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Formation Dynamics of a Fermion Pair Condensate PHYSICAL REVIEW LETTERS week ending PRL 94, 180401 (2005) 13 MAY 2005 Formation Dynamics of a Fermion Pair Condensate M. W. Zwierlein, C. H. Schunck, C. A. Stan, S. M. F. Raupach, and W. Ketterle Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA (Received 23 December 2004; published 9 May 2005) The dynamics of pair condensate formation in a strongly interacting Fermi gas close to a Feshbach resonance was studied. We employed a phase-shift method in which the delayed response of the many- body system to a modulation of the interaction strength was recorded. The observable was the fraction of condensed molecules in the cloud after a rapid magnetic field ramp across the Feshbach resonance. The measured response time was slow compared to the rapid ramp, which provides final proof that the molecular condensates reflect the presence of fermion pair condensates before the ramp. DOI: 10.1103/PhysRevLett.94.180401 PACS numbers: 03.75.Ss, 05.30.Fk Atomic Fermi gases close to a Feshbach resonance [1] servable is again the molecular condensate fraction after a offer the unique possibility of studying many-body phe- rapid sweep to the BEC side of the Feshbach resonance. Its nomena in a strongly interacting system with tunable in- sensitivity to changes in the scattering length on the BCS teractions. Recently a major focus has been on condensates side [6,7] arises through the dependence of the critical tem- of pairs of fermionic atoms [2–8]. By changing the mag- perature for pair condensation on the interaction strength. netic field, the interaction strength between atoms in two By showing that the delayed response time of the molecu- spin states can be varied. That way, condensates of either lar condensate fraction is long compared to the sweep tightly bound molecules or of extended pairs of fermions times used in the present and previous experiments, we in- can be created, whose size can become comparable or even fer that the observed condensates could not have been cre- larger than the interparticle spacing. The description of this ated during the rapid transfer and thus must originate from so-called BEC-BCS crossover [9] is an active frontier in preexisting fermion pair condensates. However, we do find many-body physics with still controversial interpretations evidence that condensed pairs are more likely to be trans- [10–13]. ferred into molecules than thermal pairs. Therefore, in con- The control of interactions via magnetic fields does not trast to assumptions made in previous work [6,7], the mo- only give access to very different physical regimes, it also lecular condensate fraction after the ramp may not equal allows one to apply a time-varying interaction strength the fraction of condensed atom pairs above resonance. [14,15] and to study the dynamics of a many-body system The experimental setup was the same as in our previous in novel ways. This was used in recent experiments in work [7]. A degenerate cloud of 6Li, sympathetically which molecular condensates were observed after a rapid cooled with 23Na, was loaded into an optical dipole trap field ramp from the BCS to the Bose-Einstein condensate to access a broad Feshbach resonance at 834 G [17,18] (BEC) side of the Feshbach resonance [6,7]. It was argued between the two lowest hyperfine states of 6Li, labeled j1i that if the ramp time was faster than the formation time of a and j2i. An equal mixture of these states was evaporatively molecular condensate, its presence after the sweep neces- cooled at 770 G using an exponential ramp-down of the sarily reflected a preexisting condensate of fermion pairs. optical trap to 15 mW. This resulted in an essentially pure However, without access to that formation time, secondary Bose-Einstein condensate of 3 106 molecules. An upper evidence was gathered, namely, the invariance of the con- limit for the temperature of the gas is T < 0:2, with the densate fraction under variations of the sweep rate [6] or of TF the density immediately before the ramp [7]. This excluded Fermi temperature TF given by the zero-temperature, ideal 1=3 simple models of the molecular condensate formation gas relation TF h! 3N , !=2 is the geometric mean during the ramp, but left room for more sophisticated of the trapping frequencies, and N is the total atom number. many-body effects. In particular, the time to cross the Next, the trap was recompressed to 25 mWp (trap frequen- Feshbach resonance in these experiments was not faster cies: x y 580 Hz, z 12:1Hz 0:2 B with the ÿ1 than the unitarity limited collision time / hE F , and there- magnetic field B in kG) and the magnetic field was adia- fore dynamics during the sweep could not be ruled out. batically increased in 500 ms to 1000 G, the starting point Here we present an experimental study of the formation for the following experiments. Here, in the wings of the dynamics of a fermion pair condensate on the BCS side of Feshbach resonance, the scattering length a was still suffi- the Feshbach resonance [16]. We employ a novel phase- ciently large and negative for the gas to be in the strongly shift method, which records the delayed response of the interacting regime, with kFjaj1:6 at a Fermi energy of many-body system to a modulation of the magnetic field EF 2:0 K and a Fermi wave number kF 1=2700a0. that changes periodically its interaction strength. The ob- The temperature at this point could therefore not be reli- 0031-9007=05=94(18)=180401(4)$23.00 180401-1 2005 The American Physical Society PHYSICAL REVIEW LETTERS week ending PRL 94, 180401 (2005) 13 MAY 2005 ably determined, but is expected to be significantly lower ramp did not follow the magnetic field modulation instan- than the one on the BEC side due to adiabatic cooling [19]. taneously, but lagged behind. At a Fermi energy of EF Subsequently, the magnetic field and thus the interaction 2 K, the peak condensate fraction was delayed by R strength in the gas were modulated at frequencies in the 500 100 s with respect to the magnetic field’s closest range of 100–500 Hz, and an amplitude of about 50 G [20]. approach to resonance [22]. This time scale was indepen- At a variable time t after the start of the modulation, the dent of the modulation frequency [compare Figs. 2 and fraction of condensed fermion pairs was recorded by time- 4(a), below]. This also rules out that our results are affected of-flight analysis. by the excitation of collective modes. R equals 130 times ÿ1 To identify fermionic condensates across the resonance the unitarity limited collision time, hE F 3:8 s. The region, we proceeded as in [6,7]. Immediately after the rapid magnetic field ramp utilized here and in [7] traversed release of the cloud from the optical potential, the magnetic the Feshbach resonance in less than 10 s, which is much field was switched to zero field (initial ramp rate smaller than R. 30 G=s), where further expansion of the cloud took This delay time can be interpreted as the relaxation time place. This rapid ramp out of the resonance region trans- of the fermionic condensate. In a normal Fermi gas of N formed large fermion pairs into deeply bound molecules particles at temperatures much smaller than the Fermi with high efficiency [21]. Figure 1 details the imaging temperature TF, relaxation occurs through collisions be- procedure used to determine molecular condensate frac- tween the thermally excited particles close to the Fermi tions and the number of unpaired atoms in each state after surface, whose number scales as N ’ N kBT . The number th EF the ramp. In our previous work, we showed that the con- of available scattering states again being proportional to densate fractions had a peak around the Feshbach reso- kBT EF , the relaxation time will be R ’ h 2 . In general, if nance and fell off on either side [7]. Here, this dependence EF kBT the Fermi surface is smeared out over an energy width E, was exploited to observe the delayed response of the the relaxation time is ’ h EF . This formula with E system to the magnetic field modulation on the BCS side. E2 Figure 2 shows the main result of this Letter: The should apply also to the superfluid state [23] when the gap condensate fraction in the molecular clouds after the rapid parameter is rapidly changed to a much smaller value. Generally, one would expect E to be the larger of and kBT. Using R 500 s, we obtain the estimate E 0:1EF which may set an upper bound for both temperature and pairing gaps. A decay is superimposed to the periodic modulation of the condensate fraction. It could be caused by heating due to the nonadiabaticity of the process. Another source of heating could be the excitation of the cloud via the small accompanying variation of the magnetic field curvature. 0.6 0.5 0.4 0.3 Magnetic Field [G] 0.2 840 Molecular Condensate Fraction 880 920 FIG. 1. Imaging of molecular condensates. The rapid ramp to 960 0 2 4 6 8 10 12 14 16 zero field after release from the trap created a cloud containing Time [ms] both molecules and unpaired atoms. A Stern-Gerlach field 1 gradient separated atoms (magnetic moment 3 B for states FIG. 2. Measurement of the relaxation time of fermionic pair j1i and j2i, respectively) from molecules, which are purely condensates.
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