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SWITCH EFFECT OF NONCLASSICAL LIGHT
J. Janszky, C. Sibilia, M. Bertolotti, Y. Yushin
To cite this version:
J. Janszky, C. Sibilia, M. Bertolotti, Y. Yushin. SWITCH EFFECT OF NONCLASSICAL LIGHT.
Journal de Physique Colloques, 1988, 49 (C2), pp.C2-337-C2-339. �10.1051/jphyscol:1988280�. �jpa-
00227697�
JOURNAL DE PHYSIQUE
Colloque C2, Suppl6ment au n06, Tome 49, juin 1988
SWITCH EFFECT OF NONCLASSICAL LIGHT
J. JANSZKY, C. SIBILIA', M. BERTOLOTTI* and Y. WSHIN*"
Research Laboratory for Crystal Physics of the Hungarian Academy of Science, PO Box 132, H-1502 Budapest, Hungary
"~ipartimento di Energetics, Via Scarpa 16, I-00161 Roma, Italy and GNEQP of CNR, Italy
* * Institute of Crystallography, Moscow 117333, USSR
R6sum6
-
On dtude la propagation de la lumigre avec statistique complexe (avec proprietds de squeezing, coh6rent et chaotique) dans un coupleur directionnel optique lineaire. Le state de squeezing peut&re commutd d'une sortie a l'autre et sa component de squeezing peut chang6 en raison du parametre de dephasage.
Abstract
-
We have studied the behavior of light with complex statistics (having squeezed, coherent and chaotic features) propagating inside a linear coupler. We show that the squeezed state can be switched from one channel to the other one, changing its squeezing properties, depending on the detuning parameter.We have studied the propagation through a linear directional coupler of light with complex statistics , ( having sq~eezed~coherent and chaotic features),looking at quantum effectssuch assqueezing.
Light with complex statistics can be described by the following characteristic function
=
1~ ( 7 )
= exp [ - M I ? \+ r
cs*q 2
+s
r*2j +?w*
+i W]
1
where M I S and W are statistical characteristic parameters describing chaotic (M) ,squeezing (S) and coherent ( W = W eiq ) part of the field / I /.
In particular if a field is in a pure squeezed state we have
r being the squeezing parameter.
A field in a mixed state ( superposition of chaotic, coherent and squeezed state) is given by
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988280
C2-338 JOURNAL DE PHYSIQUE
being N the noise photon number.
In the case of a directional coupler it is possible to evaluate each of the previous quantities starting from the solution of the Heisenberg equations. In fact assuming a single mode propagation in each waveguide the Heisenberg operatorial equations look like the classical one obtained in the frame of the " coupled mode theory" :
=
-
i ~a exp A ( 2 i 6 z 1-
i 6 b-
f bh A
where a and b are the field annijiilatiog operators in channel 2 and
b
respecti-vely,
5
is the detuning parameter, Q and Qb are noise operatbrsra
andgb
are damping constants, and K is the c8upling constant.
Solutions of these equations can be found analitically neglecting the last two terms / 2 / .
We assume that the input statistics of light of both modes can be described by the normally ordered characteristic function as given by eq.(l).
From the solution of eqs.(4) we find the statistical properties of the output field.
We are interested to the squeezing behavior of the structure. The squeezing can be defined as usually using the following operators:
The field is squeezed if + < 1 or < I
.
These variances are connected to the statistical characteristics /3/ by the following equation
From the solutions of eqs.(4) we can evaluate M and S and obtain the squeezing behavior of the field through the structure.
Of course different results can be obtained depending on the input field.
We have studied several different input field situations as for example equal field in both channels, i.e. the same Mo, S and W values, and other situations in which also the effect of the detuning papameterohas been taken into account.
The nost interesting case is the one in which we suppose a pure squeezed state in channel
b
as an input, and a vacuum state or a pure coherent state in the other channel (i.e. M = S = 0 ) . If the detuning parameter is zero we find at the output of the structurg zego noise andi.e. in channel 2 we have an opposite squeezing that it was the input of channel b
,
while the output in channelb
shows no squeezing. Changing the detuning pa- rameter we change the switching conditions of the squeezing. In fact for another special value of the detuning parameter5
= K we have again no outputnoise in both channel and
1.e. changing the detuning parameter from zero to K we have the same output con- ditions as the input.
Other values of the detuning parameter modify the switch possibility of squeezing, because noise can be added.
This effect is shown in Fig.1
,
where the noise level in channel 5 is plotted against the length of the directional coupler,
for three different values of the detuning parameter. For &=0 i there are two critical lengths ( z = H / 2 cm and z = fl cm, if K = 1 cm-I ) of the structure forwhich the noise level is zero (i.e.a squeezed state is found)
,
for = 0 - 2 cm-1,
and6
= 0.5 cm-1,
noise level is zero only for z = f f cm, while for any other length noise is added.This behaviour,diPectly connected to the phase shift introduced by the directio- nal coupler,shows that i.t is possible to use the coupler as a switch device for,nog classical light.
Fig.1
-
Noise level (a.u.1 in channel 5 vs length of the linear coupler for thre~~different values of detuning parameter ( d = 0, b = 0.2, b = 0.5 Cm,
K = I c m ) .
REFERENCES
/I/ Marcuse, D." Theory of Optical Dielectric Waveguides", A.D.,N.Y.,(1974) /2/ Janszky,J., Sibilia, C., Bertolotti, M.,Yushin, Y., to be published.
/3/ Janszky,J., Yushin, Y.Phys.Rev.
