Abstract

The displacement of micro-electro-mechanical-systems (MEMS) cantilevers is used to measure a broad variety of phenomena in devices ranging from force microscopes to biochemical sensors to thermal imaging systems. We demonstrate, to the best of our knowledge, the first direct measurement of a MEMS cantilever displacement with a noise floor 4 dB below the shot-noise limit (SNL) at an equivalent optical power. By combining multi-spatial-mode quantum light sources with a simple differential measurement, we show that sub-SNL MEMS displacement sensitivity is highly accessible compared to previous efforts that measured the displacement of macroscopic mirrors with very distinct spatial structures crafted with multiple optical parametric amplifiers and locking loops. These results support a new class of quantum MEMS sensors with an ultimate signal-to-noise ratio determined by quantum correlations, enabling ultratrace sensing, imaging, and microscopy applications in which signals were previously obscured by shot noise.

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References

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  43. S. M. Barnett, C. Fabre, A. Maıtre, “Ultimate quantum limits for resolution of beam displacements,” Eur. Phys. J. D. 22, 513–519 (2003).
    [Crossref]
  44. O. Hosten, P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
    [Crossref]
  45. P. B. Dixon, D. J. Starling, A. N. Jordan, J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
    [Crossref]
  46. N. Treps, V. Delaubert, A. Maître, J. M. Courty, C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
    [Crossref]
  47. C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
    [Crossref]
  48. C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36, 2979–2981 (2011).
    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (2)

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

R. Pooser, J. Jing, “Continuous-variable cluster-state generation over the optical spatial mode comb,” Phys. Rev. A 90, 043841 (2014).
[Crossref]

2013 (5)

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88, 033845 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

B. Lawrie, P. Evans, R. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110, 156802 (2013).
[Crossref]

B. Lawrie, R. C. Pooser, “Toward real-time quantum imaging with a single pixel camera,” Opt. Express 21, 7549–7559 (2013).
[Crossref]

U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, U. L. Andersen, “Quantum-enhanced micromechanical displacement sensitivity,” Opt. Lett. 38, 1413–1415 (2013).
[Crossref]

2012 (6)

J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, P. D. Lett, “Imaging using quantum noise properties of light,” Opt. Express 20, 17050–17058 (2012).
[Crossref]

Z. Qin, J. Jing, J. Zhou, C. Liu, R. C. Pooser, Z. Zhou, W. Zhang, “Compact diode-laser-pumped quantum light source based on four-wave mixing in hot rubidium vapor,” Opt. Lett. 37, 3141–3143 (2012).
[Crossref]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012).
[Crossref]

O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A 85, 010101 (2012).
[Crossref]

J. Tamayo, V. Pini, P. Kosaka, N. F. Martinez, O. Ahumada, M. Calleja, “Imaging the surface stress and vibration modes of a microcantilever by laser beam deflection microscopy,” Nanotechnology 23, 315501 (2012).
[Crossref]

R. Garcia, E. T. Herruzo, “The emergence of multifrequency force microscopy,” Nat. Nanotechnol. 7, 217–226 (2012).
[Crossref]

2011 (4)

H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
[Crossref]

P. E. Rutten, “High speed two-dimensional optical beam position detector,” Rev. Sci. Instrum. 82, 073705 (2011).
[Crossref]

J. Arlett, E. Myers, M. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol. 6, 203–215 (2011).
[Crossref]

C. Liu, J. Jing, Z. Zhou, R. C. Pooser, F. Hudelist, L. Zhou, W. Zhang, “Realization of low frequency and controllable bandwidth squeezing based on a four-wave-mixing amplifier in rubidium vapor,” Opt. Lett. 36, 2979–2981 (2011).
[Crossref]

2010 (5)

W. Hiebert, D. Vick, V. Sauer, M. Freeman, “Optical interferometric displacement calibration and thermomechanical noise detection in bulk focused ion beam-fabricated nanoelectromechanical systems,” J. Micromech. Microeng. 20, 115038 (2010).
[Crossref]

L. Tetard, A. Passian, T. Thundat, “New modes for subsurface atomic force microscopy through nanomechanical coupling,” Nat. Nanotechnol. 5, 105–109 (2010).
[Crossref]

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref]

P. Verlot, A. Tavernarakis, T. Briant, P.-F. Cohadon, A. Heidmann, “Backaction amplification and quantum limits in optomechanical measurements,” Phys. Rev. Lett. 104, 133602 (2010).
[Crossref]

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

2009 (2)

J. Teufel, T. Donner, M. Castellanos-Beltran, J. Harlow, K. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4, 820–823 (2009).
[Crossref]

P. B. Dixon, D. J. Starling, A. N. Jordan, J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
[Crossref]

2008 (4)

O. Hosten, P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, R. Schnabel, “Observation of squeezed light with 10-db quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref]

2007 (2)

L. Picco, L. Bozec, A. Ulcinas, D. Engledew, M. Antognozzi, M. Horton, M. Miles, “Breaking the speed limit with atomic force microscopy,” Nanotechnology 18, 044030 (2007).
[Crossref]

O. Sahin, S. Magonov, C. Su, C. F. Quate, O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2, 507–514 (2007).
[Crossref]

2006 (2)

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref]

M. C. LeMieux, M. E. McConney, Y.-H. Lin, S. Singamaneni, H. Jiang, T. J. Bunning, V. V. Tsukruk, “Polymeric nanolayers as actuators for ultrasensitive thermal bimorphs,” Nano Lett. 6, 730–734 (2006).
[Crossref]

2005 (3)

T. Fukuma, M. Kimura, K. Kobayashi, K. Matsushige, H. Yamada, “Development of low noise cantilever deflection sensor for multienvironment frequency-modulation atomic force microscopy,” Rev. Sci. Instrum. 76, 053704 (2005).
[Crossref]

G. S. Shekhawat, V. P. Dravid, “Nanoscale imaging of buried structures via scanning near-field ultrasound holography,” Science 310, 89–92 (2005).
[Crossref]

N. Treps, V. Delaubert, A. Maître, J. M. Courty, C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

2004 (2)

D. Rugar, R. Budakian, H. Mamin, B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[Crossref]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

2003 (2)

S. M. Barnett, C. Fabre, A. Maıtre, “Ultimate quantum limits for resolution of beam displacements,” Eur. Phys. J. D. 22, 513–519 (2003).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[Crossref]

2002 (2)

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett. 88, 203601 (2002).
[Crossref]

R. S. Bennink, R. W. Boyd, “Improved measurement of multimode squeezed light via an eigenmode approach,” Phys. Rev. A 66, 053815 (2002).

2000 (2)

M. T. Cuberes, H. Assender, G. A. D. Briggs, O. Kolosov, “Heterodyne force microscopy of PMMA/rubber nanocomposites: nanomapping of viscoelastic response at ultrasonic frequencies,” J. Phys. D 33, 2347–2355 (2000).
[Crossref]

C. Fabre, J. B. Fouet, A. Maître, “Quantum limits in the measurement of very small displacements in optical images,” Opt. Lett. 25, 76–78 (2000).
[Crossref]

1997 (2)

T. Miyatani, M. Fujihira, “Calibration of surface stress measurements with atomic force microscopy,” J. Appl. Phys. 81, 7099–7115 (1997).
[Crossref]

F. Dinelli, S. Biswas, G. Briggs, O. Kolosov, “Ultrasound induced lubricity in microscopic contact,” Appl. Phys. Lett. 71, 1177–1179 (1997).
[Crossref]

1995 (1)

D. Smith, “Limits of force microscopy,” Rev. Sci. Instrum. 66, 3191–3195 (1995).
[Crossref]

1994 (1)

K. Yamanaka, H. Ogiso, O. Kolosov, “Ultrasonic force microscopy for nanometer resolution subsurface imaging,” Appl. Phys. Lett. 64, 178–180 (1994).
[Crossref]

1992 (1)

C. A. Putman, B. G. De Grooth, N. F. Van Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
[Crossref]

1990 (1)

M. T. Jaekel, S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
[Crossref]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
[Crossref]

Ahumada, O.

J. Tamayo, V. Pini, P. Kosaka, N. F. Martinez, O. Ahumada, M. Calleja, “Imaging the surface stress and vibration modes of a microcantilever by laser beam deflection microscopy,” Nanotechnology 23, 315501 (2012).
[Crossref]

Andersen, U.

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett. 88, 203601 (2002).
[Crossref]

Andersen, U. L.

Anetsberger, G.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

Antognozzi, M.

L. Picco, L. Bozec, A. Ulcinas, D. Engledew, M. Antognozzi, M. Horton, M. Miles, “Breaking the speed limit with atomic force microscopy,” Nanotechnology 18, 044030 (2007).
[Crossref]

Arcizet, O.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref]

Arlett, J.

J. Arlett, E. Myers, M. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol. 6, 203–215 (2011).
[Crossref]

Arnold, W.

H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
[Crossref]

Assender, H.

M. T. Cuberes, H. Assender, G. A. D. Briggs, O. Kolosov, “Heterodyne force microscopy of PMMA/rubber nanocomposites: nanomapping of viscoelastic response at ultrasonic frequencies,” J. Phys. D 33, 2347–2355 (2000).
[Crossref]

Bache, M.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Bachor, H.-A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
[Crossref]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett. 88, 203601 (2002).
[Crossref]

Barnett, S. M.

S. M. Barnett, C. Fabre, A. Maıtre, “Ultimate quantum limits for resolution of beam displacements,” Eur. Phys. J. D. 22, 513–519 (2003).
[Crossref]

Bedorf, D.

H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
[Crossref]

Bennink, R. S.

R. S. Bennink, R. W. Boyd, “Improved measurement of multimode squeezed light via an eigenmode approach,” Phys. Rev. A 66, 053815 (2002).

Biswas, S.

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Mamin, H.

D. Rugar, R. Budakian, H. Mamin, B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
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Marino, A. M.

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88, 033845 (2013).
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J. B. Clark, Z. Zhou, Q. Glorieux, A. M. Marino, P. D. Lett, “Imaging using quantum noise properties of light,” Opt. Express 20, 17050–17058 (2012).
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C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
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V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
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Martinez, N. F.

J. Tamayo, V. Pini, P. Kosaka, N. F. Martinez, O. Ahumada, M. Calleja, “Imaging the surface stress and vibration modes of a microcantilever by laser beam deflection microscopy,” Nanotechnology 23, 315501 (2012).
[Crossref]

Matsushige, K.

T. Fukuma, M. Kimura, K. Kobayashi, K. Matsushige, H. Yamada, “Development of low noise cantilever deflection sensor for multienvironment frequency-modulation atomic force microscopy,” Rev. Sci. Instrum. 76, 053704 (2005).
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Mavalvala, N.

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
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R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
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McConney, M. E.

M. C. LeMieux, M. E. McConney, Y.-H. Lin, S. Singamaneni, H. Jiang, T. J. Bunning, V. V. Tsukruk, “Polymeric nanolayers as actuators for ultrasensitive thermal bimorphs,” Nano Lett. 6, 730–734 (2006).
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McCormick, C. F.

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
[Crossref]

Mehmet, M.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, R. Schnabel, “Observation of squeezed light with 10-db quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
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Miles, M.

L. Picco, L. Bozec, A. Ulcinas, D. Engledew, M. Antognozzi, M. Horton, M. Miles, “Breaking the speed limit with atomic force microscopy,” Nanotechnology 18, 044030 (2007).
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T. Miyatani, M. Fujihira, “Calibration of surface stress measurements with atomic force microscopy,” J. Appl. Phys. 81, 7099–7115 (1997).
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Myers, E.

J. Arlett, E. Myers, M. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol. 6, 203–215 (2011).
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Nielsen, B. M.

Ogiso, H.

K. Yamanaka, H. Ogiso, O. Kolosov, “Ultrasonic force microscopy for nanometer resolution subsurface imaging,” Appl. Phys. Lett. 64, 178–180 (1994).
[Crossref]

Ou, Z.

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
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A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012).
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L. Tetard, A. Passian, T. Thundat, “New modes for subsurface atomic force microscopy through nanomechanical coupling,” Nat. Nanotechnol. 5, 105–109 (2010).
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M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88, 033845 (2013).
[Crossref]

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L. Picco, L. Bozec, A. Ulcinas, D. Engledew, M. Antognozzi, M. Horton, M. Miles, “Breaking the speed limit with atomic force microscopy,” Nanotechnology 18, 044030 (2007).
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Pinard, M.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
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O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A 85, 010101 (2012).
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J. Tamayo, V. Pini, P. Kosaka, N. F. Martinez, O. Ahumada, M. Calleja, “Imaging the surface stress and vibration modes of a microcantilever by laser beam deflection microscopy,” Nanotechnology 23, 315501 (2012).
[Crossref]

Pooser, R.

R. Pooser, J. Jing, “Continuous-variable cluster-state generation over the optical spatial mode comb,” Phys. Rev. A 90, 043841 (2014).
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B. Lawrie, P. Evans, R. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110, 156802 (2013).
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Pooser, R. C.

Putman, C. A.

C. A. Putman, B. G. De Grooth, N. F. Van Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
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O. Sahin, S. Magonov, C. Su, C. F. Quate, O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2, 507–514 (2007).
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M. T. Jaekel, S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
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Roukes, M.

J. Arlett, E. Myers, M. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol. 6, 203–215 (2011).
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Rugar, D.

D. Rugar, R. Budakian, H. Mamin, B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
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P. E. Rutten, “High speed two-dimensional optical beam position detector,” Rev. Sci. Instrum. 82, 073705 (2011).
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O. Sahin, S. Magonov, C. Su, C. F. Quate, O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2, 507–514 (2007).
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H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
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W. Hiebert, D. Vick, V. Sauer, M. Freeman, “Optical interferometric displacement calibration and thermomechanical noise detection in bulk focused ion beam-fabricated nanoelectromechanical systems,” J. Micromech. Microeng. 20, 115038 (2010).
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Schnabel, R.

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, R. Schnabel, “Observation of squeezed light with 10-db quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
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H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
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G. S. Shekhawat, V. P. Dravid, “Nanoscale imaging of buried structures via scanning near-field ultrasound holography,” Science 310, 89–92 (2005).
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M. C. LeMieux, M. E. McConney, Y.-H. Lin, S. Singamaneni, H. Jiang, T. J. Bunning, V. V. Tsukruk, “Polymeric nanolayers as actuators for ultrasensitive thermal bimorphs,” Nano Lett. 6, 730–734 (2006).
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D. Smith, “Limits of force microscopy,” Rev. Sci. Instrum. 66, 3191–3195 (1995).
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O. Sahin, S. Magonov, C. Su, C. F. Quate, O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2, 507–514 (2007).
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P. B. Dixon, D. J. Starling, A. N. Jordan, J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
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O. Sahin, S. Magonov, C. Su, C. F. Quate, O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2, 507–514 (2007).
[Crossref]

Tamayo, J.

J. Tamayo, V. Pini, P. Kosaka, N. F. Martinez, O. Ahumada, M. Calleja, “Imaging the surface stress and vibration modes of a microcantilever by laser beam deflection microscopy,” Nanotechnology 23, 315501 (2012).
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M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
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L. Tetard, A. Passian, T. Thundat, “New modes for subsurface atomic force microscopy through nanomechanical coupling,” Nat. Nanotechnol. 5, 105–109 (2010).
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J. Teufel, T. Donner, M. Castellanos-Beltran, J. Harlow, K. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4, 820–823 (2009).
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L. Tetard, A. Passian, T. Thundat, “New modes for subsurface atomic force microscopy through nanomechanical coupling,” Nat. Nanotechnol. 5, 105–109 (2010).
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O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, C. Fabre, “Ultimate sensitivity of precision measurements with intense Gaussian quantum light: a multimodal approach,” Phys. Rev. A 85, 010101 (2012).
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N. Treps, V. Delaubert, A. Maître, J. M. Courty, C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
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N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
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N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett. 88, 203601 (2002).
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M. C. LeMieux, M. E. McConney, Y.-H. Lin, S. Singamaneni, H. Jiang, T. J. Bunning, V. V. Tsukruk, “Polymeric nanolayers as actuators for ultrasensitive thermal bimorphs,” Nano Lett. 6, 730–734 (2006).
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M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88, 033845 (2013).
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L. Picco, L. Bozec, A. Ulcinas, D. Engledew, M. Antognozzi, M. Horton, M. Miles, “Breaking the speed limit with atomic force microscopy,” Nanotechnology 18, 044030 (2007).
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G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
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H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, R. Schnabel, “Observation of squeezed light with 10-db quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
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C. A. Putman, B. G. De Grooth, N. F. Van Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
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P. Verlot, A. Tavernarakis, T. Briant, P.-F. Cohadon, A. Heidmann, “Backaction amplification and quantum limits in optomechanical measurements,” Phys. Rev. Lett. 104, 133602 (2010).
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Vick, D.

W. Hiebert, D. Vick, V. Sauer, M. Freeman, “Optical interferometric displacement calibration and thermomechanical noise detection in bulk focused ion beam-fabricated nanoelectromechanical systems,” J. Micromech. Microeng. 20, 115038 (2010).
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H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
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G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
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A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012).
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T. Fukuma, M. Kimura, K. Kobayashi, K. Matsushige, H. Yamada, “Development of low noise cantilever deflection sensor for multienvironment frequency-modulation atomic force microscopy,” Rev. Sci. Instrum. 76, 053704 (2005).
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K. Yamanaka, H. Ogiso, O. Kolosov, “Ultrasonic force microscopy for nanometer resolution subsurface imaging,” Appl. Phys. Lett. 64, 178–180 (1994).
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Zhang, B.

H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
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Zhang, W.

Zhou, J.

Zhou, L.

Zhou, Z.

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K. Yamanaka, H. Ogiso, O. Kolosov, “Ultrasonic force microscopy for nanometer resolution subsurface imaging,” Appl. Phys. Lett. 64, 178–180 (1994).
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M. T. Jaekel, S. Reynaud, “Quantum limits in interferometric measurements,” Europhys. Lett. 13, 301–306 (1990).
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J. Appl. Phys. (2)

C. A. Putman, B. G. De Grooth, N. F. Van Hulst, J. Greve, “A detailed analysis of the optical beam deflection technique for use in atomic force microscopy,” J. Appl. Phys. 72, 6–12 (1992).
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W. Hiebert, D. Vick, V. Sauer, M. Freeman, “Optical interferometric displacement calibration and thermomechanical noise detection in bulk focused ion beam-fabricated nanoelectromechanical systems,” J. Micromech. Microeng. 20, 115038 (2010).
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M. C. LeMieux, M. E. McConney, Y.-H. Lin, S. Singamaneni, H. Jiang, T. J. Bunning, V. V. Tsukruk, “Polymeric nanolayers as actuators for ultrasensitive thermal bimorphs,” Nano Lett. 6, 730–734 (2006).
[Crossref]

Nanotechnology (2)

J. Tamayo, V. Pini, P. Kosaka, N. F. Martinez, O. Ahumada, M. Calleja, “Imaging the surface stress and vibration modes of a microcantilever by laser beam deflection microscopy,” Nanotechnology 23, 315501 (2012).
[Crossref]

L. Picco, L. Bozec, A. Ulcinas, D. Engledew, M. Antognozzi, M. Horton, M. Miles, “Breaking the speed limit with atomic force microscopy,” Nanotechnology 18, 044030 (2007).
[Crossref]

Nat. Commun. (2)

R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun. 1, 121 (2010).
[Crossref]

F. Hudelist, J. Kong, C. Liu, J. Jing, Z. Ou, W. Zhang, “Quantum metrology with parametric amplifier-based photon correlation interferometers,” Nat. Commun. 5, 3049 (2014).
[Crossref]

Nat. Mater. (1)

H. Wagner, D. Bedorf, S. Küchemann, M. Schwabe, B. Zhang, W. Arnold, K. Samwer, “Local elastic properties of a metallic glass,” Nat. Mater. 10, 439–442 (2011).
[Crossref]

Nat. Nanotechnol. (5)

J. Teufel, T. Donner, M. Castellanos-Beltran, J. Harlow, K. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4, 820–823 (2009).
[Crossref]

L. Tetard, A. Passian, T. Thundat, “New modes for subsurface atomic force microscopy through nanomechanical coupling,” Nat. Nanotechnol. 5, 105–109 (2010).
[Crossref]

O. Sahin, S. Magonov, C. Su, C. F. Quate, O. Solgaard, “An atomic force microscope tip designed to measure time-varying nanomechanical forces,” Nat. Nanotechnol. 2, 507–514 (2007).
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J. Arlett, E. Myers, M. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol. 6, 203–215 (2011).
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Nat. Photonics (2)

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
[Crossref]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012).
[Crossref]

Nature (2)

D. Rugar, R. Budakian, H. Mamin, B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[Crossref]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
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Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (7)

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010).
[Crossref]

N. Treps, V. Delaubert, A. Maître, J. M. Courty, C. Fabre, “Quantum noise in multipixel image processing,” Phys. Rev. A 71, 013820 (2005).
[Crossref]

C. F. McCormick, A. M. Marino, V. Boyer, P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78, 043816 (2008).
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R. S. Bennink, R. W. Boyd, “Improved measurement of multimode squeezed light via an eigenmode approach,” Phys. Rev. A 66, 053815 (2002).

M. T. Turnbull, P. G. Petrov, C. S. Embrey, A. M. Marino, V. Boyer, “Role of the phase-matching condition in nondegenerate four-wave mixing in hot vapors for the generation of squeezed states of light,” Phys. Rev. A 88, 033845 (2013).
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H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, R. Schnabel, “Observation of squeezed light with 10-db quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref]

B. Lawrie, P. Evans, R. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110, 156802 (2013).
[Crossref]

P. Verlot, A. Tavernarakis, T. Briant, P.-F. Cohadon, A. Heidmann, “Backaction amplification and quantum limits in optomechanical measurements,” Phys. Rev. Lett. 104, 133602 (2010).
[Crossref]

N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, C. Fabre, “Surpassing the standard quantum limit for optical imaging using nonclassical multimode light,” Phys. Rev. Lett. 88, 203601 (2002).
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O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
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P. B. Dixon, D. J. Starling, A. N. Jordan, J. C. Howell, “Ultrasensitive beam deflection measurement via interferometric weak value amplification,” Phys. Rev. Lett. 102, 173601 (2009).
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Rev. Sci. Instrum. (3)

P. E. Rutten, “High speed two-dimensional optical beam position detector,” Rev. Sci. Instrum. 82, 073705 (2011).
[Crossref]

T. Fukuma, M. Kimura, K. Kobayashi, K. Matsushige, H. Yamada, “Development of low noise cantilever deflection sensor for multienvironment frequency-modulation atomic force microscopy,” Rev. Sci. Instrum. 76, 053704 (2005).
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D. Smith, “Limits of force microscopy,” Rev. Sci. Instrum. 66, 3191–3195 (1995).
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Science (4)

V. Boyer, A. M. Marino, R. C. Pooser, P. D. Lett, “Entangled images from four-wave mixing,” Science 321, 544–547 (2008).
[Crossref]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, P. K. Lam, “A quantum laser pointer,” Science 301, 940–943 (2003).
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G. S. Shekhawat, V. P. Dravid, “Nanoscale imaging of buried structures via scanning near-field ultrasound holography,” Science 310, 89–92 (2005).
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O. Hosten, P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
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Figures (4)

Fig. 1.
Fig. 1.

Differential beam position measurements with quantum-correlated twin beams from four-wave mixing. (a) Squeezed differential beam displacement measurement using a split detector. The probe is sent to a polarizing beam splitter (PBS) where it passes through a quarter-wave retarder before being focused onto the cantilever by a microscope objective. On the return pass the probe beam is separated at the PBS and sent to a split detector (or through an aperture), which subtracts the correlated noise between each half of each beam. (b) Energy level diagram showing a double Λ system at the D1 line (795 nm) in Rb 85 . The presence of a weak probe (Pr) stimulates the coherent emission of a conjugate (C) photon for every emitted probe photon, while high nonlinear gain on the order of 5 allows for bright fields for both probe and conjugate.

Fig. 2.
Fig. 2.

Relative beam position measurement of the probe and conjugate fields. The shaded semicircles represent correlated subparts of each beam. When accessed with a split detector, the quantum correlations in these modes reduce the total noise floor. Because the probe and conjugate are mirror images of one another about the propagation axis, a single split detector (right-hand side) can be used to access the position correlations that a relative position measurement would reveal (left-hand side).

Fig. 3.
Fig. 3.

Sub-shot-noise microcantilever deflection detection. (a) Sub-shot-noise modulation for a microcantilever with an aperture in the beam path, SNL-normalized noise power (left axis, ± 0.1 dB error bars, standard deviation of 1000 averages), and SNR (right axis) as a function of conjugate transmission through an aperture with a constant probe transmission of 50% ( ± 0.1 dB , standard deviation of 1000 averages). (b) Spectrum analyzer traces of raw displacement signals on a split detector centered at 745 kHz for various displacement amplitudes, from 30 to 120 mV. The noise floor shows a broadband squeezing level of 4.0 ± 0.1 dB relative to the shot-noise level (black line, electronics noise subtracted). The spectrum analyzer settings were as follows: resolution bandwidth, 10 kHz; video bandwidth, 100 Hz; sweep time, 2 s; 20 averages. (c) Signal-to-noise ratio (with error bars of ± 0.2 dB , statistical uncertainty) on a split detector versus increasing displacement amplitude at 745 kHz for a squeezing level of 3.0 ± 0.1 dB . The squeezed SNR increases more rapidly than the coherent case to a separation of 3 dB in the limit of large displacement.

Fig. 4.
Fig. 4.

(a) Noise floor as a function of optical power for split detector measurements using coherent states (circles) and squeezed states (squares). (b) Minimum inferred displacement measurable, calculated using the SNR and measured noise floor. The curves are fits to the data from the theoretical calculations in (c), following the methods in [4,49], and [50], which show the optical noise floor, back action (blue), and SQL (dashed lines) as a function of optical power for various levels of squeezing. The purple curve is the shot noise (no squeezing), while black, brown, and gray correspond to 4, 13, and 26 dB of squeezing, respectively.

Equations (8)

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( Δ x ) 2 SQL = ( Δ x ) 2 back + ( Δ x ) 2 SNL .
( Δ x ) 2 back = 8 P h Δ f Q 2 c λ k 2 ; ( Δ x ) 2 SNL = h c λ Δ f 8 π 2 P ,
H = i χ ( 2 ) a 1 , k 1 a 2 , k 2 a p , k p + H.C. ,
a 1 ( t ) = a 1 ( 0 ) G a 2 ( 0 ) G 1 ;
a 2 ( t ) = a 2 ( 0 ) G a 1 ( 0 ) G 1 ,
Δ ( N ) 2 = 1 ( 2 G 1 ) ,
H = i χ ( 2 ) a i , k i a j , k j a p , k p + H.C.
Δ N 2 = 1 P 0 [ P s n s ( 2 G 1 ) + ( i = 1 M P i ( x ) n i ( x ) η d ( 2 G 1 ) ) ] ,

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