We investigate the real-time buildup of short-range correlations in a nondegenerate ultracold Bose gas near a narrow Fano-Feshbach resonance. Using rapid optical control, we quench the closed-channel molecular energy to resonance on sub-microsecond timescales and track the evolution of the two-body contact through photo-dissociation losses. Repeated pulse sequences enhance sensitivity to early-time two-body losses and reveal long-lived coherence between atom pairs and molecular states. The observed dynamics are accurately reproduced by our dynamical two-channel zero-range theory, which explicitly accounts for the resonance's narrow width and finite closed-channel decay, establishing a predictive framework for correlation dynamics in quantum gases near Fano-Feshbach resonances.

A fundamental quantity characterizing Fermi gases with zero-range interactions is the three-body contact C_3, which determines several observables including the number of nearby triplets of fermions and the three-body loss rate in cold atom experiments, as shown in a companion article. Here, we compute C_3 to leading order in the non-degenerate limit for the homogeneous gas with negative or infinite scattering length a. At a=∞, using a wavefunction approach, we obtain the analytical expression of C_3, which has a remarkably slow 1/T^0.22728 dependence on the temperature T. In the Feynman diagram technique, which we use for a<0, the correct three-body short-distance correlations emerge only after a non-trivial cancellation between leading order two-body and three-body correlations, and the resulting power-law scaling comes from the large-wavevector tail of the 3-body T-matrix, which we derive inspired by the analytical solution of the three-body problem at the unitary limit.

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order N and plugged into the Dyson equation, which is then solved for the propagator G_NGN. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that G_NGN converges when N\to∞N→∞ to a limit G_∞\,G∞, which coincides with the exact physical propagator G_{exact}Gexact at small enough coupling, while G_∞ ≠ G_{exact}G∞≠Gexact at strong coupling. This follows from the findings of [Phys. Rev. Lett. 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the G_∞=G_{exact}G∞=Gexact and G_∞≠G_{exact}G∞≠Gexact regimes thanks to a criterion which does not require the knowledge of G_{exact}Gexact, as proposed in [Phys. Rev. B 93, 161102 (2016)].

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Riccardo Rossi, Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett. 119, 045701 (2017).PRLTAO0031-900710.1103/PhysRevLett.119.045701]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the Néel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O(3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U/t=4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.

We consider the resonant Fermi gas, that is, two-component fermions in three dimensions interacting by a short-range potential of large scattering length. We introduce a quantity, the three-body contact, that determines several observables. Within the zero-range model, the number of nearby fermion triplets, the large-momentum tail of the center-of-mass momentum distribution of nearby fermion pairs, as well as the large-momentum tail of the two-particle momentum distribution, are expressed in terms of the three-body contact. For a small finite interaction range, the formation rate of deeply bound dimers by three-body recombination, as well as the three-body contribution to the finite-range correction to the energy, are expressed in terms of the three-body contact and of a three-body parameter. This three-body parameter, which vanishes in the zero-range limit, is defined through the asymptotic behavior of the zero-energy scattering state at distances intermediate between the range and the two-body scattering length. In general, the three-body contact has different contributions labeled by spin and angular momentum indices, and the three-body parameter can depend on those indices. We also include the generalization to unequal masses for $\uparrow$ and $\downarrow$ particles. With respect to the relation between three-body loss rate and number of nearby triplets stated in [Petrov, Salomon and Shlyapnikov, PRL 93, 090404 (2004)], the present work adds a derivation, expresses the proportionality factor in terms of the three-body parameter, and includes the general case where there are several contributions to the three-body contact and several three-body parameters.

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Phys. Rev. Lett. 119, 045701 (2017)]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the N´eel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O (3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U/t =4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.

We demonstrate that summation of connected diagrams to high order starting from a BCS hamiltonian is a viable generic unbiased approach for strongly correlated fermions in superconducting or superfluid phases. For the 3D attractive Hubbard model in a strongly correlated regime, we observe convergence of the diagrammatic series, evaluated up to 12 loops thanks to the connected determinant diagrammatic Monte Carlo algorithm. Our study includes the polarized regime, where conventional quantum Monte Carlo methods suffer from the fermion sign problem. Upon increasing the Zeeman field, we observe the first-order superconducting-to-normal phase transition at low temperature, and a thermally activated polarization of the superconducting phase well described by quasiparticle theory.

We introduce a simple determinant diagrammatic Monte Carlo algorithm to compute the ground-state properties of a particle interacting with a Fermi sea through a zero-range interaction. The fermionic sign does not cause any fundamental problem when going to high diagram orders, and we reach order N = 30. The data reveal that the diagrammatic series diverges exponentially as (-1/R)(N) with a radius of convergence R < 1. Furthermore, on the polaron side of the polaron-dimeron transition, the value of R is determined by a special class of three-body diagrams, corresponding to repeated scattering of the impurity between two particles of the Fermi sea. A power-counting argument explains why finite R is possible for zero-range interactions in three dimensions. Resumming the divergent series through a conformal mapping yields the polaron energy with record accuracy.

We provide a description of a diagrammatic Monte Carlo algorithm for the resonant Fermi gas in the normal phase. Details are given on the diagrammatic framework, Monte Carlo moves, and incorporation of ultraviolet asymptotics. Apart from the self-consistent bold scheme, we also describe a non-self-consistent scheme, for which the ultraviolet treatment is more involved.

We demonstrate that a summing up series of Feynman diagrams can yield unbiased accurate results for strongly correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of nonrelativistic fermions in three-dimensional continuous space. Diagrams are built from partially dressed or fully dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient.

A key quantity in strongly interacting resonant Fermi gases is the contact C, which characterizes numerous properties such as the momentum distribution at large momenta or the pair correlation function at short distances. The temperature dependence of C was measured at unitarity, where existing theoretical predictions differ substantially even at the qualitative level. We report accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, obtained by bold diagrammatic Monte Carlo and Borel resummation. Our results agree with experimental data within error bars and provide crucial benchmarks for the development of advanced theoretical treatments and precision measurements.

It is commonly believed that in quantum Monte Carlo approaches to fermionic many- body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with the Monte Carlo algorithm of [Rossi, arXiv:1612.05184], the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.

We study Efimov resonances via three-body loss in an ultracold two-component gas of fermionic $^{6}\mathrm{Li}$ and bosonic $^{133}\mathrm{Cs}$ atoms close to a Feshbach resonance at 843 G, extending results reported previously [Pires et al., Phys. Rev. Lett. 112, 250404 (2014)] to temperatures around 120 nK. The experimental scheme for reaching lower temperatures is based upon compensating the gravity-induced spatial separation of the mass-imbalanced gases with bichromatic optical dipole traps. We observe the first and second excited Li-Cs-Cs Efimov resonance in the magnetic field dependence of the three-body event rate constant, in good agreement with the universal zero-range theory at finite temperature [Petrov and Werner, Phys. Rev. A 92, 022704 (2015)]. Deviations are found for the Efimov ground state, and the inelasticity parameter $\ensuremath{\eta}$ is found to be significantly larger than those for single-species systems.

While bare diagrammatic series are merely Taylor expansions in powers of interaction strength, dressed diagrammatic series, built on fully or partially dressed lines and vertices, are usually constructed by reordering the bare diagrams, which is an a priori unjustified manipulation, and can even lead to convergence to an unphysical result [E. Kozik, M. Ferrero, and A. Georges, Phys. Rev. Lett. 114, 156402 (2015)]. Here we show that for a broad class of partially dressed diagrammatic schemes, there exists an action ${S}^{(\ensuremath{\xi})}$ depending analytically on an auxiliary complex parameter $\ensuremath{\xi}$, such that the Taylor expansion in $\ensuremath{\xi}$ of correlation functions reproduces the original diagrammatic series. The resulting applicability conditions are similar to the bare case. For fully dressed skeleton diagrammatics, analyticity of ${S}^{(\ensuremath{\xi})}$ is not granted, and we formulate a sufficient condition for converging to the correct result.

Recently, Kozik, Ferrero and Georges discovered numerically that for a family of fundamental models of interacting fermions, the self-energy &Sgr; [ G ] ?> is a multi-valued functional of the fully dressed single-particle propagator G, and that the skeleton diagrammatic series &Sgr; bold [ G ] ?> converges to the wrong branch above a critical interaction strength. We consider the zero space-time dimensional case, where the same mathematical phenomena appear from elementary algebra. We also find a similar phenomenology for the fully bold formalism built on the fully dressed single-particle propagator and pair propagator.

Within the universal zero-range theory, we compute the three-body recombination rate to deep molecular states for two identical bosons resonantly interacting with each other and with a third atom of another species, in the absence of weakly bound dimers. The results allow for a quantitative understanding of loss resonances at finite temperature and, combined with experimental data, can be used for testing the Efimov universality and extracting the corresponding three-body parameters in a given system. Curiously, we find that the loss rate can be dramatically enhanced by the resonant heavy-heavy interaction, even for large mass ratios where this interaction is practically irrelevant for the Efimov scaling factor. This effect is important for analysing the recent loss measurements in the Cs-Li mixture.

By unitary Bose gas we mean a system composed of spinless bosons with s-wave interaction of infinite scattering length and almost negligible (real or effective) range. Experiments are currently trying to realize it with cold atoms. From the analytic solution of the three-body problem in a harmonic potential, and using methods previously developed for fermions, we determine the third cumulant (or cluster integral) b_3 and the third virial coefficient a_3 of this gas, in the spatially homogeneous case, as a function of its temperature and the three-body parameter R_t characterizing the Efimov effect. A key point is that, converting series into integrals (by an inverse residue method), and using an unexpected small parameter (the three-boson mass angle nu=pi/6), one can push the full analytical estimate of b_3 and a_3 up to an error that is in practice negligible.