Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement.

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a tenfold improvement in precision over the intensity-only Cramér-Rao bound.

[1]  著者なし.  16 , 1871, Animals at the End of the World.

[2]  Christine Silberhorn,et al.  Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings , 2018, 1803.04316.

[3]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[4]  K N Cassemiro,et al.  Adaptive detection of arbitrarily shaped ultrashort quantum light states. , 2012, Physical review letters.

[5]  R. Scott,et al.  Temporal magnification and reversal of 100 Gb/s optical data with an up‐conversion time microscope , 1994 .

[6]  B. M. Fulk.  MATH , 1992 .

[7]  Hugo Ferretti,et al.  Beating Rayleigh's Curse by Imaging Using Phase Information. , 2016, Physical review letters.

[8]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[9]  Pu Jian,et al.  Real-time displacement measurement immune from atmospheric parameters using optical frequency combs. , 2012, Optics express.

[10]  Christine Silberhorn,et al.  A quantum pulse gate based on spectrally engineered sum frequency generation. , 2010, Optics express.

[11]  S. Ram,et al.  Beyond Rayleigh's criterion: a resolution measure with application to single-molecule microscopy. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[13]  Christine Silberhorn,et al.  Highly efficient frequency conversion with bandwidth compression of quantum light , 2016, Nature Communications.

[14]  Adv , 2019, International Journal of Pediatrics and Adolescent Medicine.

[15]  J. Rehacek,et al.  Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution , 2017, 1709.07705.

[16]  A. Carnicer,et al.  Understanding the concept of resolving power in the Fabry–Perot interferometer using a digital simulation , 2006 .

[17]  Nicolas Treps,et al.  Quantum improvement of time transfer between remote clocks. , 2008, Physical review letters.

[18]  Jaroslav Rehacek,et al.  Achieving the ultimate optical resolution , 2016, EPJ Web of Conferences.

[19]  W. E. Sleat,et al.  Direct linear measurement of ultrashort light pulses with a picosecond streak camera , 1971 .

[20]  J. Lavoie,et al.  Quantum-inspired interferometry with chirped laser pulses , 2008, 0804.4022.

[21]  M. Tsang.  Conservative classical and quantum resolution limits for incoherent imaging , 2016, 1605.03799.

[22]  Torleiv Orhaug,et al.  On the Resolution of Imaging Systems , 1969 .

[23]  Christoph Simon,et al.  Fisher information for far-field linear optical superresolution via homodyne or heterodyne detection in a higher-order local oscillator mode , 2017, 1706.08633.

[24]  Carl W. Helstrom,et al.  Resolvability of Objects from the Standpoint of Statistical Parameter Estimation , 1970 .

[25]  W. Hager,et al.  and s , 2019, Shallow Water Hydraulics.

[26]  Z Hradil,et al.  Optimal measurements for resolution beyond the Rayleigh limit. , 2017, Optics letters.

[27]  Jonas Zmuidzinas,et al.  Cramér-Rao sensitivity limits for astronomical instruments: implications for interferometer design. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  M. Fejer,et al.  Multidimensional mode-separable frequency conversion for high-speed quantum communication , 2016, 1606.07794.

[29]  Z. Hradil,et al.  Optical resolution from Fisher information , 2016 .

[30]  D. Petz,et al.  Introduction to Quantum Fisher Information , 2010, 1008.2417.

[31]  Stefano Pirandola,et al.  Ultimate Precision Bound of Quantum and Subwavelength Imaging. , 2016, Physical review letters.

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

[33]  Brandoch Calef,et al.  Cramer-Rao bounds for intensity interferometry measurements. , 2013, Applied optics.

[34]  Mankei Tsang.  Subdiffraction incoherent optical imaging via spatial-mode demultiplexing , 2017 .

[35]  C. Fabre,et al.  Wavelength-multiplexed quantum networks with ultrafast frequency combs , 2013, Nature Photonics.

[36]  C. Fabre,et al.  Quantum-limited measurements of distance fluctuations with a multimode detector , 2017, 1703.08479.

[37]  Mankei Tsang,et al.  Quantum theory of superresolution for two incoherent optical point sources , 2015, 1511.00552.

[38]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[39]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[40]  Carsten Langrock,et al.  Amplitude modulation and apodization of quasiphase-matched interactions. , 2006, Optics letters.

[41]  Reza Salem,et al.  Application of space–time duality to ultrahigh-speed optical signal processing , 2013 .

[42]  Edward J. Farrell.  Information Content of Photoelectric Star Images , 1966 .

[43]  Jan Sijbers,et al.  Model-based two-object resolution from observations having counting statistics , 1999 .

[44]  Mankei Tsang,et al.  Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit. , 2016, Physical review letters.

[45]  Christine Silberhorn,et al.  Temporal-mode measurement tomography of a quantum pulse gate , 2017, 1702.03336.

[46]  Jerry Chao,et al.  Fisher information theory for parameter estimation in single molecule microscopy: tutorial. , 2016, Journal of the Optical Society of America. A, Optics, image science, and vision.

[47]  Jonathan Leach,et al.  Attosecond-resolution Hong-Ou-Mandel interferometry , 2017, Science Advances.

[48]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[49]  S. Qian,et al.  Joint time-frequency analysis , 1999, IEEE Signal Process. Mag..

[50]  K. Fisher,et al.  Quantum optical signal processing in diamond , 2015, 1509.05098.

[51]  Andrew G. Glen,et al.  APPL , 2001 .

[52]  Zach DeVito,et al.  Opt , 2017 .

[53]  Mankei Tsang,et al.  Interferometric superlocalization of two incoherent optical point sources. , 2015, Optics express.

[54]  Christoph Simon,et al.  Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode , 2016, 1606.02662.

[55]  Pedro Andrés,et al.  Space-Time Analogies in Optics , 2011 .

[56]  James W. Brodsky,et al.  Digit , 2020, Definitions.

[57]  M. Raymer,et al.  Engineering temporal-mode-selective frequency conversion in nonlinear optical waveguides: from theory to experiment. , 2017, Optics express.

[58]  Jin Jiang,et al.  Time-frequency feature representation using energy concentration: An overview of recent advances , 2009, Digit. Signal Process..