Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session P36: Focus Session: BCS-BEC Physics in Fermi Gases |
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Sponsoring Units: DAMOP Chair: Nicolai Nygaard, NIST Room: LACC 510 |
Wednesday, March 23, 2005 11:15AM - 11:27AM |
P36.00001: Density Profiles of Strongly Interacting Trapped Fermi Gases Jelena Stajic, Qijin Chen, Kathryn Levin We study density profiles in trapped fermionic gases, near Feshbach resonances, at all $T \leq T_c$ and in the near-BEC and unitary regimes. The component profiles from noncondensed pairs, fermionic excitations and the condensate are also presented. As a consequence of noncondensed Cooper pairs, our profiles are in the unitary regime rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature. [Preview Abstract] |
Wednesday, March 23, 2005 11:27AM - 11:39AM |
P36.00002: Thermodynamics of ultracold fermions in traps in the strongly interacting regime Qijin Chen, Jelena Stajic, Kathryn Levin We discuss the entropy $S$, energy $E$ for trapped fermionic gases, over the entire range from BCS to BEC, and over all $T$ from below to above $T_c$. Our work, which is based on the conventional mean field ground state, shows that both ``bosonic" and fermionic excitations contribute to $S$, and that boson-fermion interactions are essential. Trap edge effects lead to low $T$ power law contributions for the fermions in the unitary and BCS regimes, while bosons contribute to $S$ with a $T^{3/2}$ dependence. Comparison with recent experiments by the Thomas group (cond-mat/0409283) shows very good quantitative agreement. This lays the groundwork for implementing thermometry in strongly interacting Fermi gases. \\ 1. Q.J. Chen, J. Stajic, and K. Levin, \textit{Thermodynamics of ultracold fermions in traps}, cond-mat/0411090; submitted to \textbf{Science}. \\ 2. J. Stajic, Q.J. Chen, K.Levin, \textit{Measuring condensates in fermionic superfluids via density profiles in traps}, cond-mat/0408104. \\ 3. Q.J. Chen, J. Stajic, S.N. Tan, K. Levin, \textit{BCS-BEC crossover: From high temperature superconductors to ultracold superfluids}, cond-mat/0404274. [Preview Abstract] |
Wednesday, March 23, 2005 11:39AM - 11:51AM |
P36.00003: Feshbach Molecule Formation in Finite-Temperature Quantum Gases James E. Williams, Nicolai Nygaard, Tetsuro Nikuni, Charles W. Clark An exciting development in the field of ultracold atomic gases is the ability to create diatomic molecules by adjusting a Feshbach resonance in the interatomic potential. An extraordinary application of this capability has been to dynamically traverse the BEC-BCS crossover in Fermi gases. While a great deal of attention has focused on equilibrium properties in the {\it{superfluid}} regime, a complete theoretical understanding of the dynamics of molecule formation in a {\it{normal}} gas is still lacking. In a recent article [Williams {\it{et al.}}, J. Phys. B: At. Mol. Opt. Phys. {bf{37}}, L351 (2004)], we presented coupled Boltzmann-like kinetic equations for the atoms and molecules. In this talk, we show that our theory can be used to understand why the molecular conversion efficiency increases as the temperature is lowered, as observed in a recent experiment [Hodby {\it{et al.}}, cond- mat/0411487]. [Preview Abstract] |
Wednesday, March 23, 2005 11:51AM - 12:03PM |
P36.00004: Phase Diagrams for a Fermi Gas with a Feshbach Resonance Tetsuro Nikuni, Nicolai Nygaard, James E. Williams, Charles W. Clark We calculate the phase diagram for a system of Fermi atoms coupled to bosonic molecules by a Feshbach resonance. This work extends the recent work [Williams et al., New J. Phys. 6, 123 (2004)] on the phase diagrams for an ideal gas mixture to include the effect of the resonant interactions using the mean-field theory. We show the paths traversed in the phase diagrams when the molecular energy is varied either suddenly or adiabatically, and discuss the adiabatic phase diagrams obtained in recent experiments on the BCS-BEC crossover. [Preview Abstract] |
Wednesday, March 23, 2005 12:03PM - 12:15PM |
P36.00005: Pairing of Opposite-Spin Fermions in the BCS-BEC Crossover Regime Javier von Stecher, Chris H. Greene We consider a pair of opposite spin fermions that interact with a degenerate Fermi gas, which is trapped in a spherical oscillator potential. We magnetically tune the S-wave scattering length in the negative region through a Feshbach resonance, producing an attractive interaction between fermions. We use the Hartree-Fock approximation to study the degenerate Fermi gas and pseudopotentials to mimic the interaction between the pair of fermions in a trap and a degenerate Fermi gas in the mean field approximation. We implement hyperspherical coordinates and a model potential for the pair interaction to study the spectrum and wavefunctions of the pair as a function of the magnetic field. In particular, we consider the strongly interacting regime, close to the collapse of the Fermi gas. [Preview Abstract] |
Wednesday, March 23, 2005 12:15PM - 12:27PM |
P36.00006: Fermion-mediated BCS-BEC crossover in ultracold ${}^{40}$K gases Meera Parish, Bogdan Mihaila, Ben Simons, Peter Littlewood Feshbach resonance phenomena in atomic Fermi gases involves the multiple scattering of atoms from open channel states into a molecular bound state formed from neighbouring closed channel states. Current theories treat the closed channel molecule as a featureless boson, but it can be argued that this interpretation is inappropriate when applied to ${}^{40}$K, since the molecule shares a hyperfine spin state with the open channel states. Introducing a 3-fermion model, where a fermion is shared between the open and closed channel states, we explore how the nature of the bound state impinges on the mean- field characteristics of the system. [Preview Abstract] |
Wednesday, March 23, 2005 12:27PM - 1:03PM |
P36.00007: Single particle excitations in the BCS-BEC crossover region Invited Speaker: We present a theoretical study of the single particle excitations in the BCS-BEC crossover region of a trapped Fermi superfluid at $T=0$. We self-consistently solve the Bogoliubov-de Gennes coupled equations in a harmonic trap, including molecular bosons associated with a Feshbach resonance. We show that the single particle excitation gap $E_g$, which is the same magnitude as the order parameter in a {\it uniform} BCS superfluid, is much smaller than the magnitude of the order parameter ${\tilde \Delta}(r=0)$ at the center of the trap in the crossover region[1]. The excitation gap $E_g$ is determined by the lowest Andreev bound state localized at the edge of the trapped gas. We also calculate the rf-tunneling current spectrum and show how $E_g$ and ${\tilde \Delta}(r=0)$ appear in the spectrum. We compare our results with the recent experimental data for superfluid $^6$Li[2] as well as the recent theoretical work based on an LDA[3]. [1] Y. Ohashi and A. Griffin, cond-mat/0410220. [2] C. Chin et. at. Science {\bf 305}, 1128 (2004). [3] J. Kinnunen et. al. Science {\bf 305}, 1131 (2004). [Preview Abstract] |
Wednesday, March 23, 2005 1:03PM - 1:15PM |
P36.00008: Dynamic projection on Feshbach molecules: a probe of pairing and phase fluctuations Ehud Altman, Ashvin Vishwanath We describe and justify a simple model for the dynamics associated with rapid sweeps across a Feshbach resonance, from the atomic to the molecular side, in an ultra cold Fermi system. The model allows us to relate equilibrium properties of the initial state to properties of the final state, such as the fraction of condensed molecules, the momentum distribution of normal molecules and the conversion efficiency as a function of ramping rate. We find that this `projection' onto molecules is a very sensitive probe of pairs (both condensed and non-condensed pairs) in the initial state, and arises ultimately from the short distance singularity of the Cooper pair wave function. We find that near the resonance, phase fluctuations sharply reduce the observed condensate fraction even at zero temperature. For very fast sweeps at low temperature, we predict a surprising nonmonotonic behavior of the molecule condensate fraction versus detuning of the initial state from resonance. In addition to probing the fermion pair condensate [1,2], this approach can detect noncondensed pairs, and possibly establish the presence of a phase fluctuation induced `psuedogap' phase in these systems. \newline [1] C. A. Regal, M. Greiner, and D. S. Jin, Phys. Rev. Lett. 92, 040403 (2004). [2] M. Zwierlein, {\it et.al.}, Phys. Rev. Lett. 92, 120403 (2004) [Preview Abstract] |
Wednesday, March 23, 2005 1:15PM - 1:27PM |
P36.00009: Quantum phase transitions in a novel Fermi-Bose Hubbard model Lincoln D. Carr, Daniel E. Sheehy, Murray J. Holland We study a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this Hamiltonian for paired fermions and bosons in the two state approximation at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the model correctly reproduces the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models. Near resonance, the bosonic and fermionic Mott phases melt due to fluctuations between the two fields, giving rise to a total-number Mott state instead. [Preview Abstract] |
Wednesday, March 23, 2005 1:27PM - 1:39PM |
P36.00010: Fermion superfluids of non-zero orbital angular momentum near resonance Roberto Diener, Tin-Lun Ho The BEC-BCS crossover of fermion superfluids with near-resonance $s$-wave interactions has been extensively studied in the past year. We extend these studies to the pairing of Fermi gases near the scattering resonance of the $\ell\neq 0$ partial wave at $T=0$. Using a model potential which reproduces the actual two-body low energy scattering amplitude, we have obtained an analytic solution of the gap equation. We show that the ground state of $\ell=1$ and $\ell=3$ superfluids are orbital ferromagnets with pairing wavefunctions $Y_{11}$ and $Y_{32}$ respectively. For $\ell=2$, there is a degeneracy between $Y_{22}$ and a ``cyclic state". [Preview Abstract] |
Wednesday, March 23, 2005 1:39PM - 1:51PM |
P36.00011: Quantum phase transitions across p-wave Feshbach resonance Victor Gurarie, Leo Radzihovsky, Anton Andreev We study a single-species polarized Fermi gas tuned across a narrow $p$-wave Feshbach resonance. We show the existence of a magnetic field-tuned quantum phase transition as detuning sweeps across the Fermi energy, between a $p_x$-wave BCS superfluid and a $p_x+ i p_y$ molecular superfluid in the BEC regime. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological $p_x+ i p_y$ to $p_x+ i p_y$ transition at zero chemical potential, $\mu$. In two-dimensions, for $\mu>0$ it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems. [Preview Abstract] |
Wednesday, March 23, 2005 1:51PM - 2:03PM |
P36.00012: Characteristics of Fermion Pairs with d- and extended s-wave Symmetries around BE-BCS Crossover Dusan Volcko, Khandker Quader We study BE-BCS crossover features for electron pairs with $d_{x^2-y^2}$ and extended-s ($s^*$) symmetries on a quasi-2D square lattice. The pairing interaction is obtained from an extended Hubbard model with on-site repulsion U, and nearest-neighbor attraction V. We calculate various quantities for different filling f and V: Chemical potential $\mu$(V,f), gap $\Delta$(V,f), coherence length $\xi$(V,f). Tightly-bound BE pairs appear at some characteristic $V_b(f)$ at both small and large fillings for both symmetries. At the BE-BCS crossover, the quasiparticle distribution function $v_k^2$ for d-wave is strikingly different from that for $s^*$ wave: While for $s^*$ wave, the central peak in $v_k^2$ diminishes continuously, for $d_{x^2-y^2}$, it vanishes abruptly at the crossover, and redistributes around $(\pm \pi, 0), (0,\pm \pi)$ in the Brillouin zone. The Fourier transform, $v_r^2$ exhibits a ``checkerboard'' pattern. While the general features may be of relevance to the BE-BCS crossover in Fermi systems, the single-particle feature may be of relevance to the field of high $T_c$ cuprates near the pseudogap region. We also explore the density collective modes around the BE-BCS crossover using functional integral techniques within a 1-loop approximation. [Preview Abstract] |
Wednesday, March 23, 2005 2:03PM - 2:15PM |
P36.00013: BCS to BEC Quantum Phase Transition in Spin Polarized Fermionic Gases Sergio Botelho, Carlos Sa de Melo Recent experiments in cold fermionic gases have shown that $s$-wave magnetic field induced Feshbach resonances can be used to form diatomic molecules of $^{40}{\rm K}$ and $^6{\rm Li}$, which undergoe Bose-Einstein condensation (BEC) on the lower magnetic field side of the resonance. On the higher magnetic field side of the resonance, it has also been established that Cooper pairing takes place and a BCS condensate is formed. We discuss the possibility of a quantum phase transition in ultracold spin polarized fermionic gases which exhibit a $p$-wave Feshbach resonance. We show that when fermionic atoms form a condensate that can be externally tuned between the BCS and BEC limits, the zero temperature compressibility and the spin susceptibility of the fermionic gas are non-analytic functions of the two-body bound state energy. This non-analyticity is due to a massive rearrangement of the momentum distribution in the ground state of the system. Furthermore, we show that the low temperature superfluid density is also non-analytic, and exhibits a dramatic change in behavior when the critical value of the bound state energy is crossed. [Preview Abstract] |
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