Cross-Kerr nonlinearity between continuous-mode coherent states and single photons

Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.

[1]  G. Kurizki,et al.  Strongly interacting photons in hollow-core waveguides , 2010, 1012.3601.

[2]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[3]  Bing He,et al.  Addendum to "Single photon logic gates using minimum resources" , 2010, 1011.4814.

[4]  Yu-Bo Sheng,et al.  Complete hyperentangled-Bell-state analysis for quantum communication , 2010, 1103.0230.

[5]  B. He,et al.  Transverse multimode effects on the performance of photon-photon gates , 2010, 1006.3584.

[6]  Yong-Fan Chen,et al.  Low-light-level cross-phase modulation by quantum interference , 2010 .

[7]  Bing He,et al.  Efficient generation of universal two-dimensional cluster states with hybrid systems , 2010, 1005.1112.

[8]  B. Sanders,et al.  Uniform cross-phase modulation for nonclassical radiation pulses , 2010, 1001.1893.

[9]  Yu-Bo Sheng,et al.  Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement , 2009, 0912.0079.

[10]  J. Bergou,et al.  Processing multiphoton states through operation on a single photon: Methods and applications , 2009, 0909.3879.

[11]  Bing He,et al.  Single-photon logic gates using minimal resources , 2009, 0909.0300.

[12]  Bing He,et al.  Bi-directional mapping between polarization and spatially encoded photonic qutrits , 2009, 0905.3214.

[13]  N. Matsuda,et al.  Observation of optical-fibre Kerr nonlinearity at the single-photon level , 2009, 1211.3488.

[14]  Bing He,et al.  Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity , 2009, 0901.3505.

[15]  Jian Li,et al.  Quantum control gates with weak cross-Kerr nonlinearity , 2008, 0811.3364.

[16]  Bing He,et al.  Creation of high-quality long-distance entanglement with flexible resources , 2008, 0808.2320.

[17]  Bing He,et al.  Universal entangler with photon pairs in arbitrary states , 2008, 0806.4216.

[18]  Fuguo Deng,et al.  Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics , 2008, 0806.0115.

[19]  Fuguo Deng,et al.  Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity , 2008, 0805.0032.

[20]  T. Tyc,et al.  Highly non-Gaussian states created via cross-Kerr nonlinearity , 2007, 0709.2011.

[21]  M. Kim,et al.  Generation of a coherent superposition of a travelling wave field , 2007 .

[22]  J. Bergou,et al.  Universal discriminator for completely unknown optical qubits , 2007, 0706.2429.

[23]  J. Shapiro,et al.  Continuous-time cross-phase modulation and quantum computation , 2006, quant-ph/0612086.

[24]  B. Sanders,et al.  Large cross-phase modulation between slow copropagating weak pulses in 87Rb. , 2006, Physical review letters.

[25]  Chang-Yi Wang,et al.  Low-light-level cross-phase-modulation based on stored light pulses. , 2006, Physical review letters.

[26]  J. Marangos,et al.  Electromagnetically induced transparency : Optics in coherent media , 2005 .

[27]  Hyunseok Jeong,et al.  Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation , 2005, quant-ph/0507095.

[28]  Kae Nemoto,et al.  Weak nonlinearities: a new route to optical quantum computation , 2005, quant-ph/0507084.

[29]  G. Kurizki,et al.  Long-range interactions and entanglement of slow single-photon pulses , 2005, quant-ph/0503071.

[30]  T. Spiller,et al.  Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities , 2004, quant-ph/0408117.

[31]  W. Munro,et al.  A near deterministic linear optical CNOT gate , 2004 .

[32]  D. Petrosyan,et al.  Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration , 2004, quant-ph/0402070.

[33]  C. Ottaviani,et al.  Polarization phase gate with a tripod atomic system , 2003, quant-ph/0310148.

[34]  T. Spiller,et al.  High-efficiency quantum-nondemolition single-photon-number-resolving detector , 2003, quant-ph/0310066.

[35]  Hoonsoo Kang,et al.  Observation of large Kerr nonlinearity at low light intensities. , 2003, Physical review letters.

[36]  C. Ottaviani,et al.  Polarization qubit phase gate in driven atomic media. , 2003, Physical review letters.

[37]  M. S. Zubairy,et al.  Enhancement of Kerr nonlinearity by multiphoton coherence. , 2002, Optics letters.

[38]  G. Kurizki,et al.  Symmetric photon-photon coupling by atoms with Zeeman-split sublevels , 2001, quant-ph/0105043.

[39]  Lukin,et al.  Nonlinear optics and quantum entanglement of ultraslow single photons , 2000, Physical review letters.

[40]  L. Hau,et al.  Nonlinear Optics at Low Light Levels , 1999 .

[41]  A. Imamoğlu,et al.  Giant Kerr nonlinearities obtained by electromagnetically induced transparency. , 1996, Optics letters.

[42]  Yamamoto,et al.  Quantum nondemolition measurement of the photon number via the optical Kerr effect. , 1985, Physical review. A, General physics.

[43]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[44]  Maira Amezcua,et al.  Quantum Optics , 2012 .

[45]  M. S. Zubairy,et al.  Quantum optics: Frontmatter , 1997 .