## Experimental investigation of the intensity fluctuation joint probability and conditional distributions of the twin-beam quantum state

Optics Express, Vol. 11, Issue 1, pp. 14-19 (2003)

http://dx.doi.org/10.1364/OE.11.000014

Acrobat PDF (983 KB)

### Abstract

We give the intensity fluctuation joint probability of the twin-beam quantum state, which was generated with an optical parametric oscillator operating above threshold. Then we present what to our knowledge is the first measurement of the intensity fluctuation conditional probability distributions of twin beams. The measured inference variance of twin beams 0.62±0.02, which is less than the standard quantum limit of unity, indicates inference with a precision better than that of separable states. The measured photocurrent variance exhibits a quantum correlation of as much as -4.9±0.2 dB between the signal and the idler.

© 2002 Optical Society of America

## 1. Introduction

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

*x*at A, on the basis of the result performed at B. The predicted results for the measurement at A, based on the measurement at B, are described by a set of conditional distributions

*P*(

*x*|

*i*is used to indicate the possible result, discrete or otherwise, of the measurement

*x*

^{B}) giving the probability of a result for the measurement at A, conditional on a result

*P*(

*x*at B could not have induced the result at A. On the basis of the measurement

*x*the inference variance

*x*= Σ

_{i}

*P*(

*x*where µ

_{i}and

*x*are the mean and the variance, respectively, of the conditional probability distribution

*p*(

*x*|

_{i}) and variance (

*x*) of the conditional distribution for the various quantum states.

*x*, is less than the standard quantum limit. In this case the measurement

*x*

^{B}at B will always imply that the result of

*x*at A is within the range µ

_{i}± δ so that the result of the measurement at A is predetermined to be within a bounded range of width 2δ. After considering the below-standard quantum limit δ, the width of the conditional distribution of the quantum inferable state is narrower than that of the separable state; that is, quantum inference with a precision is better than the standard quantum limit. To our knowledge, the narrow distributions over the outcome domain have not been experimentally established. In this paper we will give the narrower conditional distribution of twin beams, which were generated by a NOPO.

*et al.*[6

6. J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng, “Generation and application of twin beams from an optical parametric oscillator including an a-cut KTP crystal,” Opt. Lett. **23**, 870–872 (1998). [CrossRef]

*n*〉 of photoelectrons being counted as 〈

*i*〉 = 〈

*n*〉

*e*/

*T*, where

*e*and

*T*are the charge of an electron and the time interval, respectively. The variance of the current will be 〈(Δ

*i*)

^{2}〉 = 〈

*i*

^{2}〉 - 〈

*i*〉

^{2}= (

*e*/

*T*)

^{2}[〈

*n*

^{2}〉 - 〈

*n*〉

^{2}] = (2

*e*Δƒ)

^{2}〈(Δ

*n*)

^{2}〉, where Δƒ = 1/(2

*T*) is the electrical bandwidth of the detection system. Thus the variance of the photocurrent fluctuation at a particular frequency is simply proportional to the variance of the photoelectron counts, which depends on the state of light.

## 3. Experimental results

1. A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. **59**, 2555–2558 (1987). [CrossRef] [PubMed]

7. H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, “Experimental realization of a quantum measurement for intensity difference fluctuation using a beam splitter,” Phys. Rev. Lett. **82**, 1414–1417 (1999). [CrossRef]

11. Y. Zhang, K. Kasai, and M. Watanabe, “Investigation of the photon-number statistics of twin beams by direct detection,” Opt. Lett. **27**, 1244–1246 (2002). [CrossRef]

*X*

^{A}-

*X*

^{B}) = 58.5 for coherent light and

*X*

^{A}-

*X*

^{B}) = 19.0 for twin beams are obtained [11

11. Y. Zhang, K. Kasai, and M. Watanabe, “Investigation of the photon-number statistics of twin beams by direct detection,” Opt. Lett. **27**, 1244–1246 (2002). [CrossRef]

11. Y. Zhang, K. Kasai, and M. Watanabe, “Investigation of the photon-number statistics of twin beams by direct detection,” Opt. Lett. **27**, 1244–1246 (2002). [CrossRef]

*X*

^{B}at B with result

*P*(

*P*(

*X*

^{A}was sorted into 120 bins. Thus a set of probability distributions

*P*(

*P*(

*X*

^{B}. The conditional distributions of the separable state for

*X*

^{A}) = 〈

*n*〉, indicating the inherently character of coherent state. A theoretical fit is also shown for comparison. The measured mean and variance of conditional distributions for separable state were µ

_{i}= 0 and

*X*

_{coh}= 30.1±0.1, respectively. We can normalize this variance for the inference variance δ=1. These conditional distributions imply that the probability of obtaining a result X at A cannot be obtained upon measurement of

*X*

^{B}at B, in other words, the measurement at B does not allow an inference of the result of at A.

_{i}equals the measurement at subsystem B,

*X*

_{twin}= 19.0±0.1, which is variance of difference between the signal and idler,

*X*

^{A}-

*X*

_{B}). A separable state conditional distribution (solid line) with the same observed mean photon number is also shown for comparison. It indicates that the conditional distributions of twin beams are narrower than that for separable states. This indicates the inherent quantum character of the twin beams. These properties of the conditional distributions of twin beams imply that the probability of obtaining a result X at A is dependent upon measurement of

## 4. Conclusion

17. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. **68**, 3663–3667 (1992). [CrossRef] [PubMed]

19. Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. **86**, 4267–4270 (2001). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. |

2. | S. K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. , |

3. | O. Aytur and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. |

4. | Q. Pan, Y. Zhang, T. C. Zhang, C. D. Xie, and K. C. Peng, “Experimental investigation of intensity difference squeezing using Nd:YAP laser as pump source,” J. Phys. D: Appl. Phys. |

5. | K.C. Peng, Q. Pan, H. Wang, Y. Zhang, H. Su, and C.D. Xie, “Generation of two-mode quadrature-phase squeezing and intensity-difference squeezing from a cw-NOPO,” Appl. Phys. B |

6. | J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng, “Generation and application of twin beams from an optical parametric oscillator including an a-cut KTP crystal,” Opt. Lett. |

7. | H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, “Experimental realization of a quantum measurement for intensity difference fluctuation using a beam splitter,” Phys. Rev. Lett. |

8. | D. T. Smithey, M. Beck, M.G. Raymer, and A. Faridani, “measurement of the wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,” Phys. Rev. Lett. |

9. | G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature |

10. | M. Vasilyev, S. K. Choi, P. Kumar, and G. M. D’Ariano, “Tomographic measurement of joint photon statistics of the twin-beam quantum state,” Phys. Rev. Lett. |

11. | Y. Zhang, K. Kasai, and M. Watanabe, “Investigation of the photon-number statistics of twin beams by direct detection,” Opt. Lett. |

12. | D. T. Smithey, M. Beck, M. Belsley, and M. G. Raymer, “Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,” Phys. Rev. Lett. |

13. | M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,” Phys, Rev. A |

14. | M. D. Reid, “Inseparability criteria for demonstration of the Einstein-Podolsky-Rosen gedanken experiment,” Quant-ph/0103142. |

15. | M. D. Reid, “The Einstein-Podolsky-Rosen Paradox and Entanglement 1: Signatures of EPR correlations for continuous variables,” Quant-ph/0112038. |

16. | K. Kasai and M. Watanabe, in 7th International Conference on Squeezed States and Uncertainty Relations, Boston, U.S.A., June 4–8, 2001. |

17. | Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. |

18. | Y. Zhang, H. Wang, X.Y. Li, J.T. Jing, C.D. Xie, and K.C. Peng, “Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier,” Phys. Rev. A, 62, 023813 (2000). [CrossRef] |

19. | Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. |

20. | W.P. Bowen, R. Schnabel, P.K. Lam, and T.C. Ralph, “An experimental investigation of criteria for continuous variable entanglement,” Quant-ph/0209001. |

**OCIS Codes**

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 2, 2002

Revised Manuscript: December 25, 2002

Published: January 13, 2003

**Citation**

Yun Zhang, Katsuyuki Kasai, and Masayoshi Watanabe, "Experimental investigation of the intensity fluctuation joint probability and conditional distributions of the twin-beam quantum state," Opt. Express **11**, 14-19 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-1-14

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### References

- A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, �??Observation of quantum noise reduction on twin laser beams,�?? Phys. Rev. Lett. 59, 2555-2558 (1987). [CrossRef] [PubMed]
- S. K. Choi, M. Vasilyev, and P. Kumar, �??Noiseless optical amplification of images,�?? Phys. Rev. Lett. 83, 1938-1941 (1999). [CrossRef]
- O. Aytur and P. Kumar, �??Pulsed twin beams of light,�?? Phys. Rev. Lett. 65, 1551-1554(1990). [CrossRef] [PubMed]
- Q. Pan, Y. Zhang, T. C. Zhang, C. D. Xie, and K. C. Peng, �??Experimental investigation of intensity difference squeezing using Nd:YAP laser as pump source,�?? J. Phys. D: Appl. Phys. 30, 1588-1590 (1997). [CrossRef]
- K.C. Peng, Q. Pan, H. Wang, Y. Zhang, H. Su, C.D. Xie, �??Generation of two-mode quadrature-phase squeezing and intensity-difference squeezing from a cw-NOPO,�?? Appl. Phys. B 66, 755-758 (1998). [CrossRef]
- J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, K. C. Peng, �??Generation and application of twin beams from an optical parametric oscillator including an a-cut KTP crystal,�?? Opt. Lett. 23, 870-872 (1998). [CrossRef]
- H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, �??Experimental realization of a quantum measurement for intensity difference fluctuation using a beam splitter,�?? Phys. Rev. Lett. 82, 1414-1417 (1999). [CrossRef]
- D. T. Smithey, M.Beck, M.G. Raymer, and A. Faridani, �??Measurement of the wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum,�?? Phys. Rev. Lett. 70, 1244-1247 (1993). [CrossRef] [PubMed]
- G. Breitenbach, S. Schiller, and J. Mlynek, �??Measurement of the quantum states of squeezed light,�?? Nature 387, 471-475 (1997). [CrossRef]
- M. Vasilyev, S. K. Choi, P. Kumar, G. M. D�??Ariano, �??Tomographic measurement of joint photon statistics of the twin-beam quantum state,�?? Phys. Rev. Lett. 84, 2354-2357 (2000). [CrossRef] [PubMed]
- Y. Zhang, K. Kasai, and M. Watanabe, �??Investigation of the photon-number statistics of twin beams by direct detection,�?? Opt. Lett. 27, 1244-1246 (2002). [CrossRef]
- D. T. Smithey, M. Beck, M. Belsley, and M. G. Raymer, �??Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light,�?? Phys. Rev. Lett. 69, 2650-2653 (1992). [CrossRef] [PubMed]
- M. D. Reid, �??Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,�?? Phys, Rev. A 40, 913-923 (1989). [CrossRef]
- M. D. Reid, �??Inseparability criteria for demonstration of the Einstein-Podolsky-Rosen gedanken experiment,�?? Quant-ph/0103142.
- M. D. Reid, �??The Einstein-Podolsky-Rosen Paradox and Entanglement 1: Signatures of EPR correlations for continuous variables,�?? Quant-ph/0112038.
- K. Kasai and M. Watanabe, in 7th International Conference on Squeezed States and Uncertainty Relations, Boston, U.S.A., June 4-8, 2001.
- Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, �??Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,�?? Phys. Rev. Lett. 68, 3663-3667 (1992). [CrossRef] [PubMed]
- Y. Zhang, H. Wang, X.Y. Li, J.T. Jing, C.D. Xie, and K.C. Peng, �??Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier,�?? Phys. Rev. A 62, 023813 (2000). [CrossRef]
- Ch. Silberhorn, P. K. Lam, O. Wei�?, F. König, N. Korolkova, and G. Leuchs, �??Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the kerr nonlinearity in an optical fiber,�?? Phys. Rev. Lett. 86, 4267-4270 (2001). [CrossRef] [PubMed]
- W.P. Bowen, R. Schnabel, P.K. Lam, and T.C. Ralph, �??An experimental investigation of criteria for continuous variable entanglement,�?? Quant-ph/0209001.

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