Quantum interferometry with three-dimensional geometry

Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices. These can be implemented by femtosecond laser waveguide writing, recently adopted for quantum applications. In particular, multiarm interferometers include “tritter” and “quarter” as basic elements, corresponding to the generalization of a beam splitter to a 3- and 4-port splitter, respectively. By injecting Fock states in the input ports of such interferometers, fringe patterns characterized by nonclassical visibilities are expected. This enables outperforming the quantum Fisher information obtained with classical fields in phase estimation. We also discuss the possibility of achieving the simultaneous estimation of more than one optical phase. This approach is expected to open new perspectives to quantum enhanced sensing and metrology performed in integrated photonics.

[1]  A Smerzi,et al.  Phase detection at the quantum limit with multiphoton Mach-Zehnder interferometry. , 2007, Physical review letters.

[2]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[3]  R. Gill,et al.  On asymptotic quantum statistical inference , 2011, 1112.2078.

[4]  Yaron Silberberg,et al.  Publisher's Note: Classical Bound for Mach-Zehnder Superresolution , 2010 .

[5]  Keisuke Goda,et al.  A quantum-enhanced prototype gravitational-wave detector , 2008, 0802.4118.

[6]  Lipo Wang,et al.  Observation of Four-Photon Interference with a Beam Splitter by Pulsed Parametric Down-Conversion , 1999 .

[7]  G. Vallone,et al.  Two-particle bosonic-fermionic quantum walk via integrated photonics. , 2011, Physical review letters.

[8]  M. G. A. Paris,et al.  Optimal estimation of joint parameters in phase space , 2012, 1206.4867.

[9]  S. Lloyd,et al.  Quantum metrology. , 2005, Physical review letters.

[10]  S. Lloyd,et al.  Advances in quantum metrology , 2011, 1102.2318.

[11]  E. Mazur,et al.  Femtosecond laser micromachining in transparent materials , 2008 .

[12]  Jeremy L O'Brien,et al.  Heralding two-photon and four-photon path entanglement on a chip. , 2010, Physical review letters.

[13]  S. Nolte,et al.  Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics , 2003 .

[14]  Z. Y. Ou,et al.  FUNDAMENTAL QUANTUM LIMIT IN PRECISION PHASE MEASUREMENT , 1997 .

[15]  R. Osellame,et al.  Femtosecond laser microstructuring: an enabling tool for optofluidic lab‐on‐chips , 2011 .

[16]  J. Callow,et al.  Trends in the development of environmentally friendly fouling-resistant marine coatings. , 2011, Nature communications.

[17]  C. Helstrom.  Quantum detection and estimation theory , 1969 .

[18]  David Blair,et al.  A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application , 2011, 1109.2295.

[19]  Marcin Jarzyna,et al.  Quantum interferometry with and without an external phase reference , 2012 .

[20]  G. Milburn,et al.  Generalized uncertainty relations: Theory, examples, and Lorentz invariance , 1995, quant-ph/9507004.

[21]  K J Resch,et al.  Time-reversal and super-resolving phase measurements. , 2007, Physical review letters.

[22]  Marek Żukowski,et al.  Realizable higher-dimensional two-particle entanglements via multiport beam splitters , 1997 .

[23]  Weinfurter,et al.  Two-photon interference in optical fiber multiports. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[24]  J. K. Blackburn,et al.  A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application , 2011, 1109.2295.

[25]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[26]  A. Politi,et al.  Multimode quantum interference of photons in multiport integrated devices , 2010, Nature communications.

[27]  Austin G. Fowler,et al.  Experimental demonstration of topological error correction , 2009, Nature.

[28]  Roberta Ramponi,et al.  Three-dimensional Mach-Zehnder interferometer in a microfluidic chip for spatially-resolved label-free detection. , 2010, Lab on a chip.

[29]  M. J. Withford,et al.  Two-photon quantum walks in an elliptical direct-write waveguide array , 2011, 1103.0604.

[30]  Richard A. Campos,et al.  Three-photon Hong-Ou-Mandel interference at a multiport mixer , 2000 .

[31]  Yusuke Nasu,et al.  Characterization of symmetric [3 x 3] directional couplers fabricated by direct writing with a femtosecond laser oscillator. , 2006, Optics express.

[32]  G. Vallone,et al.  Integrated photonic quantum gates for polarization qubits , 2011, Nature communications.

[33]  Markus Tiersch,et al.  Zero-transmission law for multiport beam splitters. , 2010, Physical review letters.

[34]  Konrad Lehnert,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004 .

[35]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[36]  Bahaa E. A. Saleh,et al.  Quantum optical coherence tomography of a biological sample , 2008 .

[37]  Ole Steuernagel.  Comment on "Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit" , 2003 .

[38]  Marek Zukowski,et al.  Nonclassicality of pure two-qutrit entangled states , 2011, 1111.3955.

[39]  Brian J. Smith,et al.  Phase-controlled integrated photonic quantum circuits. , 2009, Optics express.

[40]  M. Paris.  Quantum estimation for quantum technology , 2008, 0804.2981.

[41]  Roberta Ramponi,et al.  Measuring protein concentration with entangled photons , 2011, 1109.3128.

[42]  J G Fujimoto,et al.  Three-dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator. , 2005, Optics letters.

[43]  Roberto Osellame,et al.  Micromachining of photonic devices by femtosecond laser pulses , 2008 .

[44]  Marco Barbieri,et al.  Multiparameter quantum metrology , 2012 .

[45]  Augusto Smerzi,et al.  Useful multiparticle entanglement and sub-shot-noise sensitivity in experimental phase estimation. , 2011, Physical review letters.

[46]  Peter C Humphreys,et al.  Multiphoton quantum interference in a multiport integrated photonic device , 2012, Nature Communications.

[47]  A. Politi,et al.  Silica-on-Silicon Waveguide Quantum Circuits , 2008, Science.

[48]  Anton Zeilinger,et al.  Similarities and Differences Between Two-Particle and Three-Particle Interference , 2000 .

[49]  H. Weinfurter,et al.  Observation of three-photon Greenberger-Horne-Zeilinger entanglement , 1998, quant-ph/9810035.

[50]  A. G. White,et al.  Creation of maximally entangled photon-number states using optical fiber multiports , 2003, quant-ph/0304135.

[51]  M. Thompson,et al.  Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit , 2012 .

[52]  Y. Silberberg,et al.  Classical bound for Mach-Zehnder superresolution. , 2010, Physical review letters.

[53]  Abrams,et al.  Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit , 1999, Physical review letters.