Abstract

The output from two grating-stabilized external-cavity diode lasers were injected into a single-mode diode laser. Operating at a wavelength of 780nm, this laser produced 50mW of power with two main frequency components of the same spectral characteristics of the seed lasers. The power ratio of the amplified components was freely adjustable due to gain saturation, and amplification was observed for frequency differences of the two seed lasers in the range from 73MHz to 6.6GHz. This system was used to realize a dual isotope magneto-optic trap (MOT) for rubidium (Rb85 and Rb87). The resulting position and cloud size of the dual isotope MOT was the same as that of the single species MOTs to within ±10 and ±20μm, respectively. We also characterized the additional spectral components produced by four wave mixing (FWM) in the diode laser amplifier and utilized a particular FWM sideband to realize hyperfine pumping and subsequent laser trapping of Rb85 in the absence of a “repump” laser dedicated to hyperfine pumping.

© 2007 Optical Society of America

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References

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  1. F. Mogensen, H. Olesen, and G. Jacobsen, "Locking conditions and stability properties for a semiconductor laser with external light injection," IEEE J. Quantum Electron. 21, 784-793 (1985).
    [CrossRef]
  2. H. Tsuchida, "Tunable, narrow-linewidth output from an injection-locked high-power AlGaAs laser diode array," Opt. Lett. 19, 1741-1743 (1994).
    [CrossRef] [PubMed]
  3. M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
    [CrossRef]
  4. A. C. Wilson, J. C. Sharpe, C. R. McKenzie, P. J. Manson, and D. M. Warrington, "Narrow-linewidth master-oscillator power amplifier based on a semiconductor tapered amplifier," Appl. Opt. 37, 4871-4875 (1998).
    [CrossRef]
  5. W. Süptitz, G. Wokurka, F. Strauch, P. Kohns, and W. Ertmer, "Simultaneous cooling and trapping of Rb85 and Rb87 in a magneto-optical trap," Opt. Lett. 19, 1571-1573 (1994).
    [CrossRef] [PubMed]
  6. M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
    [CrossRef]
  7. S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
    [CrossRef]
  8. S. B. Papp and C. E. Wieman, "Observation of heteronuclear Feshbach molecules from a Rb85-Rb87 gas," Phys. Rev. Lett. 97, 18404-1-18404-4 (2006).
    [CrossRef]
  9. G. Ferrari, M.-O. Mewes, F. Schreck, and C. Salomon, "High-power multiple-frequency narrow-linewidth laser source based on a semiconductor tapered amplifier," Opt. Lett. 24, 151-153 (1999).
    [CrossRef]
  10. G. P. Agrawal, "Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers," J. Opt. Soc. Am. B 5, 147-159 (1988).
    [CrossRef]
  11. R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
    [CrossRef]
  12. G. P. Agrawal, "Semiconductor laser amplifiers," in Semiconductor Lasers: Past, Present, and Future, G.P.Agrawal, ed., AIP Series in Theoretical and Applied Optics (AIP, 1995), pp. 243-283.
  13. J. Troger, L. Thévanz, P.-A. Nicati, and P. A. Robert, "Theory and experiment of a single-mode diode laser subject to external light from several lasers," J. Lightwave Technol. 17, 629-636 (1999).
    [CrossRef]
  14. I. Park, I. Fischer, and W. Elsäßer, "Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser," Appl. Phys. Lett. 84, 5189-5191 (2004).
    [CrossRef]
  15. A. S. Arnold, J. S. Wilson, and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69, 1236-1239 (1998).
    [CrossRef]
  16. The specified operating wavelength of the ROSA is 850nm, but we observe a sufficient sensitivity at 780nm, a differential responsivity of approximately 50V/W.
  17. When the amplifier was off, only 3.5μW from the repump seed beam, which reflected from the amplifier, was measured at the MOT, far less than that required for hyperfine repumping.
  18. H. S. Moon, J. B. Kim, J. D. Park, B. K. Kwon, H. Cho, and H. S. Lee, "Magneto-optic trap of rubidium atoms with an injection-seeded laser that operates at two frequencies," Appl. Opt. 35, 5402-5405 (1996).
    [CrossRef] [PubMed]
  19. C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
    [CrossRef] [PubMed]

2006 (1)

S. B. Papp and C. E. Wieman, "Observation of heteronuclear Feshbach molecules from a Rb85-Rb87 gas," Phys. Rev. Lett. 97, 18404-1-18404-4 (2006).
[CrossRef]

2004 (1)

I. Park, I. Fischer, and W. Elsäßer, "Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser," Appl. Phys. Lett. 84, 5189-5191 (2004).
[CrossRef]

2000 (2)

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
[CrossRef]

1999 (2)

1998 (3)

A. C. Wilson, J. C. Sharpe, C. R. McKenzie, P. J. Manson, and D. M. Warrington, "Narrow-linewidth master-oscillator power amplifier based on a semiconductor tapered amplifier," Appl. Opt. 37, 4871-4875 (1998).
[CrossRef]

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

A. S. Arnold, J. S. Wilson, and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69, 1236-1239 (1998).
[CrossRef]

1996 (1)

1994 (2)

1992 (1)

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

1989 (1)

R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
[CrossRef]

1988 (1)

1985 (1)

F. Mogensen, H. Olesen, and G. Jacobsen, "Locking conditions and stability properties for a semiconductor laser with external light injection," IEEE J. Quantum Electron. 21, 784-793 (1985).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, "Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers," J. Opt. Soc. Am. B 5, 147-159 (1988).
[CrossRef]

G. P. Agrawal, "Semiconductor laser amplifiers," in Semiconductor Lasers: Past, Present, and Future, G.P.Agrawal, ed., AIP Series in Theoretical and Applied Optics (AIP, 1995), pp. 243-283.

Arnold, A. S.

A. S. Arnold, J. S. Wilson, and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69, 1236-1239 (1998).
[CrossRef]

Boshier, M. G.

A. S. Arnold, J. S. Wilson, and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69, 1236-1239 (1998).
[CrossRef]

Cho, H.

Crane, S. G.

S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
[CrossRef]

Dinneen, T. P.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

Elsäßer, W.

I. Park, I. Fischer, and W. Elsäßer, "Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser," Appl. Phys. Lett. 84, 5189-5191 (2004).
[CrossRef]

R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
[CrossRef]

Ertmer, W.

Ferrari, G.

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

G. Ferrari, M.-O. Mewes, F. Schreck, and C. Salomon, "High-power multiple-frequency narrow-linewidth laser source based on a semiconductor tapered amplifier," Opt. Lett. 24, 151-153 (1999).
[CrossRef]

Fischer, I.

I. Park, I. Fischer, and W. Elsäßer, "Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser," Appl. Phys. Lett. 84, 5189-5191 (2004).
[CrossRef]

Fischer, T.

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

Göbel, E. O.

R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
[CrossRef]

Gould, P. L.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

Grove, T. T.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

Hänsch, T. W.

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

Jacobsen, G.

F. Mogensen, H. Olesen, and G. Jacobsen, "Locking conditions and stability properties for a semiconductor laser with external light injection," IEEE J. Quantum Electron. 21, 784-793 (1985).
[CrossRef]

Kim, J. B.

Kohns, P.

Kwon, B. K.

Lee, H. S.

Manson, P. J.

McKenzie, C. R.

Mewes, M.-O.

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

G. Ferrari, M.-O. Mewes, F. Schreck, and C. Salomon, "High-power multiple-frequency narrow-linewidth laser source based on a semiconductor tapered amplifier," Opt. Lett. 24, 151-153 (1999).
[CrossRef]

Mogensen, F.

F. Mogensen, H. Olesen, and G. Jacobsen, "Locking conditions and stability properties for a semiconductor laser with external light injection," IEEE J. Quantum Electron. 21, 784-793 (1985).
[CrossRef]

Moon, H. S.

Nicati, P.-A.

Nietzke, R.

R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
[CrossRef]

Olesen, H.

F. Mogensen, H. Olesen, and G. Jacobsen, "Locking conditions and stability properties for a semiconductor laser with external light injection," IEEE J. Quantum Electron. 21, 784-793 (1985).
[CrossRef]

Panknin, P.

R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
[CrossRef]

Papp, S. B.

S. B. Papp and C. E. Wieman, "Observation of heteronuclear Feshbach molecules from a Rb85-Rb87 gas," Phys. Rev. Lett. 97, 18404-1-18404-4 (2006).
[CrossRef]

Park, I.

I. Park, I. Fischer, and W. Elsäßer, "Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser," Appl. Phys. Lett. 84, 5189-5191 (2004).
[CrossRef]

Park, J. D.

Praeger, M.

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

Robert, P. A.

Salomon, C.

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

G. Ferrari, M.-O. Mewes, F. Schreck, and C. Salomon, "High-power multiple-frequency narrow-linewidth laser source based on a semiconductor tapered amplifier," Opt. Lett. 24, 151-153 (1999).
[CrossRef]

Schreck, F.

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

G. Ferrari, M.-O. Mewes, F. Schreck, and C. Salomon, "High-power multiple-frequency narrow-linewidth laser source based on a semiconductor tapered amplifier," Opt. Lett. 24, 151-153 (1999).
[CrossRef]

Sharpe, J. C.

Sinatra, A.

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

Strauch, F.

Süptitz, W.

Tan, K.-Y. N.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

Taylor, W.

S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
[CrossRef]

Thévanz, L.

Troger, J.

Tsuchida, H.

Vieira, D. J.

S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
[CrossRef]

Vuletic, V.

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

Wallace, C. D.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

Warrington, D. M.

Wieman, C. E.

S. B. Papp and C. E. Wieman, "Observation of heteronuclear Feshbach molecules from a Rb85-Rb87 gas," Phys. Rev. Lett. 97, 18404-1-18404-4 (2006).
[CrossRef]

Wilson, A. C.

Wilson, J. S.

A. S. Arnold, J. S. Wilson, and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69, 1236-1239 (1998).
[CrossRef]

Wokurka, G.

Zhao, X.

S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
[CrossRef]

Zimmermann, C.

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

M. Praeger, V. Vuletic, T. Fischer, T. W. Hänsch, and C. Zimmermann, "A broad emitter diode laser system for lithium spectroscopy," Appl. Phys. B 67, 163-166 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

I. Park, I. Fischer, and W. Elsäßer, "Highly nondegenerate four-wave mixing in a tunable dual-mode semiconductor laser," Appl. Phys. Lett. 84, 5189-5191 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Nietzke, P. Panknin, W. Elsäßer, and E. O. Göbel, "Four-wave mixing in gaas/algaas semiconductor lasers," IEEE J. Quantum Electron. 25, 1399-1406 (1989).
[CrossRef]

F. Mogensen, H. Olesen, and G. Jacobsen, "Locking conditions and stability properties for a semiconductor laser with external light injection," IEEE J. Quantum Electron. 21, 784-793 (1985).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Lett. (3)

Phys. Rev. A (2)

M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, and C. Salomon, "Simultaneous magneto-optical trapping of two lithium isotopes," Phys. Rev. A 61, 011403 (2000).
[CrossRef]

S. G. Crane, X. Zhao, W. Taylor, and D. J. Vieira, "Trapping an isotopic mixture of fermionic Rb84 and bosonic Rb87 atoms," Phys. Rev. A 62, 011402 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

S. B. Papp and C. E. Wieman, "Observation of heteronuclear Feshbach molecules from a Rb85-Rb87 gas," Phys. Rev. Lett. 97, 18404-1-18404-4 (2006).
[CrossRef]

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, "Isotopic difference in trap loss collisions of laser cooled rubidium atoms," Phys. Rev. Lett. 69, 897-900 (1992).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. S. Arnold, J. S. Wilson, and M. G. Boshier, "A simple extended-cavity diode laser," Rev. Sci. Instrum. 69, 1236-1239 (1998).
[CrossRef]

Other (3)

The specified operating wavelength of the ROSA is 850nm, but we observe a sufficient sensitivity at 780nm, a differential responsivity of approximately 50V/W.

When the amplifier was off, only 3.5μW from the repump seed beam, which reflected from the amplifier, was measured at the MOT, far less than that required for hyperfine repumping.

G. P. Agrawal, "Semiconductor laser amplifiers," in Semiconductor Lasers: Past, Present, and Future, G.P.Agrawal, ed., AIP Series in Theoretical and Applied Optics (AIP, 1995), pp. 243-283.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup. The output from two ECDL lasers, M 1 and M 2 , were combined and injected into a diode laser amplifier. The amplifier spectrum was characterized by mixing it with an independent ECDL laser, M c , onto a high speed photodetector (ROSA) and the resulting rf spectrum was recorded on a spectrum analyzer (RFSA). A FP interferometer and a saturated absorption spectrometer (SAS) provided additional diagnostics. Symbols: M, mirrors; OI, optical isolator; FC1, FC2, FC3, fiber optic; PBS, polarizing beam splitter cube; GS, glass slide.

Fig. 2
Fig. 2

(a) Rf heterodyne and (b) FP spectrum of the laser diode amplifier. The two seed beams were 0.7 mW each and Δ = 73 MHz apart. After amplification more than 80% of the total optical power ( 50 mW at a diode current of 100 mA ) was contained at the seed frequencies, ν 1 and ν 2 , labeled by ( ) and ( ) , respectively. The additional FWM components generated in the amplifier are labeled by ( ) and ( ) for the positive and negative orders, respectively. The comparator frequency ν c was chosen to be δ = 53 MHz below ν 1 to provide a distinct heterodyne beat note for each of the FWM components. The amplifier homodyne beat notes are labeled by ( ) . For this heterodyne spectrum, the power incident on the ROSA from the amplified beam and from M c was 11.5 and 12.0 μ W , respectively.

Fig. 3
Fig. 3

Relative amplifier power output in the two seed frequencies, ν 1 ( ) and ν 2 ( ) , as a function of the injected power at ν 2 from M 2 with the input power from M 1 held fixed at 0.67 ( 3 ) mW . The sum of the power contained in the FWM components is also shown ( ) . At almost equal injection power, the amplified seeds were equal in amplitude and contained approximately 80% of the total output power. The dashed curves are a guide to the eye.

Fig. 4
Fig. 4

Heterodyne beat frequency width (FWHM) as a function of the FWM order for both positive and negative orders, labeled by ( ) and ( ) , respectively. The inset shows the beat center frequency versus FWM order, and the slopes for the positive and negative orders provide a measure of Δ = 72.88 and 72.85 [ MHz ] , respectively. These data were extracted from the heterodyne spectrum shown in Fig. 2.

Fig. 5
Fig. 5

Fluorescence observed from the dual isotope rubidium MOT. The isotope loading was controlled by independently blocking the output of either the Rb 85 or the Rb 87 repumping laser ( M 3 or M 4 ), which left the amplifier output unchanged. (a) Rb 87 MOT was loaded by introducing its repumping light, and then the Rb 85 repumping light was introduced after 30 s . After the dual isotope MOT fluorescence reached steady state, the Rb 85 repumping light was extinguished. Immediately after, the Rb 87 fluorescence (proportional to the number of atoms) was observed to be lower than its steady state value in the absence of a Rb 85 MOT. After 3 s , the Rb 87 fluorescence recovered to its steady state value. In (b) after loading both isotopes, the Rb 87 repumping light was extinguished, and the Rb 85 fluorescence level was observed to be unchanged by the presence of the Rb 87 MOT.

Fig. 6
Fig. 6

Images and line profiles of the atomic fluorescence from a Rb 87 ( ) , Rb 85 ( ) , and dual species ( ) MOT. The (a) x axis and (b) y axis center of mass of the single species MOTs was the same as the dual species MOT to within ± 10 μ m ( ± 0.5 pixels where the magnification was 18 μ m pixel ). The FWHM of the atomic cloud grew from a size of 220 μ m for the single Rb 87 MOT to a size of 260 μ m for the dual species MOT. We estimate that the atom numbers were 2 × 10 5 , 1 × 10 5 for the single isotope Rb 85 and Rb 87 MOTs, and 2.6 × 10 5 for the dual isotope MOT.

Equations (3)

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ν n ( FWM ) = ν i + n Δ ,
f + n ( rf ) = ν c ν + n ( FWM ) = δ + n Δ
f n ( rf ) = ν c ν n ( FWM ) = Δ δ + n Δ

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