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Science

Time-Resolved Measurement of Dissipation-Induced Decoherence in a Josephson Junction

Siyuan Han, Yang Yu, Xi Chu, Shih‐I Chu, Zhen Wang

Published Aug 24, 2001• 103 citations
Publisher

Abstract

We determined the dissipation-induced decoherence time (DIDT) of a superconducting Josephson tunnel junction by time-resolved measurements of its escape dynamics. Double-exponential behavior of the time-dependent escape probability was observed, suggesting the occurrence of a two-level decay-tunneling process in which energy relaxation from the excited to the ground level significantly affects the escape dynamics of the system. The observation of temporal double-exponential dependence enables direct measurements of the DIDT, a property critical to the study of quantum dynamics and the realization of macroscopic quantum coherence and quantum computing. We found that the DIDT was tau(d) > 11 micros at T = 0.55 K, demonstrating good prospects for implementing quantum computing with Josephson devices.

DOI
10.1126/science.1062266

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We determined the dissipation-induced decoherence time (DIDT) of a superconducting Josephson tunnel junction by time-resolved measurements of its escape dynamics. Double-exponential behavior of the time-dependent escape probability was observed, suggesting the occurrence of a two-level decay-tunneling process in which energy relaxation from the excited to the ground level significantly affects the escape dynamics of the system. The observation of temporal double-exponential dependence enables direct measurements of the DIDT, a property critical to the study of quantum dynamics and the realization of macroscopic quantum coherence and quantum computing. We found that the DIDT was tau(d) > 11 micros at T = 0.55 K, demonstrating good prospects for implementing quantum computing with Josephson devices.
High-resolution (sub-microsecond to nanosecond) time-resolved measurements of the dynamics of superconducting electronic devices, such as Josephson tunnel junctions and SQUIDs, are indispensable for fundamental physics research, such as quantum mechanics of macroscopic variables. We describe the development of a time-resolved measurement technique that enables direct measurements, in the time domain, of the temporal evolution of Josephson junctions with a nanosecond resolution. The technique was applied to study escape dynamics of Josephson junctions, as macroscopic quantum systems, in the quantum tunnelling regime. The measured probability of junctions remaining in the initial metastable state—the survival probability—as a function of time decayed exponentially, agrees very well with the theoretical prediction of the incoherent tunnelling process.
When a Josephson junction in the zero-voltage state is current-biased below its critical current, the rate that it escapes to the finite-voltage state depends on the quantum state of the junction. By employing a slow current sweep, it is possible to observe experimentally the emptying of the thermally populated first excited level as a well-defined feature in the escape rate. This feature provides a simple method of determining the junction's energy relaxation time T1{T}_{1}T1​, a key parameter for evaluating its utility for quantum computation. We discuss the temperature regime where this effect is readily observable and describe how the emptying depends directly on the relaxation time. Our model of the junction dynamics agrees well with the measured escape rate of a $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{AlOx}\text{\ensuremath{-}}\mathrm{Nb}$ device in the 25 to 300mK300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}300mK temperature range, yielding ${T}_{1}\ensuremath{\approx}4\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.
The zero-voltage state of a Josephson junction biased with constant current consists of a set of metastable quantum energy levels. We probe the spacings of these levels by using microwaves to induce transitions and thereby enhance the escape rate to the voltage state. The widths of the resonances give a measurement of the spectroscopic coherence time of the two metastable states involved in the transitions. We observe a decoherence time shorter than that expected from dissipation alone in resonantly isolated $20\ifmmode\times\else\texttimes\fi{}5\ensuremath{\mu}{\mathrm{m}}^{2}$ area Al/AlOx/Al\mathrm{Al}/\mathrm{AlO}x/\mathrm{Al}Al/AlOx/Al junctions at 60 mK. The data are well fit by a model that includes the dephasing effects of both low-frequency current noise and the escape rate to the voltage state. We discuss implications for quantum computation using current-biased Josephson-junction qubits, including limits on the minimum number of levels needed in the well.
The Josephson effect is a privileged access to the macroscopic quantum nature of superconductors. We review some ideas and experimental techniques on macroscopic quantum decay phenomena occurring in Josephson structures. The attention is mainly addressed to intermediate levels of dissipation which characterize a large majority of low critical current Josephson devices and are therefore an avoidable consequence of nanotechnology applied more and more to Josephson devices. Phase diffusion phenomena take over thermal activation in some temperature ranges also affecting the transition to macroscopic quantum tunneling, enriching the phase diagram mostly defined by the Josephson energy, the temperature and the level of dissipation.
The dynamics of a dissipative, quantized macroscopic two-state system have been experimentally investigated through the measurement of tunneling transitions between the adjacent, equal-energy fluxoid states of a superconducting loop containing Josephson junctions. The tunneling rate \ensuremath{\Gamma} has been observed to approach zero as a power law in the temperature, giving a damping parameter \ensuremath{\alpha}=1.44, in the incoherent relaxation regime. The predicted exponential dependence of \ensuremath{\Gamma} on barrier height has been quantitatively confirmed.
Here we present the direct observation of macroscopic quantum properties in an all high-critical-temperature superconductor d-wave Josephson junction. Although dissipation caused by low-energy excitations is expected to strongly suppress macroscopic quantum effects, we demonstrate energy level quantization in our d-wave Josephson junction. The result indicates that the role of dissipation mechanisms in high-temperature superconductors has to be revised, and it may also have consequences for the class of solid-state "quiet" quantum bits with superior coherence time.