Abstract Body

The configuration of a high-quality security system high quality random number generator has been expected. Here, high- quality random numbers mean the numbers are random, un- reproducible and unpredictable. Until recently, random numbers have been generated from pseudo random number generators. However, the pseudo random numbers are concerned had a reproducibility issue because these numbers were dependent on the initial condition of the algorithm. Conversely, using physical randomness phenomena, such as thermal noise and non-linear electronic circuits, high-quality random number generators are produced. Specially, Chaos in physical phenomena is an appropriate random-number generator. It is known that JJ under irradiation radio frequency (RF) output chaotic voltage oscillation[1]. Here, conventional RF is roughly several tens GHz.

In this study, we numerically investigated the chaotic voltage of Josephson junction (JJ) under irradiation high frequency than conventional RF for high-quality random number generators using the equivalent circuits of JJ. Particularly, first, we will optimize the parameters when chaotic voltage appears under irradiation high frequency than conventional frequency. Thereafter, random numbers are generated from output voltage of JJ and the quality of randomness are evaluated using statistical test.

For the numerical simulation of the chaotic behavior in JJ, we adopted the equivalent circuit of RF-irradiated JJ using a resistively and capacitively shunted junction (RCSJ) model, as shown in Fig.1(a). Figure 1(b) shows calculated normalized current-voltage characteristics of JJ with and without RF. The Shapiro steps appeared on current-voltage characteristics with RF, which is consistent previous study. The spiked shape voltage appeared at i = 0.25-0.35. This means the voltage has sensitive initial condition. Hence, the voltage is suggested chaotic behavior in this region.

Thereafter, we computed the Lyapunov exponent λ to judge the presence of a chaotic behavior. The λ is a factor that characterizes the rate of separation of infinitesimally close trajectories in a dynamical system. Therefore, the voltages are chaotic or non-chaotic, when λ is positive or negative. Figure 1(c) shows current dependence of the λ. In Fig. 1(c), the λ is positive at spike voltage region. This is suggested that chaotic voltage appeared in this region.

Further investigation, in the case of λ is positive, power spectrum of output voltage was calculated. Less than irradiation frequency, the spectrum is independent of frequency. i.e. the white noise region appeared. In other words, it is unpredictable random number can be generated. The generation rate is less than the irradiation frequency. Therefore, we propose white noise region broad by increasing irradiation frequency. For high-speed random number generation, irradiation frequency is increased to THz range from conventional several tens GHz. By the way, intrinsic Josephson junction (IJJ) stacks can emit the THz electromagnetic wave, which is coherent, continuous and monochromaticity[2]. The IJJs are atomically and naturally stacked in cuprate superconductor such as Bi-2212 single crystal. Therefore, we assumed the RF source is the IJJ emitter because the high-speed operation of random number generators is expected possibility.

We are planning the mesa-type sample for high speed random number generators. Specifically, the chaos generation mesa and THz emission mesa are fabricated on same superconductor chip. It makes the random-number generator using RF irradiated JJ can not only be realized but also compact and high-speed operating device.

In this presentation, we will focus on and report the random number generation rate using JJ under irradiation THz electromagnetic wave. In addition, we will discuss the quality of generated random numbers from output voltage of JJ using statistical test.

References

[1] R. L. Kautz et al., Journal of Applied Physics 57, 875 (1985).

[2] L. Ozyuzer et al., Science, 318, (2007).