We study the structure of a Bose-condensed gas after quenching interactions to unitarity. Using the method of cumulants, we decompose the evolving gas in terms of clusters. Within the quantum depletion we observe the emergence of two-body clusters bound purely by many-body effects, scaling continuously with the atomic density. As the unitary Bose gas forms, three-body Efimov clusters are first localized and then sequentially absorbed into the embedded atom-molecule scattering continuum of the surrounding depletion. These results motivate future experimental probes of a quenched Bose-condensate during evolution at unitarity.

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We study a degenerate Bose gas quenched to unitarity by solving a many-body model including three-body losses and correlations up to second order. As the gas evolves in this strongly interacting regime, the buildup of correlations leads to the formation of extended pairs bound purely by manybody effects, analogous to the phenomenon of Cooper pairing in the BCS regime of the Fermi gas. Through fast sweeps away from unitarity, we detail how the correlation growth and formation of bound pairs emerge in the fraction of unbound atoms remaining after the sweep, finding quantitative agreement with experiment. We comment on the possible role of higher-order effects in explaining the deviation of our theoretical results from experiment for slower sweeps and longer times spent in the unitary regime. though these findings, combined with studies of loss dy-52 namics in Refs. [10-12], are consistent with the univer-53 sality hypothesis, a macroscopic population of Efimov 54 trimers was observed in Ref. [11]. Understanding the 55 role of the Efimov effect [17, 18] and dynamics of higher-56 order correlations [19-21] in the quenched unitary Bose 57 gas remains however an ongoing pursuit in the commu-58 nity. 59 60The difficulties of probing the system at unitarity re-61 quire that experiments return to the more stable and 62 better-understood weakly-interacting regime. During the 63 course of the experiment, we have to distinguish differ-64 ent types of atomic pairs: (i) pairs of atoms with op-65 posite momentum, analogous to Cooper pairs in Fermi 66 gases, (ii) embedded dimers at unitarity whose size is de-67 termined by the mean interparticle separation, and (iii) 68 specific ramp, we find a molecular fraction ∼ 10%, which 472 is compatible with the experimental estimate in Ref. [12]. 473 By comparing three values A = {0.28, 0.20, 0.18} to the 474 0.3 µs/G experimental data we find that A = 0.20 pro-475 vides the best fit of the experimental results over the full 476 range of t hold considered in this work. For the slower 6 477 µs/G ramp, we find that A = 0.20 gives good agreement 478 at early-times until roughly t hold 0.5t n . We discuss 479 possible sources of this discrepancy at longer t hold at the 480 conclusion of this section. 481 Our results for N free over a range of 1/R are com-482 pared against the experimental findings in Ref. [12] as 483 shown in Fig. 5. The results shown in Fig. 5 are at 484 fixed t hold = 1.9t n , nearing the limit of validity of our 485 model [see Sec. II A]. The intuitive picture, discussed 486 in Secs. II B, II C and illustrated in Fig. 2 provides a 487 way to understand our results particularly at this later 488 time where the bound pairs at unitarity play a dom-489 inant role [see Fig. 3]. For smaller ramp rates, the 490 largest values of N free shown in Fig. 5 result from the 491 fast-sweep projection occurring further away from unitar-492 ity where the overlap between embedded dimers (φ D (k)) 493 with molecules (φ * (k)) becomes minimal. We find good 494 agreement with experiment only ...

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We consider the BCS-BEC crossover of a quantum Fermi gas at T = 0 in the presence of an energy-dependent Fano-Feshbach resonance, driving the system from broad to narrow limits. We choose a minimal microscopic potential reproducing the two-particle resonance physics in terms of the scattering length a and the effective range R * representing the resonance width, and solve the BCS mean-field equations varying a, R * and the density. We show that the condensate fraction manifests a universal behavior when the correlation length, measuring the pair size, is used as the crossover parameter. Generally, a negative effective range has the effect of stretching the crossover region between the two extreme regimes, as evidenced by the behavior of the chemical potential. These results can be useful in view of the more recent perspectives of realizing narrow resonances also by optical means and amenable as a base Quantum Monte Carlo simulations. a