Abstract

We present an efficient method for optimizing the spatial profile of entangled-photon wave function produced in a spontaneous parametric down conversion process. A deformable mirror that modifies a wavefront of a 404 nm CW diode laser pump interacting with a nonlinear β-barium borate type-I crystal effectively controls the profile of the joint biphoton function. The use of a feedback signal extracted from the biphoton coincidence rate is used to achieve the optimal wavefront shape. The optimization of the two-photon coupling into two, single spatial modes for correlated detection is used for a practical demonstration of this physical principle.

© 2013 Optical Society of America

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  1. A. V. Belinskii and D. N. Klyshko, Zh. Eksp. Teor. Fiz. 105, 487 (1994).
  2. T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
    [CrossRef]
  3. C. H. Monken, P. H. Souto Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
    [CrossRef]
  4. C. Bonato, S. Bonora, A. Chiuri, P. Mataloni, G. Milani, G. Vallone, and P. Villoresi, J. Opt. Soc. Am. B 27, A175 (2010).
    [CrossRef]
  5. A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
    [CrossRef]
  6. C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
    [CrossRef]
  7. P. Kolenderski, W. Wasilewski, and K. Banaszek, Phys. Rev. A 80, 013811 (2009).
    [CrossRef]
  8. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, Opt. Lett. 29, 207 (2004).
    [CrossRef]
  9. E. Bonabeau, M. Dorigo, and G. Theraulaz, Nature 406, 39 (2000).
    [CrossRef]
  10. S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
    [CrossRef]
  11. M. Dorigo and M. L. Gambardella, IEEE Trans. Evol. Comp. 1, 53 (1997).
    [CrossRef]
  12. M. Dorigo, V. Maniezzo, and A. Colorni, IEEE Trans. Syst. 26, 29 (1996).

2010 (1)

2009 (1)

P. Kolenderski, W. Wasilewski, and K. Banaszek, Phys. Rev. A 80, 013811 (2009).
[CrossRef]

2008 (1)

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

2006 (1)

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

2004 (2)

2000 (1)

E. Bonabeau, M. Dorigo, and G. Theraulaz, Nature 406, 39 (2000).
[CrossRef]

1998 (1)

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

1997 (1)

M. Dorigo and M. L. Gambardella, IEEE Trans. Evol. Comp. 1, 53 (1997).
[CrossRef]

1996 (2)

M. Dorigo, V. Maniezzo, and A. Colorni, IEEE Trans. Syst. 26, 29 (1996).

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

1994 (1)

A. V. Belinskii and D. N. Klyshko, Zh. Eksp. Teor. Fiz. 105, 487 (1994).

Abouraddy, A. F.

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef]

Banaszek, K.

P. Kolenderski, W. Wasilewski, and K. Banaszek, Phys. Rev. A 80, 013811 (2009).
[CrossRef]

Belinskii, A. V.

A. V. Belinskii and D. N. Klyshko, Zh. Eksp. Teor. Fiz. 105, 487 (1994).

Bonabeau, E.

E. Bonabeau, M. Dorigo, and G. Theraulaz, Nature 406, 39 (2000).
[CrossRef]

Bonato, C.

C. Bonato, S. Bonora, A. Chiuri, P. Mataloni, G. Milani, G. Vallone, and P. Villoresi, J. Opt. Soc. Am. B 27, A175 (2010).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

Bonora, S.

C. Bonato, S. Bonora, A. Chiuri, P. Mataloni, G. Milani, G. Vallone, and P. Villoresi, J. Opt. Soc. Am. B 27, A175 (2010).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, Opt. Lett. 29, 207 (2004).
[CrossRef]

Capraro, I.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

Chiuri, A.

Colorni, A.

M. Dorigo, V. Maniezzo, and A. Colorni, IEEE Trans. Syst. 26, 29 (1996).

De Silvestri, S.

Dorigo, M.

E. Bonabeau, M. Dorigo, and G. Theraulaz, Nature 406, 39 (2000).
[CrossRef]

M. Dorigo and M. L. Gambardella, IEEE Trans. Evol. Comp. 1, 53 (1997).
[CrossRef]

M. Dorigo, V. Maniezzo, and A. Colorni, IEEE Trans. Syst. 26, 29 (1996).

Gambardella, M. L.

M. Dorigo and M. L. Gambardella, IEEE Trans. Evol. Comp. 1, 53 (1997).
[CrossRef]

Klyshko, D. N.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

A. V. Belinskii and D. N. Klyshko, Zh. Eksp. Teor. Fiz. 105, 487 (1994).

Kolenderski, P.

P. Kolenderski, W. Wasilewski, and K. Banaszek, Phys. Rev. A 80, 013811 (2009).
[CrossRef]

Maniezzo, V.

M. Dorigo, V. Maniezzo, and A. Colorni, IEEE Trans. Syst. 26, 29 (1996).

Mataloni, P.

Milani, G.

Monken, C. H.

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Nisoli, M.

Padua, S.

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Pascolini, M.

Pittman, T. B.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

Poletto, L.

Romanin, M.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

Saleh, B. E. A.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef]

Sansone, G.

Sergienko, A. V.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

Shih, Y. H.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

Souto Ribeiro, P. H.

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Stagira, S.

Stone, P. R.

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

Teich, M. C.

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef]

Theraulaz, G.

E. Bonabeau, M. Dorigo, and G. Theraulaz, Nature 406, 39 (2000).
[CrossRef]

Tondello, G.

Trestino, C.

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

Vallone, G.

Villoresi, P.

C. Bonato, S. Bonora, A. Chiuri, P. Mataloni, G. Milani, G. Vallone, and P. Villoresi, J. Opt. Soc. Am. B 27, A175 (2010).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, Opt. Lett. 29, 207 (2004).
[CrossRef]

Vozzi, C.

Wasilewski, W.

P. Kolenderski, W. Wasilewski, and K. Banaszek, Phys. Rev. A 80, 013811 (2009).
[CrossRef]

IEEE Trans. Evol. Comp. (1)

M. Dorigo and M. L. Gambardella, IEEE Trans. Evol. Comp. 1, 53 (1997).
[CrossRef]

IEEE Trans. Syst. (1)

M. Dorigo, V. Maniezzo, and A. Colorni, IEEE Trans. Syst. 26, 29 (1996).

J. Opt. Soc. Am. B (1)

Nature (1)

E. Bonabeau, M. Dorigo, and G. Theraulaz, Nature 406, 39 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

P. Kolenderski, W. Wasilewski, and K. Banaszek, Phys. Rev. A 80, 013811 (2009).
[CrossRef]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, Phys. Rev. A 53, 2804 (1996).
[CrossRef]

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Bonora, I. Capraro, L. Poletto, M. Romanin, C. Trestino, and P. Villoresi, Rev. Sci. Instrum. 77, 093102 (2006).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

A. V. Belinskii and D. N. Klyshko, Zh. Eksp. Teor. Fiz. 105, 487 (1994).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. The 404 nm laser passes through a Galilean telescope (lenses D and C, with fD=250mm, fC=500mm). After reflecting from the DefM, the beam is focused onto a NL by the lens F (fF=287mm). A dichroic mirror (DM) sends 10% of the pump to a wavefront sensor (WFS) to its spatial shape evaluation. The 808 nm SPDC photons are collimated by an achromatic doublet (AD) (fAD=75mm) and sent to fiber couplers (FC) after Z1=0.5m and Z2=2m of free space propagation. Finally, SPDC light is measured by two SPAD detectors and coincidences are evaluated with a coincidence counter. The outcome is utilized in a feedback loop with a DefM by Ant evolutionary algorithm.

Fig. 2.
Fig. 2.

Coincidence evolution provided by the algorithm steps. Ant algorithm maximizes the coincidence counts as explained in the text. As a result, a pattern converging to an asymptotic value is achieved. Solid black lines illustrate the average values of initial and final coincidence counts measured over 60 s of exposure time.

Fig. 3.
Fig. 3.

Measured low order Zernike components for each wavefront, before and after the optimization. In the case of flat wavefront (RMS=0.01), all Zernike terms are less than 0.01 μm. The optimized wavefront exhibits a significant growth in both second and third order aberrations.

Fig. 4.
Fig. 4.

Comparison between SPDC beam spots at 1.5 m from the crystal, acquired with an image intensifier with nominal gain of 1000 and a low-noise CCD camera, with acquisition time of 60 s. The images correspond to (a) the flat wavefront (b) and the optimized case. A substantial reduction of beam diameter can be observed.

Fig. 5.
Fig. 5.

Coincidence evolution provided by algorithm for single-mode coupling (we only show the steps increasing the coincidences).

Equations (3)

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|ψ=d2ksd2kidωsdωiψ˜ki,ks,ωi,ωsaks,ωsaki,ωi|vac,
ψ˜ki,ks,ωi,ωs=NLAp(ks+ki,ωs+ωi)sinc(L2Δkz),
f(coinc)=N/max(N,coinc),

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