A well-collimated quasi-continuous atom laser

Science

Volumn 283, Issue 5408, 1999, Pages 1706-1709

  Hagley, E W ^a   Deng, L ^a,b   Kozuma, M ^c   Wen, J ^a   Helmerson, K ^a   Rolston, S L ^a   Phillips, W D ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

^b GEORGIA SOUTHERN UNIVERSITY   (United States)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

SODIUM;

ARTICLE; ATOM; COLLIMATOR; LASER; PHOTON; POLARIZATION; PRIORITY JOURNAL; RAMAN SPECTROMETRY;

EID: 0033548588     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.283.5408.1706     Document Type: Article

References (36)

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2. A. Einstein, Sitzungsbe. Kgl. Preuss. Akad. Was. (1924), p. 261; ibid. (1925), p. 3.
3. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
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6. C. C. Bradley, C. A. Sackett, R. G. Hulet, ibid. 78, 985 (1997); see also C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, ibid. 75, 1687 (1995).
7. D. G. Fried et al., ibid. 81, 3807 (1998).
8. J. Physique 4, 11 (1994); Appl. Phys. B. 54, 321 (1992); J. Phys. Rep. 240 (1994) (special issues on optics and interferometry with atoms).
9. J. Physique 4, 11 (1994); Appl. Phys. B. 54, 321 (1992); J. Phys. Rep. 240 (1994) (special issues on optics and interferometry with atoms).
10. J. Physique 4, 11 (1994); Appl. Phys. B. 54, 321 (1992); J. Phys. Rep. 240 (1994) (special issues on optics and interferometry with atoms).
11. M.-O. Mewes et al., Phys. Rev. Lett. 78, 582 (1997).
12. A truly cw atom laser produces a continuous, coherent matter wave output while being continuously replenished with new atoms, in direct analogy with a cw optical laser. The coherence length of such a laser would be longer than the size of the trapped condensate just as the coherence length of a cw optical laser is longer than the laser cavity.
13. G. Moy, J. Hope, C. Savage, Phys. Rev. A 55, 3631 (1997).
14. M. A. Edwards, C. W. Clark, K. Burnett, S. L. Rolston, W. D. Phillips, J. Phys. B, in press.
15. M. Kozuma et al., Phys. Rev. Lett. 82, 871 (1999).
16. 1/2π = 360 Hz.
17. W. Petrich, M. H. Anderson, J. R. Ensher, I. A. Cornell, Phys. Rev. Lett. 74, 3352 (1995).
18. Atoms in the state m = -1 are trapped by the magnetic fields, whereas those in state m = +1 are antitrapped. The state m = 0 does not feel the confining potential of the magnetic trap.
19. This was done by switching off the trap and measuring the rate of the mean-field-driven ballistic expansion of the condensate at long times (>10 ms).
20. All uncertainties reported in this paper are 1-SD combined statistical and systematic uncertainties.
21. For frequency stability, both beams are derived from a single dye laser with the frequency difference controlled by two acousto-optical modulators.
22. 2| = k. Therefore, P = 1.99ℏk ≈ 2ℏk.
23. initial = -1 is the only magnetically trapped state.
24. Assuming that the scattering lengths among all m states are the same, this can be derived from expressions found in [F. Dalfovo, S. Giorgini, L. P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 2 (1999)]. The energy needed to add one atom is μ, which has a magnetic contribution of 3/7 ν and a mean-field contribution of 4/7 μ. If a small number of atoms are ouput-coupled to m = 0, a state that is not magnetically trapped, their release energy will simply be 4/7 μ, or twice the average release energy of 2/7 μ for the whole condensate.
25. In addition, the longitudinal momentum width is reduced by about the same factor because of kinematic compression.
26. The characteristic time during which the mean field potential energy turns into kinetic energy in the released BEC is 1/ω̄ (in our case about 6 ms), where ω̄ is the geometric mean of the three trapping frequencies. For our two-photon Raman transition the characteristic time scale for leaving the region of the condensate is 300 μs.
27. This is because our TOP field rotates in x̂-ẑ plane, which includes the direction of gravity.
28. The power quoted was the average over a 3-mm-diameter aperture in the center of a somewhat inhomogeneous 7-mm beam. These powers were empirically chosen to produce good output coupling.
29. The resonance frequency, for the Δm = 2 four-photon transition discussed later, was found to be 6.15(5) MHz, in good agreement with the calculated value of 6.0(2) MHz based on measurements of the trapping magnetic fields. This additional detuning of 2 × 250 kHz = 500 kHz from the four-photon resonance frequency is large compared with the Fourier width of the Raman pulse and results in a suppression of coupling to the 4ℏkẑ, m = +1 state.
30. A stimulated Raman transition that changes the momentum state of an atom but does not change the internal energy state can be viewed as Bragg diffraction (11); see also P. J. Martin, B. G. Oldaker, A. H. Miklich, D. E. Pritchard, Phys. Rev. Lett. 60, 515 (1988).
31. Because of our choice of applying the Raman beams along the quadrupole axis of the trap (ẑ), the trajectory of the output-coupled atoms (initially along ẑ) lies in the x̂-ẑ plane because gravity is along x̂. This is the plane of the rotating magnetic field zero and so the atoms will, at some point in time, cross this circle of death.
32. In the case of θ - 180° the recoil momentum from a first-order Raman transition is exactly 2ℏkẑ, which corresponds to a frequency of 100.1 kHz.
33. This was confirmed in a separate experiment, which looked at the interference of two clouds of atoms diffracted out of the condensate.
34. If the output coupling process were made continuous, by using an optical dipole or magnetic trap with no time-dependent magnetic fields, such coupling would not occur because the Fourier width of the light pulse could be made arbitrarily small. It would therefore be a simple matter to make a continuous Raman output coupler in such a case.
35. M. R. Andrews et al., Science 273, 637 (1997).
36. Supported in part by the Office of Naval Research and NASA. M.K. acknowledges the support of the Japanese Society for the Promotion of Science for Young Scientists. We thank C. W. Clark, M. A. Edwards, and P. S. Julienne for their valuable comments and suggestions.