Decay of the Zero-Voltage State in Small-Area, High-Current-Density Josephson Junctions

Abstract

We have measured the distribution in current for the onset of voltage in small-area Josephson junctions for temperatures down to ~1.6 K. The lifetime of the (V) = 0 state for our highest current density junctions becomes temperature independent for k B T %H(j)i/20 t SLT much less than the WKB prediction (co 0 is the junction resonant frequency). This is consistent with the Caldeira-Leggett theory, which includes damping effects on the quantum tunneling rate. PACS numbers: 74.50.+r, 05.04,+j, 72.70.+m Many experiments have studied the ramifications of the classical Langevin equation, but few have probed the low-temperature, high-frequency regime where quantum corrections to the picture must be expected. High-current-density Josephson tunnel junctions 1 at temperatures of a few kelvins make possible experimental studies 2 in this regime. Biased in the {V) = 0 state at currents near the critical current, the junctions are sensitive to fluctuations in the terahertz range, centered about their natural frequency, a> 0 . Fluctuation effects may be observed by sweeping the junction current through the critical current and noting the distribution, P{i), of current values at which voltage sets in. 3 P(i) should depend on whether k B T»Hu 0 /2 (classical regime) or k B T «h(x) Q /2 (quantum regime). 4 " 6 We have measured the width, a, of P(i) for junctions in the quantum regime and found that quantum effects do not appear until k B T<Hu 0 /20, in contrast to a WKB limit of k B T<hu) 0 /l. To interpret our experiments we invoke the usual model of such junctions, a "perfect" Josephson junction with current i= i c sin<p in parallel with resistance R (which we consider constant) and capacitance C. 7 Here <p is the phase difference across the junction, and i c is the critical current. The Langevin equationthen describes the position and momentum coordinates cp and Md(p/dt=2irMV/$ 0 where Fis the voltage across the junction, y = (RC)~l, M=C($ 0 / 2?r) 2 , and $ 0 = 2.07x 10" 15 Wb the flux quantum. The phase moves in the potential U{<p) = -Mw ? cy (u)j 2 = 2m c /$ 0 C), and x is the ratio (i/i c ) of the junction current to its critical current. For the noise term f(t) the fluctuation-dissipation theorem gives the spectral density (f 2 {(*))) = yMH(jocoth(Hw/2k B T), usually interpreted classically as the high-temperature limit (/ 2 (o>)) = 2yMk B T.Without fluctuations, the phase can be trapped in a local minimum at cp^sin^x if x<l, and is prevented from escape by an energy barrier AE = 2Ma>/[(1 -x 2 ) l/2 -x cos~lx]. No dc voltage develops across the junctions since {d<p/dt) = 0. For x>l the potential wells vanish and the phase increases at a speed determined by the damping and the overall steepness of the potential. This corresponds to the finite voltage state of the junction. We are interested in x slightly less than 1, in the presence of fluctuations. The phase is now restrained by a low barrier (inset, Fig. 1) which, in the absence of fluctuations, would hold ( V) = 0 until i exceeds i c . Fluctuations, however, cause p...

Switching current measurements of large area Josephson tunnel junctions

“…5. With the low damping prefactor (15), the difference |T esc − T | is less than 75 mK in the temperature range above T ⋆ , as shown by the solid symbols in the inset of effective resistance used for the fit is in good agreement with the sub-gap resistance determined from the dc current voltage characteristic of the junction. In Fig.…”

“…1b). At finite temperatures T > 0, the particle may escape from the well at bias currents γ < 1 by thermally activated processes 7,9,10,24,25,26 and also by quantum tunneling through the barrier 12,13,14,15,27 . The rate at which both processes occur depends on the barrier height…”

“…This weak temperature dependence can be attributed to the almost constant ratio of k B T /U φ 0 (I p ) for the switching data measured at different temperatures, see Eq. (15). At a fixed bath temperature, the bias current variation within a single P (I) distribution results in a noticeable variation of a t .…”

“…In a second step, we used the thermal prefactor given by the expression (15) in the calculation of the left hand side of Eq. (12) in our data analysis scheme.…”

“…At low temperatures the quantum mechanical properties of Josephson junctions have been investigated in relation to macroscopic quantum tunneling (MQT) 13,14,15 , energy level quantization (ELQ) 12,16 and macroscopic quantum coherence (MQC) 17 . Recently, the quantum mechanical properties of Josephson junction systems have regained interest in the view of their possible application for solid state based quantum information processing 18,19,20 .…”