An ultracold gas of heteronuclear alkali dimer molecules with hyperfine structure loaded into a one-dimensional optical lattice is investigated. The \emph{Hyperfine Molecular Hubbard Hamiltonian} (HMHH), an effective low-energy lattice Hamiltonian, is derived from first principles. The large permanent electric dipole moment of these molecules gives rise to long range dipole-dipole forces in a DC electric field and allows for transitions between rotational states in an AC microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. By tuning the angle between the DC electric and magnetic fields and the strength of the AC field it is possible to control the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. The HMHH's unique features have direct experimental consequences such as quantum dephasing, tunable complexity, and the dependence of the phase diagram on the molecular state.
A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction based on the conventional mean field perturbation approach.
The interband dynamics of a two-band Bose-Hubbard model is studied with strongly correlated bosons forming single-site double occupancies referred to as doublons. Our model for resonant doublon interband coupling exhibits interesting dynamical features such as quantum Zeno effect, the generation of states such as a two-band Bell-like state and an upper-band Mott-like state. The evolution of the asymptotic state is controlled here by the effective opening of one or both of the two bands, which models decay channels.
The Molecular Hubbard Hamiltonian: Field Regimes and Molecular Species
在光晶格中，超冷基态极性碱金属二聚体分子自然产生分子哈伯德哈密顿量（MHH）。我们发现，与超冷原子，不同的分子显示不同的多体相由于分子结构的内在差异，即使当分子的对称性是相同的。我们还展示了各种各样的实验控制$^1Σ$分子通过外部领域，包括施加静电和磁场，交流微波场，和光晶格光束的偏振和强度。我们提供明确的数值计算的MHH的参数，包括隧道和直接和交换偶极-偶极相互作用能，分子{ $^{6}$ Li $^{133}$ Cs}，$^{23}$ Na $^{40}$ K，$^{87}$ Rb $^{133}$ Cs，$^{40}$ K $^{87}$ Rb，和{ $^{6}$ Li $^{23}$ Na}在弱和强的外加电场。作为多体物理的研究案例，我们利用无限尺寸矩阵乘积态方法研究了一维超流相到半满和三满晶相的量子相变。
We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics -- the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the Bose-Hubbard model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations of cold atoms where a number of experimental results are available. The review is written for non-experts and can be viewed as an int…
The repulsive Hubbard Hamiltonian is one of the foundational models describing strongly correlated electrons and is believed to capture essential aspects of high temperature superconductivity. Ultracold fermions in optical lattices allow for the simulation of the Hubbard Hamiltonian with a unique control over kinetic energy, interactions and doping. A great challenge is to reach the required low entropy and to observe antiferromagnetic spin correlations beyond nearest neighbors, for which quantum gas microscopes are ideal. Here we report on the direct, single-site resolved detection of antifer…
We apply the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) to systems of bosons or fermions in lattices described by Hubbard type Hamiltonians with long-range or short-range interparticle interactions. The wavefunction is expanded in a variationally optimized time-dependent many-body basis generated by a set of effective creation operators that are related to the original particle creation operators by a time-dependent unitary transform. We use the time-dependent variational principle for the coefficients of this transform as well as the expansion…
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time ($\mathcal{PT}$) symmetry if we compensate the system additionally an overall gain term. By solving the two-site Lindblad equation with fixed dissipation exactly, we find that the dynamics of rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in…
We address the effects of quenched disorder averaging in the time-evolution of systems of ultracold atoms in optical lattices in the presence of noise, imposed by of an environment. For bosonic systems governed by the Bose-Hubbard Hamiltonian, we quantify the response of disorder in Hamiltonian parameters in terms of physical observables, including bipartite entanglement in the ground state and report the existence of disorder-induced enhancement in weakly interacting cases. For systems of two-species fermions described by the Fermi-Hubbard Hamiltonian, we find similar results. In both cases, …
Understanding the robustness of topological phases of matter in the presence of interactions poses a difficult challenge in modern condensed matter, showing interesting connections to high energy physics. In this work, we leverage these connections to present a complete analysis of the continuum long-wavelength description of a generic class of correlated topological insulators: Wilson-Hubbard topological matter. We show that a Wilsonian renormalization group (RG) approach, combined with the so-called topological Hamiltonian, provide a quantitative route to understand interaction-induced topol…
The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials. For bosons, the Hubbard Hamiltonian has been deeply scrutinised for short-range on-site interactions. However, accessing longer-range couplings has remained elusive experimentally. This marks the frontier towards the extended Bose-Hubbard Hamiltonian that allows insulating ordered phases at fractional lattice fillings. Here we implement this Hamiltonian by confining semiconductor dip…
With use of the U(1) quantum rotor method in the path integral effective action formulation, we have confirmed the mathematical similarity of the phase Hamiltonian and of the extended Bose-Hubbard model with density-induced tunneling (DIT). Moreover, we have shown that the latter model can be mapped to a pseudospin Hamiltonian that exhibits two coexisting (single-particle and pair) superfluid phases. Phase separation of the two has also been confirmed, determining that there exists a range of coefficients in which only pair condensation, and not single-particle superfluidity, is present. The D…
We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|ψ(0)\rangle=|\cdots 2020\cdots \rangle$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the the hopping energy. We d…
