Stochastic resonance in an RF SQUID with shunted ScS junction

https://doi.org/10.1016/j.physa.2013.11.005Get rights and content

Highlights

  • We numerically simulate stochastic resonance in an RF SQUID with ScS Josephson junction.

  • We use the zero-temperature approximation for the ScS superconducting current–phase relation.

  • The potential energy has a finite-height barrier for any arbitrary small parameter βL.

  • ScS-based SQUIDs are more suitable for SR amplification at ultralow temperatures.

  • The concept of “Just-In-Place Amplification” is introduced.

Abstract

Using a point (superconductor–constriction–superconductor, ScS) contact in a single-Josephson-junction superconducting quantum interference device (RF SQUID) provides stochastic resonance conditions at any arbitrary small value of loop inductance and contact critical current, unlike SQUIDs with more traditional tunnel (superconductor–insulator–superconductor, SIS) junctions. This is due to the unusual potential energy of the ScS RF SQUID which always has a barrier between two wells, thus making the device bistable. This paper presents the results of a numerical simulation of the stochastic dynamics of the magnetic flux in an ScS RF SQUID loop affected by band-limited white Gaussian noise and low-frequency sine signals of small and moderate amplitudes. The difference in stochastic amplification of RF SQUID loops incorporating ScS and SIS junctions is discussed.

Introduction

The sensitivity of superconducting quantum interference devices (SQUIDs) and their quantum analogues, SQUBIDs, has practically reached the quantum limitation  [1], [2], [3]. However, with increase of the quantizing loop inductance up to L1091010H, thermodynamic fluctuations lead to quick deterioration of the energy resolution. As shown earlier  [4], [5], [6], [7], [8], the sensitivity of magnetometers can be enhanced in this case by using stochastic resonance (SR). The SR phenomenon whose concept was introduced in the early 1980s  [9], [10], [11] manifests itself in non-monotonic rise of a system response to a weak periodic signal when noise of a certain intensity is added to the system. Owing to extensive studies during the last two decades, the stochastic resonance effect has been revealed in a variety of natural and artificial systems, both classical and quantum. Analytical approaches and quantifying criteria for estimation of the ordering due to the noise impact were determined and described in the reviews  [12], [13], [14]. In particular, the sensitivity of a bistable stochastic system fed with a weak periodic signal can be significantly improved in the presence of thermodynamic or external noise that provides switching between the metastable states of the system. For example, it was experimentally proved  [4] that the gain of a harmonic informational signal can reach 40 dB at a certain optimal noise intensity in a SQUID with an SIS (superconductor–insulator–superconductor) Josephson junction. Moreover, the stochastic amplification in SIS-based SQUIDs can be maximized at a noise level insufficient to enter the SR mode by means of the stochastic-parametric resonance (SPR) effect  [15] emerging in the system due to the combined action of the noise, a high-frequency electromagnetic field and the weak informational signal. An alternative way of enhancing the RF SQUID sensitivity is to suppress the noise with strong (suprathreshold) periodic RF pumping of properly chosen frequency which results in a better signal-to-noise ratio in the output signal  [16]. In the latter case the switching between metastable states is mainly due to strong regular RF pumping  [17] unlike SR where the dominating switching mechanism is the joint effect of noise and weak periodic signal  [12], [13], [14].

In recent years quantum point contacts (QPCs) with direct conductance have attracted strong interest from the point of view of both quantum channel conductance studies and building qubits with high energy level splitting. Currently, two types of point contacts are distinguished, depending on the ratio between the contact dimension d and the electron wave length λF=h/pF: dλF for a classical point contact  [18] and dλF for a quantum point contact  [19], [20], [21]. Practically, superconducting QPCs are superconductor–constriction–superconductor (ScS) contacts of atomic-size (ASCs). The critical currents of such contacts can take discrete values. The relation IsScS(φ) between the supercurrent IsScS and the order parameter phase φ in both classical and quantum cases at lowest temperatures (T0) essentially differs  [18], [20], [21] from the current–phase relation for an SIS junction described by the well-known Josephson formula IsSIS=Icsinφ. The corresponding potential energies in the motion equations are therefore different as well.

When an SIS junction is incorporated into a superconducting loop with external magnetic flux Φe=Φ0/2 (where Φ0=h/2e2.071015Wb is the magnetic flux quantum) piercing the loop, its current–phase relation IsSIS(φ) leads to the formation of a symmetric two-well potential energy USIS(Φ) of the whole loop that principally enables the SR dynamics only for βL=2πLIc/Φ0>1. βL is a dimensionless non-linearity parameter sometimes called the main SQUID parameter. In contrast, the potential energy UScS(Φ) of a superconducting loop with a QPC always has a barrier with a singularity at its top, and two metastable current states of the loop differing by internal magnetic fluxes Φ can be formally achieved at any vanishingly low βL1. In the quantum case, the most important consequences of the “singular” barrier shape are the essential rise of macroscopic quantum tunneling rate and the increased energy level splitting in flux qubits  [2], [3].

In the classical limit, the SR dynamics of a superconducting loop with ScS Josephson contact and non-trivial potential UScS(Φ) would differ substantially from the previously explored  [4], [5], [6], [8] case of the SIS junction and would be much like the 4-terminal SQUID dynamics  [7]. In the present work a numerical analysis is given of stochastic amplification of weak low-frequency harmonic signals in a superconducting loop broken by an ScS Josephson junction at low temperatures TTc. Specific focus is given to low critical currents, i.e. rather high-impedance contacts (ASCs) when βL=2πLIc/Φ0<1.

Section snippets

ScS junction loop model and numerical computation technique

The stochastic dynamics of the magnetic flux in an RF SQUID loop (inset in Fig. 1(a)) was studied by numerical solution of the motion equation (Langevin equation) in the resistively shunted junction (RSJ) model  [22]: LCd2Φ(t)dt2+LRdΦ(t)dt+LU(Φ,Φe)Φ=Φe(t), where C is the capacitance; R is the normal shunt resistance of the Josephson junction; L is the loop inductance; Φ(t) is the internal magnetic flux in the loop; U(Φ,Φe) is the loop potential energy, which is the sum U(Φ,Φe)=UM+UJ of the

Numerical simulation results and discussion

The energy barrier height ΔU, as follows from Eqs. (6), (7), is determined by βL and is different for the cases of ScS and SIS junctions (Fig. 2(a)). As can be seen, in the loop with SIS junction (referred to as SIS SQUID) the two-well potential with two metastable states needed to prepare conditions for stochastic amplification of a weak information signal exists only at βL>1 while it is finite for any βL in the ScS SQUID. Both ΔU and D, being in exponent, are the core parameters to define the

Conclusion

In this work the noise-induced stochastic amplification of weak informational signals at low temperatures TTc in RF SQUIDs containing ScS contacts (QPCs) is considered. It is shown that SR amplification of weak sine signals emerges at any, vanishingly small, value of the parameter βL. This is due to an unusual shape of the potential barrier between the two metastable states with a singularity at its top and always finite height. It should be noted that there is no noise-induced

Acknowledgment

The authors acknowledge Dr. A.A. Soroka for helpful discussions.

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