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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).