Abstract

We explore the quantum criticality in a one-dimensional quantum network, where adjacent nodes are connected by a fiber and each node consists of a cavity doped with N two-level atoms. We investigate the phase diagrams for cases of different atom numbers on resonance by making use of the mean-field approximation and find that both the fidelity and entanglement entropy for the ground state have dramatic changes near the critical points. Finally, the photon population imbalance of adjacent cavities is analytically explored via the two-node quantum network as the forerunner of phase transition.

© 2013 Optical Society of America

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  1. S. Sachdev, Quantum Phase Transitions (Cambridge University, 2001).
  2. S.-J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010).
    [CrossRef]
  3. P. Buonsante and A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007).
    [CrossRef]
  4. E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
    [CrossRef]
  5. D.-W. Luo and J.-B. Xu, Phys. Rev. A 87, 013801 (2013).
    [CrossRef]
  6. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
    [CrossRef]
  7. T. Pellizzari, Phys. Rev. Lett. 79, 5242 (1997).
    [CrossRef]
  8. A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006).
    [CrossRef]
  9. D. Rossini and R. Fazio, Phys. Rev. Lett. 99, 186401 (2007).
    [CrossRef]
  10. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
    [CrossRef]
  11. K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
    [CrossRef]
  12. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
    [CrossRef]
  13. K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
    [CrossRef]
  14. D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (2007).
    [CrossRef]
  15. A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
    [CrossRef]
  16. S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
    [CrossRef]

2013

D.-W. Luo and J.-B. Xu, Phys. Rev. A 87, 013801 (2013).
[CrossRef]

2012

E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
[CrossRef]

2010

S.-J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010).
[CrossRef]

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

2009

A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
[CrossRef]

2007

D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (2007).
[CrossRef]

P. Buonsante and A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007).
[CrossRef]

D. Rossini and R. Fazio, Phys. Rev. Lett. 99, 186401 (2007).
[CrossRef]

2006

A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

2005

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

2004

K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
[CrossRef]

2003

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

1997

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
[CrossRef]

T. Pellizzari, Phys. Rev. Lett. 79, 5242 (1997).
[CrossRef]

Aguiar, M. C. O.

E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
[CrossRef]

Angelakis, D. G.

D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (2007).
[CrossRef]

Birnbaum, K. M.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

Blatter, G.

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

Boca, A.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

Boozer, A. D.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

Bose, S.

D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (2007).
[CrossRef]

A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Buller, G. S.

K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
[CrossRef]

Buonsante, P.

P. Buonsante and A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007).
[CrossRef]

Cirac, J. I.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
[CrossRef]

Cole, J. H.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Fazio, R.

D. Rossini and R. Fazio, Phys. Rev. Lett. 99, 186401 (2007).
[CrossRef]

Fernandez, V.

K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
[CrossRef]

Fleischhauer, M.

A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
[CrossRef]

Gerace, D.

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

Gordon, K.

K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
[CrossRef]

Greentree, A. D.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Gu, S.-J.

S.-J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010).
[CrossRef]

Heaney, L.

E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
[CrossRef]

Hollenberg, L. C. L.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Houck, A. A.

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

Ivanov, P. A.

A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
[CrossRef]

Kimble, H. J.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Luo, D.-W.

D.-W. Luo and J.-B. Xu, Phys. Rev. A 87, 013801 (2013).
[CrossRef]

Mabuchi, H.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
[CrossRef]

Mancini, S.

A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Mascarenhas, E.

E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
[CrossRef]

Mering, A.

A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
[CrossRef]

Miller, R.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

Northup, T. E.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Pellizzari, T.

T. Pellizzari, Phys. Rev. Lett. 79, 5242 (1997).
[CrossRef]

Rossini, D.

D. Rossini and R. Fazio, Phys. Rev. Lett. 99, 186401 (2007).
[CrossRef]

Sachdev, S.

S. Sachdev, Quantum Phase Transitions (Cambridge University, 2001).

Santos, M. F.

E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
[CrossRef]

D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (2007).
[CrossRef]

Schmidt, S.

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

Serafini, A.

A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Singer, K.

A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Tahan, C.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Townsend, P.

K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
[CrossRef]

Türeci, H. E.

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

Vezzani, A.

P. Buonsante and A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007).
[CrossRef]

Xu, J.-B.

D.-W. Luo and J.-B. Xu, Phys. Rev. A 87, 013801 (2013).
[CrossRef]

Zoller, P.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
[CrossRef]

IEEE J. Quantum Electron.

K. Gordon, V. Fernandez, P. Townsend, and G. S. Buller, IEEE J. Quantum Electron. 40, 900 (2004).
[CrossRef]

Int. J. Mod. Phys. B

S.-J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010).
[CrossRef]

Nat. Phys.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Nature

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
[CrossRef]

New J. Phys.

E. Mascarenhas, L. Heaney, M. C. O. Aguiar, and M. F. Santos, New J. Phys. 14, 043033 (2012).
[CrossRef]

Phys. Rev. A

D.-W. Luo and J.-B. Xu, Phys. Rev. A 87, 013801 (2013).
[CrossRef]

D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805 (2007).
[CrossRef]

A. Mering, M. Fleischhauer, P. A. Ivanov, and K. Singer, Phys. Rev. A 80, 053821 (2009).
[CrossRef]

Phys. Rev. B

S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Phys. Rev. B 82, 100507 (2010).
[CrossRef]

Phys. Rev. Lett.

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
[CrossRef]

T. Pellizzari, Phys. Rev. Lett. 79, 5242 (1997).
[CrossRef]

A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

D. Rossini and R. Fazio, Phys. Rev. Lett. 99, 186401 (2007).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

P. Buonsante and A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007).
[CrossRef]

Other

S. Sachdev, Quantum Phase Transitions (Cambridge University, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

Order parameters (a) ψa and (b) ψb as functions of (ωμ)/g and κ/g for atom number N=1.

Fig. 2.
Fig. 2.

Same as Fig. 1 but for N=2. The red-dashed line corresponds to the phase boundary in Fig. 1.

Fig. 3.
Fig. 3.

Same as Fig. 1 but for N=3. The red-dashed line denotes the phase boundary in Fig. 1.

Fig. 4.
Fig. 4.

Fidelity F as a function of (ωμ)/g and κ/g with (a) δκ/g=0.01 and (b) δκ/g=0.1. Here, we choose N=1 and the red point plot corresponds to the phase boundary in Fig. 1.

Fig. 5.
Fig. 5.

Entanglement E (a) as a function of (ωμ)/g and κ/g with N=1 and (b) as a function of κ/g with (ωμ)/g=0.1 and N=1 (solid line), 2 (dashed line), 3 (dotted line). The red-dashed line corresponds to the phase boundary in Fig. 1.

Fig. 6.
Fig. 6.

Photon population imbalance z(t) of photons in the two Jaynes–Cummings cavities (N=1) as a function of t for different hopping rates κ/g.

Equations (1)

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

HiMF=(ωμ)(Jiz+N2+aiai+bibi)+g(Ji+ai+Jiai)zκ[ψb(ai+ai)+ψa(bi+bi)2ψaψb],

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