Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

We consider strongly interacting boson-boson mixtures on one-dimensional lattices and, by adopting a qualitative mean-field approach, investigate their quantum phases as the interspecies repulsion is increased. In particular, we analyze the low-energy quantum emulsion metastable states occurring at large values of the interspecies interaction, which are expected to prevent the system from reaching its true ground state. We argue a significant decrease in the visibility of the time-of-flight images in the case of these spontaneously disordered states.     

Atomic fermi-bose mixtures in inhomogeneous and random lattices: from fermi glass to quantum spin glass and quantum percolation

We investigate strongly interacting atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. We derive an effective Hamiltonian for the system and discuss its low temperature physics. We demonstrate the possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin-glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices.     

How the effective boson-boson interaction works in Bose-Fermi mixtures in periodic geometries

We study mixtures of spinless bosons and not spin-polarized fermions loaded in two dimensional optical lattices. We approach the problem of the ground state stability within the framework of the linear response theory; by the mean of an iterative procedure, we are able to obtain a relation for the dependence of boson-boson effective interaction on the absolute temperature of the sample. Proceeding from such a formula, we write down analytical expressions for supersolid (SS) and phase separation (PS) transition temperatures, and plot the phase diagrams.     

Soluble models of strongly interacting ultracold gas mixtures in tight waveguides

A Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.     

Magnetic properties of commensurate Bose-Bose mixtures in one-dimensional optical lattices

We investigate magnetic properties of strongly interacting bosonic mixtures confined in one dimensional geometries, focusing on recently realized ⁸⁷Rb-⁴¹K gases with tunable interspecies interactions. By combining analytical perturbation theory results with density-matrix-renormalization group calculations, we provide quantitative estimates of the ground state phase diagram as a function of the relevant microscopic quantities, identifying the more favorable experimental regimes in order to access the various magnetic phases. Finally, we qualitatively discuss the observability of such phases in realistic setups when finite temperature effects have to be considered.     

High-temperature atomic superfluidity in lattice Bose-Fermi mixtures

We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always attractive if the boson-boson on-site interaction is repulsive, and predict the existence of an enhanced BEC-BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion repulsion, the induced attraction can give rise to superfluidity via s-wave pairing at striking variance with the case of pure systems of fermionic atoms with direct repulsive interactions.     

Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

Largest lyapunov exponents for lattices of interacting classical spins

We investigate how generic the onset of chaos in interacting many-body classical systems is in the context of lattices of classical spins with nearest-neighbor anisotropic couplings. Seven large lattices in different spatial dimensions were considered. For each lattice, more than 2000 largest Lyapunov exponents for randomly sampled Hamiltonians were numerically computed. Our results strongly suggest the absence of integrable nearest-neighbor Hamiltonians for the infinite lattices except for the trivial Ising case. In the vicinity of the Ising case, the largest Lyapunov exponents exhibit a power-law growth, while further away they become rather weakly sensitive to the Hamiltonian anisotropy. We also provide an analytical derivation of these results.     

Exact results for strongly correlated fermions in 2 + 1 dimensions

We derive exact results for a model of strongly interacting spinless fermions hopping on a two-dimensional lattice. By exploiting supersymmetry, we find the number and type of ground states exactly. Exploring various lattices and limits, we show how the ground states can be frustrated, quantum critical, or combine frustration with a Wigner crystal. We show that on generic lattices the model is in an exotic "superfrustrated" state characterized by an extensive ground-state entropy.     

Orbital order in Mott insulators of spinless p-band fermions

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.     

Nonadiabatic preparation of spin crystals with ultracold polar molecules

We study the growth dynamics of ordered structures of strongly interacting polar molecules in optical lattices. Using a dipole blockade of microwave excitations, we map the system onto an interacting spin-1/2 model possessing ground states with crystalline order, and describe a way to prepare these states by nonadiabatically driving the transitions between molecular rotational levels. The proposed technique bypasses the need to cross a phase transition and allows for the creation of ordered domains of considerably larger size compared to approaches relying on adiabatic preparation.     

Bosonic superfluid-insulator transition in continuous space

We investigate the zero-temperature phase diagram of interacting Bose gases in the presence of a simple cubic optical lattice, going beyond the regime where the mapping to the single-band Bose-Hubbard model is reliable. Our computational approach is a new hybrid quantum Monte?Carlo method which combines algorithms used to simulate homogeneous quantum fluids in continuous space with those used for discrete lattice models of strongly correlated systems. We determine the critical interaction strength and optical lattice intensity where the superfluid-to-insulator transition takes place, considering also the regime of shallow optical lattices and strong interatomic interactions. The implications of our findings for the supersolid state of matter are discussed.     

Drag effect and topological complexes in strongly interacting two-component lattice superfluids

The mutual drag in strongly interacting two-component superfluids in optical lattices is discussed. Two competing drag mechanisms are the vacancy-assisted motion and proximity to a quasimolecular state. In a case of strong drag, the lowest energy topological excitation (vortex or persistent current) can consist of several circulation quanta. In the SQUID-type geometry, the circulation can become fractional. We present both the mean field and Monte Carlo results. The drag effects in optical lattices are drastically different from the Galilean-invariant Andreev-Bashkin effect in liquid helium.     

Integrative models for asymmetric fermi superfluids: emergence of a new exotic pairing phase

We introduce an exactly solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair excitations. It is proven that this phase is the exact ground state in the strong-coupling limit, while numerical examples in finite lattices show that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.     

Quantum emulsion: a glassy phase of bosonic mixtures in optical lattices

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely, a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.     

Kinetic energy of a trapped Fermi gas interacting with a Bose-Einstein condensate

We study a confined mixture of bosons and fermions in the regime of quantal degeneracy, with particular attention to the effects of the interactions on the kinetic energy of the fermionic component. We are able to explore a wide region of system parameters by identifying two scaling variables which completely determine its state at low temperature. These are the ratio of the boson-fermion and boson-boson interaction strengths and the ratio of the radii of the two clouds. We find that the effect of the interactions can be sizeable for reasonable choices of the parameters and that its experimental study can be used to infer the sign of the boson-fermion scattering length. The interplay between interactions and thermal effects in the fermionic kinetic energy is also discussed. Received 13 September 1999 and Received in final form 22 February 2000     

Towards a realistic equation of state of strongly interacting matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.     

Optimal lattice configurations for interacting spatially extended particles

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and the mass concentration depends on the density we have fixed. In the second case, both interacting potential and density of the distribution of mass are described by completely monotone functions in which case the optimality holds at any fixed density.     

Optimal control of charge with local gates in quantum-dot lattices

Semiconductor quantum dots are among the leading candidates for next-generation nanoscale devices due to their tunable size, shape, and low energy consumption. Here we apply quantum optimal control theory to coherently manipulate the single-electron charge distribution in quantum-dot lattices of various sizes. In particular, we show that to control the charge distribution it is sufficient to optimize the gate voltage acting on a single quantum dot in the lattice. We generally find yields around 99% in the picosecond time scale when using realistic models for the quantum-dot lattices on a real-space grid. We analyze and discuss both the limitations of the model regarding the gate parameters as well as the potential of the scheme for applications as quantum-dot cellular automata.     

Metastability range of the Bose condensate in 7Li-fermion mixtures at T = 0

We evaluate the ground state of a mixture of bosons and spin-polarized fermions in the case of attractive boson-boson interactions, using a variational Ansatz for the Bose condensate wave function and the Thomas-Fermi approximation for the fermions in the mean field of the condensate. Within this approximation we show that the presence of the fermions tends to restrict the metastability range of the condensate, irrespectively of the sign of the boson-fermion interactions. Numerical illustrations are reported for mixtures of ⁷Li atoms with fermions having the ⁶Li mass.