Abstract

We describe several experimental studies of Bose-Einstein condensation in a dilute gas of sodium atoms. These include studies of static and dynamic behavior of the condensate, and of its coherence properties.

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References

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  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor", Science 269, 198 (1995).
    [CrossRef] [PubMed]
  2. K. B. Davis, M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Bose-Einstein condensation in a gas of sodium atoms", Phys. Rev. Lett. 75, 3969 (1995).
    [CrossRef] [PubMed]
  3. C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number", Phys. Rev. Lett. 78, 985 (1997).
    [CrossRef]
  4. K. Huang, "Imperfect Bose Gas", in Studies in Statistical Mechanics, vol. II, edited by J. de Boer and G. E. Uhlenbeck (North-Holland, Amsterdam, 1964) p. 3.
  5. A. Griffin, D. W. Snoke, and S. Stringari (editors), Bose-Einstein Condensation (Cambridge University Press, Cambridge, 1995).
  6. K. Huang, Statistical Mechanics, second edition (Wiley, New York, 1987).
  7. M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, "Bose-Einstein condensation in a tightly confining dc magnetic trap", Phys. Rev. Lett. 77, 416 (1996).
    [CrossRef] [PubMed]
  8. Background information for the 1997 Nobel prize in physics for laser cooling, http://www.nobel.se/announcement-97/phyback97.html
  9. Links to research groups with atom traps, http://www-atoms.physics.wisc.edu/OtherSites.html
  10. C. G. Townsend, N. J. van Druten, M. R. Andrews, D. S. Durfee, D. M. Kurn, M. -O. Mewes, and W. Ketterle, "Bose-Einstein condensation of a weakly-interacting gas", in Ultracold Atoms and Bose-Einstein-Condensation, 1996, K. Burnett, ed. , OSA Trends in Optics and Photonics Series, Vol. 7 (Optical Society of America, Washington D. C. , 1996) p. 2.
  11. Indirect evidence was reported in: C. C. Bradley, C. A. Sackett, J. J. Tollet, and R. G. Hulet, "Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions", Phys. Rev. Lett. 75, 1687 (1995).
    [CrossRef] [PubMed]
  12. W. Ketterle, M. R. Andrews, K. B. Davis, D. S. Durfee, D. M. Kurn, M. -O. Mewes, and N. J. van Druten, "Bose-Einstein condensation of ultracold atomic gases", Phys. Scr. T66, 31 (1996).
    [CrossRef]
  13. BEC home page of the Georgia Southern University, http://amo.phy.gasou.edu/bec.html
  14. Home page of our group, http://amo.mit.edu/~bec
  15. N. J. van Druten, C. G. Townsend, M. R. Andrews, D. S. Durfee, D. M. Kurn, M. -O. Mewes, and W. Ketterle, "Bose-Einstein condensates - a new form of quantum matter", Czech. J. Phys. 46 (S6), 3077 (1996).
    [CrossRef]
  16. D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Quantitative Studies of Bose-Einstein Condensation in a Dilute Atomic Vapor", Czech. J. Phys. 46 (S6), 3070 (1996).
    [CrossRef]
  17. C. A. Sackett, C. C. Bradley, M. Welling, and R. G. Hulet, "Bose-Einstein Condensation of Lithium", Braz. J. Phys. 27, 154 (1997).
  18. N. P. Proukakis, K. Burnett, M. Edwards, R. J. Dodd, and C. W. Clark, "Theory of Bose-Einstein condensed trapped atoms", in Ultracold Atoms and Bose-Einstein-Condensation, 1996, K. Burnett, ed. , OSA Trends in Optics and Photonics Series, Vol. 7 (Optical Society of America, Washington D. C. , 1996) p. 14.
  19. A. Einstein, "Quantentheorie des einatomigen idealen Gases. II", Sitzungsber. K. Preuss. Akad. Wiss. Phys. Math. Kl, 3 (1925).
  20. M. R. Andrews, M. -O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Non-Destructive Observation of a Bose Condensate", Science 273, 84 (1996).
    [CrossRef] [PubMed]
  21. M. R. Andrews, D. M. Kurn, H. -J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, "Propagation of sound in a Bose-Einstein condensate", Phys. Rev. Lett. 79, 553 (1997).
    [CrossRef]
  22. E. Hecht, Optics, 2nd edition (Addison-Wesley, Reading, 1989).
  23. Y. Castin and R. Dum, "Bose-Einstein condensation in time dependent traps", Phys. Rev. Lett. 77, 5315 (1996).
    [CrossRef] [PubMed]
  24. A. Griffin, Excitations in a Bose-condensed liquid (Cambridge University Press, Cambridge, 1993).
    [CrossRef]
  25. D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Collective Excitations of a Bose-Einstein Condensate in a Dilute Gas", Phys. Rev. Lett. 77, 420 (1996).
    [CrossRef] [PubMed]
  26. M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, "Collective Excitations of a Bose-Einstein condensate in a Magnetic Trap", Phys. Rev. Lett. 77, 988 (1996).
    [CrossRef] [PubMed]
  27. S. Stringari, "Collective excitations of a trapped Bose-condensed gas", Phys. Rev. Lett. 77, 2360 (1996).
    [CrossRef] [PubMed]
  28. D. Stamper-Kurn, H. -J. Miesner, S. Inouye, M. R. Andrews, and W. Ketterle, "Excitations of a Bose-Einstein Condensate at Non-Zero Temperature: A Study of Zeroth, First, and Second Sound", Phys. Rev. Lett. (1998), submitted.
  29. D. S. Jin, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, "Temperature-Dependent Damping and Frequency Shifts in Collective Excitations of a Dilute Bose-Einstein Condensate", Phys. Rev. Lett. 78, 764 (1997).
    [CrossRef]
  30. H. M. Wiseman, "Defining the (atom) laser", Phys. Rev. A 56, 2068 (1997).
    [CrossRef]
  31. D. Kleppner, Phys. Today, Aug. 1997, p. 11; Jan. 1998, p. 90.
  32. M. -O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, "Output coupler for Bose-Einstein condensed atoms", Phys. Rev. Lett. 78, 582 (1997).
    [CrossRef]
  33. P. W. Anderson, "Measurement in Quantum Theory and the Problem of Complex Systems", in The Lesson of Quantum Theory, J. d. Boer, E. Dal, and O. Ulfbeck, ed. (Elsevier, Amsterdam, 1986) p. 23.
  34. J. Javanainen and S. M. Yoo, "Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms", Phys. Rev. Lett. 76, 161 (1996).
    [CrossRef] [PubMed]
  35. M. R. Andrews, C. G. Townsend, H. -J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Observation of interference between two Bose condensates", Science 275, 637 (1997).
    [CrossRef] [PubMed]
  36. W. Ketterle and H. -J. Miesner, "Coherence properties of Bose-Einstein condensates and atom lasers", Phys. Rev. A 56, 3291 (1997).
    [CrossRef]
  37. E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, "Coherence, Correlations, and Collisions: What One Learns About Bose-Einstein Condensates form Their Decay", Phys. Rev. Lett. 79, 337 (1997).
    [CrossRef]
  38. P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzazewski, "Fourth Statistical Ensemble for the Bose-Einstein Condensate", Phys. Rev. Lett. 79, 1789 (1997).
    [CrossRef]
  39. P. A. Ruprecht, M. J. Holland, K. Burnett, and M. Edwards, "Time-dependent solution of the nonlinear Schrdinger equation for Bose-condensed trapped neutral atoms", Phys. Rev. A 51, 4704 (1995).
    [CrossRef] [PubMed]
  40. Y. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, "Bose-Einstein condensation in trapped atomic gases", Phys. Rev. Lett. 76, 2670 (1996).
    [CrossRef] [PubMed]

Other

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor", Science 269, 198 (1995).
[CrossRef] [PubMed]

K. B. Davis, M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Bose-Einstein condensation in a gas of sodium atoms", Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef] [PubMed]

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number", Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

K. Huang, "Imperfect Bose Gas", in Studies in Statistical Mechanics, vol. II, edited by J. de Boer and G. E. Uhlenbeck (North-Holland, Amsterdam, 1964) p. 3.

A. Griffin, D. W. Snoke, and S. Stringari (editors), Bose-Einstein Condensation (Cambridge University Press, Cambridge, 1995).

K. Huang, Statistical Mechanics, second edition (Wiley, New York, 1987).

M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, "Bose-Einstein condensation in a tightly confining dc magnetic trap", Phys. Rev. Lett. 77, 416 (1996).
[CrossRef] [PubMed]

Background information for the 1997 Nobel prize in physics for laser cooling, http://www.nobel.se/announcement-97/phyback97.html

Links to research groups with atom traps, http://www-atoms.physics.wisc.edu/OtherSites.html

C. G. Townsend, N. J. van Druten, M. R. Andrews, D. S. Durfee, D. M. Kurn, M. -O. Mewes, and W. Ketterle, "Bose-Einstein condensation of a weakly-interacting gas", in Ultracold Atoms and Bose-Einstein-Condensation, 1996, K. Burnett, ed. , OSA Trends in Optics and Photonics Series, Vol. 7 (Optical Society of America, Washington D. C. , 1996) p. 2.

Indirect evidence was reported in: C. C. Bradley, C. A. Sackett, J. J. Tollet, and R. G. Hulet, "Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions", Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

W. Ketterle, M. R. Andrews, K. B. Davis, D. S. Durfee, D. M. Kurn, M. -O. Mewes, and N. J. van Druten, "Bose-Einstein condensation of ultracold atomic gases", Phys. Scr. T66, 31 (1996).
[CrossRef]

BEC home page of the Georgia Southern University, http://amo.phy.gasou.edu/bec.html

Home page of our group, http://amo.mit.edu/~bec

N. J. van Druten, C. G. Townsend, M. R. Andrews, D. S. Durfee, D. M. Kurn, M. -O. Mewes, and W. Ketterle, "Bose-Einstein condensates - a new form of quantum matter", Czech. J. Phys. 46 (S6), 3077 (1996).
[CrossRef]

D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Quantitative Studies of Bose-Einstein Condensation in a Dilute Atomic Vapor", Czech. J. Phys. 46 (S6), 3070 (1996).
[CrossRef]

C. A. Sackett, C. C. Bradley, M. Welling, and R. G. Hulet, "Bose-Einstein Condensation of Lithium", Braz. J. Phys. 27, 154 (1997).

N. P. Proukakis, K. Burnett, M. Edwards, R. J. Dodd, and C. W. Clark, "Theory of Bose-Einstein condensed trapped atoms", in Ultracold Atoms and Bose-Einstein-Condensation, 1996, K. Burnett, ed. , OSA Trends in Optics and Photonics Series, Vol. 7 (Optical Society of America, Washington D. C. , 1996) p. 14.

A. Einstein, "Quantentheorie des einatomigen idealen Gases. II", Sitzungsber. K. Preuss. Akad. Wiss. Phys. Math. Kl, 3 (1925).

M. R. Andrews, M. -O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Non-Destructive Observation of a Bose Condensate", Science 273, 84 (1996).
[CrossRef] [PubMed]

M. R. Andrews, D. M. Kurn, H. -J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, "Propagation of sound in a Bose-Einstein condensate", Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

E. Hecht, Optics, 2nd edition (Addison-Wesley, Reading, 1989).

Y. Castin and R. Dum, "Bose-Einstein condensation in time dependent traps", Phys. Rev. Lett. 77, 5315 (1996).
[CrossRef] [PubMed]

A. Griffin, Excitations in a Bose-condensed liquid (Cambridge University Press, Cambridge, 1993).
[CrossRef]

D. S. Jin, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Collective Excitations of a Bose-Einstein Condensate in a Dilute Gas", Phys. Rev. Lett. 77, 420 (1996).
[CrossRef] [PubMed]

M. -O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, "Collective Excitations of a Bose-Einstein condensate in a Magnetic Trap", Phys. Rev. Lett. 77, 988 (1996).
[CrossRef] [PubMed]

S. Stringari, "Collective excitations of a trapped Bose-condensed gas", Phys. Rev. Lett. 77, 2360 (1996).
[CrossRef] [PubMed]

D. Stamper-Kurn, H. -J. Miesner, S. Inouye, M. R. Andrews, and W. Ketterle, "Excitations of a Bose-Einstein Condensate at Non-Zero Temperature: A Study of Zeroth, First, and Second Sound", Phys. Rev. Lett. (1998), submitted.

D. S. Jin, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, "Temperature-Dependent Damping and Frequency Shifts in Collective Excitations of a Dilute Bose-Einstein Condensate", Phys. Rev. Lett. 78, 764 (1997).
[CrossRef]

H. M. Wiseman, "Defining the (atom) laser", Phys. Rev. A 56, 2068 (1997).
[CrossRef]

D. Kleppner, Phys. Today, Aug. 1997, p. 11; Jan. 1998, p. 90.

M. -O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, "Output coupler for Bose-Einstein condensed atoms", Phys. Rev. Lett. 78, 582 (1997).
[CrossRef]

P. W. Anderson, "Measurement in Quantum Theory and the Problem of Complex Systems", in The Lesson of Quantum Theory, J. d. Boer, E. Dal, and O. Ulfbeck, ed. (Elsevier, Amsterdam, 1986) p. 23.

J. Javanainen and S. M. Yoo, "Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms", Phys. Rev. Lett. 76, 161 (1996).
[CrossRef] [PubMed]

M. R. Andrews, C. G. Townsend, H. -J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Observation of interference between two Bose condensates", Science 275, 637 (1997).
[CrossRef] [PubMed]

W. Ketterle and H. -J. Miesner, "Coherence properties of Bose-Einstein condensates and atom lasers", Phys. Rev. A 56, 3291 (1997).
[CrossRef]

E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, "Coherence, Correlations, and Collisions: What One Learns About Bose-Einstein Condensates form Their Decay", Phys. Rev. Lett. 79, 337 (1997).
[CrossRef]

P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzazewski, "Fourth Statistical Ensemble for the Bose-Einstein Condensate", Phys. Rev. Lett. 79, 1789 (1997).
[CrossRef]

P. A. Ruprecht, M. J. Holland, K. Burnett, and M. Edwards, "Time-dependent solution of the nonlinear Schrdinger equation for Bose-condensed trapped neutral atoms", Phys. Rev. A 51, 4704 (1995).
[CrossRef] [PubMed]

Y. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, "Bose-Einstein condensation in trapped atomic gases", Phys. Rev. Lett. 76, 2670 (1996).
[CrossRef] [PubMed]

Supplementary Material (7)

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Figures (15)

Fig. 1.
Fig. 1.

Criterion for Bose-Einstein condensation. At high temperatures, a weakly interacting gas can be treated as a system of “billiard balls”. In a simplified quantum description, the atoms can be regarded as wavepackets with an extension Δx, approximately given by Heisenberg’s uncertainty relation Δx= ħ/Δp, where Δp denotes the width of the thermal momentum distribution. Δx is approximately equal to the thermal de Broglie wavelength λdB, the matter wavelength for an atom moving with the thermal velocity. When the gas is cooled down the de Broglie wavelength increases. At the BEC transition temperature, λdB becomes comparable to the distance between atoms, and the Bose condensates forms which is characterized by a macroscopic population of the ground state of the system. As the temperature approaches absolute zero, the thermal cloud disappears leaving a pure Bose condensate.

Fig. 2.
Fig. 2.

Observation of Bose-Einstein condensation by absorption imaging. Shown is absorption vs. two spatial dimensions. The Bose-Einstein condensate is characterized by its slow expansion observed after 6 msec time of flight. The left picture shows an expanding cloud cooled to just above the transition point; middle: just after the condensate appeared; right: after further evaporative cooling has left an almost pure condensate. The width of the images is 1.0 mm. The total number of atoms at the phase transition is about 7×105, the temperature at the transition point is 2 μK.

Fig. 3.
Fig. 3.

Formation of a Bose-Einstein condensate. Two-dimensional probe absorption images, after 6 msec time of flight, show the sharpness of the phase transition. This sequence includes the three images of Fig. 2. The evaporative cooling was induced by an externally applied rf field. As the final rf frequency (labeled on the plots) was lowered, lower temperatures and higher phase space densities were reached. The cloud at the start of the animation had a temperature of about 5 μK. Above the phase transition (frequency >700 kHz) the clouds expanded spherically, as expected for a normal thermal distribution. As the frequency was reduced, the spherical cloud shrank in size, due to the lower temperatures reached. Below the transition point (frequency <700 kHz, 2 μK) an elliptical core appeared, which is the signature of the condensate. As the frequency was lowered the spherical part became invisible, corresponding to a pure condensate. Finally, when the threshold for evaporation reached the bottom of the trap (around 300 kHz), the condensate itself was lost by evaporation. Note that the color scale here has been chosen to represent optical density (OD) instead of absorption (A), as used in the other images. The two are related by OD=-ln(1-A). The rf frequency displayed in the animation changes when a new original frame is displayed and stays constant when interpolated frames are shown. The size of the frame is 1.1 by 1.6 mm. [Media 1]

Fig. 4.
Fig. 4.

Direct observation of the formation of a Bose-Einstein condensate using dispersive light scattering (phase contrast images). The intensity of the scattered light is a measure of the density of atoms (integrated along the line-of-sight). The left picture shows the cloud slightly above the BEC transition temperature. When the temperature was lowered, a dense core formed in the center of the trap - the Bose condensate. Further cooling increased the condensate fraction to close to 100% (right).

Fig. 5.
Fig. 5.

Time-of-flight expansion of a Bose condensate. The first observations of BEC were made by suddenly turning off the trapping fields and allowing the atoms to expand ballistically. Absorption images were taken after a variable delay time. The earliest images show the pencillike shape of the initial cloud. In the early phase of the expansion, the clouds appeared larger than their true sizes due to complete absorption of the probe laser light. Between 10 and 25 msec, the isotropic expansion of the normal component was observed. After 15 msec, the slower strongly anisotropic expansion of the Bose condensate became visible. At 60 msec, the signal was lost because the clouds had fallen almost 2 cm due to gravity. They were no longer illuminated by an optical pumping beam, which transferred the atoms from the lower to the upper hyperfine state, where they are detected by absorption imaging. When the cloud has expanded to many times its original size, such time-of-flight images represent the velocity distribution of the released cloud (in this figure, this applies only to the radial expansion). The width of the field of view is 1.8 mm. [Media 2]

Fig. 6.
Fig. 6.

Observation of collective excitations. The first studies of collective excitations in a dilute Bose condensate were done using time-of-flight imaging. In this example, the condensate was driven by modulating the strength of the magnetic trap. Then, after the condensate oscillated freely for a variable amount of time, the trap was turned off allowing the condensate to ballistically expand. By stringing together many time-of-flight pictures, a movie was created which shows the free oscillation of the trapped condensate. For very long time-of-flight and an ideal gas, the observed shape oscillations reflect oscillations of the velocity distribution of the trapped condensate. In the case shown here, they depend on both the initial spatial and velocity distributions. From such data the frequency and damping rate of the excitation was determined. The width of the field of view is 3.3 mm. [Media 3]

Fig. 7.
Fig. 7.

Phase contrast images of the dipole oscillation. Using non-destructive techniques, the dipole oscillation was observed directly for a single trapped condensate. This oscillation is a collective “sloshing” of the entire cloud back and forth in the trap. The frames were taken with a separation of 10 msec between frames. The length of the condensate was 200 μm. From these images, the frequency of the dipole motion was determined to be 19 Hz.

Fig. 8.
Fig. 8.

Phase contrast images of the quadrupole-type shape oscillation. In this mode, the radial width and the axial length of the condensate oscillate out of phase. The images were taken of a single condensate at a rate of 200 frames per second. From this data, the frequency of the shape oscillation was determined to be 30 Hz.

Fig. 9.
Fig. 9.

“Real time” movie of the oscillations of a Bose-Einstein condensate. Frames in the movie were taken at a rate of 200 per second, and played back at 10 frames per second. Beginning in the first frame, the condensate was excited by a 3 cycle 30 Hz modulation of the trapping potential. Both the quadrupole-type “shape” oscillation (Fig. 8) and the dipole “sloshing” oscillation (Fig. 7) were excited. Near the end of the movie, the shape oscillation had damped away, but the undamped dipole oscillation continued. The damping time of the quadrupole-type mode has been determined to be about 250 msec. [Media 4]

Fig. 10.
Fig. 10.

The rf output coupler. Figure (a) shows a Bose condensate trapped in a magnetic trap. All the atoms have their (electron) spin up, i.e. parallel to the magnetic field. (b) A short pulse of rf radiation tilts the spins of the atoms. (c) Quantum-mechanically, a tilted spin is a superposition of spin up and down. Since the spin-down component experiences a repulsive magnetic force, the cloud is split into a trapped cloud and an out-coupled cloud. (d) Several output pulses can be extracted, which spread out and are accelerated by gravity.

Fig. 11.
Fig. 11.

The MIT atom laser operating at 200 Hz. The movie (field of view 1.8 mm × 3.9 mm) shows pulses of coherent sodium atoms coupled out from a Bose-Einstein condensate confined in a magnetic trap. Every five milliseconds, a short rf pulse rotated the magnetic moment of the trapped atoms, transferring a fraction of these atoms into a quantum state which is no longer confined (“non-magnetic”m=0 state). These atoms were accelerated downward by gravity and spread out. The atom pulses were observed by absorption imaging. Each of them contained between 105 and 106 atoms. [Media 5]

Fig. 12.
Fig. 12.

Top view of the atom laser. This movie shows a singe output pulse of the atom laser viewed from above with absorption imaging. The rf pulse used to outcouple atoms can put atoms into both of the untrapped magnetic states. This movie has finer time resolution than Fig. 11, allowing both the m=1 and m=0 outcoupled components to be observed. The m=1 component is strong field seeking, and is rapidly accelerated out of the magnetic trap. The m=0 component has very little interaction with the magnetic fields of the trap, so it expands almost ballistically and falls away from the camera under gravity, as seen in Fig. 11 (The lateral motion at the end of the top-view movie is due to the small angle between the probe light and the vertical axis). [Media 6]

Fig. 13.
Fig. 13.

Schematic setup for the observation of the interference of two Bose condensates, created in a double well potential. The two condensates were separated by a laser beam which exerted a repulsive force on the atoms. After switching off the trap, the condensates were accelerated by gravity, expanded ballistically, and overlapped. In the overlap region, a high-contrast interference pattern was observed by using absorption imaging. An additional laser beam selected absorbing atoms in a thin layer by optical pumping. This tomographic method prevented blurring of the interference pattern due to integration along the probe laser beam.

Fig. 14.
Fig. 14.

Two expanding condensates. The first frames show a phase contrast picture of two trapped condensates, followed by their ballistic expansion after the magnetic trap has been turned off (observed with resonant absorption imaging). In the early frames, the absorption was saturated (red color) and the separation between the condensates is not visible. Since the trapped clouds were much more tightly confined in the radial direction, their internal energy was released mainly in the radial direction during expansion. The two condensates overlapped due to the slow axial expansion. After 40 msec, an interference pattern was observed (Fig. 15). The period of the interference fringes is the matter wavelength associated with the relative motion of the two condensates. Fringes are not visible in this movie because of the lower resolution and because of the blurring due to line-of-sight integration across the cloud (Fig. 13). [Media 7]

Fig. 15.
Fig. 15.

Interference pattern of two expanding condensates observed after 40 msec time of flight. The width of the absorption image is 1.1 mm. The interference fringes have a spacing of 15 μm and are strong evidence for the long-range coherence of Bose-Einstein condensates.

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