Observation of stochastic resonance in percolative Josephson media
Measurements of the electrical response of granular Sn-Ge thin films below the superconducting transition temperature are reported. Addition of an external noise to the magnetic field applied to the sample is found to increase the sample voltage response to a small externally applied ac signal. The...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2002
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| Цитувати: | Observation of stochastic resonance in percolative Josephson media / A.M. Glukhov, A.G. Sivakov, A.V. Ustinov // Физика низких температур. — 2002. — Т. 28, № 6. — С. 543-547. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1302142018-02-10T03:03:42Z Observation of stochastic resonance in percolative Josephson media Glukhov, A.M. Sivakov, A.G. Ustinov, A.V. Свеpхпpоводимость, в том числе высокотемпеpатуpная Measurements of the electrical response of granular Sn-Ge thin films below the superconducting transition temperature are reported. Addition of an external noise to the magnetic field applied to the sample is found to increase the sample voltage response to a small externally applied ac signal. The gain coefficient for this signal as well as the signal-to-noise ratio displays clear maxima at particular noise levels. We interpret these observations as a stochastic resonance in the percolative Josephson media that occurs close to the percolation threshold. 2002 Article Observation of stochastic resonance in percolative Josephson media / A.M. Glukhov, A.G. Sivakov, A.V. Ustinov // Физика низких температур. — 2002. — Т. 28, № 6. — С. 543-547. — Бібліогр.: 8 назв. — англ. 0132-6414 PACS: 74.40.+k, 74.80.Bj, 64.40.Ak http://dspace.nbuv.gov.ua/handle/123456789/130214 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Glukhov, A.M. Sivakov, A.G. Ustinov, A.V. Observation of stochastic resonance in percolative Josephson media Физика низких температур |
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Measurements of the electrical response of granular Sn-Ge thin films below the superconducting transition temperature are reported. Addition of an external noise to the magnetic field applied to the sample is found to increase the sample voltage response to a small externally applied ac signal. The gain coefficient for this signal as well as the signal-to-noise ratio displays clear maxima at particular noise levels. We interpret these observations as a stochastic resonance in the percolative Josephson media that occurs close to the percolation threshold. |
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Article |
| author |
Glukhov, A.M. Sivakov, A.G. Ustinov, A.V. |
| author_facet |
Glukhov, A.M. Sivakov, A.G. Ustinov, A.V. |
| author_sort |
Glukhov, A.M. |
| title |
Observation of stochastic resonance in percolative Josephson media |
| title_short |
Observation of stochastic resonance in percolative Josephson media |
| title_full |
Observation of stochastic resonance in percolative Josephson media |
| title_fullStr |
Observation of stochastic resonance in percolative Josephson media |
| title_full_unstemmed |
Observation of stochastic resonance in percolative Josephson media |
| title_sort |
observation of stochastic resonance in percolative josephson media |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2002 |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная |
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http://dspace.nbuv.gov.ua/handle/123456789/130214 |
| citation_txt |
Observation of stochastic resonance in percolative Josephson media / A.M. Glukhov, A.G. Sivakov, A.V. Ustinov // Физика низких температур. — 2002. — Т. 28, № 6. — С. 543-547. — Бібліогр.: 8 назв. — англ. |
| series |
Физика низких температур |
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AT glukhovam observationofstochasticresonanceinpercolativejosephsonmedia AT sivakovag observationofstochasticresonanceinpercolativejosephsonmedia AT ustinovav observationofstochasticresonanceinpercolativejosephsonmedia |
| first_indexed |
2025-07-09T13:04:45Z |
| last_indexed |
2025-07-09T13:04:45Z |
| _version_ |
1837174659147104256 |
| fulltext |
Fizika Nizkikh Temperatur, 2002, v. 28, No. 6, p. 543–547Glukhov A. M., Sivakov A. G., and Ustinov A. V.Observation of stochastic resonance in percolative Josephson mediaGlukhov A. M., Sivakov A. G., and Ustinov A. V.Observation of stochastic resonance in percolative Josephson media
Observation of stochastic resonance in percolative
Josephson media
A. M. Glukhov and A. G. Sivakov
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: glukhov@ilt.kharkov.ua
A. V. Ustinov
Physikalisches Institut III, Universitat Erlangen-Nu..rnberg
Erwin-Rommel-Str. 1, D-91058 Erlangen, Germany
Received February 27, 2002
Measurements of the electrical response of granular Sn–Ge thin films below the supercon-
ducting transition temperature are reported. Addition of an external noise to the magnetic
field applied to the sample is found to increase the sample voltage response to a small
externally applied ac signal. The gain coefficient for this signal as well as the signal-to-noise
ratio displays clear maxima at particular noise levels. We interpret these observations as a
stochastic resonance in the percolative Josephson media that occurs close to the percolation
threshold.
PACS: 74.40.+k, 74.80.Bj, 64.40.Ak
1. Introduction
The phenomenon of stochastic resonance has
been discussed in relation to diverse problems in
nonlinear science, physics, chemistry and biolo-
gy [1]. Generally speaking, stochastic resonance is
the enhancement of the output signal-to-noise ratio
caused by injection of an optimal amount of noise
into a periodically driven nonlinear system. This
kind of behavior is often thought as counterintui-
tive, since a stochastic force amplifies a small peri-
odic signal here. Its mechanism is usually explained
in terms of motion of a particle in a double-well
potential subjected to noise, in the presence of a
time-periodic force. The periodic forcing leads to
noise-enhanced transitions between the two wells
and thus to an enhanced output of the forcing
signal.
One of clean examples of nonlinear systems with
few degrees of freedom is a superconducting loop
with a Josephson junction, well known as a super-
conducting quantum interferometer (SQUID).
With a proper choice of the size of the loop, this
system undergoes bistable dynamics for magnetic
flux trapped in the loop. There have been already
experiments that reported operating SQUIDs under
stochastic resonance conditions, both with the ex-
ternal noise injection [2] and with the thermally
generated intrinsic noise [3]. The stochastic reso-
nance effect can be considerably enhanced in a
system of coupled bistable oscillators (see, e.g. [4]).
Therefore, it is interesting to study stochastic am-
plification for a Josephson media consisting of many
superconducting loops with Josephson junctions.
Earlier we observed quantum interference effects
in macroscopically inhomogeneous superconducting
Sn–Ge thin-film composites near the percolation
threshold [5]. This system exhibits a considerable
voltage noise under dc current bias and a rectifi-
cation of ac current, which arise below the super-
conducting transition temperature. According to
Ref. 6, a dc voltage is observed when an ac current
larger than the critical current passes through a
system of two superconductors weakly connected by
an asymmetric double point contact, i.e., the mag-
netic flux quantization induces the critical current
oscillations and the respective voltage oscillations.
We have argued [5], that the oscillatory depen-
© A. M. Glukhov, A. G. Sivakov, and A. V. Ustinov, 2002
dence Vdc(H) in Sn–Ge thin-film composites is
related to quantum interference in randomly distri-
buted asymmetric superconducting contours inter-
rupted by Josephson weak links. In Ref. 5 we re-
ported measurements of Vdc(H) dependence for
various orientations of the film relative to the field.
The scale of the oscillatory structure in Vdc(H) is
inversely proportional to the cosine of the angle
between the applied magnetic field and the normal
to the sample plane. The emergence of the normal
magnetic field component alone as well as the
antisymmetry of the oscillatory structure relative to
H = 0 indicate the quantum-interference origin of
Vdc(H). Moreover, it appears feasible to relate these
active contours to the percolative cluster that has a
well-known fractal structure. The existence of a
wide and self-similar distribution of Josephson con-
tour areas leads to the fractal character of the
dependence Vdc(H). We have suggested and veri-
fied the model of the voltage 1/f noise origin by a
passive transformation of magnetic field oscillations
with the fractal transfer function Vdc(H) [5].
In this paper, we study the noise-induced electri-
cal response of granular Sn–Ge thin-film compo-
sites. We argue that a distributed network contain-
ing many superconducting loops with Josephson
junctions may show a cooperative behavior as sto-
chastically resonating media.
2. Experimental details and results
Josephson networks may occur naturally, e.g.,
in nonuniform superconducting materials such as
granular thin films. We prepare granular Sn–Ge
thin-film composites having monotonically varying
structure by vacuum condensation of Sn on a long
(60 mm) substrate along which a temperature gra-
dient is created. Sn is deposited on the previously
prepared 50 nm thick Ge layer. The thickness of the
Sn layer is 60 nm. The metallic condensate is co-
vered from the top with amorphous Ge. The struc-
tural change results in variation of the composite
properties from metallic to insulating over the sub-
strate. This crossover in properties is observed on a
series consisting of 30 samples cut from different
parts of the substrate. For present investigations,
we chose the samples with properties near the
percolation threshold, with a characteristic struc-
ture depicted in Fig. 1.
During measurements, the samples were kept in
exchange gas inside a superconducting solenoid.
The electrical measurements were carried out ac-
cording to the standard four-probe technique. A
sinusoidal ac current of frequency f1 = 100 kHz and
amplitude Iac = 0.8 mA was produced by an
HP3245A universal source connected to the current
leads through a dc-decoupling transformer. Fast
Fourier transformation spectra of the output volt-
age are measured by using a spectrum analyzer
SR770 with Blackman–Harris window function.
We used signal-to-noise ratio (SNR) as the major
characteristic of stochastic resonance. SNR was
measured as the ratio of the voltage amplitude of
the spectral line to the voltage noise level below it.
The noise background in the signal bin is estimated
by performing a linear fit to the peak clipped
spectrum. The noise intensity (noise level) denotes
the standard deviation σN of the Gaussian white
noise signal, which was supplied by the internal
SR770 generator.
The transition of the studied sample into the
superconducting state is smeared over 1.0 K with
the center of the resistive transition at T0 = 3.8 K.
At temperatures below T0 and with ac current Iac
applied through the sample, we observed a rectified
dc voltage Vdc , which magnitude oscillated as a
function of dc magnetic field H applied perpendicu-
lar to the substrate (Fig. 2,a). The amplitude and
frequency of the current Iac did not significantly
affect the general features of the Vdc(H) depend-
ence. The results could be always readily repro-
duced.
To observe the phenomenon of stochastic reso-
nance, we study the rectified voltage dependence on
magnetic field. The applied magnetic field consisted
of three components: (i) dc field H varied in the
range between − 300 and + 300 mOe, (ii) small ac
Fig. 1. Electron micrograph of Sn–Ge sample prepared
close the percolation threshold. Black regions corre-
spond to the metallic phase.
A. M. Glukhov, A. G. Sivakov, and A. V. Ustinov
544 Fizika Nizkikh Temperatur, 2002, v. 28, No. 6
component with the frequency fH between 5 and
60 Hz and amplitude Hac = 20 mOe, and (iii) white
Gaussian noise Hnoise with the intensity σN ranging
up to 70 mOe. The Fourier spectra of voltage re-
sponse are shown in Fig. 3 together with oscillo-
grams of the input signal Hac + Hnoise . Figure 4
shows the dependence of the output SNR for the
first harmonic of fH on the intensity of input noise
Hnoise . One can see that increasing the noise ampli-
tude at first increases SNR and then decreases it.
Such maxima are rather characteristic for the phe-
nomenon of stochastic resonance. Similar measure-
ments taken at different magnetic fields and fre-
quencies often showed multiple maxima such as
those shown in Fig. 5.
3. Discussion
In summary, our experiments demonstrate the
characteristic feature of the phenomenon of stochas-
tic resonance, namely the nonmonotonic behavior of
Fig. 2. a — Oscillatory behavior of the rectified voltage
across Sn–Ge sample versus dc magnetic field:
T = 3.0 K, f1 = 100 kHz and Iac = 0.8 mA. b — Illustra-
tion of the stochastic resonance detection scheme. Mag-
netic field components Hac and Hnoise are added to dc
magnetic field H.
Fig. 3. Input signal Hac + Hnoise (insets) and the
Fourier spectrum of the output voltage for different le-
vels of input noise Hnoise: σN = 0 (a); σN = 16 mOe (b);
σN = 31 mOe (c); σN = 47 mOe (d). The input signal
amplitude remains constant Hac = 20 mOe. Signal fre-
quency fH = 18.5 Hz, dc magnetic field H = 0.17 Oe.
Observation of stochastic resonance in percolative Josephson media
Fizika Nizkikh Temperatur, 2002, v. 28, No. 6 545
SNR. At the optimum noise level SNR increases up
to 40. The presence of multiple maxima (Figs. 4
and 5) can be due to the effect of different Joseph-
son contours in our structure that is operated at the
border of the percolation threshold.
We suppose that the nonmonotonic dependence
of SNR on frequency fH (Fig. 5) excludes other
possible explanations (such as, e.g., a simple recti-
fication effect due to a nonlinearity of the response)
for the observed gain of small input signal.
Detailed measurements taken at different fre-
quencies shown in Fig. 5 indicate, at least in some
ranges of the dc magnetic field, the existence of
parameter regions characterized by a significant
gain for a relatively broadband signal. We interpret
this behavior as a property of percolative Josephson
media with a wide range of self-similar contours.
The SNR gain in our system can be tuned to a
desired operation frequency fH by changing the dc
magnetic field H.
The nature of the stochastic resonance in the
studied system can be related to the commonly
known bistable oscillator behavior of the magnetic
flux quantization contours. Moreover, in the pres-
ence of current bias Iac at relatively high frequency
(at f1 about 100 kHz) with amplitude larger than
critical, our samples show a dynamical chaos. Such
a regime is commonly characterized by a coexistence
of multiple attractors in the phase space. Indeed,
calculation of Lyapunov exponents from the time
evolution of the voltage measured at constant cur-
rent indicates presence of chaos in our system [7].
In this case, the «phase trajectory» of the system
may stay long time in any of the attractors and
perform irregular transitions between them. A syn-
chronization of such intermittent transitions by a
small input signal may lead as well to stochastic
resonance [8]. Yet, these speculations require fur-
ther investigations to be firmly justified.
Fig. 4. Output signal-to-noise ratio (SNR) versus input
noise level σN for the first harmonic of the input signal
frequency fH = 18.5 Hz. Magnetic field H = 0.17 Oe.
Fig. 5. SNR dependence on input noise level σN and
input signal frequency fH at different dc magnetic fields
H, Oe: 0.17 (a); 0.18 (b); 0.19 (c).
A. M. Glukhov, A. G. Sivakov, and A. V. Ustinov
546 Fizika Nizkikh Temperatur, 2002, v. 28, No. 6
This work was supported by the German-Ukrai-
nian collaboration grant of the Bundesministerium
fur Bildung, Wissenschaft, Forschung und Tech-
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