Abstract

Laser fluorescence spectroscopy has been performed on the two-photon 62S1/2 to 52D3/2 transition in Ba+. Using signals from an individual laser-cooled ion in a rf trap, a laser limited linewidth of less than 3 MHz has been achieved with an effective wavelength of 2.07 μm. The absence of any sidebands in the spectra spaced at the 5.5-MHz oscillation frequency of the ion in the rf quadrupole trap indicates that the ion vibrational motion must be well into the Lamb–Dicke regime. An upper limit of 165 nm is given to the vibrational amplitude.

© 1985 Optical Society of America

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References

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  1. R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
    [CrossRef]
  2. H. Dehmelt, “Stored ion spectroscopy,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, and H. Walther, eds. (Plenum, New York, 1983).
    [CrossRef]
  3. W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
    [CrossRef]
  4. D. J. Wineland and W. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75 (1981).
  5. W. Nagourney, G. Janik, and H. Dehmelt, “Linewidth of single laser-cooled 24Mg+ ion in radiofrequency trap,” Proc. Nat. Acad. Sci. USA 80, 643 (1983).
    [CrossRef]
  6. W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, “Resonance fluorescence from single ions at rest,” in Spectral Line Shapes, B. Wende, ed. (de Gruyter, Berlin, 1981).
  7. R. Schneider and G. Werth, “Ion storage technique for very long living states: the decay rate of the 5D3/2state of Ba II,” Z. Phys. A 293, 103 (1979).
    [CrossRef]
  8. H. Dehmelt and P. Toschek, “Proposed visual detection laser spectroscopy on single Ba+ ion,” Bull. Am. Phys. Soc. 20, 61 (1975).
  9. G. Janik, “Laser cooled single ion spectroscopy of magnesium and barium,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1984).
  10. W. M. Itano and D. J. Wineland, “Laser cooling of ions stored in harmonic and Penning traps,” Phys. Rev. A 25, 35 (1982).
    [CrossRef]
  11. R. M. Whitley and C. R. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498 (1976).
    [CrossRef]
  12. H. R. Gray, R. M. Whitley, and C. R. Stroud, “Coherent trapping of atomic populations,” Opt. Lett. 3, 218 (1978).
    [CrossRef] [PubMed]

1983 (1)

W. Nagourney, G. Janik, and H. Dehmelt, “Linewidth of single laser-cooled 24Mg+ ion in radiofrequency trap,” Proc. Nat. Acad. Sci. USA 80, 643 (1983).
[CrossRef]

1982 (1)

W. M. Itano and D. J. Wineland, “Laser cooling of ions stored in harmonic and Penning traps,” Phys. Rev. A 25, 35 (1982).
[CrossRef]

1981 (1)

D. J. Wineland and W. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75 (1981).

1980 (1)

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
[CrossRef]

1979 (1)

R. Schneider and G. Werth, “Ion storage technique for very long living states: the decay rate of the 5D3/2state of Ba II,” Z. Phys. A 293, 103 (1979).
[CrossRef]

1978 (1)

1976 (1)

R. M. Whitley and C. R. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498 (1976).
[CrossRef]

1975 (1)

H. Dehmelt and P. Toschek, “Proposed visual detection laser spectroscopy on single Ba+ ion,” Bull. Am. Phys. Soc. 20, 61 (1975).

1953 (1)

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
[CrossRef]

Dehmelt, H.

W. Nagourney, G. Janik, and H. Dehmelt, “Linewidth of single laser-cooled 24Mg+ ion in radiofrequency trap,” Proc. Nat. Acad. Sci. USA 80, 643 (1983).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
[CrossRef]

H. Dehmelt and P. Toschek, “Proposed visual detection laser spectroscopy on single Ba+ ion,” Bull. Am. Phys. Soc. 20, 61 (1975).

H. Dehmelt, “Stored ion spectroscopy,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, and H. Walther, eds. (Plenum, New York, 1983).
[CrossRef]

Dehmelt, H. G.

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, “Resonance fluorescence from single ions at rest,” in Spectral Line Shapes, B. Wende, ed. (de Gruyter, Berlin, 1981).

Dicke, R. H.

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
[CrossRef]

Gray, H. R.

Hohenstatt, M.

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, “Resonance fluorescence from single ions at rest,” in Spectral Line Shapes, B. Wende, ed. (de Gruyter, Berlin, 1981).

Itano, W.

D. J. Wineland and W. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75 (1981).

Itano, W. M.

W. M. Itano and D. J. Wineland, “Laser cooling of ions stored in harmonic and Penning traps,” Phys. Rev. A 25, 35 (1982).
[CrossRef]

Janik, G.

W. Nagourney, G. Janik, and H. Dehmelt, “Linewidth of single laser-cooled 24Mg+ ion in radiofrequency trap,” Proc. Nat. Acad. Sci. USA 80, 643 (1983).
[CrossRef]

G. Janik, “Laser cooled single ion spectroscopy of magnesium and barium,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1984).

Nagourney, W.

W. Nagourney, G. Janik, and H. Dehmelt, “Linewidth of single laser-cooled 24Mg+ ion in radiofrequency trap,” Proc. Nat. Acad. Sci. USA 80, 643 (1983).
[CrossRef]

Neuhauser, W.

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, “Resonance fluorescence from single ions at rest,” in Spectral Line Shapes, B. Wende, ed. (de Gruyter, Berlin, 1981).

Schneider, R.

R. Schneider and G. Werth, “Ion storage technique for very long living states: the decay rate of the 5D3/2state of Ba II,” Z. Phys. A 293, 103 (1979).
[CrossRef]

Stroud, C. R.

Toschek, P.

H. Dehmelt and P. Toschek, “Proposed visual detection laser spectroscopy on single Ba+ ion,” Bull. Am. Phys. Soc. 20, 61 (1975).

Toschek, P. E.

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, “Resonance fluorescence from single ions at rest,” in Spectral Line Shapes, B. Wende, ed. (de Gruyter, Berlin, 1981).

Werth, G.

R. Schneider and G. Werth, “Ion storage technique for very long living states: the decay rate of the 5D3/2state of Ba II,” Z. Phys. A 293, 103 (1979).
[CrossRef]

Whitley, R. M.

Wineland, D. J.

W. M. Itano and D. J. Wineland, “Laser cooling of ions stored in harmonic and Penning traps,” Phys. Rev. A 25, 35 (1982).
[CrossRef]

D. J. Wineland and W. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75 (1981).

Bull. Am. Phys. Soc. (1)

H. Dehmelt and P. Toschek, “Proposed visual detection laser spectroscopy on single Ba+ ion,” Bull. Am. Phys. Soc. 20, 61 (1975).

Opt. Lett. (1)

Phys. Lett. (1)

D. J. Wineland and W. Itano, “Spectroscopy of a single Mg+ ion,” Phys. Lett. 82A, 75 (1981).

Phys. Rev. (1)

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472 (1953).
[CrossRef]

Phys. Rev. A (3)

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. Dehmelt, “Localized visible Ba+ mono-ion oscillator,” Phys. Rev. A 22, 1137 (1980).
[CrossRef]

W. M. Itano and D. J. Wineland, “Laser cooling of ions stored in harmonic and Penning traps,” Phys. Rev. A 25, 35 (1982).
[CrossRef]

R. M. Whitley and C. R. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498 (1976).
[CrossRef]

Proc. Nat. Acad. Sci. USA (1)

W. Nagourney, G. Janik, and H. Dehmelt, “Linewidth of single laser-cooled 24Mg+ ion in radiofrequency trap,” Proc. Nat. Acad. Sci. USA 80, 643 (1983).
[CrossRef]

Z. Phys. A (1)

R. Schneider and G. Werth, “Ion storage technique for very long living states: the decay rate of the 5D3/2state of Ba II,” Z. Phys. A 293, 103 (1979).
[CrossRef]

Other (3)

G. Janik, “Laser cooled single ion spectroscopy of magnesium and barium,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1984).

W. Neuhauser, M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, “Resonance fluorescence from single ions at rest,” in Spectral Line Shapes, B. Wende, ed. (de Gruyter, Berlin, 1981).

H. Dehmelt, “Stored ion spectroscopy,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, and H. Walther, eds. (Plenum, New York, 1983).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Perspective view of trap assembly showing one of the two barium ovens used. A close-up of the trap is shown, along with the approximate position of the barium ion. The ion is illuminated by two collinear, focused laser beams directed upward; the fluorescence is observed at right angles to the incident beams.

Fig. 2
Fig. 2

Schematic of the barium optical system. Fractions of the red and blue beams are split off, combined, and sent through the trap. Two variable attenuators control the laser intensities. Two field coils (not shown) are mounted above and below the trap to enable a magnetic field to be applied parallel to the laser beam. The entire vacuum tube is enclosed in a magnetic shield.

Fig. 3
Fig. 3

Level structure of Ba+. Only the P1/2 and D3/2 states are excited in the experiment. The intermediate D3/2 state has a measured lifetime of 17 sec.

Fig. 4
Fig. 4

Result of the three-level Bloch equation calculation. The Rabi frequencies are equal, with ΩB = ΩR = 2π × 10 MHz. The blue detuning is ΔB = −2π × 40 MHz. This is the pure-dip regime.

Fig. 5
Fig. 5

Result of the three-level Bloch equation calculation. The blue Rabi frequency is much larger than the red with ΩB = 2π × 10 MHz and ΩR = 2π × 2 MHz. The blue detuning is ΔB = −2π × 40 MHz. These conditions are similar to those used while taking the spectra shown in Figs. 810.

Fig. 6
Fig. 6

Result of the eight-level Bloch equation calculation. Linear laser polarization and a magnetic field parallel to the laser beam are assumed. This is the pure-dip regime, with ΩB = ΩR = 2π × 7 MHz. The magnetic field is 0.86 G, and ΔB = −2π × 10 MHz.

Fig. 7
Fig. 7

A scan of Ba+ fluorescence taken without the external frequency-stabilization system. The laser intensities are relatively high to produce a good signal-to-noise ratio. The static magnetic field is about 1 G. The two-photon peak is the smaller one on the left.

Fig. 8
Fig. 8

A stabilized high-resolution barium scan. The two-photon peak is less than 3 MHz wide, which is about the limit of our resolution. The applied magnetic field is about 0.15 G, and the integration time is 2 sec per point, which represents 0.25 MHz of scan. The rise to the right is the start of the main (one-photon) peak. The blue detuning is roughly −30 MHz. Note the absence of sidebands separated from the peak by the trap frequencies of 5.5 and 2.7 MHz.

Fig. 9
Fig. 9

Another stabilized barium scan, this time with an approximately symmetrized trap. The two-photon peak is about 5.5 MHz wide. The blue detuning is about −50 MHz. The magnetic field is about 150 mG, and the integration time is 1 sec per point. There is no sign of sidebands at the oscillation frequency of 5.3 MHz.

Fig. 10
Fig. 10

A stabilized barium scan, taken with the same parameters as for Fig. 9 except that the red laser power has been increased. The peak has broadened to about 7.6 MHz, but the signal-to-noise ratio is improved. There is still no sign of sidebands.

Fig. 11
Fig. 11

A stabilized barium scan in the pure-dip regime. The blue detuning is roughly −10 MHz, and the magnetic field is 0.86 G. The dip has split into four parts, as shown in the similar theoretical plot in Fig. 6.

Fig. 12
Fig. 12

A barium scan taken with counterpropagating laser beams and relatively high laser power. The magnetic field is about 0.6 G, and the trap frequencies are 8.6 and 4.3 MHz. The blue detuning is roughly −50 MHz. Notice the complex structure over a wide frequency range.

Equations (17)

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d σ 1 d t = T 13 ( σ 3 - σ 1 ) + Γ B σ 3 ,
d σ 2 d t = T 23 ( σ 3 - σ 2 ) + Γ R σ 3 ,
σ 3 = 1 3 + Γ B / T 13 + Γ R / T 23 .
T 13 = Ω B 2 Γ 4 Δ B 2 + Γ 2 ,
T 23 = Ω R 2 Γ 4 Δ R 2 + Γ 2 ,
σ 3 = Ω R 2 ( 1 + κ ) 4 Δ R 2 + Γ 2 + 3 ( 1 + κ ) Ω R 2 + κ ( 4 Δ B 2 + Γ 2 ) Ω R 2 / Ω B 2 ,
½ k T MIN = Γ / 4.
d ρ 11 d t = i Ω B 2 ( ρ 13 - ρ 31 ) + Γ B ρ 33 ,
d ρ 22 d t = i Ω R 2 ( ρ 23 - ρ 32 ) + Γ R ρ 33 ,
d ρ 12 d t = i [ ( Δ R - Δ B ) ρ 12 + Ω R 2 ρ 13 - Ω B 2 ρ 32 ] ,
d ρ 13 d t = i [ Ω B 2 ( ρ 11 - ρ 33 ) + Ω R 2 ρ 12 - Δ B ρ 13 ] - Γ 2 ρ 13 ,
d ρ 23 d t = i [ Ω R 2 ( ρ 22 - ρ 33 ) + Ω B 2 ρ 21 - Δ R ρ 23 ] - Γ 2 ρ 23 .
ρ 33 = 4 ( Δ B - Δ R ) 2 Ω B 2 Ω R 2 Γ Z ,
Z 8 ( Δ B - Δ R ) 2 Ω B 2 Ω R 2 Γ + 4 ( Δ B - Δ R ) 2 Γ 2 Y + 16 ( Δ B - Δ R ) 2 [ Δ B 2 Ω R 2 Γ B + Δ R 2 Ω B 2 Γ R ] - 8 Δ B ( Δ B - Δ R ) Ω R 4 Γ B + 8 Δ R ( Δ B - Δ R ) Ω B 4 Γ R + ( Ω B 2 + Ω R 2 ) 2 Y
Y Ω B 2 Γ R + Ω R 2 Γ B .
β EFF = 2 π x 0 / λ EFF
1 λ EFF 1 λ B 1 λ R ,

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