We model collisionless collective conversion of a degenerate Fermi gas of atoms into bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a classical field and seeding the pairing amplitudes with random phases. A dynamical instability of the Fermi sea against association with molecules drives the conversion. The model qualitatively reproduces several experimental observations [Regal et al., Nature (London), (2003)]. We predict that the initial temperature of the Fermi gas sets the limit for the efficiency of atom-molecule conversion.

We theoretically examine the creation of a Fermi-degenerate gas of molecules by considering a photoassociation or Feshbach resonance applied to a degenerate Bose-Fermi mixture of atoms. This problem raises interest because, unlike bosons, fermions in general do not behave cooperatively, so that the collective conversion of a degenerate gas atoms into a macroscopic number of diatomic molecules is not to be expected. Nevertheless, we find that the coupled Fermi system displays collective Rabi-like oscillations and a rapid adiabatic passage between atoms and molecules, thereby mimicking Bose-Einstein statistics. Cooperative association of a degenerate mixture of Bose and Fermi gases could therefore serve as a shortcut to a degenerate gas of Fermi molecules.

We theoretically investigate Raman photoassociation of a degenerate Bose-Fermi mixture of atoms and the subsequent prospect for anomalous (Cooper) pairing between atoms and molecules. Stable fermionic molecules are created via free-bound-bound stimulated Raman adiabatic passage which, in contrast to purely bosonic systems, can occur in spite of collisions. With the leftover atomic condensate to enhance intrafermion interactions, the superfluid transition to atom-molecule Cooper pairs occurs at a temperature that is roughly an order of magnitude below what is currently feasible.PACS numbers: 03.75. Ss, 05.30.Fk, 74.20.Mn, Photoassociation occurs when two atoms absorb a laser photon [1], thereby jumping from the free twoatom continuum to a bound molecular state. Neutralatom statistics is determined by the number of neutrons in the nucleus-odd for fermions and even for bosons. Similarly, the sum of the total number of neutrons in the nuclei of the constituent atoms determines neutralmolecule statistics. Molecules formed by photoassociation of two fermions will accordingly result in a boson, whereas fermionic molecules are born of a boson and a fermion. Given degenerate Bose-Fermi atoms, two questions arise: Will the atoms photoassociate with into an arbitrary number of stable Fermi molecules? If so, is it possible to realize atom-molecule Cooper pairing?First introduced to explain superconductivity, anomalous quantum correlations between two degenerate electrons with equal and opposite momenta-Cooper pairsare due physically to an electron-electron attraction mediated by the exchange of lattice-vibration-generated phonons [2], and are a manifestation of fermionic superfluidity [3]. Anomalous pairing between different chemical species was immediately suggested to explain the larger excitation energy for nuclei with even rather than odd numbers of nucleons [4], although it turned out that interspecies pairing plays the dominant role. Today quantum matter optics offers a means to explore condensed-matter and nuclear physics by proxy, such as the pairing of fermions in atomic traps and nuclei [5].Here we investigate Raman photoassociation [6, 7, 8, can be negligible. Density fluctuations in the condensate leftover from the photoassociation process then replace the vibrating ion lattice of the superconductor [13], and the subsequent phonon exchange can enhance the intrafermion attraction. We find that a typical attraction is enhanced, but this enhancement is insufficient for a transition to atom-molecule Cooper pairs within reach of present ultracold technology.We model a Bose-Fermi mixture of atoms coupled by heteronuclear photoassociation to electronically-excited Fermi molecules, which is favored over homonuclear transitions for well resolved resonances [14]. The excited molecules are themselves coupled by a second laser to electronically stable molecules. The light-matter coupling due to laser 1 (2) is K + (Ω − ), and the intermediate (two-photon) laser detuning, basically the binding energy of the excited (stable)...

We theoretically examine two-color photoassociation of a Bose-Einstein condensate, focusing on the role of rogue decoherence in the formation of macroscopic atom-molecule superpositions. Rogue dissociation occurs when two zero-momentum condensate atoms are photoassociated into a molecule, which then dissociates into a pair of atoms of equal-and-opposite momentum, instead of dissociating back to the zero-momentum condensate. As a source of decoherence that may damp quantum correlations in the condensates, rogue dissociation is an obstacle to the formation of a macroscopic atom-molecule superposition. We study rogue decoherence in a setup which, without decoherence, yields a macroscopic atom-molecule superposition, and find that the most favorable conditions for said superposition are a density ρ ∼ 10 12 cm −3 and temperature T ∼ 10 −10 K.