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arXiv:cond-mat/9604160 · Journal of the Physical Society of Japan

Macroscopic Quantum Tunneling of a Fluxon in a Long Josephson Junction

Takeo Kato, Masatoshi Imada

Published Sep 15, 1996• 51 citations
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Abstract

Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.

DOI
10.1143/jpsj.65.2963

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Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.
We investigate the effects of a high-quality resonant cavity on macroscopic quantum tunneling (MQT) of fluxons from both a metastable state to continuum and from one degenerate ground state of a double-well potential to the other. By using a set of two coupled perturbed sine-Gordon equations, we describe the tunneling processes in linear long Josephson junctions and find that MQT in the resonant cavity increases due to potential renormalization, induced by the interaction between the fluxon and the cavity. Enhancement of the MQT rate in the weak-coupling regime is estimated by using the experimentally accessible range of the model parameters. The tunneling rate from the metastable state is found to increase weakly with increasing junction-cavity interaction strength. However, the energy splitting between the two degenerate ground states of the double-well potential increases significantly with increasing both the interaction strength and the frequency of the resonant cavity mode. Finally, we discuss how the resonant cavity may be used to tune the property of Josephson vortex quantum bits.
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.
We report an experimental observation of the macroscopic quantum tunnelling (MQT) in a d-wave high-temperature superconductor (HTSC) Bi2Sr2CaCu2O8+δ intrinsic Josephson junction (IJJs). It is well known that the current-biased Josephson tunnel junction provides an ideal stage for studying a variety of macroscopic quantum phenomena such as MQT. They have been studied and observed in low-temperature superconductor (LTSC) Josephson junctions since the early 1980s and have been established well by now. On the other hand, in the case of HTSC the d-wave pairing symmetry allows for dissipative quasiparticle excitations within the superconducting energy gap, which is expected to severely interfere with an observation of MQT. Contrary to this naive conception, our experimental results have explained that the effects of the nodal quasiparticles are not strong enough to obscure the observation of the MQT. Furthermore, we found that the MQT in IJJs was observed at approximately 1 K, which was ten times higher than that of LTSC Josephson junctions. This higher classical-to-quantum crossover temperature is due to their high plasma frequency. We also discuss the resonant activation of IJJs in the presence of microwave radiation.
Ten years ago, coherent oscillations between two quantum states of a superconducting circuit differing by the presence or absence of a single Cooper pair on a metallic island were observed for the first time. This result immediately stimulated the development of several other types of superconducting quantum circuits behaving as artificial atoms, thus bridging mesoscopic and atomic physics. Interestingly, none of these circuits fully implements the now almost 30 year old proposal of A. J. Leggett to observe coherent oscillations between two states differing by the presence or absence of a single fluxon trapped in the superconducting loop interrupted by a Josephson tunnel junction. This phenomenon of reversible quantum tunneling between two classically separable states, known as Macroscopic Quantum Coherence (MQC), is regarded crucial for precision tests of whether macroscopic systems such as circuits fully obey quantum mechanics. In this article, we report the observation of such oscillations with sub-GHz frequency and quality factor larger than 500. We achieved this result with two innovations. First, our ring has an inductance four orders of magnitude larger than that considered by Leggett, combined with a junction in the charging regime, a parameter choice never addressed in previous experiments. Second, readout is performed with a novel dispersive scheme which eliminates the electromagnetic relaxation process induced by the measurement circuit (Purcell effect). Moreover, the reset of the system to its ground state is naturally built into this scheme, working even if the transition energy is smaller than that of temperature fluctuations. As we argue, the MQC transition could therefore be, contrary to expectations, the basis of a superconducting qubit of improved coherence and readout fidelity.
We theoretically investigate the macroscopic quantum dynamics of a $\ensuremath{\pi}$ junction with a superconductor (S) and a multiferroic material or a ferromagnetic insulator (FI). By deriving the effective action from a microscopic Hamiltonian, a $\ensuremath{\pi}$-junction qubit (a S-FI-S superconducting quantum interference device ring) is proposed. In this qubit, a quantum two-level system is spontaneously generated and the effect of the quasiparticle dissipation is found to be very weak. These features make it possible to realize a quiet qubit with high coherency. We also investigate macroscopic quantum tunneling (MQT) in current-biased S-FI-S $\ensuremath{\pi}$ junctions and show that the influence of the quasiparticle dissipation on MQT is negligibly small.
We have theoretically investigated macroscopic quantum tunneling (MQT) and the influence of nodal quasiparticles and zero energy bound states (ZESs) on MQT in sss-wave/ddd-wave hybrid Josephson junctions. In contrast to ddd-wave/ddd-wave junctions, the low-energy quasiparticle dissipation resulting from nodal quasiparticles and ZESs is suppressed due to a quasiparticle-tunneling blockade effect in an isotropic sss-wave superconductor. Therefore, the inherent dissipation in these junctions is found to be weak. We have also investigated MQT in a realistic sss-wave/ddd-wave (Nb∕Au∕YBCO)(\mathrm{Nb}∕\mathrm{Au}∕\mathrm{YBCO})(Nb∕Au∕YBCO) junction in which Ohmic dissipation in a shunt resistance is stronger than the inherent dissipation and find that MQT is observable within the current experimental technology. This result suggests the high potential of sss-wave/ddd-wave hybrid junctions for applications in quantum information devices.