Phys. Rev. Lett. 102, 250402 (2009): Inelastic Collisions of a Fermi ...

PRL 102, 250402 (2009) PHYSICAL REVIEW LETTERS
week ending
26 JUNE 2009
resonance at B ¼ 877 G, we find K 3 ¼ 3:5 0:9
10 28 cm 6 =s at hx 2 i=x 2 F ¼ 1:9 and K 3 ¼ 1:9 0:3
10 28 cm 6 =s at hx 2 i=x 2 F ¼ 0:8. In this case, K 3ðhx 2 i=
x 2 F ¼ 1:9Þ=K 3ðhx 2 i=x 2 F
¼ 0:8Þ ¼1:8 0:6, while the
ratio of the mean square widths is 1:9=0:8 ¼ 2:4. For
data taken below resonance at a magnetic field of 780 G
at hx 2 i=x 2 F ¼ 2:1, we find K 3 ¼ð17:3 3:2Þ
10 28 cm 6 =s. Athx 2 i=x 2 F ¼ 0:9, we obtain K 3 ¼ð9:4
3:1Þ10 28 cm 6 =s. Then K 3 ðhx 2 i=x 2 F ¼ 1:8Þ=
K 3 ðhx 2 i=x 2 F
¼ 0:9Þ ¼1:8 0:7, while the ratio of the
mean square widths is 2:1=0:9 ¼ 2:3, again consistent
with linear scaling with energy [14].
We observe two-body loss rates at low energy
hx 2 i=x 2 F
1, in addition to the three-body rate. In contrast,
at high energy, hx 2 i=x 2 F ’ 2, we find K 2 ¼ 0. At
780 G we obtain K 2 ¼ð0:57 0:22Þ10 14 cm 3 =s at
hx 2 i=x 2 F
¼ 0:9. On the BEC side of the Feshbach resonance,
we expect that two-body inelastic collisions arise
from molecule-atom or molecule-molecule [17]. We also
observe a two-body rate in the unitary regime at B ¼
823 G for E =E F ¼ 0:7 as noted above, K 2 ¼ð0:42
0:16Þ10 14 cm 3 =s. This is reasonable, since at low
energy, pair-atom or pair-pair inelastic collisions are possible.
Therefore, both two-body decay and three-body
decay processes can play a role in the atom loss. Above
the Feshbach resonance, we do not observe a two-body
decay process for 1=ðk F aÞ 0:04, i.e., B>848 G.
This suggests that no pairs are formed for B>848 G at
the lowest energy E =E F ¼ 0:7 we achieve.
In conclusion, we have measured two- and three-body
inelastic collision rates for a Fermi gas near a Feshbach
resonance. The study of the two-body rate is quite interesting.
Below resonance, it is known that inelastic atommolecule
or molecule-molecule collisions arise from decay
to lower molecular vibrational states. Since the crossover
regime involves tightly bound pairs, it is not farfetched to
suggest that inelastic processes near and just above resonance
arise from collisions involving correlated pairs. It is
now accepted that the unitary Fermi gas system has preformed
pairs [24], which exist at temperatures above the
superfluid transition. These pairs share properties of
Cooper pairs (they do not exist in free space) but they are
small enough to behave much like molecules. Hence, a
decay of a pair to a bound molecular state appears reasonable
conjecture. That fact that the two-body rate just below
resonance (molecular regime) is similar to the rate at
resonance (no bound molecules) supports this conjecture,
as does the vanishing of the two-body rate at high temperature.
In this case, a many-body theory of inelastic
collisions will be needed to replace the few-body theory
that is valid far from resonance. The investigation of the
energy (or temperature [21]) dependence of K 3 and K 2 ,
will be an important topic for future work.
This research is supported by the Physics Divisions of
the Army Research Office and the National Science
Foundation, and the Chemical Sciences, Geosciences,
and Biosciences Division of the Office of Basic Energy
Sciences, Office of Science, U.S. Department of Energy.
We are indebted to Le Luo and Bason Clancy for help in
the initial stages of this work.
*jet@phy.duke.edu
[1] E. Tiesinga, A. J. Moerdijk, B. J. Verhaar, and H. Stoof,
Phys. Rev. A 46, R1167 (1992).
[2] E. Tiesinga, B. J. Verhaar, and H. Stoof, Phys. Rev. A 47,
4114 (1993).
[3] J. L. Roberts, N. R. Claussen, S. L. Cornish, and C. E.
Wieman, Phys. Rev. Lett. 85, 728 (2000).
[4] C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, Phys.
Rev. Lett. 90, 053201 (2003).
[5] C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. 92,
083201 (2004).
[6] K. Dieckmann, C. A. Stan, S. Gupta, Z. Hadzibabic, C. H.
Schunck, and W. Ketterle, Phys. Rev. Lett. 89, 203201
(2002).
[7] T. Bourdel, L. Khaykovich, J. Cubizolles, J. Zhang,
F. Chevy, M. Teichmann, L. Tarruell, S. J. J. M. F.
Kokkelmans, and C. Salomon, Phys. Rev. Lett. 93,
050401 (2004).
[8] K. M. O’Hara, S. L. Hemmer, M. E. Gehm, S. R. Granade,
and J. E. Thomas, Science 298, 2179 (2002).
[9] S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod.
Phys. 80, 1215 (2008).
[10] E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland,
E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 79,
337 (1997).
[11] E. Braaten and H.-W. Hammer, Phys. Rep. 428, 259
(2006).
[12] P. Bedaque, E. Braaten, and H.-W. Hammer, Phys. Rev.
Lett. 85, 908 (2000).
[13] B. Esry, C. Greene, and J. Burke, Phys. Rev. Lett. 83, 1751
(1999).
[14] J. P. D’Incao and B. D. Esry, Phys. Rev. Lett. 94, 213201
(2005).
[15] E. Nielsen and J. Macek, Phys. Rev. Lett. 83, 1566
(1999).
[16] D. S. Petrov, Phys. Rev. A 67, 010703(R) (2003).
[17] D. S. Petrov, C. Salomon, and G. V. Shlyapnikov, Phys.
Rev. Lett. 93, 090404 (2004).
[18] P. Massignan and H. T. C. Stoof, Phys. Rev. A 78, 030701
(R) (2008).
[19] K. Helfrich and H.-W. Hammer, arXiv:0902.3410v1.
[20] J. E. Thomas, Phys. Rev. A 78, 013630 (2008).
[21] L. Luo and J. E. Thomas, J. Low Temp. Phys. 154, 1
(2009).
[22] F. Werner, Phys. Rev. A 78, 025601 (2008).
[23] M. Bartenstein, A. Altmeyer, S. Riedl, R. Geursen,
S. Jochim, C. Chin, J. H. Denschlag, R. Grimm,
A. Simoni, E. Tiesinga, C. J. Williams, and P. S.
Julienne, Phys. Rev. Lett. 94, 103201 (2005).
[24] Q. Chen, J. Stajic, S. Tan, and K. Levin, Phys. Rep. 412, 1
(2005).
250402-4