Abstract

We analyse a novel squeezing and entangling mechanism which is due to correlated Stokes and anti-Stokes photon forward scattering in a multi-level atom vapour. We develop a full quantum model for an alkali atomic vapour including quantized collective atomic states which predicts high degree of squeezing for attainable experimental conditions. Following the proposal we present an experimental demonstration of 3.5 dB pulsed frequency nondegenerate squeezed (quadrature entangled) state of light using room temperature caesium vapour. The source is very robust and requires only a few milliwatts of laser power. The squeezed state is generated in the same spatial mode as the local oscillator and in a single temporal mode. The two entangled modes are separated by twice the Zeeman frequency of the vapour which can be widely tuned. The narrow-band squeezed light generated near an atomic resonance can be directly used for atom-based quantum information protocols. Its single temporal mode characteristics make it a promising resource for quantum information processing.

© 2009 Optical Society of America

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References

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  1. T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303R (1999).
    [Crossref]
  2. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
    [Crossref] [PubMed]
  3. S. Lloyd and S. L. Braunstein, “Quantum Computation over Continuous Variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
    [Crossref]
  4. A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of Spin Squeezing via Continuous Quantum Nondemolition Measurement,” Phys. Rev. Lett. 85, 1594 (2000).
    [Crossref] [PubMed]
  5. S. L. Braunstein, “Quantum error correction for communication with linear optics,” Nature (London)  394, 47 (1998).
    [Crossref]
  6. S. Lloyd and J.-J. E. Slotine,“Analog Quantum Error Correction,” Phys. Rev. Lett. 80, 4088–4091 (1998).
    [Crossref]
  7. L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
    [Crossref]
  8. D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
    [Crossref]
  9. Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
    [Crossref] [PubMed]
  10. C. Schori, J. L. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A 66, 033802 (2002).
    [Crossref]
  11. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
    [Crossref] [PubMed]
  12. 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 (1985).
    [Crossref] [PubMed]
  13. A. Lambrecht, T. Coudreau, A. M. Steinberg, and E. Giacobino, “Squeezing with cold atoms,” Europhys. Lett. 36, 93–98 (1996).
    [Crossref]
  14. V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
    [Crossref] [PubMed]
  15. 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]
  16. J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation,” Phys. Rev. A 68, 025801 (2003).
    [Crossref]
  17. E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. 33, 1213–1215 (2008).
    [Crossref] [PubMed]
  18. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
    [Crossref] [PubMed]
  19. J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
    [Crossref] [PubMed]
  20. M. Sasaki and S. Suzuki, “Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula,” Phys. Rev. A 73, 043807 (pages 18) (2006).
    [Crossref]
  21. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
    [Crossref] [PubMed]
  22. D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
    [Crossref]
  23. O. Mishina, D. Kuprianov, and E. S. Polzik, “Macroscopic quantum information channel via the polarization-sensitive interaction between the light and spin subsystems,” in NATO Advanced research workshop: Quantum information processing from theory to experiment, vol. 199, p. 346 (2006).
  24. J. Sherson, B. Julsgaard, and E. S. Polzik, Advances in Atomic, Molecular, and Optical Physics, chap. Deterministic atom-light quantum interface (2006).
  25. B. Julsgaard, A. Kozhekin, and E. S. Polzik,“Experimental long-lived entanglement of two macroscopic objects,” Nature (London)  413, 400 (2001).
    [Crossref] [PubMed]
  26. K. Hammerer, A. Sorensen, and E. Polzik, “Quantum interface between light and atomic ensembles,” arXiv:0807.3358v3, http://arxiv.org/abs/0807.3358.
  27. B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
    [Crossref] [PubMed]
  28. J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
    [Crossref] [PubMed]
  29. L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
    [Crossref] [PubMed]
  30. T. Opatrny, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 53813 (2002).
    [Crossref]

2008 (3)

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

E. E. Mikhailov and I. Novikova, “Low-frequency vacuum squeezing via polarization self-rotation in Rb vapor,” Opt. Lett. 33, 1213–1215 (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]

2006 (4)

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
[Crossref] [PubMed]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[Crossref] [PubMed]

M. Sasaki and S. Suzuki, “Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula,” Phys. Rev. A 73, 043807 (pages 18) (2006).
[Crossref]

2005 (1)

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

2004 (2)

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

2003 (2)

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation,” Phys. Rev. A 68, 025801 (2003).
[Crossref]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[Crossref]

2002 (2)

C. Schori, J. L. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A 66, 033802 (2002).
[Crossref]

T. Opatrny, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 53813 (2002).
[Crossref]

2001 (2)

B. Julsgaard, A. Kozhekin, and E. S. Polzik,“Experimental long-lived entanglement of two macroscopic objects,” Nature (London)  413, 400 (2001).
[Crossref] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
[Crossref] [PubMed]

2000 (3)

L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
[Crossref]

A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of Spin Squeezing via Continuous Quantum Nondemolition Measurement,” Phys. Rev. Lett. 85, 1594 (2000).
[Crossref] [PubMed]

L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
[Crossref] [PubMed]

1999 (2)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303R (1999).
[Crossref]

S. Lloyd and S. L. Braunstein, “Quantum Computation over Continuous Variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

1998 (3)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

S. L. Braunstein, “Quantum error correction for communication with linear optics,” Nature (London)  394, 47 (1998).
[Crossref]

S. Lloyd and J.-J. E. Slotine,“Analog Quantum Error Correction,” Phys. Rev. Lett. 80, 4088–4091 (1998).
[Crossref]

1996 (1)

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

1992 (1)

Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
[Crossref] [PubMed]

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 (1985).
[Crossref] [PubMed]

Bigelow, N. P.

A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of Spin Squeezing via Continuous Quantum Nondemolition Measurement,” Phys. Rev. Lett. 85, 1594 (2000).
[Crossref] [PubMed]

Boyer, V.

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]

Bramati, A.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Braunstein, S. L.

S. Lloyd and S. L. Braunstein, “Quantum Computation over Continuous Variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

S. L. Braunstein, “Quantum error correction for communication with linear optics,” Nature (London)  394, 47 (1998).
[Crossref]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

Brezger, B.

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation,” Phys. Rev. A 68, 025801 (2003).
[Crossref]

Browne, D. E.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[Crossref]

Chelkowski, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Cirac, I.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
[Crossref] [PubMed]

Cirac, J. I.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
[Crossref] [PubMed]

L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
[Crossref]

Coudreau, T.

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

Dantan, A.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Danz-mann, K.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Duan, L.-M.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
[Crossref] [PubMed]

L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
[Crossref] [PubMed]

L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
[Crossref]

Eisert, J.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[Crossref]

Fiurasek, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

Franzen, A.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

Giacobino, E.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

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

Giedke, G.

L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
[Crossref] [PubMed]

Grangier, P.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
[Crossref] [PubMed]

Hage, B.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Hammerer, K.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

K. Hammerer, A. Sorensen, and E. Polzik, “Quantum interface between light and atomic ensembles,” arXiv:0807.3358v3, http://arxiv.org/abs/0807.3358.

Hettich, C.

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[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 (1985).
[Crossref] [PubMed]

Josse, V.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Julsgaard, B.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

B. Julsgaard, A. Kozhekin, and E. S. Polzik,“Experimental long-lived entanglement of two macroscopic objects,” Nature (London)  413, 400 (2001).
[Crossref] [PubMed]

J. Sherson, B. Julsgaard, and E. S. Polzik, Advances in Atomic, Molecular, and Optical Physics, chap. Deterministic atom-light quantum interface (2006).

Kimble, H.

Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
[Crossref] [PubMed]

Kimble, H. J.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

Korolkova, N.

T. Opatrny, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 53813 (2002).
[Crossref]

Kozhekin, A.

B. Julsgaard, A. Kozhekin, and E. S. Polzik,“Experimental long-lived entanglement of two macroscopic objects,” Nature (London)  413, 400 (2001).
[Crossref] [PubMed]

Krauter, H.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

Kuprianov, D.

O. Mishina, D. Kuprianov, and E. S. Polzik, “Macroscopic quantum information channel via the polarization-sensitive interaction between the light and spin subsystems,” in NATO Advanced research workshop: Quantum information processing from theory to experiment, vol. 199, p. 346 (2006).

Kupriyanov, D. V.

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

Kuzmich, A.

A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of Spin Squeezing via Continuous Quantum Nondemolition Measurement,” Phys. Rev. Lett. 85, 1594 (2000).
[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]

Lastzka, N.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Laurat, J.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
[Crossref] [PubMed]

ler, S. G.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Lett, P. D.

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]

Leuchs, G.

T. Opatrny, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 53813 (2002).
[Crossref]

Lloyd, S.

S. Lloyd and S. L. Braunstein, “Quantum Computation over Continuous Variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

S. Lloyd and J.-J. E. Slotine,“Analog Quantum Error Correction,” Phys. Rev. Lett. 80, 4088–4091 (1998).
[Crossref]

lmer, K. M.

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[Crossref] [PubMed]

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
[Crossref] [PubMed]

Lvovsky, A. I.

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation,” Phys. Rev. A 68, 025801 (2003).
[Crossref]

Mandel, L.

A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of Spin Squeezing via Continuous Quantum Nondemolition Measurement,” Phys. Rev. Lett. 85, 1594 (2000).
[Crossref] [PubMed]

Marino, A. M.

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]

Mehmet, M.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (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 (1985).
[Crossref] [PubMed]

Mikhailov, E. E.

Mishina, O.

O. Mishina, D. Kuprianov, and E. S. Polzik, “Macroscopic quantum information channel via the polarization-sensitive interaction between the light and spin subsystems,” in NATO Advanced research workshop: Quantum information processing from theory to experiment, vol. 199, p. 346 (2006).

Mishina, O. S.

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

Neergaard-Nielsen, J. S.

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[Crossref] [PubMed]

Nielsen, B. M.

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[Crossref] [PubMed]

Novikova, I.

Olsson, R. K.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

Opatrny, T.

T. Opatrny, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 53813 (2002).
[Crossref]

Ou, Z.

Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
[Crossref] [PubMed]

Ourjoumtsev, A.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
[Crossref] [PubMed]

Peng, K. C.

Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
[Crossref] [PubMed]

Pereira, S.

Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
[Crossref] [PubMed]

Pinard, M.

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

Plenio, M. B.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[Crossref]

Polzik, E.

K. Hammerer, A. Sorensen, and E. Polzik, “Quantum interface between light and atomic ensembles,” arXiv:0807.3358v3, http://arxiv.org/abs/0807.3358.

Polzik, E. S.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[Crossref] [PubMed]

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

C. Schori, J. L. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A 66, 033802 (2002).
[Crossref]

B. Julsgaard, A. Kozhekin, and E. S. Polzik,“Experimental long-lived entanglement of two macroscopic objects,” Nature (London)  413, 400 (2001).
[Crossref] [PubMed]

L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
[Crossref]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

O. Mishina, D. Kuprianov, and E. S. Polzik, “Macroscopic quantum information channel via the polarization-sensitive interaction between the light and spin subsystems,” in NATO Advanced research workshop: Quantum information processing from theory to experiment, vol. 199, p. 346 (2006).

J. Sherson, B. Julsgaard, and E. S. Polzik, Advances in Atomic, Molecular, and Optical Physics, chap. Deterministic atom-light quantum interface (2006).

Pooser, R. C.

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]

Ralph, T. C.

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303R (1999).
[Crossref]

Ries, J.

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation,” Phys. Rev. A 68, 025801 (2003).
[Crossref]

Sasaki, M.

M. Sasaki and S. Suzuki, “Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula,” Phys. Rev. A 73, 043807 (pages 18) (2006).
[Crossref]

Scheel, S.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[Crossref]

Schnabel, R.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Schori, C.

C. Schori, J. L. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A 66, 033802 (2002).
[Crossref]

Sherson, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

J. Sherson, B. Julsgaard, and E. S. Polzik, Advances in Atomic, Molecular, and Optical Physics, chap. Deterministic atom-light quantum interface (2006).

Sherson, J. F.

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

Slotine, J.-J. E.

S. Lloyd and J.-J. E. Slotine,“Analog Quantum Error Correction,” Phys. Rev. Lett. 80, 4088–4091 (1998).
[Crossref]

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 (1985).
[Crossref] [PubMed]

Sokolov, I. M.

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

Sorensen, A.

K. Hammerer, A. Sorensen, and E. Polzik, “Quantum interface between light and atomic ensembles,” arXiv:0807.3358v3, http://arxiv.org/abs/0807.3358.

Sorensen, J. L.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

Sørensen, J. L.

C. Schori, J. L. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A 66, 033802 (2002).
[Crossref]

Steinberg, A. M.

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

Suzuki, S.

M. Sasaki and S. Suzuki, “Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula,” Phys. Rev. A 73, 043807 (pages 18) (2006).
[Crossref]

Tualle-Brouri, R.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
[Crossref] [PubMed]

Vahlbruch, H.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, 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 (1985).
[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 (1985).
[Crossref] [PubMed]

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
[Crossref] [PubMed]

L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
[Crossref] [PubMed]

L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
[Crossref]

Europhys. Lett. (1)

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

Nature (5)

S. L. Braunstein, “Quantum error correction for communication with linear optics,” Nature (London)  394, 47 (1998).
[Crossref]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London)  414, 413 (2001).
[Crossref] [PubMed]

B. Julsgaard, A. Kozhekin, and E. S. Polzik,“Experimental long-lived entanglement of two macroscopic objects,” Nature (London)  413, 400 (2001).
[Crossref] [PubMed]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurasek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature (London)  432, 482–486 (2004).
[Crossref] [PubMed]

J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, I. Cirac, and E. S. Polzik, “Quantum teleportation between light and matter,” Nature (London)  443, 557–560 (2006).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (7)

J. Ries, B. Brezger, and A. I. Lvovsky, “Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation,” Phys. Rev. A 68, 025801 (2003).
[Crossref]

C. Schori, J. L. Sørensen, and E. S. Polzik, “Narrow-band frequency tunable light source of continuous quadrature entanglement,” Phys. Rev. A 66, 033802 (2002).
[Crossref]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[Crossref]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61, 010303R (1999).
[Crossref]

D. V. Kupriyanov, O. S. Mishina, I. M. Sokolov, B. Julsgaard, and E. S. Polzik, “Multimode entanglement of light and atomic ensembles via off-resonant coherent forward scattering,” Phys. Rev. A 71, 032348 (2005).
[Crossref]

M. Sasaki and S. Suzuki, “Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light: Analytical formula,” Phys. Rev. A 73, 043807 (pages 18) (2006).
[Crossref]

T. Opatrny, N. Korolkova, and G. Leuchs, “Mode structure and photon number correlations in squeezed quantum pulses,” Phys. Rev. A 66, 53813 (2002).
[Crossref]

Phys. Rev. Lett. (10)

L.-M. Duan, G. Giedke, I. Cirac, and P. Zoller, “Inseparability Criterion for Continuous Variable Systems,” Phys. Rev. Lett.,  84, 2722–2725 (2000).
[Crossref] [PubMed]

S. Lloyd and S. L. Braunstein, “Quantum Computation over Continuous Variables,” Phys. Rev. Lett. 82, 1784–1787 (1999).
[Crossref]

A. Kuzmich, L. Mandel, and N. P. Bigelow, “Generation of Spin Squeezing via Continuous Quantum Nondemolition Measurement,” Phys. Rev. Lett. 85, 1594 (2000).
[Crossref] [PubMed]

Z. Ou, S. Pereira, H. Kimble, and K. C. Peng, “Realization of the Einten-Podolsy-rosen Paradox for Continuous Variables,” Phys. Rev. Lett. 68, 3663 (1992).
[Crossref] [PubMed]

S. Lloyd and J.-J. E. Slotine,“Analog Quantum Error Correction,” Phys. Rev. Lett. 80, 4088–4091 (1998).
[Crossref]

L.-M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, “Quantum Communication between Atomic Ensembles Using Coherent Light,” Phys. Rev. Lett. 85, 5643 (2000).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. G. ler, K. Danz-mann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (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 (1985).
[Crossref] [PubMed]

V. Josse, A. Dantan, A. Bramati, M. Pinard, and E. Giacobino,“Continuous variable entanglement using cold atoms,” Phys. Rev. Lett. 92, 123601 (2004).
[Crossref] [PubMed]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. M. lmer, and E. S. Polzik, “Generation of a Superposition of Odd Photon Number States for Quantum Information Networks,” Phys. Rev. Lett. 97, 083604 (pages 4) (2006).
[Crossref] [PubMed]

Science (3)

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating Optical Schrodinger Kittens for Quantum Information Processing,” Science 312, 83–\86 (2006).
[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. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706 (1998).
[Crossref] [PubMed]

Other (3)

K. Hammerer, A. Sorensen, and E. Polzik, “Quantum interface between light and atomic ensembles,” arXiv:0807.3358v3, http://arxiv.org/abs/0807.3358.

O. Mishina, D. Kuprianov, and E. S. Polzik, “Macroscopic quantum information channel via the polarization-sensitive interaction between the light and spin subsystems,” in NATO Advanced research workshop: Quantum information processing from theory to experiment, vol. 199, p. 346 (2006).

J. Sherson, B. Julsgaard, and E. S. Polzik, Advances in Atomic, Molecular, and Optical Physics, chap. Deterministic atom-light quantum interface (2006).

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Figures (7)

Fig. 1.
Fig. 1.

Off-resonant double A interaction in caesium in the presence of the magnetic field. The interaction is driven by linearly polarized light beam detuned by ∆ = 0.85GHz from the extreme atomic resonance. The ground state levels are split by Ω L = 322kHz. The collective scattering leads to weak atomic excitation to the mF=3 state described by an annihilation operator b̂ and Ω L sidebands of the driving light described by annihilation operators â+ and â-.

Fig. 2.
Fig. 2.

Pictorial representation of the interaction. The light in the exponentially rising mode at the input of the cell is mapped onto the atoms, and it assumes a form of an exponentially falling mode onto which the atoms have contributed.

Fig. 3.
Fig. 3.

Experimental setup. Cells 1 and 2 are placed in magnetic shields in equal magnetic fields B⃗ oriented along x. The atoms are pumped with circularly polarized pump beams of opposite helicity. The probe beam propagates perpendicular to the B⃗ field, interacts with the atoms and is detected by a balanced homodyne detector.

Fig. 4.
Fig. 4.

The decay of the mean values 〈x̂ L (t)〉 (solid) and 〈p̂ L (t)〉 (dash-dot line) measured by the homodyne detector. Prior to this measurement the atoms are prepared in a CSS state and subsequently displaced in both X̂ A and P̂ A by an RF pulse.

Fig. 5.
Fig. 5.

Average power spectrum 〈p̂2 L,c (Ω) + p̂2 L,s (Ω)〉 = Var(p̂+p̂) + Var(x̂-x̂) of the homodyne signal p̂L(t) , Frequencies around Ω L = 322kHz are shown. The atoms are initialised to the CSS state and then a 15 ms long probe pulse is sent through them. Solid curve is taken with atoms in both cells tuned to the 322 kHz Larmor frequency, while dash-dot curve is the shot noise level reference, taken with atoms detuned far away from the detection bandwidth. The Gaussian shape of the reference spectrum is due to the detection bandwidth, mainly limited by the lock-in amplifier used to demodulate the homodyne signal, while the dip in the middle is the fingerprint of the narrowband squeezing produced in the interaction with the atoms.

Fig. 6.
Fig. 6.

Noise reduction 101og10 (2〈(P̂ L,c (n))2 + (P̂ L,s (n))2〉) in the characteristic output modes.

Fig. 7.
Fig. 7.

Characteristic output mode functions for the most squeezed mode (blue solid line), the next mode (green dashed line) and an exponential fit for the most squeezed mode (red dash-dot line).

Equations (25)

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

Ĥint=ħχaâb̂+ħχpâb̂+H.c.,
Ĥint=ħL0Ldz(χaâb̂+χpâ+b̂)+H.c.
b̂=eiΩLtnNaLk=1nmF=4kmF=3k
â+(t)=â+(t)iχpb̂(t),
â(t)=â(t)iχab̂(t),
b̂(t)t=iχpâ+(t)+iχaâ(t)γSWb̂(t),
âc(t)=âc(t)iχpb̂c(t)+iχab̂c(t),
b̂c(t)t=iχpâc(t)+iχaâc(t)γSWb̂c(t),
âc(t)=âc(t)2γSW0tdteγSW(tt)âc(t)+ieγSWt(χpb̂c(0)+χab̂c(0)),
b̂c(t)=i0tdteγSW(tt)(χpâc(t)+χaâc(t))+eγSWtb̂c(0).
X̂L+iP̂L2=Nin0Tâc(t)eγSWtdt,X̂L+iP̂L2=Nout0Tâc(t)eγSWtdt,
b̂c(0)=X̂A+iP̂A2 , b̂c(T)=X̂A+iP̂A2 .
X̂A=1ξ2κ2X̂A+κP̂L,X̂L=1ξ2κ2X̂L+κP̂A,
P̂A=1ξ2κ2P̂Aξ2κX̂L,P̂L=1ξ2κ2P̂L+ξ2κX̂A.
x̂L(t)=2γSWξeγSWtP̂A(t=0) ,
p̂L(t)=2γSWξeγSWtX̂A(t=0) .
Ĥint=ħγ8Δλ22πNaAL0Ldz[a0ϕ+a1Szjz+a2(ϕjz2Sj+2S+j2)].
Ĥint=ħγ8Δλ22πNaAL0Ldz{a1szjz14a2(Syjy+2Sxjx)+ϕ[a0a2(1672jx)]+56a2Sx}
Sy=Φ2(â+â)Sz=Φ2i(ââ)
jy=2LNa (b̂+b̂)jz=i2LNa (b̂b̂ )
Ĥintappr=ħL2γSW 0Ldz [1ξb̂b̂i2ââi2+ξb̂+b̂2â+â2] ,
γSW=14a1a2ΦNaA2(γ8Δλ22π)2 , ξ=14a2a1 .
C(t,t)=pc(t)pc(t)pc(t)pc(t)
QnQmQnQm=dtdtun(t)C(t,t)um(t)
C(t,t)=nξnun(t)un(t)

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