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arXiv:1011.0388 · Physical Review A

Repulsively bound exciton-biexciton states in high-spin fermions in optical lattices

Arturo Argüelles, Luis Santos

Published Mar 25, 2011• 0 citations
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Abstract

We show that the interplay between spin-changing collisions and quadratic Zeeman coupling provides a mechanism for the formation of repulsively bound composites in high-spin fermions, which we illustrate by considering spin flips in an initially polarized hard-core one-dimensional Mott insulator of spin-$3/2$ fermions. We show that after the flips the dynamics is characterized by the creation of two types of exciton-biexciton composites. We analyze the conditions for the existence of these bound states and discuss their intriguing properties. In particular we show that the effective mass and stability of the composites depends nontrivially on spin-changing collisions, on the quadratic Zeeman effect, and on the initial exciton localization. Finally, we show that the composites may remain stable against inelastic collisions, opening the possibility of interesting quantum composite phases.

DOI
10.1103/physreva.83.033624

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We show that the interplay between spin-changing collisions and quadratic Zeeman coupling provides a mechanism for the formation of repulsively bound composites in high-spin fermions, which we illustrate by considering spin flips in an initially polarized hard-core one-dimensional Mott insulator of spin-3/23/23/2 fermions. We show that after the flips the dynamics is characterized by the creation of two types of exciton-biexciton composites. We analyze the conditions for the existence of these bound states and discuss their intriguing properties. In particular we show that the effective mass and stability of the composites depends nontrivially on spin-changing collisions, on the quadratic Zeeman effect, and on the initial exciton localization. Finally, we show that the composites may remain stable against inelastic collisions, opening the possibility of interesting quantum composite phases.
We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2)⊗SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-1/2 gases.
We investigate the phase separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of the density-matrix renormalization method. The phase separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between intercomponent fermions. We find the existence of a critical repulsive interaction strength above which the phase separation evolves. By increasing the trap imbalance, the composite phase of the Mott-insulating core is changed into one of the ferromagnetic insulating core, which is incompressible and originates from the Pauli exclusion principle.
We present a comprehensive study of a one-dimensional two-orbital model at and below quarter filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasicondense with finite center-of-mass momentum and an order parameter that changes phase with wave vector QQQ. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge- density-wave instability. When pairing dominates over the interorbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin-gapped superconductor, a genuine orbital-selective paired state. All these results are supported by both analytical and numerical calculations. By assuming a quasiclassical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from k=0k=0k=0. The full characterization of the different phases is obtained by means of extensive density-matrix renormalization-group calculations.
We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.
We study the phase diagram of repulsively interacting spin-1 bosons in optical lattices at unit filling, showing that an externally induced quadratic Zeeman effect may lead to a rich physics characterized by various phases and phase transitions. We find that the main properties of the system may be described by an effective field model, which provides the precise location of the phase boundaries for any dimension, in excellent agreement with our numerical calculations for one-dimensional (1D) systems. Thus, our work provides a quantitative guide for the experimental analysis of various types of field-induced quantum phase transitions in spin-1 lattice bosons. These transitions, which are precluded in spin-1/2 systems, may be realized by using an externally modified quadratic Zeeman coupling, similar to recent experiments with spinor condensates in the continuum.
Understanding fundamentals of few-body physics provides an interesting bottom-up approach for the clarification of many-body properties. The remarkable experimental progress in realizing spin-orbit coupling (SOC) in optical Raman lattices offers a renewed thrust towards discovering novel few-body features induced by the interplay between SOC and optical lattices. Using the Wilson renormalization method to account for high-band effects, we study the low-energy two-body scattering processes of spin-1/21/21/2 fermions in spin-orbit-coupled optical lattices. We demonstrate that, under weak SOC, adding a small lattice potential would destabilize shallow two-body bound states, contrary to conventional wisdom. On the other hand, when the lattice is sufficiently deep, two-body bound states are always stabilized by increasing the lattice depth. This intriguing nonmonotonic behavior of the bound-state stability derives from the competition between SOC and optical lattices and can be explained by analyzing the low-energy density of states. We also discuss the impact of high-band effects on such a behavior, as well as potential experimental detection.