Abstract

We study two-photon transport in a one-dimensional waveguide with a side-coupled two-level system. Depending on the momentum of the incoming photons, we find that the nature of the scattering process changes considerably. We further show that bunching behavior can be found in the scattered light. As a result, we find that the waveguide dispersion has a strong influence on the photon correlations. By modifying the momentum of the pulse, the nature of the correlations can therefore be altered or optimized.

© 2013 Optical Society of America

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  1. H. J. Kimble, Nature 453, 1023 (2008).
    [CrossRef]
  2. P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
    [CrossRef]
  3. T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
    [CrossRef]
  4. L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
    [CrossRef]
  5. P. Longo, P. Schmitteckert, and K. Busch, J. Opt. A 11, 114009 (2009).
    [CrossRef]
  6. P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. Lett. 104, 023602 (2010).
    [CrossRef]
  7. P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. A 83, 063828 (2011).
    [CrossRef]
  8. J. T. Shen and S. Fan, Phys. Rev. Lett. 98, 153003 (2007).
    [CrossRef]
  9. H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. A 85, 043832 (2012).
    [CrossRef]
  10. Y. Saad, SIAM J. Numer. Anal. 29, 209 (1992).
    [CrossRef]
  11. R. B. Sidje, ACM Trans. Math. Softw. 24, 130 (1998).
    [CrossRef]
  12. S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
    [CrossRef]
  13. P. Schmitteckert, Phys. Rev. B 70, 121302 (2004).
    [CrossRef]
  14. S. T. Carr, D. A. Bagrets, and P. Schmitteckert, Phys. Rev. Lett. 107, 206801 (2011).
    [CrossRef]
  15. H. Römer, Theoretical Optics: An Introduction (Wiley-VCH, 2005).
  16. X. T. Zou and L. Mandel, Phys. Rev. A 41, 475 (1990).
    [CrossRef]

2012

H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. A 85, 043832 (2012).
[CrossRef]

2011

S. T. Carr, D. A. Bagrets, and P. Schmitteckert, Phys. Rev. Lett. 107, 206801 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. A 83, 063828 (2011).
[CrossRef]

2010

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. Lett. 104, 023602 (2010).
[CrossRef]

2009

P. Longo, P. Schmitteckert, and K. Busch, J. Opt. A 11, 114009 (2009).
[CrossRef]

2008

H. J. Kimble, Nature 453, 1023 (2008).
[CrossRef]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

2007

J. T. Shen and S. Fan, Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

2006

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

2004

P. Schmitteckert, Phys. Rev. B 70, 121302 (2004).
[CrossRef]

1998

R. B. Sidje, ACM Trans. Math. Softw. 24, 130 (1998).
[CrossRef]

1992

S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
[CrossRef]

Y. Saad, SIAM J. Numer. Anal. 29, 209 (1992).
[CrossRef]

1990

X. T. Zou and L. Mandel, Phys. Rev. A 41, 475 (1990).
[CrossRef]

Bagrets, D. A.

S. T. Carr, D. A. Bagrets, and P. Schmitteckert, Phys. Rev. Lett. 107, 206801 (2011).
[CrossRef]

Baranger, H. U.

H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. A 85, 043832 (2012).
[CrossRef]

Bermel, P.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Busch, K.

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. A 83, 063828 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. Lett. 104, 023602 (2010).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, J. Opt. A 11, 114009 (2009).
[CrossRef]

Carr, S. T.

S. T. Carr, D. A. Bagrets, and P. Schmitteckert, Phys. Rev. Lett. 107, 206801 (2011).
[CrossRef]

Fan, S.

J. T. Shen and S. Fan, Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

Forchel, A.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Gauthier, D. J.

H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. A 85, 043832 (2012).
[CrossRef]

Gong, Z. R.

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Joannopoulos, J. D.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Johnson, S. G.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Julsgaard, B.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Kamp, M.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Kimble, H. J.

H. J. Kimble, Nature 453, 1023 (2008).
[CrossRef]

Liu, Y.-X.

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Lodahl, P.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Longo, P.

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. A 83, 063828 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. Lett. 104, 023602 (2010).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, J. Opt. A 11, 114009 (2009).
[CrossRef]

Lund-Hansen, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Mandel, L.

X. T. Zou and L. Mandel, Phys. Rev. A 41, 475 (1990).
[CrossRef]

Nori, F.

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Rodriguez, A.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Römer, H.

H. Römer, Theoretical Optics: An Introduction (Wiley-VCH, 2005).

Saad, Y.

Y. Saad, SIAM J. Numer. Anal. 29, 209 (1992).
[CrossRef]

Schmitteckert, P.

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. A 83, 063828 (2011).
[CrossRef]

S. T. Carr, D. A. Bagrets, and P. Schmitteckert, Phys. Rev. Lett. 107, 206801 (2011).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. Lett. 104, 023602 (2010).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, J. Opt. A 11, 114009 (2009).
[CrossRef]

P. Schmitteckert, Phys. Rev. B 70, 121302 (2004).
[CrossRef]

Shen, J. T.

J. T. Shen and S. Fan, Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

Sidje, R. B.

R. B. Sidje, ACM Trans. Math. Softw. 24, 130 (1998).
[CrossRef]

Soljacic, M.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Stobbe, S.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Sun, C. P.

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Sünner, T.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

Thyrrestrup, H.

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

White, S. R.

S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
[CrossRef]

Zheng, H.

H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. A 85, 043832 (2012).
[CrossRef]

Zhou, L.

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Zou, X. T.

X. T. Zou and L. Mandel, Phys. Rev. A 41, 475 (1990).
[CrossRef]

ACM Trans. Math. Softw.

R. B. Sidje, ACM Trans. Math. Softw. 24, 130 (1998).
[CrossRef]

J. Opt. A

P. Longo, P. Schmitteckert, and K. Busch, J. Opt. A 11, 114009 (2009).
[CrossRef]

Nature

H. J. Kimble, Nature 453, 1023 (2008).
[CrossRef]

Phys. Rev. A

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. A 74, 043818 (2006).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. A 83, 063828 (2011).
[CrossRef]

H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. A 85, 043832 (2012).
[CrossRef]

X. T. Zou and L. Mandel, Phys. Rev. A 41, 475 (1990).
[CrossRef]

Phys. Rev. B

P. Schmitteckert, Phys. Rev. B 70, 121302 (2004).
[CrossRef]

Phys. Rev. Lett.

S. T. Carr, D. A. Bagrets, and P. Schmitteckert, Phys. Rev. Lett. 107, 206801 (2011).
[CrossRef]

S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
[CrossRef]

J. T. Shen and S. Fan, Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

P. Longo, P. Schmitteckert, and K. Busch, Phys. Rev. Lett. 104, 023602 (2010).
[CrossRef]

T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, Phys. Rev. Lett. 101, 113903 (2008).
[CrossRef]

L. Zhou, Z. R. Gong, Y.-X. Liu, C. P. Sun, and F. Nori, Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

SIAM J. Numer. Anal.

Y. Saad, SIAM J. Numer. Anal. 29, 209 (1992).
[CrossRef]

Other

H. Römer, Theoretical Optics: An Introduction (Wiley-VCH, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

Final states after scattering for (a) k=(3π/4) at time t=70/J and (b) k=(π/2) at t=55/J. In the first case, the occupation of the atom after scattering is much higher, and less light is transmitted into the right lead of the waveguide.

Fig. 2.
Fig. 2.

(a) and (b) Final state after scattering in the two-dimensional representation of the wave function and the position of the second photon while the first has been absorbed to excite the atom in the case k=(3π/4) at time t=70/J. (c) and (d) The same for the case k=(π/2) at t=55/J. In the first case one photon is trapped at the site x=100 while the other photon propagates, whereas in the second case both photons are trapped in the same position or propagate alongside one another [enlarged in the inset in (c)].

Fig. 3.
Fig. 3.

Second-order correlation function for (a) k=(3π/4) and (b) k=(π/2) at different times. In (b) we clearly observe photon bunching.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

H=Jx(ax+1ax+axax+1)+Ω2σz+V(σ+ax0+σax0),
|ψ(t)=eiH(tt0)|ψ(t=t0).
|ψ(t)=i=1Mj=1Mugij(t)axiaxj|0,g+i=1Muei(t)axi|0,e.
|ψ(t0)=1Ni=1Mj=1Meikx1ieikx2j×e(x1ix¯)2/2σ2e(x2jx¯)2/2σ2ax1iax2j|0,g.
Ω=2Jcos(k).
(ugM1ugM2ugMMug21ug22ug11),(ue1ue2ueM).
g(2)(xi,ti;xj,tj)=axi(ti)axj(tj)axj(tj)axi(ti)axi(ti)axi(ti)axj(tj)axj(tj).
g(2)(xi,t;xj,t)=nxinxjnxiδijnxinxj.
g(2)(xi,t,xj,t)=11n,n=2,3,

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