## Measurement of fluorescence emission spectrum of few strongly driven atoms using an optical nanofiber |

Optics Express, Vol. 18, Issue 16, pp. 17154-17164 (2010)

http://dx.doi.org/10.1364/OE.18.017154

Acrobat PDF (1042 KB)

### Abstract

We show that the fluorescence emission spectrum of few atoms can be measured by using an optical nanofiber combined with the optical heterodyne and photon correlation spectroscopy. The observed fluorescence spectrum of the atoms near the nanofiber shows negligible effects of the atom-surface interaction and agrees well with the Mollow triplet spectrum of free-space atoms at high excitation intensity.

© 2010 OSA

## 1. Introduction

4. C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. **65**(1), 33–36 (1990). [CrossRef] [PubMed]

5. P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. **69**(1), 49–52 (1992). [CrossRef] [PubMed]

6. J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, “Heterodyne measurement of the resonance fluorescence of a single ion,” J. Mod. Opt. **44**(10), 1999–2010 (1997). [CrossRef]

7. Ch. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett. **85**(3), 538–541 (2000). [CrossRef] [PubMed]

*et al*. have proposed to combine both the OHD and PCR methods to realize high resolution and high sensitivity. Using such a combined method they have demonstrated the measurement of the spectrum of an extremely weak coherent light [8

8. H. G. Hong, W. Seo, M. Lee, W. Choi, J. H. Lee, and K. An, “Spectral line-shape measurement of an extremely weak amplitude-fluctuating light source by photon-counting-based second-order correlation spectroscopy,” Opt. Lett. **31**(21), 3182–3184 (2006). [CrossRef] [PubMed]

9. F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, “Spontaneous emission of a cesium atom near a nanofiber: efficient coupling of light to guided modes,” Phys. Rev. A **72**(3), 032509 (2005). [CrossRef]

11. K. P. Nayak and K. Hakuta, “Single atoms on an optical nanofiber,” N. J. Phys. **10**(5), 053003 (2008). [CrossRef]

9. F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, “Spontaneous emission of a cesium atom near a nanofiber: efficient coupling of light to guided modes,” Phys. Rev. A **72**(3), 032509 (2005). [CrossRef]

10. K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express **15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

11. K. P. Nayak and K. Hakuta, “Single atoms on an optical nanofiber,” N. J. Phys. **10**(5), 053003 (2008). [CrossRef]

13. K. P. Nayak, F. Le Kien, M. Morinaga, and K. Hakuta, “Antibunching and bunching of photons in resonance fluorescence from a few atoms into guided modes of an optical nanofiber,” Phys. Rev. **79**(2), 021801 (2009). [CrossRef]

10. K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express **15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

11. K. P. Nayak and K. Hakuta, “Single atoms on an optical nanofiber,” N. J. Phys. **10**(5), 053003 (2008). [CrossRef]

15. F. Kien, S. Gupta, and K. Hakuta, “Optical excitation spectrum of an atom in a surface-induced potential,” Phys. Rev. A **75**(3), 032508 (2007). [CrossRef]

## 2. Theoretical outline

*S*(ω), can be directly obtained from the Fourier transform of the first-order correlation function

*E*(

*t*) as,where ‹…› denotes the time average and

*τ*the delay time. We consider the case where the atom-position distribution is random and the atom number has a Poissonian distribution. The phases of photons emitted by different atoms are random and the total fluorescence field can be written as the sum of the fields emitted by individual atoms. For simplicity, we consider a single polarization of the guided field. The first- and second-order correlation functions for nanofiber single-mode observation have the forms [12

12. F. Le Kien and K. Hakuta, “Correlations between photons emitted by multiatom fluorescence into a nanofiber,” Phys. Rev. A **77**(3), 033826 (2008). [CrossRef]

*I*is the intensity of the fluorescence field emitted by all the atoms combined.

*n*is the mean atom number. The parameter

*ω*

_{0}is the atomic transition frequency. The coefficients

*μ*are determined by the mode profile function of the nanofiber guided modes. We point out here that the above equations reduce to free-space single-mode observations for

*n*is large enough. But in our present case, where the number of atoms is small, the intensity correlation is dominated by

*et al*., one can selectively obtain the

*g*

^{(1)}(

*τ*) information from the intensity correlations by using the combined method of OHD and PCR spectroscopy [8

8. H. G. Hong, W. Seo, M. Lee, W. Choi, J. H. Lee, and K. An, “Spectral line-shape measurement of an extremely weak amplitude-fluctuating light source by photon-counting-based second-order correlation spectroscopy,” Opt. Lett. **31**(21), 3182–3184 (2006). [CrossRef] [PubMed]

*E*(

*t*) with

*ω*is the LO-frequency. The intensity correlation is then given aswhere

_{LO}*S*(ω), which is given by Eq. (1), expression (4) for the second-order correlation function

*S*(ω) information is down-shifted by

*ω*in the frequency domain. The shifted spectrum appears around the frequency

_{LO}*ω*

_{0}-ω

*. So, we can obtain the spectral density*

_{LO}*S*(

*ω*) by taking the Fourier transform of the correlation signal

*ω*should be chosen such that there is no overlap between the second term and the other terms of Eq. (6) in the frequency domain and also such that the shifted spectrum frequency falls within the measurable bandwidth of the detector.

_{LO}## 3. Experiments

### 3.1 Experimental setup

10. K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express **15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

*μ*s in every 200

*μ*s and repeating this process for many cycles. For the initial state preparation of the atoms, the MOT repump beam is switched off 200 ns after the cooling beam during each observation period so that any residual atoms in the F=3 state can be pumped into the F=4 state. During the observation period of 10

*μ*s, atoms around the nanofiber are excited by a laser beam irradiated perpendicularly to the nanofiber in the travelling wave configuration.

*D*

_{2}line transition 6

*S*

_{1/2}

*F*=3 ↔ crossover of 6

*P*

_{3/2}

*F*=2→

*F*′=3, using saturated absorption spectroscopy. Thus, the frequency of the excitation beam can be varied around the closed cycle transition of Cs

*D*

_{2}line, 6

*S*

_{1/2}

*F*=4 ↔ 6

*P*

_{3/2}

*F*=5, by tuning the RF-frequency generator. The frequency stability of the excitation laser is limited by the line-width of the reference laser, which is better than 1 MHz, and is enough for resolving the natural line-width of Cs atom of 5.2 MHz. The intensity fluctuation of the excitation laser is less than 2%. Part of the ECDL-output is fiber-coupled to the signal fiber-line, as shown in Fig. 1, and is used as the LO-light. Thus, the fluorescence spectrum frequency falls in the frequency range around 80 MHz (=

*ω*

_{0}-ω

*).*

_{LO}*μ*s [11

**10**(5), 053003 (2008). [CrossRef]

### 3.2 Settings for the excitation beam frequency

**10**(5), 053003 (2008). [CrossRef]

9. F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, “Spontaneous emission of a cesium atom near a nanofiber: efficient coupling of light to guided modes,” Phys. Rev. A **72**(3), 032509 (2005). [CrossRef]

**15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

*μ*K is 117 kHz. In addition to the above mechanisms, the vdW potential also leads to an increase in the linewidth by about 1.5 MHz [15

15. F. Kien, S. Gupta, and K. Hakuta, “Optical excitation spectrum of an atom in a surface-induced potential,” Phys. Rev. A **75**(3), 032508 (2007). [CrossRef]

### 3.3 Estimation of atom number

13. K. P. Nayak, F. Le Kien, M. Morinaga, and K. Hakuta, “Antibunching and bunching of photons in resonance fluorescence from a few atoms into guided modes of an optical nanofiber,” Phys. Rev. **79**(2), 021801 (2009). [CrossRef]

*g*

^{(2)}(

*τ*) as following [13

13. K. P. Nayak, F. Le Kien, M. Morinaga, and K. Hakuta, “Antibunching and bunching of photons in resonance fluorescence from a few atoms into guided modes of an optical nanofiber,” Phys. Rev. **79**(2), 021801 (2009). [CrossRef]

*μ*

_{0}is determined experimentally as

*μ*

_{0}= 0.36 [13

**79**(2), 021801 (2009). [CrossRef]

^{2}. We have fitted the observed curve using the above formula to obtain the average atom number

*n*by assuming the theoretical form of

*g*

^{(2)}(

*τ*) as given in Refs [1,12

12. F. Le Kien and K. Hakuta, “Correlations between photons emitted by multiatom fluorescence into a nanofiber,” Phys. Rev. A **77**(3), 033826 (2008). [CrossRef]

*n=*14 ± 2.

## 4. Results

### 4.1 Resonant excitation

*S*

_{1/2}

*F*=4 ↔ 6

*P*

_{3/2}

*F′*=5. Figures 4(a) and 4(c) show the normalized coincidences measured for two excitation beam intensities 30 mW/cm

^{2}and 153 mW/cm

^{2}respectively, for time delay

*τ*= ±2

*μ*s. Figures 4(b) and 4(d) show the enlarged view of the center region of Figs. 4(a) and 4(c) respectively, for

*τ*= ±100 ns.

^{5}counts/s. Following the equation shown in Ref [10

**15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

*n*is the fluorescence photon count,

_{p}*n*the atom number,

*R*the atomic scattering rate,

*η*the average coupling efficiency of fluorescence into nanofiber guided mode,

_{fiber}*T*is the effective transmission of the fluorescence photons through the signal fiber-line which includes the nanofiber transmission and the losses associated with various optics and fiber couplers and

*η*is the quantum efficiency of the APD’s.

_{D}*T*and

*η*are 12% and 45% respectively. The number of atoms,

_{D}*n*≈14 and the atomic scattering rate

*R*is estimated as 1.7 ×10

^{7}

*s*

^{−1}with a saturation intensity of 2 mW/cm

^{2}. For the above calculation we used an effective spontaneous emission rate of 3.6 ×10

^{7}

*s*

^{−1}which includes the QED-enhancement factor [9

**72**(3), 032509 (2005). [CrossRef]

**15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

*η*≈2.3%.

_{fiber}*g*

^{(1)}(

*τ*) is clearly seen at zero time delay in Figs. 4(a) and 4(c). In Figs. 4(b) and 4(d), one can readily recognize the oscillations with a period of around 12 ns which reflects the difference frequency of ~80 MHz between the fluorescence frequency and the LO frequency. Envelope of the oscillation is mainly given by the first-order correlation function as shown in Eq. (5). By comparing Figs. 4(b) and 4(d), one can see that at low excitation intensity, the envelope which peaks at τ =0 falls-off smoothly. Whereas Fig. 4(d) at high excitation intensity shows a dip at around τ =25 ns.

16. B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. **188**(5), 1969–1975 (1969). [CrossRef]

17. R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A **15**(1), 227–233 (1977). [CrossRef]

### 4.2 Off-resonant excitation

^{2}. Figure 6 shows the measured emission spectra for three excitation beam detuning marked in Fig. 2 by (a), (b), and (d). Results are plotted by gray curves. The spectra for off-resonant excitation are found to be shifted from the resonant case by the respective excitation beam detuning. In the observed spectra, the central-peak appears at the excitation frequency and the separation between the side-peaks and the central-peak increases with increase in detuning of the excitation beam. This is due to the increase in the effective Rabi-frequency,

## 5. Discussions

4. C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. **65**(1), 33–36 (1990). [CrossRef] [PubMed]

**72**(3), 032509 (2005). [CrossRef]

15. F. Kien, S. Gupta, and K. Hakuta, “Optical excitation spectrum of an atom in a surface-induced potential,” Phys. Rev. A **75**(3), 032508 (2007). [CrossRef]

**15**(9), 5431–5438 (2007). [CrossRef] [PubMed]

**10**(5), 053003 (2008). [CrossRef]

**75**(3), 032508 (2007). [CrossRef]

18. F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A **70**(6), 063403 (2004). [CrossRef]

19. E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. **104**(20), 203603 (2010). [CrossRef] [PubMed]

## 6. Conclusions

## Acknowledgements

## References and links

1. | M. O. Scully, and M. Suhail Zubairy, |

2. | R. Loudon, |

3. | W. Demtröder, |

4. | C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. |

5. | P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. |

6. | J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, “Heterodyne measurement of the resonance fluorescence of a single ion,” J. Mod. Opt. |

7. | Ch. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett. |

8. | H. G. Hong, W. Seo, M. Lee, W. Choi, J. H. Lee, and K. An, “Spectral line-shape measurement of an extremely weak amplitude-fluctuating light source by photon-counting-based second-order correlation spectroscopy,” Opt. Lett. |

9. | F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, “Spontaneous emission of a cesium atom near a nanofiber: efficient coupling of light to guided modes,” Phys. Rev. A |

10. | K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express |

11. | K. P. Nayak and K. Hakuta, “Single atoms on an optical nanofiber,” N. J. Phys. |

12. | F. Le Kien and K. Hakuta, “Correlations between photons emitted by multiatom fluorescence into a nanofiber,” Phys. Rev. A |

13. | K. P. Nayak, F. Le Kien, M. Morinaga, and K. Hakuta, “Antibunching and bunching of photons in resonance fluorescence from a few atoms into guided modes of an optical nanofiber,” Phys. Rev. |

14. | F. Le Kien, K. P. Nayak, and K. Hakuta, “Second-order correlations of fluorescence from an atomic gas into a nanofiber,” Comm. in Phys. |

15. | F. Kien, S. Gupta, and K. Hakuta, “Optical excitation spectrum of an atom in a surface-induced potential,” Phys. Rev. A |

16. | B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. |

17. | R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A |

18. | F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A |

19. | E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. |

**OCIS Codes**

(020.0020) Atomic and molecular physics : Atomic and molecular physics

(270.0270) Quantum optics : Quantum optics

(300.2140) Spectroscopy : Emission

(300.2530) Spectroscopy : Fluorescence, laser-induced

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: June 18, 2010

Revised Manuscript: July 16, 2010

Manuscript Accepted: July 16, 2010

Published: July 28, 2010

**Citation**

Manoj Das, A. Shirasaki, K. P. Nayak, M. Morinaga, Fam Le Kien, and K. Hakuta, "Measurement of fluorescence emission spectrum of few strongly driven atoms using an optical nanofiber," Opt. Express **18**, 17154-17164 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17154

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### References

- M. O. Scully, and M. Suhail Zubairy, Quantum Optics (Cambridge University Press, 1997).
- R. Loudon, The Quantum Theory of Light (Oxford Science Publications, 2000).
- W. Demtröder, Laser Spectroscopy –Basic Concepts and Instrumentation (Springer, 2003).
- C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65(1), 33–36 (1990). [CrossRef] [PubMed]
- P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. 69(1), 49–52 (1992). [CrossRef] [PubMed]
- J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, “Heterodyne measurement of the resonance fluorescence of a single ion,” J. Mod. Opt. 44(10), 1999–2010 (1997). [CrossRef]
- Ch. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett. 85(3), 538–541 (2000). [CrossRef] [PubMed]
- H. G. Hong, W. Seo, M. Lee, W. Choi, J. H. Lee, and K. An, “Spectral line-shape measurement of an extremely weak amplitude-fluctuating light source by photon-counting-based second-order correlation spectroscopy,” Opt. Lett. 31(21), 3182–3184 (2006). [CrossRef] [PubMed]
- F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, “Spontaneous emission of a cesium atom near a nanofiber: efficient coupling of light to guided modes,” Phys. Rev. A 72(3), 032509 (2005). [CrossRef]
- K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, and K. Hakuta, “Optical nanofiber as an efficient tool for manipulating and probing atomic Fluorescence,” Opt. Express 15(9), 5431–5438 (2007). [CrossRef] [PubMed]
- K. P. Nayak and K. Hakuta, “Single atoms on an optical nanofiber,” N. J. Phys. 10(5), 053003 (2008). [CrossRef]
- F. Le Kien and K. Hakuta, “Correlations between photons emitted by multiatom fluorescence into a nanofiber,” Phys. Rev. A 77(3), 033826 (2008). [CrossRef]
- K. P. Nayak, F. Le Kien, M. Morinaga, and K. Hakuta, “Antibunching and bunching of photons in resonance fluorescence from a few atoms into guided modes of an optical nanofiber,” Phys. Rev. 79(2), 021801 (2009). [CrossRef]
- F. Le Kien, K. P. Nayak, and K. Hakuta, “Second-order correlations of fluorescence from an atomic gas into a nanofiber,” Comm. in Phys. 19, 35–48 (2009).
- F. Kien, S. Gupta, and K. Hakuta, “Optical excitation spectrum of an atom in a surface-induced potential,” Phys. Rev. A 75(3), 032508 (2007). [CrossRef]
- B. R. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188(5), 1969–1975 (1969). [CrossRef]
- R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15(1), 227–233 (1977). [CrossRef]
- F. Le Kien, V. I. Balykin, and K. Hakuta, “Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber,” Phys. Rev. A 70(6), 063403 (2004). [CrossRef]
- E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104(20), 203603 (2010). [CrossRef] [PubMed]

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