Session H14: Cold Gases: One Dimensional Phenomena

Feshbach physics in a one-dimensional optical lattice

We consider a pair of atoms in a one-dimensional optical lattice interacting via a Feshbach resonance. Using a two-channel description of the resonance, we derive the analytic form of the Fano scattering resonance inside the continuum band and the discrete bound states outside the band. We suggest experiments to probe and utilize the special properties of the system, which arise from the continuum having an upper edge.   

Pairing states of a polarized Fermi gas trapped in a one-dimensional optical lattice

We study the properties of a one-dimensional (1D) gas of fermions trapped in a lattice by means of the density matrix renormalization group method, focusing on the case of unequal spin populations, and strong attractive interaction. In the low density regime, the system phase-separates into a well defined superconducting core and a fully polarized metallic cloud surrounding it. We argue that the superconducting phase corresponds to a 1D analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of tightly bound bosonic pairs with a finite center-of-mass momentum that scales linearly with the magnetization. In the large density limit, the system allows for four phases: in the core, we either find a Fock state of localized pairs or a metallic shell with free spin-down fermions moving in a fully filled background of spin-up fermions. As the magnetization increases, the Fock state disappears to give room for a metallic phase, with a partially polarized superconducting FFLO shell and a fully polarized metallic cloud surrounding the core.   

The FFLO Phase in Imbalanced Spin Fermions in 1-d

Pairing in imbalanced spin populations has lately been the focus of many experimental and theoretical studies. Different mechanisms have been proposed to explain how pairing takes place between the two fermionic species. In this talk we will present exact Quantum Monte Carlo simulations of imbalanced spin populations in one dimension. We will first discuss the case where no confining potential is imposed. Here we have found that the pair-pair correlation function develops oscillations at nonzero polarizations, corresponding to a pair momentum distribution that, instead of being peaked at zero, is peaked at a momentum equal to the difference in the Fermi momenta. This indicates that the pairing mechanism is described by the Fulde Fuerrel Larkin Ovchinnikov (FFLO) picture, and not by other proposed phases which require zero-momentum pairing. When a confining potential is included in the simulations, we find that the FFLO oscillations are still present. In addition, we show that the local polarization displays a dip in the center of the trap, similar to experimental observations performed with 3-dimensional optical traps.   

One dimensional trapped fermions with attractive contact interactions

Recent advancements in cold atomic physics allow creation of optical lattices which reproduce well defined model Hamiltonians. This opens the route to resolve the phases of strongly correlated systems by carrying out experiments with trapped cold atoms. In this work, we study the properties of one dimensional trapped spin 1/2 fermions with attractive contact interactions by means of exact quantum Monte Carlo techniques. According to the local density approximation (LDA), such a system is expected to show phase separation between a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state and either fully polarized or fully paired outer shells.$[1]$ Here we show how the size and temperature affect the LDA phase boundaries. Mapping out the dependence on the number of particles, temperature, and interaction strength is extremely useful to benchmark experiments where cold atoms are trapped in arrays of cigar-shaped tubes, and understand whether the related setup will be able to detect the signatures of the FFLO state. \newline [1] G. Orso, Phys. Rev. Lett. 98, 070402 (2007).   

Quantum Monte Carlo study of the visibility of one-dimensional Bose-Fermi mixtures

The study of ultra-cold, optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility ${\cal V}_b$, and quantum Monte Carlo (QMC) calculations which show ${\cal V}_b$ increasing. In this talk, we present new QMC simulations which evaluate the density profiles and ${\cal V}_b$ of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where ${\cal V}_b$ is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott insulating domains before and after the fermions are included. Finally, we show that ${\cal V}_b$ exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of composite boson-fermion particles.   

Molecular superfluid phase in one-dimensional multicomponent fermionic cold atoms

We study a simple model of $N$-component fermions with contact interactions which describes fermionic atoms with $N = 2F + 1$ hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound-states made of $N$ fermions.   

Spin and charge velocities of one-dimensional boson-fermion mixture

We study the ground state and elementary excitations of a one-dimensional mixture of scalar bosons and spin-1/2 fermions with repulsive delta-function interaction by the Bethe-ansatz method. Though the ground state properties are dramatically changed once bosons are mixed into fermions, the spin and charge excitations still feature linear dispersions, and their velocities satisfy a simple universal relation.   

The ground state properties of two-component ultra-cold Fermi gas in hard wall confinement

We investigate the ground state properties of a one-dimensional two-component ultra-cold Fermi gas subjected to a hard wall trap. The explicit form of the wave function is obtained by solving the Bethe Ansatz equations numerically. Then we obtain the one-body density matrix of the system for different interaction strengths. Results of the momentum distribution of the atoms, which are obtained from the Fourier transform of the one-body density matrix, are reported for different interaction strengths. This interacting system may be experimentally accessible using ultra-cold atoms.   

Quantum Phase Transition between (Luttinger) Liquid and Gas of Cold Molecules

We consider cold polar molecules confined in a helical optical lattice similar to those used in holographic microfabrication. An external electric field polarizes molecules along the axis of the helix. The large-distance inter-molecular dipolar interaction is attractive but the short-scale interaction is repulsive due to geometric constraints and thus prevents collapse. The interaction strength depends on the electric field. We show that a zero-temperature liquid-gas transition occurs at a critical field. It can be observed under experimentally accessible conditions.   

Dynamics of excitations in a one-dimensional Bose liquid

We studied the dynamical structure factor $S(q,\omega)$ of interacting bosons in one-dimension. The sharp resonant peak $S(q,\omega) \propto \delta(\omega - \epsilon(q))$ as predicted by the Bogolubov theory is transformed into a power law singularity, $S(q,\omega) \propto (\omega - \epsilon(q))^{-\mu(q)}$ due to the strong quantum fluctuations. The corresponding momentum dependent exponent $\mu(q)$ is evaluated using the Lieb-Liniger model. The full momentum dependence $\mu(q)$ has been found in the strongly interaction regime using the Fermi Bose mapping. For the large momentum $q$ the different method allows us to express the exponent through the Luttinger liquid parameters. The two results agree in their common region of applicability.   

Probing the excitations of a one dimensional topological Bose insulator

We investigate the dynamic response of a system of ultracold dipolar atoms or molecules in the one dimensional Haldane Bose insulator phase. This phase, which was recently predicted theoretically [1], is characterized by non-local string order and its elementary excitations are domain walls in this order. We compute experimentally relevant response functions and we derive asymptotically exact expressions near the quantum critical points separating the Haldane insulator from the conventional Mott and density wave insulators. In particular, we predict a narrow absorption peak in Bragg spectroscopy experiments, due to the excitation of a single domain wall in the string order. \newline [1] E.G. Dalla Torre, E. Berg, E. Altman, {\it Phys. Rev Lett.} {\bf 97}, 260401 (2006)   

Adiabatic loading of a one dimensional system of interacting bosons into an optical lattice

We study excitations from the ground state of a system of bosons confined to one dimension (1D) and interacting via contact repulsion, while loading them adiabatically into an optical lattice. In particular, we analyze the dependence of the density of created excitations on the ramp rate $\delta$. We find that for strongly interacting commensurate bosons this density scales as $\sqrt{\delta}$, while for weakly interacting bosons it scales as $\delta^{2}$.   

Bosonic Mixtures in one-dimensional optical lattices I.

We study binary bosonic mixtures of ultra-cold atoms, confined to one dimension in an optical lattice, for various densities. Within a Luttinger liquid description, using renormalization group equations at second order, we determine both ordered and quasi-ordered phases of these mixtures. At commensurate filling, e.g. unit-filling and half-filling, we find different types of localized phases, whereas for densities that are incommensurate to the lattice, but equal for the two species, we find the behavior of a spin gap transition. We discuss the properties of the various phases, and how they could be detected in experiment.   

Bosonic Mixtures in one-dimensional optical lattices II

Using a Time-evolving Block Decimation (TEBD) approach, we study the quantum phases of bosonic mixtures in one dimension. With this numerical approach we determine how various phases appear for both finite and infinite systems. In particular, we relate the different phases of this system to the microscopic parameters of the underlying Bose-Hubbard model and calculate the correlation functions that characterize the phases in different parameter regions. Furthermore, for a finite system, we discuss the effects of a global trap on the state of the system.