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.>
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature
Tcr the thermal fluctuations of the Josephson phase induce such a switching, and as
T<Tcr the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature
Tcr between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux
Φ. Beyond that we predict a narrow peak in the dependence of
Tcr(Φ) occurring in the intermediate range of
Φ. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
A macroscopic variable, the phase difference across a Josephson junction, is shown to obey quantum mechanics by observing the phenomena of energy-level quantization and quantum tunneling.The relevant parameters of the junction were determined .!.!! .ill!:!, in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves.The first observation of quantized energy levels for this system is reported.The positions of these energy levels are in quantitative agreement with the quantum mechanical predictions based on the measured junction parameters.A model is presented that predicts correctly the observed resonance shapes.The measured value of the escape rate out of the zero-voltage state for an underdamped (Q -30) junction was found to be independent of temperature at low temperatures.This low temperature escape rate was in excellent agreement with the prediction for macroscopic quantum tunneling, with no adjustable parameters.Jolw rJt..
The escape rate from the zero voltage state in a superconducting Josephson junction (JJ) is determined by the temperature, but it saturates at low temperature due to macroscopic quantum tunneling (MQT). Complications due to d-wave symmetry in a high temperature superconductor, like low energy quasiparticles and an unconventional current-phase relation, may influence the escape rate. We report, for the first time to our knowledge, the observation of MQT in a YBa(2)Cu(3)O(7-delta) grain boundary biepitaxial JJ. This proves that dissipation can be significantly reduced by a proper junction configuration, which is of significance for quantum coherence.
We employ a functional integral technique to calculate the macroscopic quantum tunneling rate at zero temperature of a current-biased Josephson junction weakly coupled to a resonator. We allow for the effects of environmental dissipation on both the junction and the resonator via baths of harmonic oscillators, and we consider both cases of weak and strong junction damping. The resonator can be, in principle, any quantum harmonic oscillator that couples to the junction bilinearly in either the coordinate or the velocity. The Josephson phase difference $\ensuremath{\phi}$ is the tunneling variable in this system, and the low-lying bound states in the junction's potential energy well are weakly metastable due to tunneling through a finite-width energy barrier. There has been some interest in using such biased junctions as qubits with the resonator providing multiqubit coupling. The main result of this work is that coupling to the resonator has a suppressive effect on the junction's tunneling: the stronger the coupling strength between the junction and resonator, the greater the reduction of the tunneling rate. Including damping to the junction also suppresses tunneling, a well-known result, but damping of the resonator actually reduces the magnitude of suppression; i.e., damping the resonator partially counteracts the suppression provided directly by the junction-resonator coupling. Details of the junction-resonator coupling yield interesting variations on this theme that may be useful for qubit design. For example, the coupling
Uint between a current-biased junction and an AlN dilatational resonator should depend on the angular frequency of the resonator ${\ensuremath{\omega}}_{R}$ in a power-law fashion [A. N. Cleland and M. R. Geller, Phys. Rev. Lett. 93, 070501 (2004)], specifically ${U}_{\mathit{int}}\ensuremath{\propto}{({\ensuremath{\omega}}_{R})}^{n}$, where
n=1∕2. We find that for any value of
n in the range
0<n<1 the junction's tunneling rate exhibits a nonmonotonic dependence on ${\ensuremath{\omega}}_{R}$, and for
n=1∕2, the tunneling rate is maximally suppressed for ${\ensuremath{\omega}}_{R}∕{\ensuremath{\omega}}_{J}\ensuremath{\approx}1$, where ${\ensuremath{\omega}}_{J}$ is the bias current-dependent plasma frequency of the junction.