Abstract

We predict a strong enhancement of the capture rate and the friction force for atoms crossing a driven high-Q cavity field if several near degenerate cavity modes are simultaneously coupled to the atom. In contrast to the case of a single TEM 00 mode, circular orbits are not stable and damping of the angular and radial motion occurs. Depending on the chosen atom-field detuning the atoms phase lock the cavity modes to create a localized field minimum or maximum at their current positions. This corresponds to a local potential minimum which the atom drags along with its motion. The stimulated photon redistribution between the modes then creates a large friction force. The effect is further enhanced if the atom is directly driven by a coherent field from the side. Several atoms in the field interact via the cavity modes, which leads to a strongly correlated motion.

© 2002 Optical Society of America

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References

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  1. R. J. Thompson, G. Rempe, and H. J. Kimble, �??Observation of normal-mode splitting for an atom in an optical cavity,�?? Phys. Rev. Lett. 68, 1132 (1992).
    [CrossRef] [PubMed]
  2. M. Hennrich, T. Legero, A. Kuhn and G. Rempe, �??Vacuum-Stimulated Raman Scattering Based on Adiabatic Passage in a High-Finesse Optical Cavity,�?? Phys. Rev. Lett. 85, 4872 (2000).
    [CrossRef] [PubMed]
  3. P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, �??Cavity-induced Atom Cooling in the Strong Coupling Regime,�?? Phys. Rev. Lett. 79, 4974�??4977 (1997).
    [CrossRef]
  4. V. Vuleti´c, H. W. Chan, and A. T. Black, �??Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,�?? Phys. Rev. A 64, 033405 (2001).
    [CrossRef]
  5. P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, �??Trapping an atom with single photons,�?? Nature (London) 404, 365 (2000).
    [CrossRef]
  6. C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, �??The Atom-Cavity Microscope: Single-Atoms Bound in Orbit by Single Photons,�?? Science 287, 1447 (2000).
    [CrossRef] [PubMed]
  7. A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, �??Trapping of single atoms with single photons in cavity QED,�?? Phys. Rev. A 63, 013401 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. M. Gangl and H. Ritsch, �??Cold atoms in a high-Q ring cavity,�?? Phys. Rev. A 61, 043405 (2000).
    [CrossRef]
  11. P. Horak, H. Ritsch, T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, �??Optical Kaleidoscope Using a Single Atom,�?? Phys. Rev. Lett. 88, 043601 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. P. Domokos, T. Salzburger, and H. Ritsch �??Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,�?? Phys. Rev. A 66, 043406 (2002).
    [CrossRef]
  14. P. M¨unstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, �??Observation of Cavity-Mediated Long-Range Light Forces between Strongly Coupled Atoms,�?? Phys. Rev. Lett. 84, 4068�??4071 (2000).
    [CrossRef] [PubMed]

J. Phys. B: At. Mol. Opt. Phys. (1)

P. Domokos, P. Horak, and H. Ritsch, �??Semiclassical theory of cavity-assisted atom cooling,�?? J. Phys. B: At. Mol. Opt. Phys. 34, 187�??198 (2001).
[CrossRef]

Nature (1)

P. W. H. Pinkse, T. Fischer, P. Maunz, and G. Rempe, �??Trapping an atom with single photons,�?? Nature (London) 404, 365 (2000).
[CrossRef]

Phys. Rev. A (5)

A. C. Doherty, T. W. Lynn, C. J. Hood, and H. J. Kimble, �??Trapping of single atoms with single photons in cavity QED,�?? Phys. Rev. A 63, 013401 (2000).
[CrossRef]

S. J. van Enk, J. McKeever, H. J. Kimble, and J. Ye, �??Cooling of a single atom in an optical trap inside a resonator,�?? Phys. Rev. A 64, 013407 (2001).
[CrossRef]

M. Gangl and H. Ritsch, �??Cold atoms in a high-Q ring cavity,�?? Phys. Rev. A 61, 043405 (2000).
[CrossRef]

P. Domokos, T. Salzburger, and H. Ritsch �??Dissipative motion of an atom with transverse coherent driving in a cavity with many degenerate modes,�?? Phys. Rev. A 66, 043406 (2002).
[CrossRef]

V. Vuleti´c, H. W. Chan, and A. T. Black, �??Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering,�?? Phys. Rev. A 64, 033405 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

P. M¨unstermann, T. Fischer, P. Maunz, P. W. H. Pinkse, and G. Rempe, �??Observation of Cavity-Mediated Long-Range Light Forces between Strongly Coupled Atoms,�?? Phys. Rev. Lett. 84, 4068�??4071 (2000).
[CrossRef] [PubMed]

P. Horak, H. Ritsch, T. Fischer, P. Maunz, T. Puppe, P. W. H. Pinkse, and G. Rempe, �??Optical Kaleidoscope Using a Single Atom,�?? Phys. Rev. Lett. 88, 043601 (2002).
[CrossRef] [PubMed]

T. Fischer, P. Maunz, P. W. H. Pinkse, T . Puppe, and G. Rempe, �??Feedback on the Motion of a Single Atom in an Optical Cavity,�?? Phys. Rev. Lett. 88, 163002 (2002).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, and H. J. Kimble, �??Observation of normal-mode splitting for an atom in an optical cavity,�?? Phys. Rev. Lett. 68, 1132 (1992).
[CrossRef] [PubMed]

M. Hennrich, T. Legero, A. Kuhn and G. Rempe, �??Vacuum-Stimulated Raman Scattering Based on Adiabatic Passage in a High-Finesse Optical Cavity,�?? Phys. Rev. Lett. 85, 4872 (2000).
[CrossRef] [PubMed]

P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, �??Cavity-induced Atom Cooling in the Strong Coupling Regime,�?? Phys. Rev. Lett. 79, 4974�??4977 (1997).
[CrossRef]

Science (1)

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, �??The Atom-Cavity Microscope: Single-Atoms Bound in Orbit by Single Photons,�?? Science 287, 1447 (2000).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic representation of the system composed of an laser-driven atom strongly coupled to the field of a coherently pumped cavity.

Fig. 2.
Fig. 2.

Steady-state field intensity for a fixed laser-driven atom where Δ c = 2U 0 = -20 μs -1, corresponding to Δ a = -1440 μs -1 and g = 120 μs -1. The other parameters are (κ, γ) = (10, 20) μs -1 and the pumping strength ζ is chosen such that s = 0.03. The arrow indicates the position of the atom.

Fig. 3.
Fig. 3.

Steady-state field intensity for a fixed atom in a driven cavity, where (a) Δ c = 2U 0 = -20 μs -1 and (b) Δ a = 0, Δ c = -20 μs -1. Only η 00 is different from zero and chosen such that s = 0.03. The other parameters are the same as in Fig. 2. The arrows indicate the positions of the atom.

Fig. 4.
Fig. 4.

Steady-state field intensity for two laser-driven atoms simultaneously inside a cavity where Δ c = 2U 0 = -20 μs -1. The other parameters are the same as in Fig. 2. The arrows indicate the positions of the atoms.

Fig. 5.
Fig. 5.

Trajectory of a Rubidium atom with initial velocity v = 12 cm/s for (a) the ground mode and (b) the first six modes. In both cases, the ground mode is pumped. The blue curves shows asymmetric oscillations for 0 ≤ t ≤ 2 ms, the red circles a few rotations after t = 5 ms. The other parameters are the same as in Fig. 2.

Fig. 6.
Fig. 6.

Trajectory of a driven Rubidium atom initial at rest for (a) the ground mode and (b) the first six modes. The atom is trapped in y-direction within about a quarter of a wavelength already for 0 < t < 1 ms (blue curve). The atomic motion after t = 5 ms, which is indicated by the red curve, is much more damped in the multimode case.

Fig. 7.
Fig. 7.

Influence of an incoming atom (blue curve) on an initial trapped one (green curve) in the atom driving case for Δ c = -30 μs -1 and U 0 = -3.33 μs -1. The atom initially at rest starts to oscillate in phase with the incoming one (a) and after a few milliseconds the kinetic energy is periodically exchanged between the two atoms (b).

Equations (24)

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ρ ˙ = i ħ [ H , ρ ] + L ρ ,
H = p ̂ 2 2 m ħ Δ a σ + σ ħ Δ c n = 1 M a n a n i ħ n = 1 M g n ( x ̂ ) ( σ + a n a n σ )
i ħ ζ h ( x ̂ ) ( σ + σ ) i ħ n = 1 M η n ( a n a n )
L ρ = n = 1 M κ n ( 2 a n ρ a n { a n a n , ρ } + )
+ γ ( 2 N ( u ) σ e i u x ̂ ρ e i u x ̂ σ + du { σ + σ , ρ } + ) .
σ g n = 1 M f n ( x ̂ ) a n + ζ h ( x ̂ ) i Δ a γ .
x ˙ = p m
p ˙ = ħ U 0 ( ε * ( x ) ε ( x ) + ε ( x ) ε * ( x ) )
i ħ Γ 0 ( ε * ( x ) ε ( x ) ε ( x ) ε * ( x ) )
ħ ( η eff + i γ eff ) ( h ( x ) ε ( x ) + ε * ( x ) h ( x ) )
ħ ( η eff i γ eff ) ( h ( x ) ε * ( x ) + ε ( x ) h ( x ) )
ħ Δ a ζ 2 Δ a 2 + γ 2 h 2 ( x )
α ˙ n = ( i Δ c κ ) α n ( Γ 0 + i U 0 ) f n ( x ) ε ( x )
( γ eff + i η eff ) h ( x ) f n ( x ) + η n
ε ( x ) = n = 1 M f n ( x ) α n .
τ < 1 ω rec Δ a γ ,
s = σ + σ
= g 2 ε ( x ) 2 + ζ g h ( x ) ( ε ( x ) + ε * ( x ) ) + ζ 2 h 2 ( x ) Δ a 2 + γ 2
I x y = n , m f n x y f m x y α n * α m .
f nm x y z = H n ( 2 x w 0 ) H m ( 2 y w 0 )
× exp ( x 2 + y 2 w 0 2 ) cos ( k z ) .
M ( α 1 α M ) = v
M i j = δ i j Γ 0 + i U 0 i Δ c κ f i ( x ) f j ( x )
v i = ( γ eff + i η eff ) h ( x ) f i ( x ) η i i Δ c κ .

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