Stochastic resonance in an RF SQUID with shunted ScS junction
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 , 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 and the electron wave length : for a classical point contact [18] and 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 between the supercurrent and the order parameter phase in both classical and quantum cases at lowest temperatures () essentially differs [18], [20], [21] from the current–phase relation for an SIS junction described by the well-known Josephson formula . 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 (where is the magnetic flux quantum) piercing the loop, its current–phase relation leads to the formation of a symmetric two-well potential energy of the whole loop that principally enables the SR dynamics only for . is a dimensionless non-linearity parameter sometimes called the main SQUID parameter. In contrast, the potential energy 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 can be formally achieved at any vanishingly low . 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 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 . Specific focus is given to low critical currents, i.e. rather high-impedance contacts (ASCs) when .
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]: where is the capacitance; is the normal shunt resistance of the Josephson junction; is the loop inductance; is the internal magnetic flux in the loop; is the loop potential energy, which is the sum of the
Numerical simulation results and discussion
The energy barrier height , as follows from Eqs. (6), (7), is determined by 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 while it is finite for any in the ScS SQUID. Both and , 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 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 . 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.
References (34)
- et al.
Physica C
(2002) - et al.
Phys. Rep.
(2003) - et al.
The superconducting quantum point contacts
Physica
(1940)- et al.
Physica A
(1996) - et al.
Superlattices Microstruct.
(1999) - et al.
Appl. Phys. Lett.
(1982) - et al.
Phys. Rev. B
(2012) - et al.
J. Low Temp. Phys.
(2012) - et al.
Appl. Phys. Lett.
(1995)
J. Appl. Phys.
Appl. Supercond.
J. Low Temp. Phys.
J. Phys. A
J. Phys. A
Tellus
Rev. Modern Phys.
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