Method for amplifying voltage in Josephon junction

The present invention discloses a method for amplifying voltage to which a test will be given in Josephon junction having external current, and more particularly, to a method for amplifying voltage in Josephon junction in which the voltage in a simple Josephon junction having an external current can be amplified by inserting an external colored noise into the external current.

FIELD OF THE INVENTION 
The present invention relates to a method for amplifying voltage in 
Josephon junction in which the voltage to which a test will be given can 
be amplified by inserting an external noise. 
BACKGROUND OF THE INVENTION 
A typical Josephon junction includes two separated superconductors, an 
insulator (called "gap") connecting them, and an external current. 
Electrons within superconductors are same in size and opposite directions 
in momentum, and they may form a stable shape when their cooper pair are 
consisted of two electrons having opposite spins. However, the cooper pair 
may break and the excited electrons or holes created due to the breakage 
are referred as quasi-particles. 
When two superconductors are near enough, the cooper pair located at one 
superconductor exits the gap toward the other superconductor, and this is 
referred as a Josephon tunneling. Movement of the cooper pair is called a 
super current having no resistance. If the external current is less than a 
critical current, the external current appears as a super current that is 
movement of the cooper pairs. However, if the external current is greater 
than the critical current, current (called "common current") due to the 
tunneling of quasi-particles other than the super current is generated 
because the cooper pairs will break, and accordingly there exists a 
resistance and it will cause a voltage to occur. 
SUMMARY OF THE INVENTION 
The object of the present invention to provide a method for amplifying 
voltage in Josephon junction used for a device such as a superconductor 
quantum device sensing a very weak magnetic field or measuring the amount 
thereof, by which the voltage could be maximized by inserting color noise 
into the external current. 
The another object of the present invention to provide a method for 
amplifying voltage in Josephon junction comprising the steps of 
determining a voltage in Josephon junction; adding a colored noise to an 
external current; and controlling given parameter values and the intensity 
of the colored noise or the flip vibration number to amplify the voltage 
determined in the first step. 
In the present invention, an external current is applied to Josephon 
junction circuit having a resistance, and then a symmetric telegraph noise 
or a more general colored noise is applied to the external current. The 
voltage can be amplified by controlling the intensity of the noise and the 
flip vibration number.

Similar reference characters refer to similar parts in the several views of 
the drawings. 
DESCRIPTION OF THE INVENTION 
Embodiments of the present invention will be explained below in detail by 
reference to the accompanying drawings. 
FIG. 1 is a circuit diagram to illustrate one Josephon junction. In the 
drawing, two circles indicate a first and a second superconductors 1 and 2 
respectively. R indicates the resistance of the current due to movement of 
the quasi-particles. I and V indicate external current and voltage 
respectively. 
The circuit of FIG. 1 can be represented as a differential equation such as 
Mathematical Equation 1! referred as a Josephon relationship, assuming 
that the constants such as Planck's constant, the resistance and the 
charge amount of electrons are all 1. 
Mathematical Equation 1! 
EQU d.psi./dt=-b sin .psi.+I. 
Mathematical Equation 1! is obtained by resealing Planck's constant, the 
resistance and the charge amount of electrons from an original equation 
having these constants and by setting the resistance R to be 1. Where p is 
a phase difference between the phase of the cooper pair wave function on 
one superconductor that on the other superconductor. The super current due 
to the cooper pair is caused by the interference of the wave function at 
the cooper pairs located on both side superconductors. 
Mathematical Equation 1! represents the amount of common current on the 
left side. Where R=1, the left side in Mathematical Equation 1! also 
represents the voltage. The first term on the left side in Mathematical 
Equation 1! represents a super current, and the term b represents a 
critical current of the gap. If external current is not applied thereto 
(I=0), the super current and the common current both have the values of 0 
since the stable fixed point of Mathematical Equation 1! is when .psi.=0. 
In the present invention, taking Josephson junction having an external 
current not 0 and a color noise I(t) into considerations. For brief 
explanation of this invention, the simplest telegraph noise (or 
dichotomous noise) among the colored noises is selected for I (t). 
However, the results may be derived through the general colored noise. The 
symmetric telegraph noise I(t) has two values .DELTA. and -.DELTA. and it 
also has a specific value as in Mathematical Equation 2!. 
Mathematical Equation 2! 
EQU &lt;I(t)=0&gt;, &lt;I(t)I(t-.tau.)=.DELTA..sup.2 exp (-.gamma. .tau.) 
where &lt;.&gt; is the average of the noise ensemble, and .DELTA. and .gamma./2 
each represents the intensity of I(t) and the flip vibration number of 
.DELTA..fwdarw.-.DELTA.(or -.DELTA..fwdarw..DELTA.). 
When representing the Josephon junction used in the present invention as a 
differential equation, it will give the following Mathematical Equation 
3!. 
Mathematical Equation 3! 
EQU d.psi./dt=-b sin .psi.+I+I(t)+.eta.(t) 
.eta.(t) is an external Gaussian white noise caused by temperature 
variation etc. and is given as the following Mathematical Equation 4!. 
Mathematical Equation 4! 
EQU &lt;.eta.(t)&gt;=0,&lt;.eta.(t).eta.(t-.tau.)&gt;=2D.delta.(.tau.) 
Where &lt;. &gt;is the average of the noise ensemble and D is the intensity of an 
external noise .eta.(t). 
The relationship between the phase difference .psi. and the voltage V(t) is 
given as V(t)=d.psi./dt. The stationary voltage v after enough long time 
may be calculated using the solution of the stationary probability density 
function in the ensemble equation derived from Mathematical Equation 3!. 
That is, it will result in V=&lt;V(t)&gt; and &lt;.&gt; is the average of the 
stationary probability density, P.sub.s (.phi.). 
Mathematical Equation 5B! 
EQU 0=-.gamma.(P.sub.+ (.phi.)-P.sub.- (.phi.))+d/d.phi.(b sin 
.phi.-I+.DELTA.)P.sub.+ (.phi.)+D.dP.sub.+ (.phi.)/d.phi.! 
Mathematical Equation 5B! 
EQU 0=.gamma.(P.(.phi.)-P.(.phi.))+d/d.phi.(b sin 
.phi.-I+.DELTA.)P.(.phi.)+D.dP.sub.- (.phi.)/d.phi.! 
Next, the sum of the stationary solution P.sub.+ (100 )+P.sub.- (.phi.) in 
the combined ensemble equations Mathematical Equation 5A! and 
Mathematical Equation 5B! becomes the stationary probability density 
function P.sub.s (.phi.). That is, it will result in P.sub.s 
(.phi.)=P.sub.+ (.phi.) +P.sub.- (.phi.) and V is given as the following 
Mathematical Equation 6! 
Mathematical Equation 6! 
EQU V=.intg..sub.0.sup.2.pi. d.phi.(-b sin .phi.+I+.DELTA.)P.sub.s (.phi.) 
where, when solving Mathematical Equation 5A! and Mathematical Equation 
5B! so as to find P.sub.+ (.phi.)+P.sub.- (.phi.), a periodic boundary 
condition is used. 
FIG. 2 is a characteristic view to illustrate a stationary voltage in 
accordance with the intensity (.DELTA.) of the telegraph noise at the flip 
vibration number of given telegraph noise, showing the variation of the 
voltage (V) in accordance with the intensity of the telegraph noise where 
b=2.0, I=1.0 and D=0.25. In these parameter values, if a colored noise 
does not exist, V=1. 
A solid line A, a wavelike line B and a dotted line C each represent the 
voltages V where the flip vibration number of the telegraph noise, log 
.gamma.=-5.0, 0.5, 8.0. In the drawing, the solid line A and the wavelike 
line B have their peak values of V at .DELTA.=2.6 and .DELTA.=3.6, 
respectively. And the peak value of V is amplified more than 1 that is the 
value of voltage if any telegraph noise does not exist. As may be 
understood from FIG. 2, if the flip vibration number of the telegraph 
noise is small, i.e., if the telegraph noise belongs to a noise process 
occurring slowly, a great amplification effect can be obtained. If the 
flip vibration number is very large, the telegraph noise effect is offset 
to each other and thereby the value of V is given as 1 without any 
amplification effect. 
FIG. 3 is a characteristic view to illustrate a stationary voltage in 
accordance with the flip vibration number of the telegraph noise at the 
intensity of given telegraph noise, showing the variation of the voltage 
(V) in accordance with the flip vibration number of the telegraph noise 
.gamma. where b=2.0, I=1.0 and D=0.25. A solid line D, a wavelike line E 
and a dotted line F each show the voltages V where .DELTA.=1.4, 0.4 and 
2.0. When .DELTA.&lt;b, that is, if the intensity of the telegraph noise is 
small, there is no amplifying effect because the value of the peak voltage 
V is less than 1. When .DELTA.&gt;b,. voltage V is amplified at a small flip 
vibration number. The dotted line F of FIG. 3 shows V&gt;1 where log 
.gamma.&lt;-0.7. That is, if the intensity of the telegraph noise is large 
and also the noise process occurs slowly, the value of the voltage V is 
amplified. 
As discussed earlier, the present invention has an outstanding effect of 
improving the commercialization and the efficiency in the manufacture of 
the device using Josephon junction in which the voltage can be maximized 
by adding a colored noise to the external current. 
The foregoing description, although described in its preferred embodiment 
with a certain degree of particularity, is only illustrative of the 
principles of the present invention. It is to be understood that the 
present invention is not to be limited to the preferred embodiments 
disclosed and illustrated herein. Accordingly, all expedient variations 
that may be made within the scope and spirit of the present invention are 
to be encompassed as further embodiments of the present invention.