The emergent phases of strongly correlated spin-$\frac{1}{2}$ Fermi gases of Rydberg-dressed atoms in a one-dimensional optical lattice are theoretically investigated. At weak coupling a bosonization description is used to demonstrate the ability to drive alternating quantum phase transitions between distinct Luttinger liquids. At strong coupling the ground state develops nontrivial phase separation exhibiting Luttinger liquid ``puddles'' separated by magnetic domain walls due to the interplay of the incommensurate filling and the Rydberg core length scale. These phases can be detected in ultracold gases of Rydberg atoms made from $^{6}\mathrm{Li}$.
The emergent phases of strongly correlated spin-21 Fermi gases of Rydberg-dressed atoms in a one-dimensional optical lattice are theoretically investigated. At weak coupling a bosonization description is used to demonstrate the ability to drive alternating quantum phase transitions between distinct Luttinger liquids. At strong coupling the ground state develops nontrivial phase separation exhibiting Luttinger liquid ``puddles'' separated by magnetic domain walls due to the interplay of the incommensurate filling and the Rydberg core length scale. These phases can be detected in ultracold gases of Rydberg atoms made from 6Li.
Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter K>1 to hard-rod-like behavior with K<1, with a quasi-supersolid phase emerging for K<1/2. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.
Interacting ultracold atomic quantum gases provide an ideal test bed to study strongly correlated quantum matter. The interactions between atoms in such an ultracold quantum gas are typically short-ranged and well described by an effective contact potential. Introducing longer-range interactions promises the realization of novel quantum phases which are absent in systems with only short-range interactions. Trapped atoms, resonantly laser-coupled to highly excited, strongly interacting Rydberg states have been proposed as a versatile platform to realize such long-range interacting quantum matter. In a first experiment presented in this thesis, we combined the single-atom-sensitive local preparation and detection enabled by a quantum gas microscope to prepare and microscopically characterize an ensemble of rubidium-87 atoms trapped in an optical lattice in the regime of strong Rydberg blockade. There, we observe collectively enhanced optical coupling in an effective two-level system, the so-called “superatom”, and infer the presence of entanglement. Detuned optical coupling to Rydberg states, termed “Rydberg dressing”, has been proposed as an alternative approach to induce long-range interactions. Rather than directly exciting an atom to a Rydberg state, the properties of the latter are admixed to a ground state, which consequently acquires long-range interactions. In the context of this thesis, we have designed a laser system in the ultraviolet spectral range to admix Rydberg P-state character to the ground state of atoms in an optical lattice. In an emerging Ising quantum magnet, the presence of Rydberg-dressed interactions was demonstrated by an interferometric technique combined with spatially resolved spin correlation measurements. The theoretically predicted tunability of the isotropy and range of the interaction were confirmed experimentally. While these initial measurements exhibited unexpected dissipation, in a subsequent experiment in a one-dimensional spin chain this dissipation was overcome. We substantiated the improved coherence times by tracking the time evolution of the magnetization upon suddenly switching on interactions and observing coherent collapse and revival dynamics, one of the hallmarks of coherent quantum evolution. Our results establish Rydberg-dressed interactions in ultracold gases and pave the way to realize and study novel exotic quantum phases.
We study the quantum phase diagrams of Bose-Fermi mixtures of ultracold atoms confined to one dimension in an optical lattice. For systems with incommensurate densities, various quantum phases, e.g., spin- or charge-density waves, pairing, phase separation, and the Wigner crystal, are found to be dominant in different parameter regimes within a bosonization approach. The structure of the phase diagram leads us to propose that the system is best understood as a Luttinger liquid of polarons (i.e., atoms of one species surrounded by screening clouds of the other species). Special fillings, half filling for fermions, and unit filling for bosons, and the resulting gapped phases are also discussed, as well as the properties of the polarons and the experimental realization of these phases.
Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbor interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a ``spin-locked'' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a ``polarized holonic'' phase, and a crystalline phase at the filling 2/5, that we address via a semiclassical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.
We investigate the zero-temperature phases of bosonic and fermionic gases confined to one dimension and interacting via a class of finite-range soft-shoulder potentials (i.e., soft-core potentials with an additional hard-core onsite interaction). Using a combination of analytical and numerical methods, we demonstrate the stabilization of critical quantum liquids with qualitatively new features with respect to the Tomonaga-Luttinger liquid paradigm. These features result from frustration and cluster formation in the corresponding classical ground state. Characteristic signatures of these liquids are accessible in state-of-the-art experimental setups with Rydberg-dressed ground-state atoms trapped in optical lattices.
We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k F → 4k F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.