## Uniform cross-phase modulation for nonclassical radiation pulses

JOSA B, Vol. 27, Issue 6, pp. A36-A45 (2010)

http://dx.doi.org/10.1364/JOSAB.27.000A36

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### 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

**OCIS Codes**

(190.3270) Nonlinear optics : Kerr effect

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(270.5530) Quantum optics : Pulse propagation and temporal solitons

(270.5580) Quantum optics : Quantum electrodynamics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Nonlinear Optics

**History**

Original Manuscript: September 22, 2009

Manuscript Accepted: December 13, 2009

Published: March 12, 2010

**Citation**

Karl-Peter Marzlin, Zeng-Bin Wang, Sergey A. Moiseev, and Barry C. Sanders, "Uniform cross-phase modulation for nonclassical radiation pulses," J. Opt. Soc. Am. B **27**, A36-A45 (2010)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-6-A36

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### References

- H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936-1938 (1996). [CrossRef] [PubMed]
- 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] [PubMed]
- 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]
- 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] [PubMed]
- H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003). [CrossRef] [PubMed]
- M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419-1422 (2000). [CrossRef] [PubMed]
- D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by atoms with Zeeman-split sublevels,” Phys. Rev. A 65, 033833 (2002). [CrossRef]
- 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] [PubMed]
- C. Ottaviani, D. Vitali, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003). [CrossRef] [PubMed]
- 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]
- 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] [PubMed]
- I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489-3496 (1995). [CrossRef] [PubMed]
- K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004). [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]
- 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] [PubMed]
- E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46-52 (2001). [CrossRef] [PubMed]
- 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]
- 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]
- 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).
- 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] [PubMed]
- 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]
- 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] [PubMed]
- 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] [PubMed]
- 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. E. Rothenberg, “Complete all-optical switching of visible picosecond pulses in birefringent fiber,” Opt. Lett. 18, 796-798, (1993). [CrossRef] [PubMed]
- G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed., (Academic, 2007).
- 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]
- 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]
- 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]
- 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]
- 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.
- B. C. Sanders and G. J. Milburn, “Complementarity in a quantum nondemolition measurement,” Phys. Rev. A 39, 694-702 (1989). [CrossRef] [PubMed]
- T. Tyc and B. C. Sanders, “Operational formulation of homodyne detection,” J. Phys. A 37, 7341-7357 (2004). [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]
- 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.
- W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245-2248 (1998). [CrossRef]
- G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119-130 (1976). [CrossRef]
- J. D. Jackson, Classical Electrodynamics, 3rd Ed. (Wiley, 1999).
- 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] [PubMed]
- 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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