Interference of holon strings in 2D Hubbard model.

The 2D Hubbard model with large repulsion is an important problem in condensed matter physics. At half filling, its ground state is an antiferromagnet (AMF). The dope AMF below half filling is believed to capture the physics of highTcsuperconductors. And the fermion excitation of this dope AMF is theorized as splitting up into holons and spinons that carry charge and spin separately. It is believed that these exotic holons and spinons are the origins of the unusual properties of highTcsuperconductors. Despite the interests in holons and spinons, the direct observations of these excitations remain difficult in solid state experiments. Here, we show that with the rapid advances in the experimental techniques in cold atoms, the direct observation of holons is possible in quantum quench dynamic processes in cold atom settings. We show that the well-known holon-strings generated by the motion of a holon as well as their interferences can be detected by the measurements spin-spin correlations and demonstrate the presence of the Marshall phase associated with a holon string reflecting an underlying AMF background. Moreover, we show that the interferences of the holon strings make a holon propagate anisotropically, with a diffusion pattern clearly distinct from that of spinless fermions. At the same time, we show that these interferences lead to a large suppression in magnetic order in the region swept through by the strings (even to about 95% for some bond). We further demonstrate the Marshall phase of the holon-strings by comparing the dynamics of holon in thetJmodel with that of the so-calledσtJ-model, which is thetJmodel with the Marshall phase removed. The holons in these models propagate entirely differently.

Imaging the Holon string of the Hubbard model.

It has been a long-sought goal of quantum simulation to find answers to outstanding questions in condensed-matter physics. A famous example is finding the ground state and the excitations of the two-dimensional (2D) Hubbard model with strong repulsion below half-filling. This system is a doped antiferromagnet and is of great interest because of its possible relation to high-[Formula: see text] superconductors. Theoretically, the fermion excitations of this model are believed to split up into holons and spinons, and a moving holon is believed to leave behind it a string of "wrong" spins that mismatch with the antiferromagnetic background. Here, we show that the properties of the ground-state wavefunction and the holon excitation of the 2D Hubbard model can be revealed in unprecedented detail by using the imaging and the interference technique in atomic physics. They allow one to reveal the Marshall sign of the doped antiferromagnet. The region of wrong Marshall sign indicates the location of the holon string.

Spinor Condensates on a Cylindrical Surface in Synthetic Gauge Fields.

We show that by modifying the setup of the recent experiment that creates a "Dirac string" one can engineer a quasi-2D spinor Bose-Einstein condensate on a cylindrical surface, with a synthetic magnetic field normal to the surface. Because of the muticonnectivity of the surface, there are two types of vortices (called A and B) with the same vorticity. This is very different from the planar case, which only has one kind of vortex for fixed circulation. As the strength of the synthetic gauge field increases, the ground states will form a necklace of alternating AB vortices surrounding the lateral midpoint of the cylinder, and will split into two A and B necklaces at higher synthetic gauge fields. The fact that even the basic vortex structure of a Bose-Einstein condensate is altered in a cylindrical surface implies that richer phenomena are in store for quantum gases in other curved surfaces.

Phase separation in mixtures of repulsive Fermi gases driven by mass difference.

We show that phase separation must occur in a mixture of fermions with repulsive interaction if their mass difference is sufficiently large. This phenomenon is highly dimension dependent. Consequently, the density profiles of phase separated 3D mixtures are very different from those in 1D. Noting that the ferromagnetic transition of a spin-1/2 repulsive Fermi gas is the equal mass limit of the phase separation in mixtures, we show from the Bethe ansatz solution that a ferromagnetic transition will take place in the scattering states when the interaction passes through the strongly repulsive regime and becomes attractive.

Bose gases near unitarity.

We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e., the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length a(s)<0), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length a(s)*<0. For a(s)

Alternative route to strong interaction: narrow Feshbach resonance.

We show that a narrow resonance produces strong interaction effects far beyond its width on the side of the resonance where the bound state has not been formed. This is due to a resonance structure of its phase shift, which shifts the phase of a large number of scattering states by π before the bound state emerges. As a result, the magnitude of the interaction energy when approaching the resonance on the "upper" and "lower" branch from different side of the resonance is highly asymmetric, unlike their counterpart in wide resonances. Measurements of these effects are experimentally feasible.

Nature and properties of a repulsive Fermi gas in the upper branch of the energy spectrum.

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.

Bose-Einstein condensates with spin-orbit interaction.

Motivated by recent experiments carried out by Spielman's group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.

Universal thermometry for quantum simulation.

Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattices to simulate models for unsolved strongly correlated systems, so as to deduce their properties directly from experimental data. An important step in this effort is to determine the temperature of the system, which is essential for deducing all thermodynamic functions. This step, however, remains difficult for lattice systems at the moment. Here, we propose a method based on a generalized fluctuation-dissipation theorem. It does not rely on numerical simulations and gives a universal thermometry scheme for quantum gas systems including mixtures and spinor gases, provided that the local density approximation is valid.

Signature of quantum criticality in the density profiles of cold atom systems.

In recent years, there has been considerable experimental effort using cold atoms to study strongly correlated many-body systems. One class of phenomena of particular interest is quantum critical (QC) phenomena. While prevalent in many materials, these phenomena pose notoriously difficult theoretical problems due to the vanishing of energy scales in the QC region. So far, there are no systematic ways to deduce the QC behavior of bulk systems from the data of trapped atomic gases. Here, we present a simple algorithm to use the experimental density profile to determine the T=0 phase boundary of bulk systems, as well as the scaling functions in the QC regime. We also present another scheme for removing finite-size effects of the trap. We demonstrate the validity of our schemes using exactly soluble models.

Squeezing out the entropy of fermions in optical lattices.

At present, there is considerable interest in using atomic fermions in optical lattices to emulate the mathematical models that have been used to study strongly correlated electronic systems. Some of these models, such as the 2-dimensional fermion Hubbard model, are notoriously difficult to solve, and their key properties remain controversial despite decades of studies. It is hoped that the emulation experiments will shed light on some of these long-standing problems. A successful emulation, however, requires reaching temperatures as low as 10(-12) K and beyond, with entropy per particle far lower than what can be achieved today. Achieving such low-entropy states is an essential step and a grand challenge of the whole emulation enterprise. In this article, we point out a method to literally squeeze the entropy out from a Fermi gas into a surrounding Bose-Einstein condensed gas, which acts as a heat reservoir. This method allows one to reduce the entropy per particle of a lattice Fermi gas to a few percent of the lowest value obtainable today.

Superfluid-insulator transition of strongly interacting fermi gases in optical lattices.

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in lattice height Vo/ER between 2.23 and 4.14. The latter is the prediction of mean-field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF-Mott-insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-insulator transition for the BCS-BEC family.

Intrinsic heating and cooling in adiabatic processes for bosons in optical lattices.

We show that by raising the lattice "adiabatically" as in many current optical lattice experiments on bosons, even though the temperature may decrease initially, it will eventually rise linearly with lattice height, taking the system farther away from quantum degeneracy. This increase has nothing to do with the entropy of the bulk Mott phase and is caused by the adiabatic compression of the mobile atoms between Mott layers. Our studies show that one can reverse the temperature rise to reach quantum degeneracy by adiabatic expansion, which can be achieved by a variety of methods.

Criterion for bosonic superfluidity in an optical lattice.

We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution n(k) can be misleading, for even a normal Bose gas can have a similarly sharp n(k). We show that superfluidity in a homogeneous system can be detected from the so-called visibility (v) of n(k)--that v must be 1 within O(N(-2/3)), where N is the number of bosons. We also show that the T=0 visibility of trapped lattice bosons is far higher than what is obtained in some current experiments, suggesting strong temperature effects and that these states can be normal. These normal states allow one to explore the physics in the quantum critical region.

Critical rotational frequency for superfluid fermionic gases across a Feshbach resonance.

We present a method to determine the critical rotational frequencies for superfluidity of both uniform and trapped Fermi gases across a wide Feshbach resonance. It is found that as one approaches the resonance from the BCS side, beyond a critical scattering length, pairing is so robust that superfluidity cannot be destroyed by rotation. Moreover, the critical frequency has a sequence of jumps revealing the appearance of Landau levels, which are particularly prominent for systems up to a few thousand particles. For rotational frequency below an ultimate critical frequency, defined to be the lowest frequency at which the center of the cloud goes normal, a trapped gas has a superfluid core surrounded by a normal gas, as seen in recent experiments (C. H. Schunck, cond-mat/0607298).

52Cr spinor condensate: a biaxial or uniaxial spin nematic.

We show that the newly discovered 52Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: a "maximum" polar state, a "colinear" 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.

Vortices in superfluid fermi gases through the BEC to BCS crossover.

We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: k(F)(-1)and the coherence length xi, while only variation on the scale of xi is seen away from the BCS limit. The circulating current has a peak value jmax which is a nonmonotonic function of 1/k(F)a(s) implying a maximum critical velocity approximately v(F) at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to the BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.

Fermions in optical lattices swept across Feshbach resonances.

We point out that the recent experiments at ETH 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 explain why only specific regions in k space can be populated after the sweep as found at ETH.

Fermion superfluids of nonzero orbital angular momentum near resonance.

We study the pairing of Fermi gases near the scattering resonance of the l not equal 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 l=1 and l=3 superfluids are orbital ferromagnets with pairing wave functions Y11 and Y32, respectively. For l=2, there is a degeneracy between Y22 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.