Collective Excitations of a Degenerate Gas at the BEC-BCS Crossover

Bartenstein, M.; Altmeyer, A.; Riedl, Stefan; Jochim, Selim; Chin, Cheng; Denschlag, Johannes Hecker; Grimm, Rudolf

doi:10.1103/physrevlett.92.203201

Cited by 824 publications

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References 29 publications

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“…This finding could (at least partially) explain the absence of beyond-mean-field corrections on the bosonic side of the BCS-BEC crossover, recently reported in experiments with ultracold Fermi gases 16 .…”

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confidence: 77%

Comparison between a diagrammatic theory for the BCS-BEC crossover and quantum Monte Carlo results

2005

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Predictions for the chemical potential and the excitation gap recently obtained by our diagrammatic theory for the BCS-BEC crossover in the superfluid phase are compared with novel Quantum Monte Carlo results at zero temperature now available in the literature. A remarkable agreement is found between the results obtained by the two approaches.PACS numbers: 03.75. Ss, 03.75.Hh, 05.30.Jp The recent experimental realization of the BCS-BEC crossover with ultracold trapped Fermi atoms 1 has given impetus to theoretical investigations of this crossover. In a recent paper 2 , the t-matrix self-energy approach (originally conceived for the normal phase 3 ) was extended to the superfluid phase, aiming at improving the description of the BCS-BEC crossover by including pairing fluctuations on top of the BCS mean-field approach considered in Refs. 4 and 5.In this theory, the effects of the collective BogoliubovAnderson mode is explicitly included in the fermionic self-energy, thus generalizing the theory due to Popov for a weakly-interacting (dilute) superfluid Fermi gas 6 . The theory is based on a judicious choice of the fermionic self-energy, such that it reproduces the fermionic meanfield BCS behavior plus pairing fluctuations in the weakcoupling limit as well as the Bogoliubov description for the composite bosons which form in the strong-coupling limit. In the intermediate-coupling region of interest about the unitarity limit, where no small parameter exists to control the many-body approximations, the theory is able to capture the essential physics of the problem, as the excellent agreement with a previously available QMC calculation 7 at the unitarity point (k F a F ) −1 = 0 has already shown 8 , and as more extensively demonstrated by the present comparison with more recent QMC data 9,10 spanning the whole crossover region. The theory of Ref. 2 is completely ab initio and it contains no adjustable parameter. Although the comparison with QMC data is here limited to the zero-temperature limit where they are available, the predictions of the theory of Ref.

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confidence: 77%

Comparison between a diagrammatic theory for the BCS-BEC crossover and quantum Monte Carlo results

2005

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“…Such departures from the predicted binding energies are indeed observed [21] in high-precision Ramsey spectroscopy for 85 Rb. Similarly, recent collective-mode spectroscopy in 6 Li has revealed BCS-like behavior near threshold with reduced mode frequencies [26], quite different to that expected for a conventional molecular BEC.…”

Section: ͑5͒mentioning

confidence: 99%

Coherent molecular bound states of bosons and fermions near a Feshbach resonance

Drummond

Kheruntsyan

2004

Phys. Rev. A

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We analyze molecular bound states of atomic quantum gases near a Feshbach resonance. A simple, renormalizable field theoretic model is shown to have exact solutions in the two-body sector, whose binding energy agrees well with observed experimental results in both Bosonic and Fermionic cases. These solutions, which interpolate between BEC and BCS theories, also provide a more general variational ansatz for resonant superfluidity and related problems. Since these are many-body systems, it is useful to try to develop the simplest possible field-theoretic model that can explain their behavior. An essential feature of any correct many-body treatment is that the basic theory must be able to reproduce the physics of the two-body interactions. In this paper, we combine previous analytic solutions of a coherently coupled field theory [7-9] with an exact renormalization of the coupling constants [10], in order to obtain analytic predictions for the two-body bound states. This gives a unified picture of any Feshbach resonance experiment and related studies [7][8][9][10][11][12][13][14][15][16][17][18][19][20], provided a small number of observable parameters are available. The predictions will be compared with experimental data and with coupled-channel calculations.To quantitatively model these experiments, consider an effective Hamiltonian for the molecular field ͑⌿ 0 ͒ in the closed channel and the atomic fields ͑⌿ 1͑2͒ ͒ in the free-atom dissociation limit of the open channel:with the commutation (ϩ) or anticommutation (Ϫ) relation ͓⌿ i ͑x , t͒ , ⌿ j † ͑xЈ , t͔͒ ± = ␦ ij ␦͑x − xЈ͒ for Bosonic or Fermionic field operators ⌿ i , respectively. The free Hamiltonian Ĥ 0 includes the usual kinetic energy terms and the potential energies (including internal energies) due to the trap potential បV i ͑x͒, while U ij is the atom-atom, atom-molecule, and molecule-molecule coupling due to s-wave scattering. The atomic and molecular masses are m 1,2 and m 0 = m 1 + m 2 , andgives the bare energy detuning of the molecular state with respect to free atoms. Next, we consider a coherent process of Raman photoassociation or a magnetic Feshbach resonance coupling, giving rise to an overall effective Hamiltonian term in the homo-nuclear case (only with Bosons) [7,8],or, for the case of heteronuclear dimer formation involving either fermions or bosons [9],Here, is the bare atom-molecule coupling responsible for the conversion of free atom pairs into molecules and vice versa. The heteronuclear case can be applied to Fermionic atom pairs in different spin states (⌿ 1 , ⌿ 2 ) combining into a Bosonic molecule ͑⌿ 0 ͒, or pairs of Bosonic and Fermionic atoms combining into a Fermionic molecule, or else to a fully Bosonic case where the atom pairs are not identical. Bosonic homonuclear case. First we consider the fully Bosonic uniform case of Eq. (2), i.e., a single-species atomic BEC (with m 1 ϵ m) coupled to a molecular BEC, where the atomic background energy is chosen to be zero. We ignore inelastic collisions-which is a reasonable approximati...

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“…It indicates that the TF approximation of the kinetic energy density is a very good approximation for the experimental conditions of Ref. [11], N Ϸ 10 4 (inclusion of the OWD gives a negligible effect, Ͻ0.5%) [37][38][39][40][41]. It can be proved [24] that every solution of Eq.…”

Section: ͑3͒mentioning

confidence: 99%

Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

2004

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The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing ) is investigated in a single-equation approach to the time-dependent density-functional theory. Our results are in good agreement with recent experimental data in the BCS-BEC crossover regime.It is also shown that the calculated corrections to the hydrodynamic approximation may be important even for systems with a rather large number of atoms.

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Collective Excitations of a Degenerate Gas at the BEC-BCS Crossover

Cited by 824 publications

References 29 publications

Comparison between a diagrammatic theory for the BCS-BEC crossover and quantum Monte Carlo results

Comparison between a diagrammatic theory for the BCS-BEC crossover and quantum Monte Carlo results

Coherent molecular bound states of bosons and fermions near a Feshbach resonance

Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

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