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arXiv:cond-mat/0101445 · Physical Review Letters

Pauli Blocking of Collisions in a Quantum Degenerate Atomic Fermi Gas

Brian DeMarco, Scott B. Papp, D. S. Jin

Published Jun 11, 2001• 141 citations
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Abstract

We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin states of magnetically trapped 40K. The relative Fermi energies are adjusted by controlling the population in each spin state. Thermodynamic measurements reveal a resulting imbalance in the mean energy per particle between the two species, which is a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of 2 reduction in the effective collision cross section in the quantum degenerate regime.

DOI
10.1103/physrevlett.86.5409

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We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin states of magnetically trapped 40K. The relative Fermi energies are adjusted by controlling the population in each spin state. Thermodynamic measurements reveal a resulting imbalance in the mean energy per particle between the two species, which is a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of 2 reduction in the effective collision cross section in the quantum degenerate regime.
Transition rates between coupled states in a quantum system depend on the density of available final states. The radiative decay of an excited atomic state has been suppressed by reducing the density of electromagnetic vacuum modes near the atomic transition. Likewise, reducing the density of available momentum modes of the atomic motion when it is embedded inside a Fermi sea will suppress spontaneous emission and photon scattering rates. Here we report the experimental demonstration of suppressed light scattering in a quantum degenerate Fermi gas. We systematically measured the dependence of the suppression factor on the temperature and Fermi energy of a strontium quantum gas and achieved suppression of scattering rates by up to a factor of 2 compared with a thermal gas.
The Pauli exclusion principle forbids indistinguishable fermions from occupying the same quantum mechanical state. The implications of this are profound; for example, it accounts for the electronic shell structure of atoms. Here, we performed measurements on the scattering of light from ultracold ensembles of atoms. For a Fermi gas in the quantum degenerate regime, we observed a marked suppression in scattering compared with a similarly prepared Bose gas. The observed decrease in fluorescence and the corresponding increase in light transmission results from Pauli blocking, where Fermi-Dirac statistics limits the number of accessible states for a scattering atom in a large Fermi sea. Our work confirms a fundamental result on the optical response of quantum gases and may contribute to cooling and thermometry schemes.
The work described in this thesis can be divided into two parts. The first part is concerned with the production of degenerate Fermi gases and Bose-Fermi mixtures. The second part of the thesis describes studies of strongly interacting spin-mixtures of ultracold fermions. We have cooled a magnetically trapped spin-polarized 6Li Fermi gas into quantum degeneracy by sympathetic cooling with bosonic 23Na. In order to do this, we have converted our previously developed apparatus for Bose-Einstein condensation of 23Na into a two-species cooling facility. We have produced 6Li samples with up to 7 × 107 atoms at temperatures below 0.5TF , and up to 3× 107 atoms at temperatures as low as 0.05TF . Further, we have also produced stable quantum degenerate mixtures of 23Na and 6Li, with several million atoms of each species. In a second set of experiments, we have studied strongly interacting spin-mixtures of 6Li. The strength of interactions was resonantly controlled by applying a magnetic field and tuning to “Feshbach resonances”, which occur when the total energy of the colliding particles coincides with the energy of a bound molecular state. These studies are relevant for the continuing quest for a superfluid transition in a Fermi gas. By studying the inelastic decay of the cloud, we have experimentally identified two Feshbach resonances for the inter-state interactions of the two lowest ground states of 6Li. Most importantly, we found that the lifetime of the strongly interacting system is long enough to observe a superfluid transition in the future. The effects of the coherent collisions in 6Li spin-mixtures were studied using radiofrequency (RF) spectroscopy. We demonstrated the absence of mean field “clock shifts” in a two-state mixture of fermions, and have introduced a three-level method to observe the interaction energy shifts. In the strongly interacting regime, near a Feshbach resonance, we have observed universal behavior of the interaction energy, independent of the value of the scattering length. Finally, we have theoretically studied the effects of Pauli blocking during a free expansion of a degenerate Fermi gas. We have concluded that a strongly interacting normal gas will undergo a hydrodynamic expansion even at zero temperature, due to inefficiency of the Pauli suppression of collisions. Therefore, the already observed hydrodynamic expansion cannot be conclusively interpreted as a signature of superfluidity. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics
Pauli blocking of spontaneous emission by a single excited-state atom has been predicted to be dramatic at low temperature when the Fermi energy E F exceeds the recoil energy E R . The photon scattering rate of a ground-state Fermi gas can also be suppressed by occupation of the final states accessible to a recoiling atom; however, suppression is diminished by scattering events near the Fermi edge. We analyse two new approaches to improve the visibility of Pauli blocking in a trapped Fermi gas. Focusing the incident light to excite preferentially the high-density region of the cloud can increase the blocking signature by 14%, and is most effective at intermediate temperature. Spontaneous Raman scattering between imbalanced internal states can be strongly suppressed at low temperature, and is completely blocked for a final state E F > 4 E R in the high imbalance limit.
Spin-polarized samples and spin mixtures of quantum degenerate fermionic atoms are prepared in selected excited Bloch bands of an optical checkerboard square lattice. For the spin-polarized case, extreme band lifetimes above 10 s are observed, reflecting the suppression of collisions by Pauli's exclusion principle. For spin mixtures, lifetimes are reduced by an order of magnitude by two-body collisions between different spin components, but still remarkably large values of about 1 s are found. By analyzing momentum spectra, we can directly observe the orbital character of the optical lattice. The observations demonstrated here form the basis for exploring the physics of Fermi gases with two paired spin components in orbital optical lattices, including the regime of unitarity.
The observation of Pauli blocking of atomic spontaneous decay via direct measurements of the atomic population requires the use of long-lived atomic gases where quantum statistics, atom recoil, and cooperative radiative processes are all relevant. We develop a theoretical framework capable of simultaneously accounting for all these effects in the many-body quantum degenerate regime. We apply it to atoms in a single 2D pancake or arrays of pancakes featuring an effective Λ level structure (one excited and two degenerate ground states). We identify a parameter window in which a factor of 2 extension in the atomic lifetime clearly attributable to Pauli blocking should be experimentally observable in deeply degenerate gases with ∼10^{3} atoms. We experimentally observe a suppressed excited-state decay rate, fully consistent with the theory prediction of an enhanced excited-state lifetime, on the ^{1}S_{0}-^{3}P_{1} transition in ^{87}Sr atoms.