Abstract

We show that atoms subject to laser radiation may form a non-additive many-body system on account of their long-range forces, when the atoms are trapped in the vicinity of a fiber with a Bragg grating. When the laser frequency is inside the grating’s bandgap but very close to its edge, we find that the range and strength of the laser-induced interaction becomes substantially enhanced, due to the large density of states near the edge, while the competing process of scattering to the fiber is inhibited. The dynamics of the atomic positions in this system conforms to a prominent model of statistical physics which exhibits slow relaxation. This suggests the possibility of using laser-illuminated atoms to study the characteristics of non-additive systems.

© 2014 Optical Society of America

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References

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  1. T. Dauxois, S. Ruffo, E. Arimondo, and M. Wilkens, eds., Dynamics and Thermodynamics of Systems with Long-Range Interactions (Springer, 2002).
  2. D. Mukamel, “Notes on the statistical mechanics of systems with long-range interactions,” arXiv:0905.1457 (2008).
  3. M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
    [CrossRef]
  4. D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Academic, 1984).
  5. E. Shahmoon and G. Kurizki, Phys. Rev. A 89, 043419 (2014).
    [CrossRef]
  6. D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, Phys. Rev. Lett. 90, 110402 (2003).
    [CrossRef]
  7. A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
    [CrossRef]
  8. E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
    [CrossRef]
  9. D. E. Chang, J. I. Cirac, and H. J. Kimble, Phys. Rev. Lett. 110, 113606 (2013).
    [CrossRef]
  10. C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, (Elsevier, 1992), pp. 1–164.
  11. K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).
  12. E. Shahmoon and G. Kurizki, Phys. Rev. A 87, 033831 (2013).
    [CrossRef]
  13. S. John and J. Wang, Phys. Rev. B 43, 12772 (1991).
    [CrossRef]
  14. S. Bay, P. Lambropoulos, and K. Mølmer, Phys. Rev. A 55, 1485 (1997).
    [CrossRef]
  15. Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
    [CrossRef]
  16. F. Baldovin, R.-H. Chavanis, and E. Orlandini, Phys. Rev. E 79, 011102 (2009).
    [CrossRef]
  17. M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
    [CrossRef]
  18. I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
    [CrossRef]
  19. K. P. Nayak and K. Hakuta, Opt. Express 21, 2480 (2013).
    [CrossRef]

2014 (1)

E. Shahmoon and G. Kurizki, Phys. Rev. A 89, 043419 (2014).
[CrossRef]

2013 (4)

D. E. Chang, J. I. Cirac, and H. J. Kimble, Phys. Rev. Lett. 110, 113606 (2013).
[CrossRef]

E. Shahmoon and G. Kurizki, Phys. Rev. A 87, 033831 (2013).
[CrossRef]

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

K. P. Nayak and K. Hakuta, Opt. Express 21, 2480 (2013).
[CrossRef]

2012 (1)

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

2010 (1)

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

2009 (1)

F. Baldovin, R.-H. Chavanis, and E. Orlandini, Phys. Rev. E 79, 011102 (2009).
[CrossRef]

2004 (1)

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

2003 (1)

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, Phys. Rev. Lett. 90, 110402 (2003).
[CrossRef]

2002 (1)

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

1997 (1)

S. Bay, P. Lambropoulos, and K. Mølmer, Phys. Rev. A 55, 1485 (1997).
[CrossRef]

1992 (1)

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef]

1991 (1)

S. John and J. Wang, Phys. Rev. B 43, 12772 (1991).
[CrossRef]

Alton, D. J.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Baldovin, F.

F. Baldovin, R.-H. Chavanis, and E. Orlandini, Phys. Rev. E 79, 011102 (2009).
[CrossRef]

Barré, J.

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

Bay, S.

S. Bay, P. Lambropoulos, and K. Mølmer, Phys. Rev. A 55, 1485 (1997).
[CrossRef]

Bouchet, F.

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

Buggle, Ch.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Chalony, M.

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

Chang, D. E.

D. E. Chang, J. I. Cirac, and H. J. Kimble, Phys. Rev. Lett. 110, 113606 (2013).
[CrossRef]

Chavanis, R.-H.

F. Baldovin, R.-H. Chavanis, and E. Orlandini, Phys. Rev. E 79, 011102 (2009).
[CrossRef]

Choi, K. S.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Chu, S.

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef]

Cirac, J. I.

D. E. Chang, J. I. Cirac, and H. J. Kimble, Phys. Rev. Lett. 110, 113606 (2013).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, (Elsevier, 1992), pp. 1–164.

Craig, D. P.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Academic, 1984).

Dauxois, T.

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

Dawkins, S. T.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

Dieckmann, K.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Ding, D.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Giovanazzi, S.

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, Phys. Rev. Lett. 90, 110402 (2003).
[CrossRef]

Goban, A.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Hakuta, K.

John, S.

S. John and J. Wang, Phys. Rev. B 43, 12772 (1991).
[CrossRef]

Kasevich, M.

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef]

Kemmann, M.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Kimble, H. J.

D. E. Chang, J. I. Cirac, and H. J. Kimble, Phys. Rev. Lett. 110, 113606 (2013).
[CrossRef]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Kurizki, G.

E. Shahmoon and G. Kurizki, Phys. Rev. A 89, 043419 (2014).
[CrossRef]

E. Shahmoon and G. Kurizki, Phys. Rev. A 87, 033831 (2013).
[CrossRef]

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, Phys. Rev. Lett. 90, 110402 (2003).
[CrossRef]

Lacroute, C.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Lambropoulos, P.

S. Bay, P. Lambropoulos, and K. Mølmer, Phys. Rev. A 55, 1485 (1997).
[CrossRef]

Marcos, B.

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

Mølmer, K.

S. Bay, P. Lambropoulos, and K. Mølmer, Phys. Rev. A 55, 1485 (1997).
[CrossRef]

Mukamel, D.

D. Mukamel, “Notes on the statistical mechanics of systems with long-range interactions,” arXiv:0905.1457 (2008).

Nayak, K. P.

O’Dell, D. H. J.

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, Phys. Rev. Lett. 90, 110402 (2003).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

Olivetti, A.

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

Orlandini, E.

F. Baldovin, R.-H. Chavanis, and E. Orlandini, Phys. Rev. E 79, 011102 (2009).
[CrossRef]

Petrov, D. S.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Pototschnig, M.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Rauschenbeutel, A.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

Reitz, D.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

Ruffo, S.

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

Sagué, G.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

Schmidt, R.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

Shahmoon, E.

E. Shahmoon and G. Kurizki, Phys. Rev. A 89, 043419 (2014).
[CrossRef]

E. Shahmoon and G. Kurizki, Phys. Rev. A 87, 033831 (2013).
[CrossRef]

Shlyapnikov, G. V.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Shvarchuck, I.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Stern, N. P.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Thiele, T.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

Thirunamachandran, T.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Academic, 1984).

Tiecke, T. G.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Vetsch, E.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

von Klitzing, W.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Walraven, J. T. M.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Wang, J.

S. John and J. Wang, Phys. Rev. B 43, 12772 (1991).
[CrossRef]

Wilkowski, D.

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

Yamaguchi, Y. Y.

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

Zielonkowski, M.

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (4)

E. Shahmoon and G. Kurizki, Phys. Rev. A 87, 033831 (2013).
[CrossRef]

S. Bay, P. Lambropoulos, and K. Mølmer, Phys. Rev. A 55, 1485 (1997).
[CrossRef]

M. Chalony, J. Barré, B. Marcos, A. Olivetti, and D. Wilkowski, Phys. Rev. A 87, 013401 (2013).
[CrossRef]

E. Shahmoon and G. Kurizki, Phys. Rev. A 89, 043419 (2014).
[CrossRef]

Phys. Rev. B (1)

S. John and J. Wang, Phys. Rev. B 43, 12772 (1991).
[CrossRef]

Phys. Rev. E (1)

F. Baldovin, R.-H. Chavanis, and E. Orlandini, Phys. Rev. E 79, 011102 (2009).
[CrossRef]

Phys. Rev. Lett. (6)

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef]

I. Shvarchuck, Ch. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitzing, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. 89, 270404 (2002).
[CrossRef]

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, Phys. Rev. Lett. 90, 110402 (2003).
[CrossRef]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[CrossRef]

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[CrossRef]

D. E. Chang, J. I. Cirac, and H. J. Kimble, Phys. Rev. Lett. 110, 113606 (2013).
[CrossRef]

Physica A (1)

Y. Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo, Physica A 337, 36 (2004).
[CrossRef]

Other (5)

C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, (Elsevier, 1992), pp. 1–164.

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier, 2006).

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Academic, 1984).

T. Dauxois, S. Ruffo, E. Arimondo, and M. Wilkens, eds., Dynamics and Thermodynamics of Systems with Long-Range Interactions (Springer, 2002).

D. Mukamel, “Notes on the statistical mechanics of systems with long-range interactions,” arXiv:0905.1457 (2008).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Schematic setup: atoms trapped in a cylindrical hollow trap along the z axis, and at distance r from the center of the tapered fiber [8]. The tapered fiber (central blue cylinder), of radius a, refractive index n1, and index grating with period Λ and amplitude Δn, is suspended in vacuum (index n0=1). The guided laser light and fiber modes are coupled to the atoms and induce their mutual interaction (LIDDI). (b) Spatial dependence of the LIDDI potential: F(z) from Eq. (4) (thick pink line) almost coincides with (1/2)cos2(kLz) (thin blue line) up to z8λL. Here kL=n¯2π/λL (see Cs atom realization considered in the text).

Fig. 2.
Fig. 2.

Relaxation time in the microcanonical ensemble τμc as a function of N for r=2a,1.5a,1.1a (blue solid line, blue dashed line, blue dotted line, respectively), compared to that in the canonical ensemble τc=γ1 (red horizontal dashed line) in seconds. The physical parameters used for this plot are in the text. Since τμcτc, γ0 does not limit the observation of the scaling of τμc with N.

Equations (7)

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

U=|Ω|2δ2Δ12cos[kL·(r1r2)],Δ12=kgk,1gk,2*ωkωL,
Δ12=d22πε0P0dωβωcos(βz)ωωLωA(ω)Ex(ω,r1)Ex*(ω,r2),
βkB+kBn¯Δn×{ω/ωu1;ω>ωu1ω/ωd;ω<ωd,βωn¯Δn2c×{1/ω/ωu1;ω>ωu1/1ω/ωd;ω<ωd,
U(z)=2ηRfsF(z),Rfs=|Ω|22δ2Γfsη=n¯Δn21ωL/ωu3π(cωL)2Ex(ωL,r1)Ex*(ωL,r2)A(ωL),F(z)=cos(kLz){cos(kBz)12ez/lsin(kBz)12π[ez/lEi(z/l)ez/lEi(z/l)]},l=11ωL/ωu1kBn¯Δn.
H=i=1Npi22m+12JNi,j=1N[1cos(θiθj)],θi4πn¯ziλL,
γkL2mRfsδ,D2kL2Rfs2.
θi=1Nj=1Nsin(θiθj)γ˜θi+2γ˜Tξi,

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