## Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble |

Optics Express, Vol. 19, Issue 15, pp. 14632-14641 (2011)

http://dx.doi.org/10.1364/OE.19.014632

Acrobat PDF (1128 KB)

### Abstract

We present measurements of the polarization correlation and photon statistics of photon pairs that emerge from a laser-pumped warm rubidium vapor cell. The photon pairs occur at 780 nm and 1367 nm and are polarization entangled. We measure the autocorrelation of each of the generated fields as well as the cross-correlation function, and observe a strong violation of the two-beam Cauchy-Schwartz inequality. We evaluate the performance of the system as source of heralded single photons at a telecommunication wavelength. We measure the heralded autocorrelation and see that coincidences are suppressed by a factor of ≈ 20 from a Poissonian source at a generation rate of 1500 s^{−1}, a heralding efficiency of 10%, and a narrow spectral width.

© 2011 OSA

## 1. Introduction

1. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in *Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India* (IEEE, 1984), p. 175. [PubMed]

2. A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. **67**, 661–663 (1991). [CrossRef] [PubMed]

3. L. Duan, M. Lukin, J. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature **414**, 413–418 (2001). [CrossRef] [PubMed]

## 2. System

^{85}Rb atoms which is 1.5 cm long and is maintained at a temperature of 388 K. We utilize the diamond atomic level structure [17

17. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A **79**, 033814 (2009). [CrossRef]

18. F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A **78**, 013834 (2008). [CrossRef]

*k⃗*

_{1}and

*k⃗*

_{2}respectively. The lasers are frequency locked. The 795 nm laser gets its feedback from saturation spectroscopy on an atomic cell [18

18. F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A **78**, 013834 (2008). [CrossRef]

19. W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. **69**, 3737–3740 (1998). [CrossRef]

*S*1,

*S*2) with ≈ 40% detection efficiency. The 1367-nm photons are coupled into a 200-m single mode fiber which serves to optically delay the photons 1

*μ*s. The light is split by a fiber-based 50/50 beamsplitter and then goes to two InGaAs APD detectors (

*I*1,

*I*2). The InGaAs APDs have detection efficiencies of ≈ 10% and are gated on for 1 ns. The dark count rate is 3 × 10

^{−6}counts per nanosecond gate interval.

^{85}Rb cell (Fig. 1A) is placed in the 780 nm beam path between the generation medium and the fiber coupler. This cell is 5 cm long and held at 320 K. The purpose of second cell is to spectrally filter 780-nm photons that have multiply scattered in the optically thick 4WM cell [20

20. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A **82**, 053842 (2010). [CrossRef]

## 3. Polarization correlation

### Bell State Calculation

*π*-polarized by defining the quantization axis along their polarizations. The two-photon pump process 5

*S*

_{1/2}→ 5

*P*

_{1/2}→ 6

*S*

_{1/2}then does not transfer angular momentum from the pump photons to the atoms. In this case the initial atomic state

*m*, the intermediate state

_{J}*m*and the double excited state

_{J′}*m*(with

_{J″}*J″*=

*J*) will have the same value describing the process with no angular momentum transfer.

*m*to the level

_{J}*m*, the 4WM process requires a two-photon decay from the level

_{J″}*m*back to the same level

_{J″}*m*. There are different possibilities for the polarization of the photons in this two photon decay process, but they have to satisfy the angular momentum of the atom and this is behind the the entanglement and the generation of the

_{J}*ϕ*

^{+}Bell state .

*polarized plane wave pump beams with Rabi frequencies Ω*π ^

_{1}and Ω

_{2}and detunings Δ

_{1}and Δ

_{2}. The pumps propagate in the

*x̂*direction (see Fig. 3A). The emitted photons are represented by the field operators

*λ*denotes the two polarization modes, which for the phase matched direction are horizontal ≡

*ẑ*=

*û*

_{0}and vertical ≡

*. We follow the conventions of Ref. [22*σ ^

^{ij}22. H. J. Metcalf and P. Straten, *Laser Cooling and Trapping* (Springer, 1999). [CrossRef]

*g*. The interaction Hamiltonian in the interaction picture is:

^{ij}*x̂*direction. We first take into account only one of the initial Zeeman sub-states, denoted by

*α*. The total wave-function can be written as |

*ψ*〉 = |0 0

*a*〉 + |

*ψ*

_{4}

*〉 + |*

_{WM}*ψ*

_{OTHER}〉. The first term is the vacuum with the atom in the ground state and the result for the 4WM piece is: Here the sums over

*k*and

*q*are over the frequencies of the generated photons. The

*λ*and

*γ*sums are over horizontal and vertical polarization. The

*j,k,l*sums are over all the intermediate Zeeman structure. The expression in Eqs. (2) is sum of all terms formed by stepping around the diamond, following the selection rules for the appropriate polarization, and weighting each term by the appropriate Clebsh-Gordan coefficients. The

*𝒲*(

_{α}_{jkl}*t*) factor involves the four time integrals of the fourth order term in the Dyson’s Series which after integration has the form 1/

*δ*

_{1}

*δ*

_{2}

*δ*

_{3}

*δ*

_{4}where the

*δ*are various detunings which are the same for every term up to hyperfine splittings. We assume that the pairs we observe are far from intermediate resonance compared to the respective hyperfine splittings. Under this assumption we may pull the

_{i}*𝒲*(

_{α}_{jkl}*t*) through the

*j,k,l*and

*λ*,

*γ*sums. Since the measurements we make do not depend on frequency we can, for our current purpose, ignore the sums over

*k*and

*q*. Then the answer for a single initial sub-state is where

*χ*) with

_{α}*H*replaced by

*V*. The coefficient for the HV and VH terms are zero for two horizontally polarized pumps. To take into account all of the Zeeman ground states as in Fig. 3C, we assume that the atoms begin in an incoherent mixture and the resulting state must be described by a density matrix

*ρ*= Σ

*|*

_{α}p_{α}*ψ*〉 〈

_{α}*ψ*|. The solution, after summing over all paths under the detuning condition, is the same regardless of the initial Zeeman state. It is

_{α}## 4. Autocorrelations

*P̃*

_{I1}and

*P̃*

_{I2}are the probabilities that a count occurs in detector

*I*1 and

*I*2, respectively, given that a 780-nm photon has been detected. The conditional probability that both detectors register a count at the same time is given by

*P̃*

_{I1,I2}(0). We expect

*g̃*

^{(2)}(0) = 0 for a perfect single photon state while a Poissonian source has

*g̃*

^{(2)}(0) = 1. Figure 4 shows the measured conditional autocorrelation function for different 795-nm pump powers. We see a decrease of coincidences of roughly a factor of twenty from a Poissonian source. At a pump power of 15 mW we observe

*g̃*

^{(2)}(0) = 0.06(1), a heralding efficiency of 10% and a HSP generation rate of 1500 s

^{−1}(detector and filter efficiency corrected). We have previously measured the bandwidth of the 1367-nm photons to be approximately 350 MHz [20

20. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A **82**, 053842 (2010). [CrossRef]

*et al.*[8

8. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. **96**, 093604 (2006). [CrossRef] [PubMed]

*μ*m appear in Ref. [23

23. Q. Zhou, W. Zhang, J.-R. Cheng, Y.-D. Huang, and J.-D. Peng, “Properties of optical fiber based synchronous heralded single photon sources at 1.5 *μ*m,” Phys. Lett. A **375**, 2274–2277 (2011). [CrossRef]

12. A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Express **17**, 6156–6165 (2009). [CrossRef] [PubMed]

^{4}heralded photons per second, and a high heralding efficiency of 52 % with a counts-to-accidentals ratio of 10.4. Narrowband filtering of the idler achieved a near time-bandwidth limited with a coherence length of 4 ps. This yields a HSP rate of 0.34 photons/s/MHz. In contrast, our atomic generation method, although producing fewer photons per second, has a rate of 4.3 photons/s/MHz, a substantially spectrally brighter source.

*S*1 and

*S*2 since the detectors are free running. The correlation function is then calculated offline. We observe bunching in the

*I*1 and

*I*2. The delay is changed by adding different lengths of coaxial cable between the triggering source and the detectors. We see that the light is bunched, as expected from light generated by a spontaneous process (the sample is optically thin at 1367 nm unlike at 780 nm). For a single polarization thermal source

## 5. Cross-correlations

26. M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A **34**, 1260–1276 (1986). [CrossRef] [PubMed]

## 6. Conclusion

*σ*violation of Bell’s inequality, demonstrating the entanglement of the photons. The two fields, with different wavelengths (780 nm and 1367 nm), are highly non-classical as evidenced by a strong violation of the two beam Cauchy-Schwarz inequality. We have shown that the system can function as a narrow-band, heralded single-photon source with generation rates greater than 10

^{3}s

^{−1}. This system, based on a simple vapor cell, thus produces both photons in the telecommunication band as well as narrow-band photons that can interact with atomic ensembles, suitable for application to quantum repeaters.

## Acknowledgments

## References and links

1. | C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in |

2. | A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. |

3. | L. Duan, M. Lukin, J. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

4. | A. Kuzmich, W. P. Bowen, A. D. Booze, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature |

5. | C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, “Atomic memory for correlated photon states,” Science |

6. | V. Balic, D. A. Braje, P. Kolchin, G. Yin, and S. E. Haris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. |

7. | S. Du, P. Kolchin, C. Bethangady, G. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. |

8. | T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. |

9. | K. F. Rim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, “Towards high-speed optical quantum memories,” Nat. Photonics |

10. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

11. | E. A. Goldschmidt, M. D. Eisaman, J. Fan, S. V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A |

12. | A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Express |

13. | S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” N. J. Phys. |

14. | O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-performance guided-wave asynchronous heralded single-photon source,” Opt. Lett. |

15. | A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. |

16. | Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. |

17. | R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A |

18. | F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A |

19. | W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. |

20. | R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A |

21. | J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-varible theories,” Phys. Rev. Lett. |

22. | H. J. Metcalf and P. Straten, |

23. | Q. Zhou, W. Zhang, J.-R. Cheng, Y.-D. Huang, and J.-D. Peng, “Properties of optical fiber based synchronous heralded single photon sources at 1.5 |

24. | A. F. Molisch and B. P. Oehry, |

25. | L. Mandel and E. Wolf, |

26. | M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A |

27. | Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, “Non-degenerate nonclassical photon pairs in a hot atomic ensemble,” Opt. Express |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(270.5290) Quantum optics : Photon statistics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: June 7, 2011

Revised Manuscript: July 2, 2011

Manuscript Accepted: July 3, 2011

Published: July 14, 2011

**Citation**

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, "Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble," Opt. Express **19**, 14632-14641 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14632

Sort: Year | Journal | Reset

### References

- C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, 1984), p. 175. [PubMed]
- A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef] [PubMed]
- L. Duan, M. Lukin, J. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001). [CrossRef] [PubMed]
- A. Kuzmich, W. P. Bowen, A. D. Booze, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423, 731–734 (2003). [CrossRef] [PubMed]
- C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, “Atomic memory for correlated photon states,” Science 301, 196–200 (2003). [CrossRef] [PubMed]
- V. Balic, D. A. Braje, P. Kolchin, G. Yin, and S. E. Haris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
- S. Du, P. Kolchin, C. Bethangady, G. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008). [CrossRef] [PubMed]
- T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96, 093604 (2006). [CrossRef] [PubMed]
- K. F. Rim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D. Jaksch, and I. A. Walmsley, “Towards high-speed optical quantum memories,” Nat. Photonics 4, 218–221 (2010). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]
- E. A. Goldschmidt, M. D. Eisaman, J. Fan, S. V. Polyakov, and A. Migdall, “Spectrally bright and broad fiber-based heralded single-photon source,” Phys. Rev. A 78, 013844 (2008). [CrossRef]
- A. R. McMillan, J. Fulconis, M. Halder, C. Xiong, J. G. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Express 17, 6156–6165 (2009). [CrossRef] [PubMed]
- S. Fasel, O. Alibart, S. Tanzilli, P. Baldi, A. Beveratos, N. Gisin, and H. Zbinden, “High-quality asynchronous heralded single-photon source at telecom wavelength,” N. J. Phys. 6, 163 (2004). [CrossRef]
- O. Alibart, D. B. Ostrowsky, P. Baldi, and S. Tanzilli, “High-performance guided-wave asynchronous heralded single-photon source,” Opt. Lett. 30, 1539–1541 (2005). [CrossRef] [PubMed]
- A. G. Radnaev, Y. O. Dudin, R. Zhao, H. H. Jen, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, “A quantum memory with telecom-wavelength conversion,” Nat. Phys. 6, 894–899 (2010). [CrossRef]
- Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105, 260502 (2010). [CrossRef]
- R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Four-wave mixing in the diamond configuration in an atomic vapor,” Phys. Rev. A 79, 033814 (2009). [CrossRef]
- F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: the diamond configuration,” Phys. Rev. A 78, 013834 (2008). [CrossRef]
- W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998). [CrossRef]
- R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82, 053842 (2010). [CrossRef]
- J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-varible theories,” Phys. Rev. Lett. 23, 880–884 (1969). [CrossRef]
- H. J. Metcalf and P. Straten, Laser Cooling and Trapping (Springer, 1999). [CrossRef]
- Q. Zhou, W. Zhang, J.-R. Cheng, Y.-D. Huang, and J.-D. Peng, “Properties of optical fiber based synchronous heralded single photon sources at 1.5 μm,” Phys. Lett. A 375, 2274–2277 (2011). [CrossRef]
- A. F. Molisch and B. P. Oehry, Radiation Trapping in Atomic Vapours (Oxford University Press, 1998).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- M. D. Reid and D. F. Walls, “Violations of classical inequalities in quantum optics,” Phys. Rev. A 34, 1260–1276 (1986). [CrossRef] [PubMed]
- Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, “Non-degenerate nonclassical photon pairs in a hot atomic ensemble,” Opt. Express 16, 21708–21713 (2008). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.