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arXiv:cond-mat/0505740 · Physical Review B

Mott states under the influence of fermion-boson conversion

Fei Zhou

Published Dec 1, 2005• 17 citations
arXivHTMLPDF

Abstract

The author has studied the influence of fermion-boson conversion on Mott states near Feshbach resonances. It is demonstrated that Mott states are unstable with respect to fermion-boson conversion. A branch of collective modes in superfluids has been found, which involve antisymmetric phase oscillations in fermionic and bosonic channels and are always gapped. The low-energy quantum dynamics of a Fermi-Bose superfluid can be fully characterized by either an effective coupled $\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)$ quantum rotor Hamiltonian or a coupled $XXZ\ensuremath{\bigotimes}XXZ$ spin model.

DOI
10.1103/physrevb.72.220501

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The author has studied the influence of fermion-boson conversion on Mott states near Feshbach resonances. It is demonstrated that Mott states are unstable with respect to fermion-boson conversion. A branch of collective modes in superfluids has been found, which involve antisymmetric phase oscillations in fermionic and bosonic channels and are always gapped. The low-energy quantum dynamics of a Fermi-Bose superfluid can be fully characterized by either an effective coupled U(1)\ensuremath⨂U(1)\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)U(1)\ensuremath⨂U(1) quantum rotor Hamiltonian or a coupled XXZ\ensuremath⨂XXZXXZ\ensuremath{\bigotimes}XXZXXZ\ensuremath⨂XXZ spin model.
We study the quantum dynamics of superfluids of bosons hybridized with Cooper pairs near Feshbach resonances and the influence of fermion–boson conversion on Mott states. We derive a set of equations of motion which describe novel low energy dynamics in superfluids and obtain a new distinct branch of gapped collective modes in superfluids which involve anti-symmetric phase oscillations in fermionic and bosonic channels. We also find that Mott states in general are unstable with respect to fermion–boson conversion; particles become delocalized and the off-diagonal long-range order of superfluids can be developed when a finite conversion is present. We further point out a possible hidden order in Mott states. It is shown that the quantum dynamics of Fermi–Bose states can be characterized by either an effective coupled U (1) ⊗ U (1) quantum rotor Hamiltonian in a large- N limit or a coupled XXZ ⊗ XXZ spin Hamiltonian in a single-orbit limit.
We discuss the phase transitions of fermions in one dimension with a narrow Feshbach resonance described by the boson–fermion resonance model. By means of the bosonization technique, we derive a low-energy Hamiltonian of the system and show that a strongly correlated state exists, where the order parameters of the Bose condensation and superfluidity decay with the same critical exponent. We also show that density fluctuations near the Fermi wavevector are strongly suppressed as a consequence of a spin gap and a gap against the formation of phase slips. We find a Luther–Emery point where the phase slips and the spin excitations can be described in terms of pseudofermions, providing closed form expressions of the density–density correlations and the spectral functions. The relevance of our results for experiments with ultracold atomic gases subject to one-dimensional confinement is also discussed.
We study the ground-state properties of one-dimensional mixtures of bosonic and fermionic atoms resonantly coupled to fermionic Feshbach molecules. When the particle densities of fermionic atoms and Feshbach molecules differ, the system undergoes various depletion transitions between binary and ternary mixtures as a function of the detuning parameter. However, when the particle densities of fermionic atoms and Feshbach molecules are identical, the molecular conversion and disassociation processes induce a gap in a sector of low-energy excitations, and the remaining system can be described by a two-component Tomonaga-Luttinger liquid. Using a bosonization scheme, we derive the effective low-energy Hamiltonian for the system, which has a similar form as that of the two-chain problem of coupled Tomonaga-Luttinger liquids. With the help of improved perturbative renormalization group analysis of the latter problem, we determine the ground-state phase diagram and find that it contains a phase dominated by composite superfluid or pairing correlations between the open and closed resonant channels.
We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.
Collective oscillations of superfluid mixtures of ultracold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation models and ordinary differential equation models for the dynamics. An application to the recent experiment with fermionic 6Li^{6}\mathrm{Li}6Li and bosonic 7Li^{7}\mathrm{Li}7Li atoms, which approximately have the same masses, is discussed.
Near Feshbach resonances, n | a | 3 ≫ 1, systems of Bose and Fermi particles become strongly interacting/dense. In this unitary limit both bosons and fermions have very different properties than in a dilute gas, e.g., the energy per particle approaches a value ℏ 2 n 2/3 / m times a universal many-body constant. Calculations based upon an approximate Jastrow wavefunction can quantitatively describe recent measurements of trapped Bose and Fermi atoms near Feshbach resonances. The pairing gap between attractive fermions also scales as Δ ∼ ℏ 2 n 2/3 / m near Feshbach resonances and is a large fraction of the Fermi energy—promising for observing BCS superfluidity in traps. Pairing undergoes several transitions depending on interaction strength and the number of particles in the trap and can also be compared with pairing in nuclei.