arXiv subjects
Publications and source records attributed to Tin-Lun Ho.
We present the theory of bosonic systems with multiple condensates, unifying disparate models which are found in the literature, and discuss how degeneracies, interactions, and symmetries conspire to give rise to this unusual behavior. We show that as degeneracies multiply, so do the types of fragmentation, eventually leading to strongly correlated states with no trace of condensation.
For decades, the conventional view is that an s-wave BCS superfluid can not support uniform spin polarization due to a gap $Δ$ in the quasiparticle excitation spectrum. We show that this is an artifact of the dismissal of quasiparticle interactions $V_{qp}^{}$ in the conventional approach at the outset. Such interactions can cause triplet fluctuations in the ground state and hence non-zero spin polarization at "magnetic field" $h<Δ$. The resulting ground state is a pairing state of quasiparticles on the ``BCS vacuum". For sufficiently large $V_{qp}$, the spin polarization of at unitarity has the simple form $m\propto μ^{1/2}$. Our study is motivated by the recent experiments at Rice which found evidence of a homogenous superfluid state with uniform spin polarization.
We show that the newly discovered $^{52}$Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: A "maximum" polar state, a "co-linear" polar state, or a biaxial nematic ferromagnetic state. We also present the phase diagram with a magnetic field in the interaction subspace containing the Chromium condensate. It contains many uniaxial and biaxial spin nematic phases, which often but not always break time reversal symmetry, and can exist with or without spontaneous magnetization.
We point out some logical inconsistencies in the model proposed in [Phys. Rev. A 71, 043604 (2005)] as well as in the calculations performed on it. The proposed model is not able to describe Feshbach resonances in optical lattices.
We point out that the recent experiments at ETH \cite{Esslinger} on fermions in optical lattices, where a band insulator evolves continuously into states occupying many bands as the system is swept adiabatically across Feshbach resonance, have implications on a wide range of fundamental issues in condensed matter. We derive the effective Hamiltonian of these systems, obtain expressions for their energies and band populations, and point out the increasing quantum entanglement of the ground state during the adiabatic sweep. Our results also explains why only specific regions in $k$-space can be populated after the sweep as found in ref. \cite{Esslinger}.
We show that the high temperature behavior of atomic gases near Feshbach Resonance with non-zero orbital angular momentum $(\ell >0)$ belong to a universality class different from that of s-wave resonances. The universal interaction energy is $2(2\ell +1)$ times larger than that of the s-wave when approaching the resonance from the atomic side, but is essentially zero on the molecular side; contrary to s-wave resonances where interaction energies on both sides are the same except for a sign change. The measurement of these universality properties should be feasible in current experiments.
We study the pairing of Fermi gases near the scattering resonance of the $\ell\neq 0$ partial wave. 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 $\ell=3$ superfluid 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". Dipole energy will orient the angular momentum axis. The gap function can be determined by the angular dependence of the momentum distribution of the fermions.
We show that when the Fermi energy of a Fermi gas is much smaller than the intrinsic energy width of a Fashbach resonance, the system behaves like a Fermi gas interacting with contact potential. This in turn implies universality at resonance, and large fermionic pairs in the strongly interacting regime. The recent experiments of JILA (PRL. 92, 040403 (2004)) and MIT (PRL. 92, 120403 (2004)) turn out to be deep inside this universal regime, which explains the perfect fit of these experiments by the BEC-BCS crossover theory with contact potential (cond-mat/0404517). We also show that rf spectrocopy can be used to map out the pair wavefunction directly.
We offer strong evidence that the recent observations by M. Greiner, C. Regal, and D. Jin and by MIT group are signatures of a fermion superfluid in the strongly interacting regime made up of large fermion pairs. Our conclusions are based on calculations using crossover theory for different potentials including those with the characteristics of two-channel models. Our results demonstrate clearly universality near resonance. The $T_{c}$ predicted by crossover theory is a perfect match with the observed boundary of vanishing condensate fraction with no adjustable parameters.
We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a scaling structure in the energy spectrum. Our demonstration is relevant to the Efimov problem in nuclear physics where similar scaling appears.
We show that, apart from a difference in scale, all of the surprising recently observed properties of a degenerate Fermi gas near a Feshbach resonance persist in the high temperature Boltzmann regime. In this regime, the Feshbach resonance is unshifted. By sweeping across the resonance, a thermal distribution of bound states (molecules) can be reversibly generated. Throughout this process, the interaction energy is negative and continuous. We also show that this behavior must persist at lower temperatures unless there is a phase transition as the temperature is lowered. We rigorously demonstrate universal behavior near the resonance.
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported by recent experiments and can be proven in Boltzmann regime. It implies a universal form for the grand potential which is characterized by only a few universal numbers in degenerate limit. This universal form provides a simple way to determine the density profile of a trapped fermion superfluid as well as the second sound velocity of a homogeneous superfluid at unitarity.
We analyze recent experiments at JILA which observe periodic formation of stripes in a rotating Bose condensate [Engels et al. Phys. Rev. Lett. {\bf 89}, 100403 (2002)], and explain this behavior as a consequence of kinetic energy driven evolution, where the vortices follows a quadrupolar flow. We demonstrate that the structure of vortex lattices in the lowest Landau level is a useful tool for understanding such complex phenomena, even when the system is not in the quantum Hall regime.
We propose a simple scheme of generating rotating atomic clusters in an optical lattices which produces states with quantum Hall and spin liquid properties. As the rotation frequencies increases, the ground state of a rotating cluster of spin-1 Bose atoms undergoes a sequence of (spin and orbit) transitions, which terminates at an angular momentum $L^{\ast}$ substantially lower than that of the boson Laughlin state. The spin-orbit correlations reflect "fermionization" of bosons facilitated by their spin degrees of freedom. We also show that the density of an expanding group of clusters has a scaling form which reflects the quantum Hall and the spin structure of a single cluster.
We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.
We show that as the number of vortices in a three dimensional Bose-Einstein Condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy-plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.
We show that the ground state of an attractive Bose gas in a double well evolves from a coherent state to a Schrodinger Cat like state as the tunneling barrier is decreased. The latter exhibits super- fragmentation as spin-1 Bose gas with antiferromagnetic interaction, which is caused by the same physics. We also show that the fragmented condensates of attractive and repulsive Bose gases in double wells lead to very different interference patterns.
We show that the density profile of a Fermi gas in rapidly rotating potential will develop prominent features reflecting the underlying Landau level like energy spectrum. Depending on the aspect ratio of the trap, these features can be a sequence of ellipsoidal volumes or a sequence of quantized steps.