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arXiv:1207.3013 · Physical Review Letters

Experimental Evidence of a φ Josephson Junction

H. Sickinger, A. Lipman, Martin P. Weides, R. G. Mint︠s︡, H. Kohlstedt, D. Koelle, R. Kleiner, E. Goldobin

Published Sep 7, 2012• 142 citations
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Abstract

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The value of $\ensuremath{\varphi}$ can be chosen by design in the interval $0<\ensuremath{\varphi}<\ensuremath{\pi}$. The junctions used in our experiments are fabricated as 0-$\ensuremath{\pi}$ Josephson junctions of moderate normalized length with asymmetric 0 and $\ensuremath{\pi}$ regions. We show that (a) these $\ensuremath{\varphi}$ Josephson junctions have two critical currents, corresponding to the escape of the phase $\ensuremath{\psi}$ from $\ensuremath{-}\ensuremath{\varphi}$ and $+\ensuremath{\varphi}$ states, (b) the phase $\ensuremath{\psi}$ can be set to a particular state by tuning an external magnetic field, or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.

DOI
10.1103/physrevlett.109.107002

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We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase \ensuremathψ=\ifmmode±\else\textpm\fi\ensuremathφ\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}\ensuremathψ=\ifmmode±\else\textpm\fi\ensuremathφ. The value of \ensuremathφ\ensuremath{\varphi}\ensuremathφ can be chosen by design in the interval 0<\ensuremathφ<\ensuremathπ0<\ensuremath{\varphi}<\ensuremath{\pi}0<\ensuremathφ<\ensuremathπ. The junctions used in our experiments are fabricated as 0-\ensuremathπ\ensuremath{\pi}\ensuremathπ Josephson junctions of moderate normalized length with asymmetric 0 and \ensuremathπ\ensuremath{\pi}\ensuremathπ regions. We show that (a) these \ensuremathφ\ensuremath{\varphi}\ensuremathφ Josephson junctions have two critical currents, corresponding to the escape of the phase \ensuremathψ\ensuremath{\psi}\ensuremathψ from \ensuremath−\ensuremathφ\ensuremath{-}\ensuremath{\varphi}\ensuremath−\ensuremathφ and +\ensuremathφ+\ensuremath{\varphi}+\ensuremathφ states, (b) the phase \ensuremathψ\ensuremath{\psi}\ensuremathψ can be set to a particular state by tuning an external magnetic field, or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.
We consider a short Josephson junction with a phase discontinuity $\ensuremath{\kappa}$ created, e.g., by a pair of tiny current injectors, at some point x0{x}_{0}x0​ along the width of the junction. We derive the effective current-phase relation (CPR) for the system as a whole, i.e., reduce it to an effective pointlike junction. From the effective CPR we obtain the ground state of the system and predict the dependence of its critical current on $\ensuremath{\kappa}$. We show that in a large range of $\ensuremath{\kappa}$ values the effective junction behaves as a ${\ensuremath{\varphi}}_{0}$ Josephson junction, i.e., has a unique ground state phase ${\ensuremath{\varphi}}_{0}$ within each $2\ensuremath{\pi}$ interval. For $\ensuremath{\kappa}\ensuremath{\approx}\ensuremath{\pi}$ and x0{x}_{0}x0​ near the middle of the junction one obtains a ${\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$ junction, i.e., a Josephson junction with degenerate ground state phase ${\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$ within each $2\ensuremath{\pi}$ interval. Further, in view of possible escape experiments especially in the quantum domain, we investigate the scaling of the energy barrier and eigenfrequency close to the critical currents and predict the behavior of the escape histogram width $\ensuremath{\sigma}(\ensuremath{\kappa})$ in the regime of the macroscopic quantum tunneling.
We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.
The φ Josephson junction has a doubly degenerate ground state with the Josephson phases ±φ. We demonstrate the use of such a φ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic field and reading by applying a bias current. In the “store” state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with rapid single flux quantum logic is possible.
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 have performed a quantitative electrodynamic experiment on a Josephson oxide tunneling junction. Using a current source at 30 Mc/sec, we have verified the time dependence of the Josephson equation, j=j0j={j}_{0}j=j0​ $sin [{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]$, where $(\frac{\ensuremath{\partial}}{\ensuremath{\partial}t})[{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}{l}^{r}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]=\ensuremath{-}(\frac{2eV}{\ensuremath{\hbar}})$. Thus the limiting voltage is shown to obey the quantum relationship relationship, $2eV=\ensuremath{\hbar}\ensuremath{\omega}$. Measurements were made completely in the coherent state showing the diffraction nature of the junction as a function of applied magnetic field. The Josephson (parametric) inductance of the junction was directly observed and is in good agreement with the theory.