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VOLUME 86, NUMBER 20

PHYS ICAL REVIEW LETTERS
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2001

Comment on "Dispersion-Independent High-Visibility Quantum Interference in Ultrafast Parametric Down-Conversion"
Recently AtatЭre et al. claimed to "recover" highvisibility quantum interference in femtosecond pulse pumped type-II spontaneous parametric down-conversion (SPDC ) using neither spectral postselection nor a thin nonlinear crystal [1]. We show in this Comment that the interpretation of experimental data as well as the theory presented in Ref. [1] are incorrect and discuss why such a scheme cannot be used to recover high-visibility quantum interference. Let us first discuss the theory presented in Ref. [1]. Equation (8) is incorrect and, consequently, so is Eq. (10). According to Eq. (10), the coincidence counting rate should have a sin2 u1 1 u2 modulation with 100% visibility for arbitrary angles of u1 and u2 when t 0. As we shall see in our experiment, this is not so. This is because, for arbitrary u1 and u2 , there should be two more terms, i.e., cos p 4 2 u1 sin p 4 2 u2 A t1 , t2 1 t 2 A t2 1 t , t1 2 sin p 4 2 u1 cos p 4 2 u2 A t1 1 t , t2 2 A t2 , t1 1 t , which cannot be ignored in Eq. (8). These two terms have no overlap if t 0. This will reduce the visibility of the polarization correlation at arbitrary u1 and u2 , except at the H and V settings of the analyzers. To demonstrate that Eq. (10) in Ref. [1] is incorrect, we performed an experiment which is identical to Fig. 1 in Ref. [1] in which the polarization correlation is measured. When u1 90± H or 0± V , high-visibility modulation is observed as u2 is varied [see Fig. 1(a)]. This is what AtatЭre et al. observed in Ref. [1]. However, at u1 45±, the visibility is immediately reduced to 16% [Fig. 1( b)]. This means that the "X -Y delay" at t 0 does not recover the quantum interference as the authors expected. In fact, one can observe the same interference pattern when the X -Y delay is absent. To show this, we removed the X -Y delay from the setup, set u1 90±, and varied u2 . The "visibility" is 100% [see Fig. 1(c)]. By setting u1 45± H and varying u2 again, as evident from Fig. 1(d), the visibility is as low as 16%. This demonstrates that the X -Y delay has no net physical effect when t 0. This also shows that what is observed in Ref. [1] is not quantum interference. It simply shows that the signal is V polarized and the idler is H polarized. These data clearly show that jV jH has not been transformed to jX jX 2 jY jY , as the authors claim [Eq. (10)]. In fact, such a "cascaded transformation of the two-photon state" cannot occur unless proper longitudinal compensation is made first [2]. Therefore, it is obvious that this type of scheme cannot be used to recover quantum interference. We also note that Fig. 3 in Ref. [1] might lead to confusion since readers might mistakenly consider it to show space-time interference. In fact,
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FIG. 1. Experimental data. With X -Y delay t 45±. Without X -Y delay: (c) u1 90±, (b) u1 (a) u1 (d) u1 45±.

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only polarization correlation measurement is observed in Ref. [1] at a fixed angle u1 0±. It is true that AtatЭre et al. made some type of polarization state transformation of biphotons. Certainly these transformations are related to t and the pump pulse duration (for a general description of polarization transformation of biphotons, see Ref. [3]). It, however, has nothing to do with the "recovery" of quantum interference as they claim. In conclusion, we have experimentally and theoretically shown AtatЭre et al.'s claim to be in error. Neither the experimental data nor the correct theory support their claim. Finally, we would like to mention that we have recently developed a new method of generating entangled photon pairs pumped by femtosecond pulses which shows true high-visibility quantum interference [4]. Yoon-Ho Kim, Sergei P. Kulik,* Morton H. Rubin, and Yanhua Shih
Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250 Received 31 May 2000 DOI: 10.1103 / PhysRevLett.86.4710 PACS numbers: 42.50.Dv, 03.65.Ta

[1] [2] [3] [4]

*Permanent address: Department of Physics, Moscow State University, Moscow, 119899, Russia. M. AtatЭre, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 84, 618 (2000). M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, Phys. Rev. A 50, 5122 (1994). A. V. Burlakov and D. N. Klyshko, JETP Lett. 69, 839 (1999). Y.-H. Kim, S. P. Kulik, and Y. H. Shih, Phys. Rev. A 62, 011802(R) (2000); quant-ph /0007067.

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0031 - 9007 01 86(20) 4710(1) $15.00

© 2001 The American Physical Society