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arXiv:0901.1723 · Physical Review B

Theory of two-dimensional macroscopic quantum tunneling in YBa2Cu3O7−δ Josephson junctions coupled to an LC circuit

Shiro Kawabata, Thilo Bauch, Takeo Kato

Published Nov 13, 2009• 10 citations
arXivHTMLPDF

Abstract

We investigate classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) Josephson junction coupled to an LC circuit theoretically. Due to the coupling between the junction and the LC circuit, the macroscopic phase dynamics can be described as the escape process of a fictitious particle with an anisotropic mass moving in a two-dimensional potential. We analytically calculate the escape rate including both the TA and MQT regime by taking into account the peculiar dynamical nature of the system. In addtion to large suppression of the MQT rate at zero temperature, we study details of the temperature dependence of the escape rate across a crossover region. These results are in an excellent agreement with recent experimental data for the MQT and TA rate in a YBCO biepitaxial Josephson junction. Therefore the coupling to the LC circuit is essential in understanding the macroscopic quantum dynamics and the qubit operation based on the YBCO biepitaxial Josephson junctions.

DOI
10.1103/physrevb.80.174513

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We investigate classical thermal activation (TA) and macroscopic quantum tunneling (MQT) for a YBa2Cu3O7\ensuremath−\ensuremathδ{\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}YBa2​Cu3​O7\ensuremath−\ensuremathδ​ (YBCO) Josephson junction coupled to an LC circuit theoretically. Due to the coupling between the junction and the LC circuit, the macroscopic phase dynamics can be described as the escape process of a fictitious particle with an anisotropic mass moving in a two-dimensional potential. We analytically calculate the escape rate including both the TA and MQT regime by taking into account the peculiar dynamical nature of the system. In addtion to large suppression of the MQT rate at zero temperature, we study details of the temperature dependence of the escape rate across a crossover region. These results are in an excellent agreement with recent experimental data for the MQT and TA rate in a YBCO biepitaxial Josephson junction. Therefore the coupling to the LC circuit is essential in understanding the macroscopic quantum dynamics and the qubit operation based on the YBCO biepitaxial Josephson junctions.
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 study macroscopic quantum tunneling (MQT) in ccc-axis twist Josephson junctions made of high-Tc{T}_{c}Tc​ superconductors in order to clarify the influence of the anisotropic order parameter symmetry (OPS) on MQT. The dependence of the MQT rate on the twist angle $\ensuremath{\gamma}$ about the ccc axis is calculated by using the functional integral and the bounce method. Due to the ddd-wave OPS, the $\ensuremath{\gamma}$ dependence of standard deviation of the switching current distribution and the crossover temperature from thermal activation to MQT are found to be given by $\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}$ and $\sqrt{\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}}$, respectively. We also show that a dissipative effect resulting from the nodal quasiparticle excitation on MQT is negligibly small, which is consistent with recent MQT experiments using ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ intrinsic junctions. These results indicate that MQT in ccc-axis twist junctions becomes a useful experimental tool for testing the OPS of high-Tc{T}_{c}Tc​ materials at low temperature, and suggest high potential of such junctions for qubit applications.
We study $\mathrm{Nb}\ensuremath{-}{\mathrm{AlO}}_{x}$-Nb Josephson junctions (JJs) with a phase-discontinuity $\ensuremath{\kappa}$ created by a pair of current injectors attached to one of the Nb electrodes. For $\ensuremath{\kappa}\ensuremath{\approx}\ensuremath{\pi}$ the Josephson potential energy UUU as a function of the average phase $\ensuremath{\psi}$ across the JJ has the form of a $2\ensuremath{\pi}$-periodic double-well potential. Thus, the device behaves as a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$ (the value of $\ensuremath{\varphi}$ depends on the system parameters). Experimentally, the existence of two wells of the potential is confirmed by the observation of two different critical currents ${I}_{\mathrm{c}\ifmmode\pm\else\textpm\fi{}}$, corresponding to the escape from different wells. We investigate the escape of the Josephson phase from both wells by collecting statistics of the switching currents. The histogram of switching current exhibits two peaks corresponding to ${I}_{\mathrm{c}\ifmmode\pm\else\textpm\fi{}}$. The dependence of the width ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ of each peak on the bath temperature TTT indicates the transition from thermal activation to macroscopic quantum tunneling (MQT) at ${T}^{★}\ensuremath{\approx}260\phantom{\rule{0.28em}{0ex}}\mathrm{mK}$ as TTT decreases. We argue that the observed saturation value of ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ below T★{T}^{★}T★ is indeed related to quantum tunneling rather than to parasitic noise in the system, as the histogram width can be reduced by tuning the value of $\ensuremath{\kappa}$ away from $\ensuremath{\pi}$. The comparison of the experimental escape rate $\mathrm{\ensuremath{\Gamma}}$ with theoretical predictions further confirms MQT of the phase $\ensuremath{\psi}$ from both wells.
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{T}_{cr}Tcr​ the thermal fluctuations of the Josephson phase induce such a switching, and as T<TcrT<{T}_{cr}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.
A nanometer-thick small mesa consiting of only two or three Bi 2 Sr 2 CaCu 2 O y intrinsic Josephson junctions (IJJs) is studied through the switching current distribution measurements down to 0.4 K. Experimental results clearly show that the first switching events from the zero-voltage state for 1 K < T < 4 K are successfully described by a conventional thermal activation (TA) theory for a single Josephson junction, and that they become independent of temperature below T* ∼ 0.7 K. We observe the microwave-induced peak in the switching distribution at 0.4 K, which is induced by the microwave irradiation at 55 GHz. These results strongly suggest that the system crossovers to macroscopic quantum tunneling (MQT) regime below T* , which is as high as the previously reported value for a stacked IJJs with several tens of junctions, in contrast to the recent result on a similar mesa-structured surface IJJ.