A spin-1 atomic gas in an optical lattice, in the unit-filling Mott Insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a disordered rotationally-invariant spin-1 bilinear-biquadratic model. We study, via the density matrix renormalization group algorithm, a bounded disorder model such that the spin interactions can be locally either ferromagnetic or antiferromagnetic. Random interactions induce the appearance of a disordered ferromagnetic phase characterized by a non-vanishing value of spin-glass order parameter across the boundary between a ferromagnetic phase and a dimer phase exhibiting random singlet order. The study of the distribution of the block entanglement entropy reveals that in this region there is no random singlet order.
A 2D Fock-state lattice (FSL is constructed from the many-body states of two interacting two-mode quantum gases. By periodically driving the interspecies interactions and pulsing the tunneling between the two modes of each gas, a synthetic gauge field is generated. We derive an effective Hamiltonian in the short pulse limit which resembles the Harper-Hofstadter Hamiltonian where the magnetic flux per plaquette is controlled by the ratio of the interaction energy and the driving frequency. The quasispectrum of the Floquet operator of the driving sequence shows the celebrated Hofstadter's butter…
We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit the translational symmetry from the Hamiltonian, within sufficiently short excitation times minimizing detrimental decoherence effects. For the GHZ states, we propose a two-step detection protocol to experimentally verify the optimal preparation of the target state based only on standard measurement tec…
Emerging dynamical constraints resulting from inter-site interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the $1/r^3$ tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body …
We review recent developments in the use of magnetic lattices as a complementary tool to optical lattices for trapping periodic arrays of ultracold atoms and degenerate quantum gases. Recent advances include the realisation of Bose-Einstein condensation in multiple sites of a magnetic lattice of one-dimensional microtraps, the trapping of ultracold atoms in square and triangular magnetic lattices, and the fabrication of magnetic lattice structures with sub-micron period suitable for quantum tunnelling experiments. Finally, we describe a proposal to utilise long-range interacting Rydberg atoms …
We present an experimental study demonstrating the manipulation of atom-number distributions of spinor gases after nonequilibrium quantum quenches across superfluid to Mott-insulator phase transitions in cubic optical lattices. Our data indicate that atom distributions in individual Mott lobes can be tuned by properly designing quantum quench sequences, which suggests methods of maximizing the fraction of atoms in Mott lobes of even occupation numbers and has applications in attaining different quantum magnetic phases including massively entangled states. Spatial distributions of gases in thre…
Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here we demonstrate the possibility to reconstruct the momentum-space distribution of three-dimensional interacting lattice gases atom-by-atom. This is achieved by detecting individual metastable Helium atoms in the far-field regime of expansion, when released from an optical lattice. We benchmark our technique with Quantum Monte-Carlo calculations, demonstrating the ability to resolve momentum distributions of superfluids oc…
Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being developed and explored all the time, the prospects for probing exotic topological phases would be greatly enhanced if they could be realized in systems that were easily tuned. The flexibility offered by ultracold atoms could provide such a platform. Here, we review the tools available for creating topological states using ultracold atoms in optical …
Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted a lot of attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a …
We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterize…
We map out the interaction effects on the first six virial coefficients of one-dimensional Fermi gases with zero-range attractive and repulsive interactions, and the first four virial coefficients of the two-dimensional analog with attractive interactions. To that end, we use two non-perturbative stochastic methods: projection by complex stochastic quantization, which allows us to determine high-order coefficients at weak coupling and estimate the radius of convergence of the virial expansion; and a path-integral representation of the virial coefficients. To complement our numerical calculatio…
We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices computed via Density Functional Theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional optical lattices, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to under…
We investigate thermodynamic properties of lattice Bose gases in optical cavities in the Mott-insulator limit. We find the system assumes anomalous thermodynamic behavior that can be traced back to the breaking of fundamental additivity by its infinite-long range interaction. Specifically, the system shows striking ensemble inequivalence between the canonical ensemble and the grand canonical one, sharply manifesting in the distinct anomalous structure of the thermodynamic phase diagram in the canonical ensemble. In particular, in the temperature regime around half of the on-site energy, the sy…
We study the effective Bloch-wave scattering of a spinless Fermi gas in one-dimensional (1D) optical lattices. By tuning the odd-wave scattering length, we find multiple resonances of Bloch-waves scattering at the bottom (and the top) of the lowest band, beyond which an attractive (and a repulsive) two-body bound state starts to emerge. These resonances exhibit comparable widths in the deep lattice limit, and the finite interaction range plays an essential role in determining their locations. Based on the exact two-body solutions, we construct an effective microscopic model for the low-energy …
We investigate the finite temperature charge density wave (CDW) transition of lattice Bose gases within optical cavities in the deep Mott-insulator limit. We find a new critical regime emerges at a temperature around one-half of the on-site interaction energy, where the first order CDW transition at low temperatures terminates at a critical point and changes to a second order one. By directly calculating the critical exponents and constructing the effective theory in the corresponding critical regime, we find the emergent criticality belongs to the five-dimensional Ising universality class. Di…
The Pauli exclusion principle is one of the most fundamental manifestations of quantum statistics. Here, we report on its local observation in a spin-polarized degenerate gas of fermions in an optical lattice. We probe the gas with single-site resolution using a new generation quantum gas microscope avoiding the common problem of light induced losses. In the band insulating regime, we measure a strong local suppression of particle number fluctuations and a low local entropy per atom. Our work opens a new avenue for studying quantum correlations in fermionic quantum matter both in and out of eq…
We introduce and investigate a system that uses temporal resonance-induced phase space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both the classical and quantum phase space of the atom cloud, even when the optical lattice potential is arbitrarily weak. The topology of the pathways, which form web-like patterns, can by controled by changing the amplitude and period of the optical lattice. In turn, this control can be used to increase and limit the BEC's center-of-mass kinetic energy …
We investigate the ground-state phase diagram of interacting binary Bose gases trapped in two-dimensional optical lattices by means of quantum Monte Carlo simulations. Our simulations reveal a magnetic phase transition from a $x-y$ ferromagnetic-order to a spin insulator inside the Mott insulating phase with two particles per site for quasi-balanced on-site inter- and intra-particle interactions, i.e., $U_{\uparrow \downarrow} \lesssim U$. This 3D-XY transition is characterized by the establishment of a finite local magnetic moment along the $z$-axis, ferromagnetic correlations in the $x-y$ pl…
