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Register a new userSuperfluid-Mott-Insulator Transition in a One-Dimensional Optical Lattice with Double-Well Potentials
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We study the superfluid-Mott-insulator transition of ultracold bosonic atoms in a one-dimensional optical lattice with a double-well confining trap using the density-matrix renormalization group. At low density, the system behaves similarly as two separated ones inside harmonic traps. At high density, however, interesting features appear as the consequence of the quantum tunneling between the two wells and the competition between the superfluid and Mott regions. They are characterized by a rich step-plateau structure in the visibility and the satellite peaks in the momentum distribution function as a function of the on-site repulsion. These novel properties shed light on the understanding of the phase coherence between two coupled condensates and the off-diagonal correlations between the two wells.
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We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e. a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.
We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases are investigated with the density matrix renormalization group technique. Novel magnetic phases are uncovered and phase transitions between them within the superfluid regime are discussed. Possible experimental detection are discussed.
We define, compute and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals $(i)$ mid-gap states related to parity-forbidden optical states, and $(ii)$ strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.
We study (by an exact numerical scheme) the single-particle density matrix of $sim 10^3$ ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to the interpretation and further development of the recent pioneering experiment by Greiner et al. In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid--Mott-insulator transition.
We study the nonequilibrium phase diagram of long-lived photo-doped states in the one-dimensional $U$-$V$ Hubbard model, where $eta$-pairing, spin density wave and charge density wave (CDW) phases are found. The photo-doped states are studied using an effective model obtained by a Schrieffer-Wolff transformation combined with separate chemical potentials for the approximately conserved pseudoparticle excitations, leading to a generalized Gibbs ensemble type description. These photo-doped states are characterized by gapless ($eta$-paring) and gapped (CDW) features in the nonequilibrium spectra. For small $V$, the $eta$-pairing correlations dominate over a wide doping range even when the SU$_c(2)$ symmetry that protects $eta$-pairing in the pure Hubbard model is absent. With increasing $V$, the CDW correlations take over in a wide doping range and are strong relative to the chemically doped case. We attribute the strong CDW correlations to the competition between intra- and inter-species repulsion and the one-dimensional configuration. Our results show that photo-doped strongly correlated systems exhibit different phases than conventional semiconductors.
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