Abstract

We propose a scheme to achieve a uniform cross-phase modulation (XPM) for two nonclassical light pulses and study its application for quantum nondemolition measurements of the photon number in a pulse and for controlled phase gates in quantum information. We analyze the scheme by quantizing a common phenomenological model for classical XPM. Our analysis first treats the ideal case of equal XPM and pure unitary dynamics. This establishes the groundwork for more-complicated studies of nonunitary dynamics and difference in phase shifts between the two pulses where decohering effects severely affect the performance of the scheme.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
    [CrossRef]
  5. S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611-4614 (1999).
    [CrossRef]
  6. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
    [CrossRef]
  7. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638-641 (2003).
    [CrossRef]
  8. H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef]
  9. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000).
    [CrossRef]
  10. D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by atoms with Zeeman-split sublevels,” Phys. Rev. A 65, 033833 (2002).
    [CrossRef]
  11. A. B. Matsko, I. Novikova, G. R. Welch, and M. S. Zubairy, “Enhancement of Kerr nonlinearity by multiphoton coherence,” Opt. Lett. 28, 96-98 (2003).
    [CrossRef]
  12. C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
    [CrossRef]
  13. D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
    [CrossRef]
  14. S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
    [CrossRef]
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  17. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
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    [CrossRef]
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  22. J. H. Shapiro and R. S. Bondurant, “Qubit degradation due to cross-phase-modulation photon-number measurement,” Phys. Rev. A 73, 022301 (2006).
    [CrossRef]
  23. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
    [CrossRef]
  24. K. Koshino, “Transitional behavior between self-Kerr and cross-Kerr effects by two photons,” Phys. Rev. A 75, 063807 (2007).
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    [CrossRef]
  27. G. M. Gehring, R. W. Boyd, A. L. Gaeta, D. J. Gauthier, and A. E. Willner, “Fiber-based slow-light technologies,” J. Lightwave Technol. 26, 3752-3762 (2008).
    [CrossRef]
  28. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
    [CrossRef]
  29. P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
    [CrossRef]
  30. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  34. F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  37. Answering the question whether the case v1V1(z)≠v2V2(z) of this phenomenological model describes a real physical system may require an ab-initio quantum description of a medium that supports XPM. This is a formidable task and beyond the aim of our work to propose schemes for QND measurements of the photon number and to generate a CPG.
  38. B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694-702 (1989).
    [CrossRef]
  39. T. Tyc and B. C. Sanders, “Operational formulation of homodyne detection,” J. Phys. A 37, 7341-7357 (2004).
    [CrossRef]
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    [CrossRef]
  41. Strictly speaking, d denotes the initial distance between the pulses inside the medium.
  42. Usually the state in which the phase shift is acquired is taken to be |11〉, but we consider |10〉 to simplify the discussion. Both gates are related by a single-qubit NOT operation that acts on the second qubit.
  43. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245-2248 (1998).
    [CrossRef]
  44. G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119-130 (1976).
    [CrossRef]
  45. J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, 1999).
  46. L. Boivin, F. X. Kärtner, and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modulation with a finite response time,” Phys. Rev. Lett. 73, 240-243 (1994).
    [CrossRef]
  47. For instance, for giant nonlinearities based on EIT we would have Δvt≫w because the light pulses would have a duration in the order of microseconds.

2009

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

2008

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

G. M. Gehring, R. W. Boyd, A. L. Gaeta, D. J. Gauthier, and A. E. Willner, “Fiber-based slow-light technologies,” J. Lightwave Technol. 26, 3752-3762 (2008).
[CrossRef]

2007

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[CrossRef]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

K. Koshino, “Transitional behavior between self-Kerr and cross-Kerr effects by two photons,” Phys. Rev. A 75, 063807 (2007).
[CrossRef]

2006

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

J. H. Shapiro and R. S. Bondurant, “Qubit degradation due to cross-phase-modulation photon-number measurement,” Phys. Rev. A 73, 022301 (2006).
[CrossRef]

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

2005

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

2004

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

T. Tyc and B. C. Sanders, “Operational formulation of homodyne detection,” J. Phys. A 37, 7341-7357 (2004).
[CrossRef]

2003

A. B. Matsko, I. Novikova, G. R. Welch, and M. S. Zubairy, “Enhancement of Kerr nonlinearity by multiphoton coherence,” Opt. Lett. 28, 96-98 (2003).
[CrossRef]

C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638-641 (2003).
[CrossRef]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

2002

D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by atoms with Zeeman-split sublevels,” Phys. Rev. A 65, 033833 (2002).
[CrossRef]

2001

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001).
[CrossRef]

2000

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000).
[CrossRef]

1999

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

1998

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245-2248 (1998).
[CrossRef]

1997

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 52(6), 36-42 (1997).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

1996

1995

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489-3496 (1995).
[CrossRef]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

1994

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

L. Boivin, F. X. Kärtner, and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modulation with a finite response time,” Phys. Rev. Lett. 73, 240-243 (1994).
[CrossRef]

1993

1992

1991

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef]

1989

B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694-702 (1989).
[CrossRef]

1976

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119-130 (1976).
[CrossRef]

Abbou, F. M.

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

Abid, A.

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed., (Academic, 2007).

Anderson, D. Z.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

Artoni, M.

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Bajcsy, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638-641 (2003).
[CrossRef]

Balic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Bhagwat, A. R.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

Boivin, L.

L. Boivin, F. X. Kärtner, and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modulation with a finite response time,” Phys. Rev. Lett. 73, 240-243 (1994).
[CrossRef]

Boller, K.-J.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef]

Bondurant, R. S.

J. H. Shapiro and R. S. Bondurant, “Qubit degradation due to cross-phase-modulation photon-number measurement,” Phys. Rev. A 73, 022301 (2006).
[CrossRef]

Boyd, R. W.

Cataliotti, F.

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Chang, D. E.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[CrossRef]

Chiang, T.-K.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

Chuah, H. T.

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

Chuang, I. L.

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489-3496 (1995).
[CrossRef]

Corbalan, R.

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Cornell, E. A.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

Di Giuseppe, G.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Fleischhauer, M.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Fong, T. K.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

Gaeta, A. L.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

G. M. Gehring, R. W. Boyd, A. L. Gaeta, D. J. Gauthier, and A. E. Willner, “Fiber-based slow-light technologies,” J. Lightwave Technol. 26, 3752-3762 (2008).
[CrossRef]

Gauthier, D. J.

Gehring, G. M.

Hafezi, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

Harris, S. E.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 52(6), 36-42 (1997).
[CrossRef]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

Haus, H. A.

L. Boivin, F. X. Kärtner, and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modulation with a finite response time,” Phys. Rev. Lett. 73, 240-243 (1994).
[CrossRef]

Hemmer, P. R.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[CrossRef]

Hiew, C. C.

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

Hofferberth, S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

Hollberg, L.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000).
[CrossRef]

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936-1938 (1996).
[CrossRef]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, 1999).

Jennewein, T.

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

Joneckis, L. G.

Kagi, N.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

Kang, H.

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

Kärtner, F. X.

L. Boivin, F. X. Kärtner, and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modulation with a finite response time,” Phys. Rev. Lett. 73, 240-243 (1994).
[CrossRef]

Kazovsky, L. G.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001).
[CrossRef]

Koshino, K.

K. Koshino, “Transitional behavior between self-Kerr and cross-Kerr effects by two photons,” Phys. Rev. A 75, 063807 (2007).
[CrossRef]

Kurizki, G.

D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by atoms with Zeeman-split sublevels,” Phys. Rev. A 65, 033833 (2002).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001).
[CrossRef]

Leung, P.

P. Leung, T. Ralph, W. J. Munro, and K. Nemoto, “Spectral effects of fast response cross Kerr non-linearity on quantum gate,” arXiv:0810.2828v2 (2008).

Lindblad, G.

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119-130 (1976).
[CrossRef]

Londero, P.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

Lukin, M. D.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638-641 (2003).
[CrossRef]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Malakyan, Y. P.

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

Marhic, M. E.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

Marzlin, K.-P.

Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

Matsko, A. B.

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001).
[CrossRef]

B. C. Sanders and G. J. Milburn, “Quantum limits to all-optical switching in the nonlinear Mach-Zehnder interferometer,” J. Opt. Soc. Am. B 9, 915-924 (1992).
[CrossRef]

B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694-702 (1989).
[CrossRef]

Montgomery, D.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

Munro, W. J.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).

P. Leung, T. Ralph, W. J. Munro, and K. Nemoto, “Spectral effects of fast response cross Kerr non-linearity on quantum gate,” arXiv:0810.2828v2 (2008).

Nemoto, K.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).

P. Leung, T. Ralph, W. J. Munro, and K. Nemoto, “Spectral effects of fast response cross Kerr non-linearity on quantum gate,” arXiv:0810.2828v2 (2008).

Novikova, I.

Ong, D. S.

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

Ottaviani, C.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Pan, J.-W.

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

Petrosyan, D.

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by atoms with Zeeman-split sublevels,” Phys. Rev. A 65, 033833 (2002).
[CrossRef]

Peyronel, T.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

Ralph, T.

P. Leung, T. Ralph, W. J. Munro, and K. Nemoto, “Spectral effects of fast response cross Kerr non-linearity on quantum gate,” arXiv:0810.2828v2 (2008).

Razavi, M.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

Rebic, S.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Renn, M. J.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

Resch, K.

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

Robinson, H. G.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Rothenberg, J. E.

Sanaka, K.

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

Sanders, B. C.

Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

T. Tyc and B. C. Sanders, “Operational formulation of homodyne detection,” J. Phys. A 37, 7341-7357 (2004).
[CrossRef]

B. C. Sanders and G. J. Milburn, “Quantum limits to all-optical switching in the nonlinear Mach-Zehnder interferometer,” J. Opt. Soc. Am. B 9, 915-924 (1992).
[CrossRef]

B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694-702 (1989).
[CrossRef]

Schmidt, H.

Scully, M. O.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Shapiro, J. H.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

J. H. Shapiro and R. S. Bondurant, “Qubit degradation due to cross-phase-modulation photon-number measurement,” Phys. Rev. A 73, 022301 (2006).
[CrossRef]

L. G. Joneckis and J. H. Shapiro, “Quantum propagation in a Kerr medium: lossless, dispersionless fiber,” J. Opt. Soc. Am. B 10, 1102-1120 (1993).
[CrossRef]

Slepkov, A. D.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[CrossRef]

Spiller, T. P.

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

Tombesi, P.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Tyc, T.

T. Tyc and B. C. Sanders, “Operational formulation of homodyne detection,” J. Phys. A 37, 7341-7357 (2004).
[CrossRef]

Vdovin, O.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

Velichansky, V. L.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Venkataraman, V.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

Vitali, D.

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Vuletic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

Wang, Z.-B.

Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

Welch, G. R.

Wieman, C. E.

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

Willner, A. E.

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245-2248 (1998).
[CrossRef]

Yamamoto, Y.

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489-3496 (1995).
[CrossRef]

Zeilinger, A.

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

Zhu, Y.

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638-641 (2003).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

Zubairy, M. S.

Commun. Math. Phys.

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119-130 (1976).
[CrossRef]

IEEE Photonics Technol. Lett.

T.-K. Chiang, N. Kagi, T. K. Fong, M. E. Marhic, and L. G. Kazovsky, “Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency,” IEEE Photonics Technol. Lett. 6, 733-736 (1994).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

J. Phys. A

T. Tyc and B. C. Sanders, “Operational formulation of homodyne detection,” J. Phys. A 37, 7341-7357 (2004).
[CrossRef]

J. Russ. Laser Res.

F. M. Abbou, C. C. Hiew, H. T. Chuah, D. S. Ong, and A. Abid, “A detailed analysis of cross-phase modulation effects on OOK and dpsk optical WDM transmission systems in the presence of GVD, SPM, and ASE noise,” J. Russ. Laser Res. 29, 57-70 (2008).
[CrossRef]

Nature

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638-641 (2003).
[CrossRef]

New J. Phys.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).
[CrossRef]

J. H. Shapiro and R. S. Bondurant, “Qubit degradation due to cross-phase-modulation photon-number measurement,” Phys. Rev. A 73, 022301 (2006).
[CrossRef]

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

S. Rebić, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A 70, 032317 (2004).
[CrossRef]

I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489-3496 (1995).
[CrossRef]

K. Koshino, “Transitional behavior between self-Kerr and cross-Kerr effects by two photons,” Phys. Rev. A 75, 063807 (2007).
[CrossRef]

D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by atoms with Zeeman-split sublevels,” Phys. Rev. A 65, 033833 (2002).
[CrossRef]

S. Rebić, C. Ottaviani, G. Di Giuseppe, D. Vitali, and P. Tombesi, “Assessment of a quantum phase-gate operation based on nonlinear optics,” Phys. Rev. A 74, 032301 (2006).
[CrossRef]

B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694-702 (1989).
[CrossRef]

Phys. Rev. B

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[CrossRef]

Phys. Rev. Lett.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef]

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103, 043602 (2009).
[CrossRef]

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef]

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, “Spectroscopy in dense coherent media: line narrowing and interference effects,” Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

M. J. Renn, D. Montgomery, O. Vdovin, D. Z. Anderson, C. E. Wieman, and E. A. Cornell, “Laser-guided atoms in hollow-core optical fibers,” Phys. Rev. Lett. 75, 3253-3256 (1995).
[CrossRef]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).

Z.-B. Wang, K.-P. Marzlin, and B. C. Sanders, “Large cross-phase modulation between slow copropagating weak pulses in Rb87,” Phys. Rev. Lett. 97, 063901 (2006).
[CrossRef]

K. Sanaka, T. Jennewein, J.-W. Pan, K. Resch, and A. Zeilinger, “Experimental nonlinear sign shift for linear optics quantum computation,” Phys. Rev. Lett. 92, 017902 (2004).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245-2248 (1998).
[CrossRef]

L. Boivin, F. X. Kärtner, and H. A. Haus, “Analytical solution to the quantum field theory of self-phase modulation with a finite response time,” Phys. Rev. Lett. 73, 240-243 (1994).
[CrossRef]

Phys. Today

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 52(6), 36-42 (1997).
[CrossRef]

Other

P. Leung, T. Ralph, W. J. Munro, and K. Nemoto, “Spectral effects of fast response cross Kerr non-linearity on quantum gate,” arXiv:0810.2828v2 (2008).

J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, 1999).

Strictly speaking, d denotes the initial distance between the pulses inside the medium.

Usually the state in which the phase shift is acquired is taken to be |11〉, but we consider |10〉 to simplify the discussion. Both gates are related by a single-qubit NOT operation that acts on the second qubit.

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed., (Academic, 2007).

Answering the question whether the case v1V1(z)≠v2V2(z) of this phenomenological model describes a real physical system may require an ab-initio quantum description of a medium that supports XPM. This is a formidable task and beyond the aim of our work to propose schemes for QND measurements of the photon number and to generate a CPG.

For instance, for giant nonlinearities based on EIT we would have Δvt≫w because the light pulses would have a duration in the order of microseconds.

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