Mesoscopic systems: classical irreversibility and quantum coherence

Abstract

Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn 12 -ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V 15 , the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of twolevel systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce t 1 -like relaxation of S z with dissipation to the bath of two-level systems with which they interact most. Finally, let us mention that these experiments on quantum oscillations are, most of the time, performed in the classical regime of Rabi oscillations, suggesting that decoherence mechanisms might also be treated classically.

Quantum Stoner-Wohlfarth Model

“…Jm, 75.45.+j, 75.50.Xx, 75.60.Jk We study the reversal of a uniaxial magnet of spin S submitted to a fixed transverse field and a longitudinal sweeping field. This model had been studied for single-molecule magnets with moderate spins S=10, in which the Landau-Zener (LZ) transition plays an important role [1][2][3][4][5]. Some years ago, the parent model of an Ising spin-chain with ferromagnetic interactions and same longitudinal and transverse fields showed a quantum spinodal phase transition where a size (spin-chain length)-independent magnetization decay was observed and attributed to independent single-spin reversals [6].In this letter, we study the quantum aspects of the Stoner-Wohlfarth (SW) transition, and more particularly the relations between the quantum dynamics and classical irreversibility of a large quantum spin S in a uniaxial anisotropy broken by a transverse field, and submitted to a sweeping longitudinal field at zero Kelvin.…”

“…We study the reversal of a uniaxial magnet of spin S submitted to a fixed transverse field and a longitudinal sweeping field. This model had been studied for single-molecule magnets with moderate spins S=10, in which the Landau-Zener (LZ) transition plays an important role [1][2][3][4][5]. Some years ago, the parent model of an Ising spin-chain with ferromagnetic interactions and same longitudinal and transverse fields showed a quantum spinodal phase transition where a size (spin-chain length)-independent magnetization decay was observed and attributed to independent single-spin reversals [6].…”

Decoherence

“…Barbara [5], an experimentalist in mesoscopic physics, reviews the current state of tunnelling experiments in large spin systems, and discusses the origin of hysteresis and of decoherence in those systems. He shows why the classical and quantum dynamics of an effective spin 1/2 are the same, and how the Landau-Zener model can be treated classically.…”

“…The paper takes its cue from a model, proposed by Diosi, for reconciling classical gravitation with quantum dynamics, and shows that similar models arise when an open quantum system is used as a classical controller for another target quantum system. Barbara [5], an experimentalist in mesoscopic physics, reviews the current state of tunnelling experiments in large spin systems, and discusses the origin of hysteresis and of decoherence in those systems. He shows why the classical and quantum dynamics of an effective spin 1/2 are the same, and how the LandauZener model can be treated classically.…”

Distribution of eigenstate populations and dissipative beating dynamics in uniaxial single-spin magnets

“…Various quantum effects have been reported in both single-molecule and single-spin magnets. One of the significant quantum effects is the stepwise magnetization process in hysteresis of blocked magnetization at low temperatures, in which quantum tunneling between the states with magnetizations in opposite directions plays an important role 7,8 . This phenomenon is understood as a quantum hybridization of discrete opposite magnetization energy levels forming an avoided level crossing.…”