum dynamics

It is shown that by incorporating the principle of detailed balance in the Lindblad dissipative quantum dynamics of the density matrix, the approach to thermal equilibrium not assured in the original formulation of this theory, can be realized. Three examples of current interest illustrate the general formalism. From the last example, we deduce for a low-power InAs HEMT device of about a tenth of a micron size, having the following estimates provided by Dr. W. Kruppa of our Laboratory, R ∼ 5 Ω, L ∼ 0.1 nH, and C ∼ 0.1 pF, the decoherence time ∼ 80 ps. Typical tunneling times in a resonant tunneling quantum device is about 0.1 ps, well below the decoherence time estimated above. With this crude estimate, we may conclude that picosecond regimes are clasical, while below that, we have quantum regimes.

Resonant magnetic quantum tunneling through thermally activated states

A theory of the magnetic relaxation of a large spin (S=10) having a large uniaxial magnetocrystalline anisotropy is outlined. The theory explains magnetic relaxation observed in Mn12 acetate. The joint action of local fields and a fourth order distortion of the magnetocrystalline anisotropy is necessary to account for the tunneling that is observed, between the m=−4 and m=4 unperturbed states. Even in resonance, tunneling takes place mainly incoherently in Mn12 acetate. It proceeds through the lowest energy state doublet which is not blocked by longitudinal local fields. The relaxation rate Γ has been calculated using a master equation. The model gives magnetization hysteresis loops and ac magnetic susceptibility curves which are in quantitative agreement with experimental results. For temperatures below 0.5 K approximately, nonresonant tunneling from the ground state becomes the dominant relaxation mechanism.

Experimental evidence of macroscopic resonant tunneling of magnetization in antiferromagnetic ferritin

Macroscopic resonant quantum tunneling of magnetization has been observed in antiferromagnetic ferritin particles. The dependence of magnetic viscosity on the applied magnetic field has been systematically investigated in the temperature range 1.8–10 K. The zero maximum in field dependence of viscosity and the maximum in the field dependent blocking temperature are interpreted to be due to the resonant spin tunneling between matching spin levels.

Resonant quantum tunnelling and coherence of the Néel vector for different crystal symmetries

The phenomena of macroscopic quantum tunnelling and coherence of the Néel vector are investigated for small single-domain antiferromagnetic particles. Both the Wentzel-Kramers-Brillouin exponents and the pre-exponential factors are found exactly for the tunnelling rates, for various forms of the magnetocrystalline anisotropy. The calculations are performed on the basis of the two-sublattice model and the instanton method applied to the spin-coherent-state path integral.

Resonant magnetic quantum tunneling through thermally activated states

We present a theory of resonant quantum tunneling of large spins through thermally activated states. It gives numerical results that are in good agreement with data from recent magnetic quantum tunneling experiments in Mn acetate. We show that neither dipolar fields nor crystal-field perturbations, acting separately, can account for the resonances observed. However, we find that these two perturbations acting jointly produce a highly nonlinear effect that enhances tunneling rates up to their observed values. Resonant tunneling through low-lying energy-state pairs is blocked. We show that the tunneling frequency ${\ensuremath{\omega}}_{T}$ and the lifetime ${\ensuremath{\tau}}_{0}$ of the thermally populated pairs of states through which tunneling proceeds fulfils ${\ensuremath{\omega}}_{T}{\ensuremath{\tau}}_{0}\ensuremath{\gg}1$. A superposition of these two states becomes incoherent approximately in time $1/{\ensuremath{\omega}}_{T}.$ Using the master equation that follows, and spin-phonon-induced transition rates that we calculate, we obtain relaxation rates and magnetization hysteresis curves that agree reasonably well with experiment.

Considerations on resonant macroscopic quantum tunneling in SQUID systems

We present a theoretical analysis of the resonant macroscopic quantum tunneling in SQUID systems including the effect of both the temperature and the sweeping rate of the external flux, and the study of the phenomenon both in quasi-stationary and non-stationary conditions. We have found a very good agreement in the comparison of our results with the experimental data.

Metastable states in classical and quantum systems

The classical vibrational metastable states in a one-dimensional two-mass system are investigated experimentally and theoretically via the transmission of a coherent wave packet propagating through the system. The Fourier transform of the vibrational signal recorded in between the masses reveals resonant excitations by the coherent wave packet. The time-resolved spectrum indicates that the lifetime of a metastable state of higher frequency is longer than that of lower frequency, which is in contrast with the quantum mechanical double-barrier system. This study, which is easily accessible to physics majors, also demonstrates quantum resonant tunneling in a very simple classical way.

Effects of evanescent modes and subband mixing in resonant tunneling transistors

We theoretically investigate a gated resonant tunneling diode as a potential new quantum resonant tunneling transistor. The resonant tunneling transistor is dimensionally controllable in the active channel using a lateral depletion region. Under bias conditions in which the resonant tunneling transistor reaches zero dimensionality in the well region, we consider the attractive and repulsive perturbation potentials (Vpe) of impurity or defect scattering in source and well regions. A transfer matrix formalism is employed to calculate the transmission probabilities and current densities through the double barrier, and we describe the scattering matrices using the presence of evanescent modes in various lateral confinement configurations. We discuss the effect of scattering and subband mixing on the current-voltage characteristics of resonant tunneling transistors.

Thermally assisted macroscopic quantum resonance on a single-crystal of Mn12-acetate

Magnetization measurements have been performed on a single monocrystal of the molecule Mn12-acetate (Mn12Ac). Steps were observed in the hysteresis loop for values of the applied field at which level crossings of the collective spin states of each manganese clusters take place. At these fields, the magnetization relaxes at short time scales, being otherwise essentially blocked. This novel behavior is interpreted in terms of resonant quantum tunneling of the magnetization from thermally activated energy levels. Hysteresis loop measurements performed for different field orientations and alternating current (ac) susceptibility experiments confirm this picture.

Resonant coherent quantum tunneling of the magnetization of spin- systems: Spin-parity effects

We perform quantum dynamical calculations to study the reversal of the magnetization for systems of a few spin- particles with a general biaxial anisotropy in the presence of an external magnetic field at T=0 and with no dissipation. Collective quantum tunneling of the magnetization is demonstrated to occur only for some specific resonant values of the magnetic field proving the invalidity of semiclassical approximations for clusters of a few spin- particles. Quantum tunneling of the magnetization direction at zero field is shown to be spin-parity dependent: whereas clusters with an odd number of particles do not exhibit quantum tunneling of the magnetization due to the degeneration between the first two levels, clusters with an even number of spins present resonant coherent quantum tunneling of the magnetization. On the contrary, resonant coherent quantum tunneling of the magnetization at finite magnetic field has no detectable parity dependence. We study the dependence of such collective tunneling of the magnetization on the magnetic field, the number of spins, and the anisotropy.

Implications of the intrinsic decoherence in quantum mechanics to nonequilibrium statistical mechanics.

The discrete-time jump model for intrinsic decoherence in quantum mechanics proposed recently by Milburn is here generalized to explicitly time-dependent Hamiltonians. In this model, a time-dependent entropy is obtained and thus it admits of an interpretation that this is a model for an open system. Unlike in the Milburn model, we introduce a minimum uncertainty phase change dictated by the minimum ``time-energy uncertainty product'' to define the shortest time scale in the system. Implications of this model to quantum nanometric devices such as quantum dots or resonant tunneling devices are indicated. \textcopyright{} 1996 The American Physical Society.

Resonant macroscopic quantum tunneling in SQUID systems.

A detailed theoretical analysis of the resonant macroscopic quantum tunneling in superconducting quantum interference device systems is presented. Our approach allows us to include the effect of both temperature and sweeping rate of the external flux, and to study the phenomenon both in quasistationary and nonstationary conditions, which can be induced by a fast sweep of the external bias. Moreover we compare our theory with the experimental data of Rouse, Han, and Lukens [Phys. Rev. Lett. {bold 75}, 1614 (1995)] referring to the quasistationary case, while other observable effects are predicted in the nonstationary case. {copyright} {ital 1996 The American Physical Society.}

Phase rigidity and h/2e oscillations in a single-ring Aharonov-Bohm experiment.

We address the results presented recently by Yacoby et al. [Phys. Rev. Lett. 74, 4047 (1995)] on the coherency and phase evolution in a resonant tunneling quantum dot embedded in an Aharonov-Bohm (AB) ring. The observed phase rigidity of the AB conductance oscillations is theoretically explained by invoking simple symmetry arguments applicable to two terminal measurements, and is corroborated experimentally in generic experiments. We show that under certain conditions h/2e oscillations dominate completely the conductance of a single AB ring. \textcopyright{} 1996 The American Physical Society.

Resonant macroscopic quantum tunneling in SQUID systems: Theoretical fitting of experimental data

A theoretical model for the effects of resonant macroscopic quantum tunneling in SQUID systems is presented. This allows us to make for the first time a comparison of theory with experiment.

Resonant macroscopic quantum tunneling in small Josephson junctions: Effect of temperature.

Within the well-established quantum picture of Josephson junctions, we study the possibility of resonant macroscopic quantum tunneling. Expressions for the lifetime of metastable states are obtained and the effects of temperature on the main features of the phenomenon are discussed. A "saturation temperature" for the process, below which any temperature effect is negligible, is identified. Quantitative considerations are also given on the actual experimental accessibility to these measurements.

Quantum dynamical calculations on the magnetization reversal in clusters of spin-1/2 particles: Resonant coherent quantum tunneling.

In the present work the reversal of magnetization and the coherence of tunneling when an external magnetic field is rotated instantaneously are studied in systems of a few spin-1/2 particles described by an anisotropic Heisenberg Hamiltonian at T=0. Our calculations demonstrate that this model for small magnetic particles exhibits collective tunneling of the magnetization only for some specific resonant values of the applied magnetic field. These resonant effects occur at fields much lower than the values corresponding to the vanishing of the barrier in the Stoner-Wohlfarth model. The former model is at variance with the exact calculations presented in this paper. \textcopyright{} 1996 The American Physical Society.

Effect of temperature on the resonant macroscopic quantum tunneling in small Josephson junctions

The study of the quantum behaviour of Josephson junctions is interesting not only by itself, but also for the technological importance in electronics employing superconducting weak links. Recently great attention has been devoted to the effects of Resonant Macroscopic Quantum Tunneling (RMQT) between levels the same energy in neighbouring wells of the potential shape describing the junction. This can produce voltage spikes along the supercurrent branch of the I-V curves and peaks in the current switching distributions. Schmidt, Clealand, and Clarke have presented a detailed analysis of the resonant tunnel dynamics for the T=0 case. The present paper is based on a different theoretical approach, first proposed by Larkin and Ovchinnikov, which allows one to include explicitly the temperature. We study the phenomenon in its time dependence and this allows us to consider the lifetime of the voltage spikes as well as the effect of the RMQT on the quantum escape rate out of the V=0 state.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Aspects of macroscopic quantum tunnelling in small Josephson junctions

We study the effect of temperature on the lifetime of the resonant macroscopic quantum tunnelling voltage state. In view of experiments we consider a merit factor in order to balance between measuring extremely small signals of longer duration or larger signals of shorter duration.