Evidence of two-dimensional macroscopic quantum tunneling of a current-biased dc SQUID

The escape probability out of the superconducting state of a hysteretic dc SQUID has been measured at different values of the applied magnetic flux. At low temperatures, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional macroscopic quantum tunneling (MQT) law but are perfectly accounted for by the two-dimensional MQT behavior as we propose here. Near zero flux, our data confirms the recent MQT observation in a dc SQUID [Phys. Rev. Lett. 89, 98301 (2002)]].     

One-shot quantum measurement using a hysteretic dc SQUID

We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.     

Quantitative study of macroscopic quantum tunneling in a dc SQUID: a system with two degrees of freedom

To test whether the theory of macroscopic quantum tunneling (MQT) is applicable to systems with 2 degrees of freedom, we experimentally investigated the switching current distribution of a dc SQUID. Using sample parameters determined from measurements at T=4.2 K, we are able to make quantitative comparison to the theories from 8 mK to 4.2 K. The excellent agreement between the data and the MQT theory demonstrates that tunneling from the zero-voltage state of the dc SQUID is well described by the quantum mechanics.     

Macroscopic quantum tunneling of a bose condensate

We study, by means of a variational method, the stability of a condensate in a magnetically trapped atomic Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the critical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropriate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly.     

Macroscopic quantum tunneling in molecular magnets

Our present understanding of the phenomenon of quantum tunneling of magnetization (QTM), is reviewed in the light of the experiments performed on the molecular complex Mn₁₂-ac. This system, in which QTM was clearly shown for the first time, consists of molecules with mesoscopic spins in dipolar interactions. Both single and many-molecule effects are essential for the observation of QTM (crystal field, hyperfine and dipolar interactions), which allows one to make a link between mesoscopic physics and magnetism.     

Macroscopic quantum tunneling in small magnetic particles

Macroscopic quantum tunneling of magnetization in small antiferromagnetic clusters is studied for the spin-1/2 anisotropic (J _z ≡ J, J _x =J _y ≡J _xy ) Heisenberg model with the use of both perturbation theory and an exact numerical diagonalization technique. Splitting of the two lowest levels due to the lifting of the degeneracy between them (in the case J _xy =0) by the in-plane exchange (J _xy ≠ 0) is found to occur in the N/2th order of perturbation theory. Tunneling is absent in systems with an odd number of sites, in which the levels are doubly degenerate in zero magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 688–693 (10 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Macroscopic theory of activated decay of metastable states

The Brownian motion of a particle over a potential barrier, a problem first solved by Kramers, is reexamined also for the case of intermediate friction, to which Kramers' solutions do not apply. The theory is macroscopic and entirely based on the Langevin equation of the particle, but it makes essential use of ideas of a recent microscopic theory of Grabert and of Pollak, Grabert, and Hänggi for a particle coupled to an infinite set of harmonic oscillators. Their result for the escape rate is recovered, but the present method seems more generally applicable. We introduce and use a new theoretical tool-the transformation to a new set of variables mixing the macroscopic and the noise variables of the Langevin equation.     

Macroscopic quantum tunneling in differently loaded Josephson junctions

In relation to the problem of quantum measurement, macroscopic quantum tunneling (MQT) in Josephson junctions is one of the most investigated topics. Although many theoretical studies have been devoted to this argument, the agreement on a single theoretical model has not yet been reached. The purpose of the present work is to analyze the load “seen” by the junction, in order to evaluate the contribution of the dissipation that modifies the decay-rate of the metastable state of the junction. The present work reports some theoretical results in relation to different kinds of loading systems, namely, the cases of capacitive, inductive and purely resistive load. The resistive load is considered also in relation to an experimental test.     

Macroscopic quantum resonance tunneling of domain walls

Results are presented of a theoretical investigation of the tunneling of magnetic domain walls, taking account of the interaction of the walls with the thermal system of the crystal. It is shown that thermal stimulation increases considerably the transmittance of the potential barriers during propagation of walls through a crystal. Fiz. Tverd. Tela (St. Petersburg) 40, 1855–1860 (October 1998)     

Low-temperature relaxation of metastable states and quantum tunneling in antiferromagnets with Ising rare-earth ions: Dysprosium orthoaluminate

The paper reports the first observation of a magnetic relaxation of metastable states in an antiferromagnet (dysprosium orthoaluminate DyAlO₃) at low temperatures in zero magnetic field made by magnetostriction measurements. The metastable states were excited with the heat shock at the transition through the λ point of liquid helium in the course of thermal cycling. A possible mesoscopic mechanism of thermally activated and quantum magnetic relaxation is discussed.     

Macroscopic spin tunneling and quantum critical behavior of a condensate in a double-well potential

In a previous work [H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001)]], we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a twofold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.     

Macroscopic quantum tunneling induced by a spontaneous field in intrinsic Josephson junctions

We theoretically study macroscopic quantum tunneling (MQT) in capacitively coupled Josephson junctions in the case that one of the junctions is in the finite voltage state. We find that the system can be mapped into a one dimensional model with a spontaneous periodic perturbation and calculate the MQT rate by using the time-dependent WKB method. Then the MQT rate is found to be resonantly enhanced and the enhancement of MQT rate is found even off the resonant point.