Abstract

We present experimental results on the generation of multi-spatial-mode, single-beam, quadrature squeezed light using four-wave mixing in hot Rb vapor. Squeezing and phase-sensitive deamplification are observed over a range of powers and detunings near the 85Rb D1 atomic transition. We observe −3 dB of vacuum quadrature squeezing, comparable to the best single-spatial mode results previously reported using atomic vapors, however, produced here in multiple spatial modes. We confirm that the squeezing is present in more than one transverse mode by studying the spatial distribution of the noise properties of the field.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  30. Note that the definitions of ? and ? used here differ from those in Ref. [22].
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    [CrossRef] [PubMed]
  32. K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).
  33. M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
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    [CrossRef]
  36. A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
    [CrossRef] [PubMed]

2011 (2)

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]

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (6)

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[CrossRef] [PubMed]

R. Pooser, A. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17, 16722–16730 (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]

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]

M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17, 11415–11425 (2009).
[CrossRef] [PubMed]

2008 (9)

N. C. Menicucci, S. T. Flammina, 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 downconvertion,” Opt. Lett. 33, 1825–1827 (2008).
[CrossRef] [PubMed]

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” IEEE J. Sel. Top. Quantum Electron. 14, 635–647 (2008).
[CrossRef]

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

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

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

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

2005 (2)

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

2002 (1)

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

1999 (2)

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

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[CrossRef]

1996 (1)

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
[CrossRef]

1995 (1)

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

1994 (1)

P. Kumar and M. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
[CrossRef]

1993 (2)

1985 (1)

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

1981 (1)

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

Abram, I.

Agha, I. H.

Aoki, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

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]

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]

Boyd, R. W.

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

Boyer, V.

R. Pooser, A. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17, 16722–16730 (2009).
[CrossRef] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[CrossRef] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

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

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

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

Brambilla, E.

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum Imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2007), Vol. 51, p. 251.
[CrossRef]

Buchler, B.

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

Buchler, B. C.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[CrossRef] [PubMed]

Campbell, G.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[CrossRef] [PubMed]

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]

Caves, C. M.

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

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]

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

Chelkowski, S.

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

Choi, S.-K.

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[CrossRef]

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]

Coudreau, T.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
[CrossRef]

Danzmann, K.

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

Davis, W. V.

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

Devaux, F.

E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” IEEE J. Sel. Top. Quantum Electron. 14, 635–647 (2008).
[CrossRef]

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
[CrossRef] [PubMed]

Ducci, S.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Eckstein, A.

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]

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Flammina, S. T.

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

Franzen, A.

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

Furusawa, A.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

Gaeta, A. L.

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

Gatti, A.

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum Imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2007), Vol. 51, p. 251.
[CrossRef]

Gehr, R. J.

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

Giacobino, E.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
[CrossRef]

Gigan, S.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Goda, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

Gossler, S.

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

Grangier, P.

Gray, M. B.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

Grosse, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

Hage, B.

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

Hiraoka, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

Hollberg, L. W.

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

Hosseini, M.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[CrossRef] [PubMed]

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]

Jones, K. M.

R. Pooser, A. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17, 16722–16730 (2009).
[CrossRef] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

Kauranen, M.

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

Kolobov, M.

Kolobov, M. I.

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

Kumar, P.

M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17, 11415–11425 (2009).
[CrossRef] [PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[CrossRef]

P. Kumar and M. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
[CrossRef]

M. Kolobov and P. Kumar, “Sub-shot-noise microscopy: imaging of faint phase objects with squeezed light,” Opt. Lett. 18, 849–851 (1993).
[CrossRef] [PubMed]

Lam, P. K.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[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]

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

Lam, P.-K.

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

Lambrecht, A.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
[CrossRef]

Lantz, E.

E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” IEEE J. Sel. Top. Quantum Electron. 14, 635–647 (2008).
[CrossRef]

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
[CrossRef] [PubMed]

Lastzka, N.

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

Lemons, K.

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

Lett, P. D.

R. Pooser, A. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Quantum correlated light beams from non-degenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of 85Rb and 87Rb,” Opt. Express 17, 16722–16730 (2009).
[CrossRef] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[CrossRef] [PubMed]

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

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

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

Levenson, J.

Lopez, L.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

Lugiato, L.

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum Imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2007), Vol. 51, p. 251.
[CrossRef]

Maitre, A.

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

Marino, A.

Marino, A. M.

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[CrossRef] [PubMed]

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

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

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

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Matre, A.

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Mavalvala, N.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

McClelland, D.

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

McClelland, D. E.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

McCormick, C. F.

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

McKenzie, K.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

Mehmet, M.

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

Menicucci, N. C.

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

Mertz, J. C.

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

Messin, G.

Mikhailov, E. E.

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

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]

Mosset, A.

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
[CrossRef] [PubMed]

Nagasako, E. M.

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[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. Flammina, and O. Pfister, “One-way quantum computing in the optical frequency comb,” Phys. Rev. Lett. 101, 130501 (2008).
[CrossRef] [PubMed]

Pooser, R.

Pooser, R. C.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[CrossRef] [PubMed]

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

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

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

Rivera, T.

Scazza, F.

Schnabel, R.

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

Shaddock, D.

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

Silberhorn, C.

Slusher, R. E.

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

Sokolov, I.

Sparkes, B. M.

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[CrossRef] [PubMed]

Steinberg, A. M.

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
[CrossRef]

Stelmakh, N.

Takei, N.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

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]

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]

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

Vahlbruch, H.

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

Valley, J. F.

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

van Loock, P.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

Vasilyev, M.

M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17, 11415–11425 (2009).
[CrossRef] [PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[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]

Wakui, K.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

Yonezawa, H.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

Yurke, B.

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

Europhys. Lett. (1)

A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” IEEE J. Sel. Top. Quantum Electron. 14, 635–647 (2008).
[CrossRef]

J. Opt. B (1)

K. McKenzie, E. E. Mikhailov, K. Goda, P. K. Lam, N. Grosse, M. B. Gray, N. Mavalvala, and D. E. McClelland, “Quantum noise locking,” J. Opt. B 7, S241–S428 (2005).

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

M. Hosseini, B. M. Sparkes, G. Campbell, P. K. Lam, and B. C. Buchler, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174 (2011).
[CrossRef] [PubMed]

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]

Nature (1)

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein–Podolsky–Rosen entanglement,” Nature 457, 859–862 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Kumar and M. Kolobov, “Degenerate four-wave mixing as a source for spatially-broadband squeezed light,” Opt. Commun. 104, 374–378 (1994).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (3)

W. V. Davis, M. Kauranen, E. M. Nagasako, R. J. Gehr, A. L. Gaeta, and R. W. Boyd, “Excess noise acquired by a laser beam after propagating through an atomic-potassium vapor,” Phys. Rev. A 51, 4152–4159 (1995).
[CrossRef] [PubMed]

M. Martinelli, N. Treps, S. Ducci, S. Gigan, A. Matre, and C. Fabre, “Experimental study of the spatial distribution of quantum correlations in a confocal optical parametric oscillator,” Phys. Rev. A 67, 023808 (2003).
[CrossRef]

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

Phys. Rev. D (1)

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

Phys. Rev. Lett. (11)

K. McKenzie, D. Shaddock, D. McClelland, B. Buchler, and P.-K. Lam, “Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection,” Phys. Rev. Lett. 88, 231102 (2002).
[CrossRef] [PubMed]

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

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef] [PubMed]

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

L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maitre, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100, 013604 (2008).
[CrossRef] [PubMed]

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

R. C. Pooser, A. M. Marino, V. Boyer, K. M. Jones, and P. D. Lett, “Low-noise amplification of a continuous-variable quantum state,” Phys. Rev. Lett. 103, 010501 (2009).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, and P. D. Lett, “Generation of spatially broadband twin beams for quantum imaging,” Phys. Rev. Lett. 100, 143601 (2008).
[CrossRef] [PubMed]

A. M. Marino, V. Boyer, R. C. Pooser, P. D. Lett, K. Lemons, and K. M. Jones, “Delocalized correlations in twin light beams with orbital angular momentum,” Phys. Rev. Lett. 101, 093602 (2008).
[CrossRef] [PubMed]

S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999).
[CrossRef]

A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94, 223603 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Science (2)

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]

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

Other (3)

A. Gatti, E. Brambilla, and L. Lugiato, “Quantum Imaging,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2007), Vol. 51, p. 251.
[CrossRef]

M. Kolobov, ed., Quantum Imaging (Springer, 2007).
[CrossRef]

Note that the definitions of ? and ? used here differ from those in Ref. [22].

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Figures (6)

Fig. 1
Fig. 1

4WM in hot 85Rb vapor. (a) Twin beam generation. The top panel shows the physical arrangement of the beams in the Rb cell. The lower panel shows the level structure of the D1 transition of 85Rb and the optical frequencies arranged in the double-Λ configuration. Here νp indicates the pump, while ν1 and ν2 indicate the probe and conjugate, respectively. (b) Corresponding diagrams for the generation of single-beam quadrature squeezing. Here ν1 and ν2 are the pumps and νp is the probe. For both (a) and (b): the width of the excited state in the level diagram represents the Doppler broadened line, Δ is the one-photon detuning, δ is the two-photon detuning, and νHF is the hyperfine splitting.

Fig. 2
Fig. 2

Experimental setup. AOM: acousto-optic modulator, TA: semiconductor tapered amplifier, SA: radio frequency spectrum analyzer, BS: non-polarizing beamsplitter, PBS: polarizing beamsplitter, BB: beam block. The beam block and the flip mirror are removed in order to seed the 4WM process and permit direct intensity detection with a single photodiode.

Fig. 3
Fig. 3

Squeezing measurements at 1 MHz as a function of one photon detuning Δ. (a) (Green squares) Amplitude-quadrature squeezing measured when the 4WM process is seeded with 60 μW. (Blue triangles) The squeezing expected for an ideal PSA, calculated from the measured gain at each value of Δ, and corrected for loss. The powers in pump 1 and pump 2 are both 190 mW. (b) (Red circles) Measured squeezing when the process is not seeded (vacuum squeezing). The power in pump 1 is 230 mW, and the power in pump 2 is 160 mW. For both (a) and (b): δ = −4 MHz, RBW = 30 kHz, VBW = 100 Hz.

Fig. 4
Fig. 4

Vacuum squeezing measured by homodyne detection at 1 MHz when (a) the phase of the local oscillator (LO) is scanned and (b) when the phase of the LO is locked. Trace (c) indicates the standard quantum limit. (RBW = 30 kHz, VBW = 100 Hz.) Comparison of the traces shows a squeezing level of (−2.8 ± 0.2) dB. Here Δ = 0.8 GHz, δ = −4 MHz, the power in pump 1 is 230 mW and the power in pump 2 is 160 mW.

Fig. 5
Fig. 5

Measured vacuum squeezing at 1 MHZ (RBW = 30 kHz, VBW = 100 kHz) as a function of pump powers. The contour lines give the squeezing in decibels. Δ = 0.8 GHz, δ = −4 MHz.

Fig. 6
Fig. 6

Vacuum squeezing measured at 1 MHz (RBW = 10 kHz, VBW = 300 Hz) for different forms of spatially-dependent losses. We show the behavior of the vacuum squeezing when we cut the LO with an iris (red circles), or with a razor blade from the top (green triangles) and from the side (blue squares). The uncertainties in the squeezing measurements are approximately the size of the symbols. We also show the expected behavior of a single-mode squeezed beam (black curve). Here Δ = 0.8 GHz, δ = −4 MHz. The power in pump 1 is 230 mW, and in pump 2 is 160 mW.

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