An optical example for classical Zeno effect

Abstract

In this brief report, we present a proposal to observe the classical zeno effect via the frequent measurement in optics. Comment: 2 pages, 2 figures

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arXiv:1003.5545v1 [quant-ph] 29 Mar 2010
An optical example for classical Zeno effect
Li-Gang Wang,1,2Shi-Jian Gu,1and Hai-Qing Lin1
1Department of Physics and ITP, The Chinese University of Hong Kong, Hong Kong, China
2Department of Physics, Zhejiang University, Hangzhou 310027, China
(Dated: March 30, 2010)
In this brief report, we present a proposal to observe the classical zeno effect via the frequent
measurement in optics.
PACS numbers: 05.40.-a, 03.65.Xp, 03.67.-a
Zeno paradox, such as the problem of the so-called fly-
ing arrow, contrary to the evidence of our senses, seems
never happen in real classical world. But this paradox
is believed to be possible realized uniquely in quantum
world, known as quantum Zeno effect proposed by Misra
and Sudarshan [1] in 1977, because of probability prop-
erties of quantum states and the projective measurement
in quantum mechanics (for a review, see Ref. [2]). Re-
cently, one of us (Gu) argued that the classical Zeno effect
is possible recovered with Super Mario’s intelligent feed-
back [3]. Later, we further showed that the decay of a
classical state in classical noise channels can be signifi-
cantly suppressed with the aid of the successive repeaters
[4], in this sense we claim that the classical Zeno effect
may exist in classical stochastic process. In this report,
we present a proposal to observe the classical zeno effect
in optics. The evolution of the polarized-light intensity
in the designed system are strongly affected by the mea-
sured times.
As shown in Fig. 1(a), when a linear polarized light
beam with initial intensity I0 is incident on a series of
successive Faraday media, the polarization direction of
the beam gradually changes with the increasing number
of the Faraday media. Assuming that the initial direction
of light polarization is in the y direction and the angle
for the polarization rotation from the input to output
changes π/2, then the intensity of the linear polarization
FIG. 1: (Color online) (a) Setup for successive polarization
rotation with a series of Faraday media and (b) setup for the
observation of optical Zeno effect with vertical-polarization
measurements after each Faraday medium.
medium with the length L/N induces a polarization rotation
angle of π/2N and L is the total length of all Faraday media.
Each Faraday
?
?
???????
?
?
?
??
FIG. 2: (Color online) (a) Intensity evolutions of the polar-
ized beam in the y component as a function of distance z for
different measurement times. (b) Dependence of the output
intensities of the polarized beam on the measurement times
N.
beam for the y component is given by
I(z) = I0cos2?πz
2L
?
,(1)
where L is the total length of all Faraday media that
induce the π/2 rotation of light polarization, and z is the
internal distance inside the Faraday media. Since there is
no measurement in (a), the intensity of polarization beam
for the y component evolutes smoothly as a function of
z.
However, once the measurements are presented in Fig.
1(b), the evolution of the resulted intensity is dramati-
cally changed. In Fig. 1(b), we do a vertical-polarization
measurement (along the y direction) after each Faraday
medium, then the resulted intensity of the polarization
beam for the y component becomes

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I(z) = I0
?
cos2(π
2N)
?i−1
cos2
?π
2L
?
z −L
N(i − 1)
??
,
(2)
where N is the total number of Faraday media with the
same polarization rotation angle π/(2N), and i denotes
the ith Faraday medium at which the distance z is lo-
cated. Therefore, the intensity for the polarization light
beam for the y component at the output end finally be-
comes
Iout= I0
?
cos2?π
2N
??N
. (3)
When the measured times increase to be infinite, i. e.,
N → ∞, the output intensity at the output end will be
close to I0. This indicates that the initial intensity of the
linear polarized light beam for the y component, passing
through numerical Faradaymedia with small polarization
rotation angles, will not decay after the infinite measure-
ments. Figure 2(a) shows clearly the changes of the in-
tensities of the linear polarized light in the y component
for different measurement times, and with the increasing
of the measurement times the decay of the intensity be-
comes slower. In Fig. 2(b), it is found that the output
intensity at the output end becomes larger and larger,
and it gradually tends to be one with the increasing of
the measurement times N.
In summary, instead of the memory effect in the pre-
vious scheme [4], in the present scenario we use the po-
larization property of light to recover the Zeno effect.
We can see that the measurement of the light polariza-
tion plays the same role of the projective measurement in
quantum mechanics. However, all the quantities involved
here are classical. In a word, Zeno effect does happen in
the classical world.
Acknowledgments
This work is supported by the Earmarked Grant Re-
search from the Research Grants Council of HKSAR,
China (Project No. CUHK 400807 and 403609).
[1] B. Misra and E. C. G. Sudarshan, J. Math. Phys. 18, 756
(1977).
[2] K. Koshino and A. Shimizu, Phys. Rep. 412, 191 (2005).
[3] S. J. Gu, EPL 88, 20007 (2009).
[4] S. J. Gu, L. G. Wang, Z. G. Wang, and H. Q. Lin,
arXiv:0911.5388 (2009).