Abstract

Nonclassical beams in high order spatial modes have attracted much interest but they exhibit much less squeezing and entanglement than the fundamental spatial modes, limiting their applications. We experimentally demonstrate the relation between pump modes and entanglement of first-order Hermite Gauss modes (HG10 entangled states) in a type II OPO and show that the maximum entanglement of high order spatial modes can be obtained by optimizing the pump spatial mode. To our knowledge, this is the first time to report this. Utilizing the optimal pump mode, the HG10 mode threshold can be reached easily without HG00 oscillation and HG10 entanglement is enhanced by 53.5% over HG00 pumping. The technique is broadly applicable to entanglement generation in high order modes.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Squeezing and entanglement in doubly resonant, type II, second-harmonic generation

Ulrik L. Andersen and Preben Buchhave
J. Opt. Soc. Am. B 20(9) 1947-1958 (2003)

Bright entanglement characteristics of subharmonic modes reflected from cavity for type II second-harmonic generation

Zehui Zhai, Hongxin Zou, Junxiang Zhang, and Jiangrui Gao
J. Opt. Soc. Am. B 22(4) 878-883 (2005)

Bright two-color tripartite entanglement with second harmonic generation

Shuqin Zhai, Rongguo Yang, Kui Liu, Hailong Zhang, Junxiang Zhang, and Jiangrui Gao
Opt. Express 17(12) 9851-9857 (2009)

References

  • View by:
  • |
  • |
  • |

  1. R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
    [Crossref] [PubMed]
  2. L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
    [Crossref] [PubMed]
  3. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
    [Crossref] [PubMed]
  4. P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
    [Crossref]
  5. S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
    [Crossref] [PubMed]
  6. H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
    [Crossref]
  7. Y. Zhou, X. Jia, F. Li, C. Xie, and K. Peng, “Experimental generation of 8.4 dB entangled state with an optical cavity involving a wedged type-II nonlinear crystal,” Opt. Express 23, 4952–4959 (2015).
    [Crossref] [PubMed]
  8. H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
    [Crossref]
  9. V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
  10. G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
    [Crossref]
  11. A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
    [Crossref]
  12. J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
    [Crossref]
  13. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H. A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7, 229–233 (2013).
    [Crossref]
  14. M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
    [Crossref]
  15. M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
    [Crossref] [PubMed]
  16. M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102, 163602 (2009).
    [Crossref] [PubMed]
  17. J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
    [Crossref]
  18. B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
    [Crossref]
  19. B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Direct generation of a multi-transverse mode non-classical state of light,” Opt. Express 19, 4405–4410 (2011).
    [Crossref] [PubMed]
  20. B. dos Santos, K. Dechoum, and A. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
    [Crossref]
  21. K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
    [Crossref] [PubMed]
  22. L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
    [Crossref] [PubMed]
  23. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [Crossref]
  24. M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
    [Crossref]
  25. M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).
  26. K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
    [Crossref] [PubMed]
  27. J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
    [Crossref]
  28. Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
    [Crossref]

2016 (5)

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
[Crossref] [PubMed]

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

2015 (1)

2014 (3)

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

2013 (2)

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

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

2012 (1)

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

2011 (1)

2010 (2)

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
[Crossref]

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

2009 (3)

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

B. dos Santos, K. Dechoum, and A. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

2008 (1)

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

2007 (1)

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

2006 (1)

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

2000 (1)

L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

1996 (1)

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

1993 (1)

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
[Crossref]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

1986 (1)

L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

1985 (1)

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Andersen, U. L.

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

Aolita, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Bachor, H.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Bachor, H. A.

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

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Barreiro, J. T.

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Berchera, I. R.

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Bowen, W. P.

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

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

Brida, G.

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Buchhave, P.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Cai, C.

K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
[Crossref] [PubMed]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Chalopin, B.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Direct generation of a multi-transverse mode non-classical state of light,” Opt. Express 19, 4405–4410 (2011).
[Crossref] [PubMed]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
[Crossref]

Chen, Z. B.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Cirac, J.

L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

D’Ambrosio, V.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Danzmann, K.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Daria, V.

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

Dechoum, K.

B. dos Santos, K. Dechoum, and A. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

Del Re, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Delaubert, V.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Ding, D. S.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

dos Santos, B.

B. dos Santos, K. Dechoum, and A. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Drummond, P. D.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
[Crossref]

Duan, L.

L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Fabre, C.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Direct generation of a multi-transverse mode non-classical state of light,” Opt. Express 19, 4405–4410 (2011).
[Crossref] [PubMed]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
[Crossref]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Friberg, S.

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

Friberg, S. R.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
[Crossref]

Gao, J.

K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
[Crossref] [PubMed]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

Genovese, M.

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Giacobino, E.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

Giedke, G.

L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Giner, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

Guo, G. C.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

Guo, J.

K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
[Crossref] [PubMed]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Guo, P.

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

Guo, S.

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

Hage, B.

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

Hall, J.

L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Harb, C.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Harb, C. C.

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Hollberg, L.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Janousek, J.

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

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Jia, X.

Khoury, A.

B. dos Santos, K. Dechoum, and A. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

Kimble, H.

L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Kimble, H. J.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Knittel, J.

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

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Kwek, L. C.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Kwiat, P. G.

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Lam, P.

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Lam, P. K.

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Lassen, M.

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Laurat, J.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

Leuchs, G.

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

Levanon, A.

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

Li, F.

Li, Y.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Liu, K.

K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
[Crossref] [PubMed]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

Liu, Z.

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

Lu, C. Y.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Lu, X. M.

M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Machida, S.

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

Marrucci, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Maxein, D.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

Mehmet, M.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Mertz, J.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Morizur, J. F.

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

Mukai, T.

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Nair, R.

M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Nicolas, A.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Pan, J. W.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Peng, K.

Peng, K. C.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Scazza, F.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Direct generation of a multi-transverse mode non-classical state of light,” Opt. Express 19, 4405–4410 (2011).
[Crossref] [PubMed]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
[Crossref]

Schnabel, R.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Sciarrino, F.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Shelby, R. M.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
[Crossref]

Shi, B. S.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

Shi, S.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

Slusher, R.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Slussarenko, S.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Spagnolo, N.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Sun, H.

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

Taylor, M. A.

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

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

Treps, N.

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Direct generation of a multi-transverse mode non-classical state of light,” Opt. Express 19, 4405–4410 (2011).
[Crossref] [PubMed]

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
[Crossref]

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Tsang, M.

M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Vahlbruch, H.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

Valley, J.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Veissier, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

Wagner, K.

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

Walborn, S. P.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Wei, T.

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Weinfurter, H.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Werner, M.

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

Wu, H.

L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Wu, L. A.

L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Xie, C.

Yamamoto, Y.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
[Crossref]

Yurke, B.

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Zeilinger, A.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Zhang, J.

K. Liu, J. Guo, C. Cai, J. Zhang, and J. Gao, “Direct generation of spatial quadripartite continuous variable entanglement in an optical parametric oscillator,” Opt. Lett. 41, 5178–5181 (2016).
[Crossref] [PubMed]

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

Zhang, W.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

Zhou, Y.

Zhou, Z. Y.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

Zoller, P.

L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

Zukowski, M.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Appl. Phys. Lett. (1)

H. Sun, K. Liu, Z. Liu, P. Guo, J. Zhang, and J. Gao, “Small-displacement measurements using high-order Hermite-Gauss modes,” Appl. Phys. Lett. 104, 121908 (2014).
[Crossref]

J. Eur. Opt. Soc. Rapid Publ. (1)

M. Lassen, V. Delaubert, C. C. Harb, P. K. Lam, N. Treps, and H. A. Bachor, “Generation of squeezing in higher order Hermite - Gaussian modes with an optical parametric amplifier,” J. Eur. Opt. Soc. Rapid Publ. 1, 06003 (2006).
[Crossref]

Light Sci. Appl. (1)

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5, e16019 (2016).
[Crossref]

Nat. Commun. (1)

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Nat. Photonics (4)

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8, 234–238 (2014).
[Crossref]

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

J. Janousek, K. Wagner, J. F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H. A. Bachor, “Optical entanglement of co-propagating modes,” Nat. Photonics 3, 399–402 (2009).
[Crossref]

Nat. Phys. (1)

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[Crossref]

Nature (1)

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, “Quantum solitons in optical fibres,” Nature 365, 307–313 (1993).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rep. (1)

M. A. Taylor and W. P. Bowen, “Quantum metrology and its application in biology,” Phys. Rep. 615, 1–59 (2016).
[Crossref]

Phys. Rev. A (1)

B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804 (2010).
[Crossref]

Phys. Rev. Lett. (10)

B. dos Santos, K. Dechoum, and A. Khoury, “Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum,” Phys. Rev. Lett. 103, 230503 (2009).
[Crossref]

K. Liu, J. Guo, C. Cai, S. Guo, and J. Gao, “Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator,” Phys. Rev. Lett. 113, 170501 (2014).
[Crossref] [PubMed]

L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[Crossref] [PubMed]

M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H. Bachor, P. Lam, N. Treps, P. Buchhave, C. Fabre, and C. Harb, “Tools for multimode quantum information: modulation, detection, and spatial quantum correlations,” Phys. Rev. Lett. 98, 083602 (2007).
[Crossref] [PubMed]

M. Lassen, G. Leuchs, and U. L. Andersen, “Continuous variable entanglement and squeezing of orbital angular momentum states,” Phys. Rev. Lett. 102, 163602 (2009).
[Crossref] [PubMed]

S. Friberg, S. Machida, M. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77, 3775–3778 (1996).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

R. Slusher, L. Hollberg, B. Yurke, J. Mertz, and J. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

L. A. Wu, H. Kimble, J. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
[Crossref] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6, 031033 (2016).

Rev. Mod. Phys. (1)

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multiphoton entanglement and interferometry,” Rev. Mod. Phys. 84, 777–838 (2012).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Theoretical inseparabilities V against normalized pump power p / p t h 00 00 for three pump modes, HG00 (blue solid line), HG20 (green dashed line) and the optimal pump mode HGopt (red dotted line) under ideal conditions. The parameters are ηdet = 1, ηesc = 1, Ω = 0.

Fig. 2
Fig. 2

Schematic of the experimental setup. NOPA: non-degenerate optical parametric amplifier, KTP: type II KTP crystal, M1 and M2: cavity mirrors, BS: beam splitter, PBS: polarizing beam splitter, MCs: mode converters, SG: signal generator, Servo: servo amplifier circuit for feedback system, PZTs: piezoelectric transducers, DBS: dichroic beam splitter, Local: local oscillator, BHDs: balanced homodyne detectors, +/−: positive/negative power combiner, and SA: spectrum analyzer.

Fig. 3
Fig. 3

The inseparabilities V versus normalized pump power p / p t h 00 00, where p t h 00 00 = 510 mW. Data points from the experiment are blue squares for HG00 pumping, green circles for HG20 pumping and red triangles for the optimal pump mode HGopt. The solid curves are the theoretical values in experimental conditions for the three pump modes.

Fig. 4
Fig. 4

The HG10 mode correlation noise powers for the amplitude sum V X s + X i (a1–a3) and the phase difference V Y s Y i (b1–b3). The top row was taken using 500 mW of HG00 pumping, the middle row with 670 mW of HG20 pumping, and the bottom row with 670 mW of the superposition HGopt pumping.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

v p ( r ) = n = 0 c n v n 0 ( r ) ,
H ^ = i ε p ( a ^ p a ^ p ) + i χ Γ ( a ^ p a ^ s a ^ i a ^ p a ^ s a ^ i ) ,
Γ = + v p ( r ) u s * ( r ) u i * ( r ) d r .
τ a ^ ˙ p ( t ) = γ p a ^ p ( t ) χ Γ a ^ s ( t ) a ^ i ( t ) + ε p e i θ p + 2 μ p b ^ i n p ( t )
τ a ^ ˙ s ( t ) = γ s a ^ s ( t ) + χ Γ a ^ p ( t ) a ^ i ( t ) + 2 γ s a ^ i n s ( t ) + 2 μ s b ^ i n s ( t )
τ a ^ ˙ i ( t ) = γ i a ^ i ( t ) + χ Γ a ^ p ( t ) a ^ s ( t ) + 2 γ i a ^ i n i ( t ) + 2 μ i b ^ i n i ( t ) .
ε p t h = γ / ( χ Γ ) .
V X ^ s X ^ i = V Y ^ s + Y ^ i = 1 η e s c 4 σ ( 1 + σ ) 2 + Ω 2 ,
V X ^ s + X ^ i = V Y ^ s Y ^ i = 1 η e s c 4 σ ( 1 + σ ) 2 + Ω 2 ,
V X ^ s + X ^ i = V Y ^ s Y ^ i = 1 η det η e s c 4 p / p t h ( 1 + p / p t h ) 2 + Ω 2 ,
V = V X s + X i + V Y s Y i = 2 η det η e s c 8 p / p t h ( 1 + p / p t h ) 2 + Ω 2 < 2 .
Γ = + v 00 ( r ) [ u 00 ( r ) ] 2 d r = 1 ,
Γ = n = 0 c n + v n 0 ( r ) [ u 10 ( r ) ] 2 d r = n = 0 c n Γ n ,
Γ 0 = + v 00 ( r ) [ u 10 ( r ) ] 2 d r = 1 / 2 ,
Γ 2 = + v 20 ( r ) [ u 10 ( r ) ] 2 d r = 1 / 2 ,
V ( d B ) = 10 log 10 V ( p e r )
V X s + X i 00 + V Y s Y i 00 = 1.13 ± 0.02 < 2 ,
V X s + X i 20 + V Y s Y i 20 = 1.04 ± 0.02 < 2 ,
V X s + X i o p t + V Y s Y i o p t = 0.98 ± 0.04 < 2 .

Metrics