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Journal of the Physical Society of Japan

Increase of Phase Retrapping Effects in the Switching Rate from the Finite Voltage State of the Underdamped Intrinsic Josephson Junctions

Haruhisa Kitano, Yusaku Takahashi, Daiki Kakehi, Hikaru Yamaguchi, Shin-ichiro Koizumi, Shin-ya Ayukawa

Published Apr 14, 2016• 11 citations
Publisher

Abstract

We report a detailed study of the phase switching rate from the first to the fourth switch for a small stack of Bi2Sr2CaCu2Oy intrinsic Josephson junctions (IJJs). Experimental results were analyzed by using the conventional single-junction model including the thermally-activated phase escape and the multiple phase retrapping. It is shown that the phase retrapping effects are more prominent for higher order switches, even for the underdamped IJJs showing a large hysteresis in the current–voltage characteristics. This clearly suggests that the tilted washboard potential representing the phase switch from the finite voltage state in IJJs can be influenced by a rapid oscillation generated in a phase-switched junction.

DOI
10.7566/jpsj.85.054703

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•Aug 22, 2008•0 citations
We report a detailed study of the phase switching rate from the first to the fourth switch for a small stack of Bi2Sr2CaCu2Oy intrinsic Josephson junctions (IJJs). Experimental results were analyzed by using the conventional single-junction model including the thermally-activated phase escape and the multiple phase retrapping. It is shown that the phase retrapping effects are more prominent for higher order switches, even for the underdamped IJJs showing a large hysteresis in the current–voltage characteristics. This clearly suggests that the tilted washboard potential representing the phase switch from the finite voltage state in IJJs can be influenced by a rapid oscillation generated in a phase-switched junction.
We study the microwave-induced phase switches from the finite voltage state for the underdamped intrinsic Josephson junctions (IJJs) made of Bi 2 Sr 2 CaCu 2 O y (Bi2212). We observe the resonant double-peak structure in the switching current distribution at low temperatures. This feature is successfully explained by a quantum mechanical model where the strong microwave field effectively suppresses the potential barrier for the phase escape from a potential well and the macroscopic quantum tunneling (MQT) is resonantly enhanced. The detailed analyses considering the effects of multiple phase retrapping processes after the phase escape strongly suggest that the intense microwave field suppresses the energy-level spacing in the potential well, by effectively decreasing the fluctuation-free critical current and the Josephson plasma frequency. This effect also reduces the number of photons required for the multiphoton transition between the ground and the first excited states, making it possible to observe the energy level quantization in the MQT state. The temperature dependence of the resonance peak emerging in the switching rate clearly demonstrates that the quantized energy state can be survived up to ~10 K, which is much higher than a crossover temperature predicted by the conventional Caldeira-Leggett theory.
The macroscopic quantum tunneling (MQT) in the current-biased intrinsic Josephson junctions (IJJs) of high- T c cuprates has attracted much attention for decades. Although the MQT for the phase switches from the zero to the first voltage state (1st SW) in the multiple-branched I-V curves is well explained by the conventional theory, the occurrence of MQT for the higher order switches such as the switch from the 1st to 2nd voltage state (2nd SW) has been still debated. Here, we present an experimental study on the phase switches of small IJJs fabricated from underdoped Bi 2 Sr 2 (Ca,Y)Cu 2 O y . We observed the single photon transition between quantized energy levels in the 3rd phase switches at 59.15 GHz and 2 K. The comparison with the previous studies on the nearly optimal-doped Bi 2 Sr 2 CaCu 2 O y clearly suggests a possibility that the MQT rate for the higher-order phase switches is commonly enhanced by the effective suppression of the energy barrier for the higher-order phase escape due to the phase-running state after the 1st SW, in spite of the large difference in a critical current density and T c .
We present a study of the first and second switches (SWs) with nearly identical switching current ISWI_{\rm SW}ISW​ in Bi2_22​Sr2_22​Ca0.85_{0.85}0.85​Y0.15_{0.15}0.15​Cu2_22​Oy_yy​ intrinsic Josephson junctions (IJJs). In contrast to early studies where a large difference between ISW1stI_{\rm SW}^{\rm 1st}ISW1st​ and ISW2ndI_{\rm SW}^{\rm 2nd}ISW2nd​ was observed, a crossover temperature TcrT_{\rm cr}Tcr​ to the quantum phase escapes for the 2nd SW is strongly reduced $(\sim$2.8~K) and agrees with that for the 1st SW. This confirms that the anomalous enhancement of Tcr2ndT_{\rm cr}^{\rm 2nd}Tcr2nd​, commonly observed in the IJJs with ISW1st<ISW2ndI_{\rm SW}^{\rm 1st} < I_{\rm SW}^{\rm 2nd}ISW1st​<ISW2nd​, originates from the phase running state after the 1st SW. Detailed analysis of the microwave-induced escapes strongly suggests that nonlinear bifurcated phenomena possibly occurs in IJJs.
We study the dynamics of multi-junction switching (MJS): several intrinsic Josephson junctions (IJJs) in an array switch to the finite voltage state simultaneously. The number of multi-switching junctions ( N ) was successfully tuned by changing the load resistance serially connected to an Bi 2 Sr 1.6 La 0.4 CuO 6+δ IJJ array. The independence of the escape rates of N in the macroscopic quantum tunneling regime indicates that MJS is a successive switching process rather than a collective process. The origin of MJS is explained by the gradient of a load curve and the relative magnitudes of the switching currents of quasiparticle branches in the current–voltage plane.
We report measurements of switching current distribution (SWCD) from a phase-diffusion branch (PDB) to a quasiparticle-tunneling branch (QTB) as a function of temperature in a cuprate-based intrinsic Josephson junction. Contrary to the thermal-activation model, the width of the SWCD increases and the corresponding switching rate shows a nonlinear behavior with a negative curvature in a semilogarithmic scale with decreasing temperature down to 1.5 K. Based on the multiple-retrapping model, we quantitatively demonstrate that the frequency-dependent junction quality factor, representing the energy dissipation in a phase-diffusion regime, determines the observed temperature dependence of the SWCD and the switching rate. We also show that a retrapping process from the QTB to the PDB is related to the low-frequency limit damping.
Measurements of macroscopic quantum tunnelling (MQT) in intrinsic Josephson junctions (IJJs) suggest that they may be suitable as qubits. An advantage of using IJJs over trilayers is the absence of any artificial barrier and hence the possible absence of decohering two-level fluctuators. A disadvantage is that it is difficult to fabricate single IJJs. Hence all IJJ MQT experiments have been carried out on arrays of many IJJs in series. Since MQT is suppressed by dissipation, it is important (a) to understand the role of dissipation on the dynamics of IJJs and (b) to consider how the dissipation and the dynamics change as a function of the number of junctions in the array which are in the voltage state. We have measured distributions of the nth-order switching current in TlBaCaCuO IJJ arrays, where n indicates switching from n to n+1 junctions being in the voltage state. The junctions show conventional underdamped behaviour at temperatures below some temperature T*, with a suppression of the width of the distribution above T*. We find that T* depends upon n. For n = 0 (i.e. switching from the supercurrent branch), T* is less than 4.2 K. For n > 0, we measured T* values between 20 K and 40 K. Calculations and simulations show that a change in T* results from a change in Q. Analysis suggests that the Q of the IJJs is determined by the environmental impedance when all junctions in the array are in the zero-voltage state, whereas having one junction or more in the voltage state isolates the array from the environment leading to a higher Q. We discuss our data in the context of possible qubit applications.