Abstract

We use the angular Doppler-effect to obtain stable frequency shifts from below one Hertz to hundreds of Hertz in the optical domain, constituting a control of 1 part in 1014. For the first time, we use these very small frequency shifts to create continuous motion in interference patterns including the scanning of linear fringe patterns and the rotation of the interference pattern formed from a Laguerre-Gaussian beam. This enables controlled lateral and rotational movement of trapped particles.

© 2002 Optical Society of America

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References

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    [CrossRef]
  2. K. MacAdam, A. Steinbach and C. E. Wieman, �??A Narrow-Band Tunable Diode-Laser System with Grating Feedback, and a Saturated Absorption Spectrometer for Cs and Rb,�?? Am. J. Phys. 60, 1098 (1992).
    [CrossRef]
  3. S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer and D. Meschede, �??Deterministic Delivery of a Single Atom,�?? Science 293, 278 (2001).
    [CrossRef] [PubMed]
  4. A. E. Chiou, W. Wang, G. J. Sonek, J. Hong and M. W. Berns, �??Interferometric optical tweezers,�?? Opt. Commun. 133, 7 (1997).
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  5. M. MacDonald, L. Paterson, W. Sibbett, P. E. Bryant and K. Dholakia, �??Trapping and manipulation of lowindex particles in a two-dimensional interferometric optical trap,�?? Opt. Lett. 26, 863 (2001).
    [CrossRef]
  6. M. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett and K. Dholakia, �??Revolving interference patterns for the rotation of optically trapped particles,�?? Opt. Commun. 201, 21 (2002).
    [CrossRef]
  7. M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett and K. Dholakia, �??Creation and Manipulation of Three-Dimensional Optically Trapped Structures,�?? Science 296, 1101 (2002).
    [CrossRef] [PubMed]
  8. L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant and K. Dholakia, �??Controlled Rotation of Optically Trapped Microscopic Particles,�?? Science 292, 912 (2001).
    [CrossRef] [PubMed]
  9. B. A. Garetz, �??Angular Doppler Effect,�?? JOSA Lett. 71, 609 (1981).
    [CrossRef]
  10. I. Bialynicki-Birula and Z. Bialynicki-Birula, �??Rotational Frequency Shift,�?? Phys. Rev. Lett. 78, 2539 (1997).
    [CrossRef]
  11. R. Simon, H. J. Kimble and E. C. G. Sudarshan, �??Evolving Geometric Phase and Its Dynamical Manifestation as a Frequency Shift: An Optical Experiment,�?? Phys. Rev. Lett. 61, 19 (1988).
    [CrossRef] [PubMed]
  12. D. Schrader, S. Kuhr, W. Alt, M. Müller, V. Gomer and D. Meschede, �??An optical conveyer belt for single neutral atoms,�?? Appl. Phys. B 73, 819 (2001).
    [CrossRef]
  13. P. Hariharan and B. Ward, �??Interferometry and the Doppler effect: An experimental verification,�?? J. Mod. Opt. 44, 221 (1997).
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  14. C. F. Buhrer, D. Baird and E. M. Conwell, �??Optical frequency shifting by the electro-optic effect,�?? Appl. Phys. Lett. 1, 46 (1962).
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Am. J. Phys. (1)

K. MacAdam, A. Steinbach and C. E. Wieman, �??A Narrow-Band Tunable Diode-Laser System with Grating Feedback, and a Saturated Absorption Spectrometer for Cs and Rb,�?? Am. J. Phys. 60, 1098 (1992).
[CrossRef]

Appl. Phys. B (1)

D. Schrader, S. Kuhr, W. Alt, M. Müller, V. Gomer and D. Meschede, �??An optical conveyer belt for single neutral atoms,�?? Appl. Phys. B 73, 819 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

C. F. Buhrer, D. Baird and E. M. Conwell, �??Optical frequency shifting by the electro-optic effect,�?? Appl. Phys. Lett. 1, 46 (1962).
[CrossRef]

J. Mod. Opt. (1)

P. Hariharan and B. Ward, �??Interferometry and the Doppler effect: An experimental verification,�?? J. Mod. Opt. 44, 221 (1997).
[CrossRef]

JOSA Lett. (1)

B. A. Garetz, �??Angular Doppler Effect,�?? JOSA Lett. 71, 609 (1981).
[CrossRef]

Opt. Commun. (2)

M. MacDonald, K. Volke-Sepulveda, L. Paterson, J. Arlt, W. Sibbett and K. Dholakia, �??Revolving interference patterns for the rotation of optically trapped particles,�?? Opt. Commun. 201, 21 (2002).
[CrossRef]

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong and M. W. Berns, �??Interferometric optical tweezers,�?? Opt. Commun. 133, 7 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

I. Bialynicki-Birula and Z. Bialynicki-Birula, �??Rotational Frequency Shift,�?? Phys. Rev. Lett. 78, 2539 (1997).
[CrossRef]

R. Simon, H. J. Kimble and E. C. G. Sudarshan, �??Evolving Geometric Phase and Its Dynamical Manifestation as a Frequency Shift: An Optical Experiment,�?? Phys. Rev. Lett. 61, 19 (1988).
[CrossRef] [PubMed]

Rev. Sci. Inst. (1)

D. Haubrich, M. Dornseifer and R. Wynands, �??Lossless beam combiners for nearly equal laser frequencies,�?? Rev. Sci. Inst. 71, 338 (2000).
[CrossRef]

Science (3)

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett and K. Dholakia, �??Creation and Manipulation of Three-Dimensional Optically Trapped Structures,�?? Science 296, 1101 (2002).
[CrossRef] [PubMed]

L. Paterson, M. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant and K. Dholakia, �??Controlled Rotation of Optically Trapped Microscopic Particles,�?? Science 292, 912 (2001).
[CrossRef] [PubMed]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer and D. Meschede, �??Deterministic Delivery of a Single Atom,�?? Science 293, 278 (2001).
[CrossRef] [PubMed]

Supplementary Material (2)

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Figures (5)

Fig. 1.
Fig. 1.

Adapted Mach-Zehnder interferometer for creating two co-propagating laser beams with a frequency shift between them of 2Ωrot. PBS, polarising beam splitter; M, mirror; λ/2, half wave plate; Rλ/2, rotating λ/2; BS, 50:50 beam splitter; +ħ , right hand circularly polarised light; - ħ , left hand circularly polarised light; Ωrot, rotation frequency of half-wave plate.

Fig. 2.
Fig. 2.

The beat signal produced by interfering two Gaussian beams separated in frequency using the angular Doppler effect.

Fig. 3.
Fig. 3.

1 μm diameter silica spheres moving from left to right as the linear fringes of an interference pattern are scanned using the angular Doppler effect. The particles are trapped (a) along the bright fringes and then move to the right (b)-(d). Continuous motion of the pattern amalgamates all of these spheres on the right hand side of the pattern region (d).

Fig. 4
Fig. 4

Rotating interference patterns: patterns produced in order between l = 1 + l = -1, l = 2 + l = -2 and l = 3 + l = -3 [see video-clip: arlt1.m1v (1,711 KB)].

Fig. 5
Fig. 5

a 5 μm long glass rod trapped in the interference pattern between one Laguerre-Gaussian beam with l = 1 and one with l = -1, is rotated continuously in water using the angular Doppler-effect [see video-clip: arlt2.m1v (1,470 KB)].

Equations (15)

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ħ + I Ω rot = ħ + I Ω rot /
ħ ω 1 + L 1 2 2 I = ħ ω 2 + L 2 2 2 I
Δ ω = ω 1 ω 2 = 2 Ω rot
V = 2 Ω λ sin α
E 1 ( r ̅ ) = E 01 p z exp [ i ( + kz ωt ) ] ;
E 2 ( r ̅ ) = E 02 p z exp [ i ( + kz ( ω + Δ ω ) t ) ]
I ( r ̅ ) = E 1 ( r ̅ ) + E 2 ( r ̅ ) 2
= E 01 2 + E 02 2 + 2 Re { E 01 E 02 * } cos ( 2 l φ + ( Δ ω ) t )
I ( p , φ , z , t ) 2 I 0 ( p , z ) [ 1 + cos ( 2 l φ + ( Δ ω ) t ) ]
= 4 I 0 p z cos 2 ( l φ + ( Δ ω 2 ) t ) .
I ( p , φ , z , t ) = 4 I 0 p z cos 2 [ ψ φ t ]
dt = ( ψ t ) φ ( ψ φ ) t = Ω rot l
E 2 ( r ̅ ) = E 02 p z exp [ i ( kz ( ω + Δ ω ) t ) ] .
I ( r ̅ ) = E 01 2 + E 02 2 + 2 Re { E 01 E 02 * } cos ( + 2 Ω rot t )
dt = 2 Ω rot l

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