Mott Plateau Research Articles

Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices

Non-equilibrium quantum phenomena are ubiquitous in nature. Yet, theoretical predictions on the real-time dynamics of many-body quantum systems remain formidably challenging, especially for high dimensions, strong interactions or disordered samples. Here we consider a notable paradigm of strongly correlated Fermi systems, the Mott phase of the Hubbard model, in a setup resembling ultracold-gases experiments. We study the three-dimensional expansion of a cloud into an optical lattice after removing the confining potential. We use time-dependent density-functional theory combined with dynamical mean-field theory, considering interactions below and above the Mott threshold, as well as disorder effects. At strong coupling, we observe multiple timescales in the melting of the Mott wedding-cake structure, as the Mott plateau persist orders of magnitude longer than the band insulating core. We also show that disorder destabilises the Mott plateau and that, compared to a clean setup, localisation can decrease, creating an interesting dynamic crossover during the expansion.

Dipolar dynamics for interacting ultracold fermions in a trapped optical lattice

Using the time-dependent density matrix renormalization group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.

Spectral properties of trapped one-dimensional ultracold fermions loaded on optical lattices

We examine spectral properties on one-dimensional (1D) trapped ultracold Fermi atoms loaded on optical lattices by using the dynamical density-matrix renormalization group (DDMRG) method. We find that spectra are very rich due to the interplay of free or repulsive interaction and the harmonic-trap potential. One of the rich examples is that a 1D Tomonaga-Luttinger (TL) liquid spectrum emerges beneath multiple bound-state flat levels in the Mott-plateau phase and the TL spectrum gradually disappears with a partial breakdown of the central Mott plateau by increasing the trap strength. A more striking example is the growth of a distinct low-energy broadened band from the bound-state flat levels together with the breakdown. It demonstrates a carrier doping effect into the Mott phase in optical lattice systems.

Magnetic structure of an imbalanced Fermi gas in an optical lattice

We analyze the repulsive fermionic Hubbard model on square and cubic lattices with spin imbalance and in the presence of a parabolic confinement. We analyze the magnetic structure as a function of the repulsive interaction strength and polarization. In the first part of the article, we perform unrestricted Hartree-Fock calculations for the two-dimensional (2D) case and find that above a critical interaction strength ${U}_{c}$ the system turns ferromagnetic at the edge of the trap, which is in agreement with the ferromagnetic Stoner instability of a homogeneous system away from half-filling. For $U<{U}_{c}$, we find a canted antiferromagnetic structure in the Mott region in the center and a partially polarized compressible edge. The antiferromagnetic order in the Mott plateau is perpendicular to the direction of the imbalance. In this regime, the same qualitative behavior is expected for 2D and three-dimensional (3D) systems. In the second part of the article, we give a general discussion of magnetic structures above ${U}_{c}$. We argue that spin conservation leads to nontrivial textures, both in the ferromagnetic polarization at the edge and for the N\'eel order in the Mott plateau. We discuss differences in magnetic structures for 2D and 3D cases.

Hubbard-model calculations of phase separation in optical lattices

Antiferromagnetic, Mott insulator, d-wave and gossamer superfluid phases are calculated for 2D square lattices from the extended Hubbard (t-J-U) model using the Gutzwiller projection method and renormalized mean field theory. Phase separation between antiferromagnetic and d-wave superfluid phases is found near half filling when the on-site repulsion exceeds $U\ga7.3t$, and coincides with a first order transition in the double occupancy. Phase separation is thus predicted for 2D optical lattices with ultracold Fermi atoms whereas it is inhibited in cuprates by Coulomb frustration which instead may lead to stripes. In a confined optical lattice the resulting density distribution is discontinuous an with extended Mott plateau which enhances the antiferromagnetic phase but suppresses the superfluid phase. Observation of Mott insulator, antiferromagnetic, stripe and superfluid phases in density and momentum distributions and correlations is discussed.

Hole localization in strongly correlated and disordered systems: DMRG studies for 1-D and 3-leg ladder random Hubbard models

We study one-dimensional and 3-leg ladder repulsive Hubbard models with random potential by using the density-matrix renormalization group method. When holes are slightly doped to the half-filling, the local Mott phase called “Mott plateau” and the local dip structure in density profile called “hole localized valley” are well-separately observable in strong on-site repulsive U / t and strong randomness for both models. We suggest that these separated structures qualitatively capture locally inhomogeneous characters seen in heavily under-doped High- T c superconductors.

Mott Plateau in Trapped Bose–Fermi Mixture

Boson–fermion mixture confined on an optical lattice is numerically studied. Mott-plateau like behavior is observed under certain conditions in the density profile of the bosons and fermions as one sees in bosonic atoms in a trap potential. In the Mott plateau area, the total number of the bosons and fermions at each site is kept to an integer value but both local density of the bosons and that of the fermions take some intermediate values. Unlike bosonic or fermionic Mott insulators, the bosons and fermions can move even in the Mott plateau area by exchanging their positions. With Monte Carlo simulations we demonstrate the formation of the Mott plateau, examine the property of the bosons and fermions by measuring the densities and local density fluctuations, and give discussion on this rather new state.

Two-dimensional dynamics of ultracold atoms in optical lattices

We analyze the dynamics of ultracold atoms in optical lattices induced by a sudden shift of the underlying harmonic trapping potential. In order to study the effect of strong interactions, dimensionality and lattice topology on transport properties, we consider bosonic atoms with arbitrarily strong repulsive interactions, on a two-dimensional square lattice and a hexagonal lattice. On the square lattice we find insulating behavior for weakly interacting atoms and slow relaxation for strong interactions, even when a Mott plateau is present, which in one dimension blocks the dynamics. On the hexagonal lattice the center of mass relaxes to the new equilibrium for any interaction strength.

Disorder-enhanced phase coherence in trapped bosons on optical lattices

The consequences of disorder on interacting bosons trapped in one-dimensional optical lattices are investigated by quantum Monte Carlo simulations. A numerical analysis of the momentum distribution function, the stiffness and the compressibility reveals a unique response to small to moderate strengths of potential disorder. If there is a Mott plateau at the centre of the trap in the clean limit, phase coherence increases as a result of disorder. The localization effects due to correlation and disorder compete against each other, resulting in a partial delocalization of the particles in the Mott region, which in turn leads to increased phase coherence. In the absence of a Mott plateau, this effect is absent. A detailed analysis of the uniform system without a trap shows that the disordered states participate in a Bose glass phase.

Probing Number Squeezing of Ultracold Atoms across the Superfluid-Mott Insulator Transition

The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.

Calculation of collective modes for the Bose-Hubbard model with confinement

The collective excitations in the Bose-Hubbard model in a trap are studied by means of numerical diagonalization in one dimension. The strength function is calculated for monopole and dipole perturbations, and moments of the strength function are utilized in order to obtain information about the collective behavior under external forces. In the superfluid regime, the spectrum is found to be exhausted by one single frequency, while in systems that contain a Mott insulating plateau several frequencies are excited. An explanation of recent experimental findings in terms of a Mott plateau is suggested.