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Current Nanomaterials

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Review Article

Weak Measurements in Nano-optics

Author(s): Niladri Modak, Ankit K. Singh, Shyamal Guchhait, Athira BS, Mandira Pal and Nirmalya Ghosh*

Volume 5, Issue 3, 2020

Page: [191 - 213] Pages: 23

DOI: 10.2174/2468187310999200723121713

open access plus

Abstract

Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to weak value that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics.

Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domains. The applications involve measuring ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics.

Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device.

Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as a natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signals or effects.

Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.

Keywords: Weak measurement, weak value, fano resonance, plasmonics, nano optics, beam shifts.

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[1]
Von Neumann J. Mathematical foundations of quantum mechanics: new edition. New Jersey: Princeton University Press 2018.
[2]
Braginsky VB, Braginski VB, Khalili FY. Quantum measurement. England: Cambridge University Press 1995.
[3]
Aharonov Y, Albert DZ, Vaidman L. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys Rev Lett 1988; 60(14): 1351-4.
[http://dx.doi.org/10.1103/PhysRevLett.60.1351] [PMID: 10038016]
[4]
Duck IM, Stevenson PM, Sudarshan EC. The sense in which a “weak measurement” of a spin-(1/2 particle’s spin component yields a value 100. Phys Rev D Part Fields 1989; 40(6): 2112-7.
[http://dx.doi.org/10.1103/PhysRevD.40.2112] [PMID: 10012041]
[5]
Ritchie NW, Story JG, Hulet RG. Realization of a measurement of a “weak value”. Phys Rev Lett 1991; 66(9): 1107-10.
[http://dx.doi.org/10.1103/PhysRevLett.66.1107] [PMID: 10043997]
[6]
Palacios-Laloy A, Mallet F, Nguyen F, et al. Experimental violation of a Bell’s inequality in time with weak measurement. Nat Phys 2010; 6(6): 442-7.
[http://dx.doi.org/10.1038/nphys1641]
[7]
Goggin ME, Almeida MP, Barbieri M, et al. Violation of the Leggett-Garg inequality with weak measurements of photons. Proc Natl Acad Sci USA 2011; 108(4): 1256-61.
[http://dx.doi.org/10.1073/pnas.1005774108] [PMID: 21220296]
[8]
Lundeen JS, Sutherland B, Patel A, Stewart C, Bamber C. Direct measurement of the quantum wavefunction. Nature 2011; 474(7350): 188-91.
[http://dx.doi.org/10.1038/nature10120] [PMID: 21654800]
[9]
Kocsis S, Braverman B, Ravets S, et al. Observing the average trajectories of single photons in a two-slit interferometer. Science 2011; 332(6034): 1170-3.
[http://dx.doi.org/10.1126/science.1202218] [PMID: 21636767]
[10]
Zhang L, Datta A, Walmsley IA. Precision metrology using weak measurements. Phys Rev Lett 2015; 114(21)210801
[http://dx.doi.org/10.1103/PhysRevLett.114.210801] [PMID: 26066422]
[11]
Hosten O, Kwiat P. Observation of the spin hall effect of light via weak measurements. Science 2008; 319(5864): 787-90.
[http://dx.doi.org/10.1126/science.1152697] [PMID: 18187623]
[12]
Salazar-Serrano LJ, Janner D, Brunner N, Pruneri V, Torres JP. Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification. Phys Rev A 2014; 89(1)012126
[http://dx.doi.org/10.1103/PhysRevA.89.012126]
[13]
Brunner N, Simon C. Measuring small longitudinal phase shifts: weak measurements or standard interferometry? Phys Rev Lett 2010; 105(1)010405
[http://dx.doi.org/10.1103/PhysRevLett.105.010405] [PMID: 20867428]
[14]
Xu XY, Kedem Y, Sun K, Vaidman L, Li CF, Guo GC. Phase estimation with weak measurement using a white light source. Phys Rev Lett 2013; 111(3)033604
[http://dx.doi.org/10.1103/PhysRevLett.111.033604] [PMID: 23909319]
[15]
Dixon PB, Starling DJ, Jordan AN, Howell JC. Ultrasensitive beam deflection measurement via interferometric weak value amplification. Phys Rev Lett 2009; 102(17)173601
[http://dx.doi.org/10.1103/PhysRevLett.102.173601] [PMID: 19518781]
[16]
Goswami S, Pal M, Nandi A, Panigrahi PK, Ghosh N. Simultaneous weak value amplification of angular Goos-Hänchen and Imbert-Fedorov shifts in partial reflection. Opt Lett 2014; 39(21): 6229-32.
[http://dx.doi.org/10.1364/OL.39.006229] [PMID: 25361321]
[17]
Kofman AG, Ashhab S, Nori F. Nonperturbative theory of weak pre-and post-selected measurements. Phys Rep 2012; 520(2): 43-133.
[http://dx.doi.org/10.1016/j.physrep.2012.07.001]
[18]
Tamir B, Cohen E. Introduction to weak measurements and weak values. Quanta 2013; 2(1): 7-17.
[http://dx.doi.org/10.12743/quanta.v2i1.14]
[19]
Pal M, Saha S, Athira B, Gupta SD, Ghosh N. Experimental probe of weak-value amplification and geometric phase through the complex zeros of the response function. Phys Rev A (Coll Park) 2019; 99(3)032123
[http://dx.doi.org/10.1103/PhysRevA.99.032123]
[20]
Singh AK, Ray SK, Chandel S, et al. Tunable Fano resonance using weak-value amplification with asymmetric spectral response as a natural pointer. Phys Rev A (Coll Park) 2018; 97(5)053801
[http://dx.doi.org/10.1103/PhysRevA.97.053801]
[21]
Griffiths DJ, Schroeter DF. Introduction to quantum mechanics. England: Cambridge University Press 2018.
[http://dx.doi.org/10.1017/9781316995433]
[22]
Gupta SD, Ghosh N, Banerjee A. Wave optics: basic concepts and contemporary trends. Florida: CRC Press 2015.
[http://dx.doi.org/10.1201/b19330]
[23]
Kim YS, Lee JC, Kwon O, Kim YH. Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat Phys 2012; 8(2): 117-20.
[http://dx.doi.org/10.1038/nphys2178]
[24]
Korotkov A, Averin D. Continuous weak measurement of quantum coherent oscillations. Phys Rev 2001; 64(16)165310
[http://dx.doi.org/10.1103/PhysRevB.64.165310]
[25]
Kim YS, Cho YW, Ra YS, Kim YH. Reversing the weak quantum measurement for a photonic qubit. Opt Express 2009; 17(14): 11978-85.
[http://dx.doi.org/10.1364/OE.17.011978] [PMID: 19582113]
[26]
Magaña-Loaiza OS, Mirhosseini M, Rodenburg B, Boyd RW. Amplification of angular rotations using weak measurements. Phys Rev Lett 2014; 112(20)200401
[http://dx.doi.org/10.1103/PhysRevLett.112.200401] [PMID: 25432026]
[27]
Bliokh KY, Aiello A. Goos-Hänchen and Imbert-Fedorov beam shifts: an overview. J Opt 2013; 15(1)014001
[http://dx.doi.org/10.1088/2040-8978/15/1/014001]
[28]
Aiello A. Goos-Hänchen and Imbert-Fedorov shifts: a novel perspective. New J Phys 2012; 14(1)013058
[http://dx.doi.org/10.1088/1367-2630/14/1/013058]
[29]
Götte JB, Dennis MR. Generalized shifts and weak values for polarization components of reflected light beams. New J Phys 2012; 14(7)073016
[http://dx.doi.org/10.1088/1367-2630/14/7/073016]
[30]
Goos F, Hänchen H. Ein neuer und fundamentaler Versuch zur Totalreflexion. Ann Phys 1947; 436(7-8): 333-46.
[http://dx.doi.org/10.1002/andp.19474360704]
[31]
Imbert C. Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam. Phys Rev D 1972; 5(4): 787.
[http://dx.doi.org/10.1103/PhysRevD.5.787]
[32]
Bliokh KY, Rodríguez-Fortuño FJ, Nori F, Zayats AV. Spin-orbit interactions of light. Nat Photonics 2015; 9(12): 796.
[http://dx.doi.org/10.1038/nphoton.2015.201]
[33]
Bliokh KY, Niv A, Kleiner V, Hasman E. Geometrodynamics of spinning light. Nat Photonics 2008; 2(12): 748.
[http://dx.doi.org/10.1038/nphoton.2008.229]
[34]
Bliokh KY, Bliokh YP. Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet. Phys Rev Lett 2006; 96(7)073903
[http://dx.doi.org/10.1103/PhysRevLett.96.073903] [PMID: 16606091]
[35]
Dressel J, Malik M, Miatto FM, Jordan AN, Boyd RW. Colloquium: understanding quantum weak values: basics and applications. Rev Mod Phys 2014; 86: 307-16.
[http://dx.doi.org/10.1103/RevModPhys.86.307]
[36]
Wu S, Li Y. Weak measurements beyond the Aharonov-Albert-Vaidman formalism. Phys Rev A 2011; 83(5)052106
[http://dx.doi.org/10.1103/PhysRevA.83.052106]
[37]
Di Lorenzo A. Full counting statistics of weak-value measurement. Phys Rev A 2012; 85(3)032106
[http://dx.doi.org/10.1103/PhysRevA.85.032106]
[38]
Aiello A, Woerdman JP. Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts. Opt Lett 2008; 33(13): 1437-9.
[http://dx.doi.org/10.1364/OL.33.001437] [PMID: 18594657]
[39]
Solli DR, McCormick CF, Ropers C, Morehead JJ, Chiao RY, Hickmann JM. Demonstration of superluminal effects in an absorptionless, nonreflective system. Phys Rev Lett 2003; 91(14)143906
[http://dx.doi.org/10.1103/PhysRevLett.91.143906] [PMID: 14611528]
[40]
Asano M, Bliokh KY, Bliokh YP, et al. Anomalous time delays and quantum weak measurements in optical micro-resonators. Nat Commun 2016; 7(1): 13488.
[http://dx.doi.org/10.1038/ncomms13488] [PMID: 27841269]
[41]
Samuel J, Bhandari R. General setting for Berry’s phase. Phys Rev Lett 1988; 60(23): 2339-42.
[http://dx.doi.org/10.1103/PhysRevLett.60.2339] [PMID: 10038326]
[42]
Tamate S, Kobayashi H, Nakanishi T, Sugiyama K, Kitano M. Geometrical aspects of weak measurements and quantum erasers. New J Phys 2009; 11(9)093025
[http://dx.doi.org/10.1088/1367-2630/11/9/093025]
[43]
Maier SA. Plasmonics: fundamentals and applications. United States: Springer 2007.
[http://dx.doi.org/10.1007/0-387-37825-1]
[44]
Yu H, Peng Y, Yang Y, Li ZY. Plasmon-enhanced light-matter interactions and applications. Comp Mater 2019; 5(1): 1-4.
[45]
Zeng S, Baillargeat D, Ho H-P, Yong K-T. Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications. Chem Soc Rev 2014; 43(10): 3426-52.
[http://dx.doi.org/10.1039/c3cs60479a] [PMID: 24549396]
[46]
Ghosh SK, Pal T. Interparticle coupling effect on the surface plasmon resonance of gold nanoparticles: from theory to applications. Chem Rev 2007; 107(11): 4797-862.
[http://dx.doi.org/10.1021/cr0680282] [PMID: 17999554]
[47]
Jain PK, Huang X, El-Sayed IH, El-Sayed MA. Review of some interesting surface plasmon resonance-enhanced properties of noble metal nanoparticles and their applications to biosystems. Plasmonics 2007; 2(3): 107-18.
[http://dx.doi.org/10.1007/s11468-007-9031-1]
[48]
Nguyen HH, Park J, Kang S, Kim M. Surface plasmon resonance: a versatile technique for biosensor applications. Sensors (Basel) 2015; 15(5): 10481-510.
[http://dx.doi.org/10.3390/s150510481] [PMID: 25951336]
[49]
El-Sayed IH, Huang X, El-Sayed MA. Surface plasmon resonance scattering and absorption of anti-EGFR antibody conjugated gold nanoparticles in cancer diagnostics: applications in oral cancer. Nano Lett 2005; 5(5): 829-34.
[http://dx.doi.org/10.1021/nl050074e] [PMID: 15884879]
[50]
Pitarke JM, Silkin VM, Chulkov EV, Echenique PM. Theory of surface plasmons and surface-plasmon polaritons. Rep Prog Phys 2006; 70(1): 1.
[http://dx.doi.org/10.1088/0034-4885/70/1/R01]
[51]
Boltasseva A, Bozhevolnyi S, Søndergaard T, Nikolajsen T, Leosson K. Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons. Opt Express 2005; 13(11): 4237-43.
[http://dx.doi.org/10.1364/OPEX.13.004237] [PMID: 19495338]
[52]
Tredicucci A, Gmachl C, Capasso F, Hutchinson AL, Sivco DL, Cho AY. Singlemode surface-plasmon laser. Appl Phys Lett 2000; 76(16): 2164-6.
[53]
Tan SJ, Campolongo MJ, Luo D, Cheng W. Building plasmonic nanostructures with DNA. Nat Nanotechnol 2011; 6(5): 268-76.
[http://dx.doi.org/10.1038/nnano.2011.49] [PMID: 21499251]
[54]
Kahraman M, Daggumati P, Kurtulus O, Seker E, Wachsmann-Hogiu S. Fabrication and characterization of flexible and tunable plasmonic nanostructures. Sci Rep 2013; 3(1): 3396.
[http://dx.doi.org/10.1038/srep03396] [PMID: 24292236]
[55]
Ray SK, Chandel S, Singh AK, et al. Polarization-tailored Fano interference in plasmonic crystals: a mueller matrix model of anisotropic Fano resonance. ACS Nano 2017; 11(2): 1641-8.
[http://dx.doi.org/10.1021/acsnano.6b07406] [PMID: 28071887]
[56]
Coleman JN, Lotya M, O’Neill A, et al. Two-dimensional nanosheets produced by liquid exfoliation of layered materials. Science 2011; 331(6017): 568-71.
[http://dx.doi.org/10.1126/science.1194975] [PMID: 21292974]
[57]
Johari P, Shenoy VB. Tunable dielectric properties of transition metal dichalcogenides. ACS Nano 2011; 5(7): 5903-8.
[http://dx.doi.org/10.1021/nn201698t] [PMID: 21707067]
[58]
Krasnok A, Lepeshov S, Alú A. Nanophotonics with 2D transition metal dichalcogenides. Opt Express 2018; 26(12): 15972-94.
[http://dx.doi.org/10.1364/OE.26.015972] [PMID: 30114850]
[59]
Fano U. Effects of configuration interaction on intensities and phase shifts. Phys Rev 1961; 124(6): 1866.
[http://dx.doi.org/10.1103/PhysRev.124.1866]
[60]
Christ A, Tikhodeev SG, Gippius NA, Kuhl J, Giessen H. Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab. Phys Rev Lett 2003; 91(18)183901
[http://dx.doi.org/10.1103/PhysRevLett.91.183901] [PMID: 14611284]
[61]
Luk’yanchuk B, Zheludev NI, Maier SA, et al. The Fano resonance in plasmonic nanostructures and metamaterials. Nat Mater 2010; 9(9): 707-15.
[http://dx.doi.org/10.1038/nmat2810] [PMID: 20733610]
[62]
Ott C, Kaldun A, Raith P, et al. Lorentz meets Fano in spectral line shapes: a universal phase and its laser control. Science 2013; 340(6133): 716-20.
[http://dx.doi.org/10.1126/science.1234407] [PMID: 23661754]
[63]
Mazumdar I, Rau AR, Bhasin VS. Efimov states and their Fano resonances in a neutron-rich nucleus. Phys Rev Lett 2006; 97(6)062503
[http://dx.doi.org/10.1103/PhysRevLett.97.062503] [PMID: 17026167]
[64]
Kobayashi K, Aikawa H, Katsumoto S, Iye Y. Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer. Phys Rev Lett 2002; 88(25 Pt 1)256806
[http://dx.doi.org/10.1103/PhysRevLett.88.256806] [PMID: 12097115]
[65]
Fan P, Yu Z, Fan S, Brongersma ML. Optical Fano resonance of an individual semiconductor nanostructure. Nat Mater 2014; 13(5): 471-5.
[http://dx.doi.org/10.1038/nmat3927] [PMID: 24747781]
[66]
Wang Y, Liao L, Hu T, et al. Exciton-polariton Fano resonance driven by second harmonic generation. Phys Rev Lett 2017; 118(6)063602
[http://dx.doi.org/10.1103/PhysRevLett.118.063602] [PMID: 28234528]
[67]
Zhang Z, Weber-Bargioni A, Wu SW, Dhuey S, Cabrini S, Schuck PJ. Manipulating nanoscale light fields with the asymmetric bowtie nano-colorsorter. Nano Lett 2009; 9(12): 4505-9.
[http://dx.doi.org/10.1021/nl902850f] [PMID: 19899744]
[68]
Wu C, Khanikaev AB, Adato R, et al. Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers. Nat Mater 2011; 11(1): 69-75.
[http://dx.doi.org/10.1038/nmat3161] [PMID: 22081082]
[69]
Zhang S, Genov DA, Wang Y, Liu M, Zhang X. Plasmon-induced transparency in metamaterials. Phys Rev Lett 2008; 101(4)047401
[http://dx.doi.org/10.1103/PhysRevLett.101.047401] [PMID: 18764363]
[70]
Chang WS, Lassiter JB, Swanglap P, et al. A plasmonic Fano switch. Nano Lett 2012; 12(9): 4977-82.
[http://dx.doi.org/10.1021/nl302610v] [PMID: 22924610]
[71]
Wu C, Khanikaev AB, Shvets G. Broadband slow light metamaterial based on a double-continuum Fano resonance. Phys Rev Lett 2011; 106(10)107403
[http://dx.doi.org/10.1103/PhysRevLett.106.107403] [PMID: 21469834]
[72]
Zheludev NI, Prosvirnin S, Papasimakis N, Fedotov V. Lasing spaser. Nat Photonics 2008; 2(6): 351-4.
[http://dx.doi.org/10.1038/nphoton.2008.82]
[73]
Chandel S, Soni J, Ray SK, et al. Complete polarization characterization of single plasmonic nanoparticle enabled by a novel Dark-field Mueller matrix spectroscopy system. Sci Rep 2016; 6: 26466.
[http://dx.doi.org/10.1038/srep26466] [PMID: 27212687]
[74]
Tadepalli S, Slocik JM, Gupta MK, Naik RR, Singamaneni S. Bio-optics and bio-inspired optical materials. Chem Rev 2017; 117(20): 12705-63.
[http://dx.doi.org/10.1021/acs.chemrev.7b00153] [PMID: 28937748]

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