Abstract

Quantum computation and communication protocols require quantum resources which are in the continuous variable regime squeezed and/or quadrature entangled optical modes. To perform more and more complex and robust protocols, one needs sources that can produce in a controlled way highly multimode quantum states of light. One possibility is to mix different single mode quantum resources. Another is to directly use a multimode device, either in the spatial or in the frequency domain. We present here the first experimental demonstration of a device capable of producing simultanuously several squeezed transverse modes of the same frequency and which is potentially scalable. We show that this device, which is an Optical Parametric Oscillator using a self-imaging cavity, produces a multimode quantum resource made of three squeezed transverse modes.

© 2011 Optical Society of America

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  1. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005.)
    [CrossRef]
  2. L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
    [CrossRef]
  3. A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
    [CrossRef] [PubMed]
  4. N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
    [CrossRef] [PubMed]
  5. A. Eckstein, and C. Silberhorn, “Broadband frequency mode entanglement in waveguided parametric downconversion,” Opt. Lett. 33, 1825–1827 (2008).
    [CrossRef] [PubMed]
  6. O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of sub-shot-noise spatial correlation in high-gain parametric down conversion,” Phys. Rev. Lett. 93, 243601 (2004).
    [CrossRef]
  7. J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
    [CrossRef] [PubMed]
  8. 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]
  9. M. D. Reid, “Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).
    [CrossRef] [PubMed]
  10. M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
    [CrossRef]
  11. M. I. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
    [CrossRef]
  12. 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]
  13. B. Chalopin, F. Scazza, C. Fabre, and N. Treps, “Multimode nonclassical light generation through the optical-parametric-oscillator threshold,” Phys. Rev. A 81, 061804(R) (2010).
    [CrossRef]
  14. L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520–2523 (1986).
    [CrossRef] [PubMed]
  15. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
    [CrossRef] [PubMed]
  16. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. 8, 189–195 (1969).
    [CrossRef] [PubMed]
  17. B. Chalopin, A. Chiummo, C. Fabre, A. Maitre, and N. Treps, “Frequency doubling of low power images using a self-imaging cavity,” Opt. Express 18, 8033–8042 (2010).
    [CrossRef] [PubMed]
  18. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
    [CrossRef] [PubMed]
  19. M. Lassen, V. Delaubert, 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]

2010 (3)

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

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

B. Chalopin, A. Chiummo, C. Fabre, A. Maitre, and N. Treps, “Frequency doubling of low power images using a self-imaging cavity,” Opt. Express 18, 8033–8042 (2010).
[CrossRef] [PubMed]

2009 (4)

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]

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (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]

2008 (4)

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[CrossRef] [PubMed]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
[CrossRef] [PubMed]

A. Eckstein, and C. Silberhorn, “Broadband frequency mode entanglement in waveguided parametric downconversion,” Opt. Lett. 33, 1825–1827 (2008).
[CrossRef] [PubMed]

2006 (1)

M. Lassen, V. Delaubert, 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]

2005 (1)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005.)
[CrossRef]

2004 (1)

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

2000 (1)

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[CrossRef] [PubMed]

1999 (1)

M. I. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

1989 (1)

M. D. Reid, “Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).
[CrossRef] [PubMed]

1986 (1)

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

1969 (1)

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]

Arnaud, J. A.

Bache, M.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and 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.

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. 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]

Barbosa, F. A. S.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

Bauchrowitz, J.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Blanchet, J.-L.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[CrossRef] [PubMed]

Brambilla, E.

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

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005.)
[CrossRef]

Cassemiro, K. N.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

Chalopin, B.

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

B. Chalopin, A. Chiummo, C. Fabre, A. Maitre, and N. Treps, “Frequency doubling of low power images using a self-imaging cavity,” Opt. Express 18, 8033–8042 (2010).
[CrossRef] [PubMed]

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

Chiummo, A.

Coelho, A. S.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

Delaubert, V.

M. Lassen, V. Delaubert, 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]

Devaux, F.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[CrossRef] [PubMed]

Di Trapani, P.

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

Eberle, T.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Eberly, J. H.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[CrossRef] [PubMed]

Eckstein, A.

Fabre, C.

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

B. Chalopin, A. Chiummo, C. Fabre, A. Maitre, and N. Treps, “Frequency doubling of low power images using a self-imaging cavity,” Opt. Express 18, 8033–8042 (2010).
[CrossRef] [PubMed]

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

Flammia, S. T.

N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
[CrossRef] [PubMed]

Furfaro, L.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[CrossRef] [PubMed]

Furusawa, A.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

Gatti, A.

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

Hall, J. L.

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

Händchen, V.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Harb, C.

M. Lassen, V. Delaubert, 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]

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]

Janousek, J.

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]

Jedrkiewicz, O.

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

Jiang, Y.-K.

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

Kimble, H. J.

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

Kolobov, M. I.

M. I. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

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. 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]

Lantz, E.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[CrossRef] [PubMed]

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, 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]

Law, C. K.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[CrossRef] [PubMed]

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]

Lopez, L.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

Lugiato, L. A.

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

Maitre, A.

Maître, A.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

Martinelli, M.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

Mehmet, M.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Menicucci, N. C.

N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
[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]

Müller-Ebhardt, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Nussenzveig, P.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

Pfister, O.

N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
[CrossRef] [PubMed]

Reid, M. D.

M. D. Reid, “Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).
[CrossRef] [PubMed]

Rivière de la Souchère, A.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

Scazza, F.

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

Schnabel, R.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Silberhorn, C.

Steinlechner, S.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Treps, N.

B. Chalopin, A. Chiummo, C. Fabre, A. Maitre, and N. Treps, “Frequency doubling of low power images using a self-imaging cavity,” Opt. Express 18, 8033–8042 (2010).
[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(R) (2010).
[CrossRef]

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[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. 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]

Ukai, R.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

Vahlbruch, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

van Loock, P.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005.)
[CrossRef]

Villar, A. S.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

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]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[CrossRef] [PubMed]

Wu, H.

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

Yukawa, M.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

Appl. Opt. (1)

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

M. Lassen, V. Delaubert, 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]

Nat. Photonics (1)

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]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (4)

M. D. Reid, “Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A 40, 913–923 (1989).
[CrossRef] [PubMed]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

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

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, “Multimode quantum properties of a self-imaging optical parametric oscillator: squeezed vacuum and Einstein–Podolsky–Rosen beams generation,” Phys. Rev. A 80, 043816 (2009).
[CrossRef]

Phys. Rev. Lett. (7)

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

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of sub-shot-noise correlations of spatial fluctuations in the photon-counting regime,” Phys. Rev. Lett. 101, 233604 (2008).
[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]

N. C. Menicucci, S. T. Flammia, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
[CrossRef] [PubMed]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304–5307 (2000).
[CrossRef] [PubMed]

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

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005.)
[CrossRef]

M. I. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71, 1539–1589 (1999).
[CrossRef]

Science (1)

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1:
Fig. 1:

Sketch of the self-imaging OPO. The cavity contains a plane mirror, a lens and a spherical mirror, and reaches complete transverse mode degeneracy for precise values of their relative distances. A non-linear crystal is placed inside the cavity. The parametric downconversion process of pump photons generate degenerate signal and idler photons in different spatial modes. The output of the OPO is a set of squeezed transverse modes.

Fig. 2:
Fig. 2:

Sketch of the experimental setup.

Fig. 3:
Fig. 3:

a) Output of the self-imaging OPO, three transverse modes of the same wavelength are squeezed. b) Fluctuations of three orthogonal output modes of the OPO measured with a homodyne detection. The phase of the local oscillator is swept, so that the fluctuations are measured on all different quadratures. The blue line indicates the shot noise level. The TEM00 (red curve) shows 1.2 dB of squeezing below shot noise, the TEM10 (cyan curve) 0.6 dB and the TEM01 (green curve) 0.3 dB.

Equations (2)

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d S ^ k d t = γ S ^ k + Λ k S ^ k + 2 γ S ^ k , in
V k , m i n = | Λ 0 | | Λ k | | Λ 0 | + | Λ k |

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