An advanced cooling scheme, incorporating entropy engineering, is vital for isolated artificial quantum systems designed to emulate the low-temperature physics of strongly correlated electron systems. This study theoretically demonstrates a cooling method employing multicomponent Fermi gases with SU(N)-symmetric interactions, focusing on the case of ^{173}Yb atoms in a two-dimensional optical lattice. Adiabatically introducing a nonuniform state-selective laser gives rise to two distinct subsystems: a central low-entropy region, exclusively composed of two specific spin components, acts as a quantum simulator for strongly correlated electron systems, while the surrounding N-component mixture retains a significant portion of the entropy of the system. The total particle numbers for each component are good quantum numbers, creating a sharp boundary for the two-component region. The cooling efficiency is assessed through extensive finite-temperature Lanczos calculations. The results lay the foundation for quantum simulations of two-dimensional systems of Hubbard or Heisenberg type, offering crucial insights into intriguing low-temperature phenomena in condensed-matter physics.
An advanced cooling scheme, incorporating entropy engineering, is vital for isolated artificial quantum systems designed to emulate the low-temperature physics of strongly correlated electron systems. This study theoretically demonstrates a cooling method employing multicomponent Fermi gases with SU(N)-symmetric interactions, focusing on the case of ^{173}Yb atoms in a two-dimensional optical lattice. Adiabatically introducing a nonuniform state-selective laser gives rise to two distinct subsystems: a central low-entropy region, exclusively composed of two specific spin components, acts as a quantum simulator for strongly correlated electron systems, while the surrounding N-component mixture retains a significant portion of the entropy of the system. The total particle numbers for each component are good quantum numbers, creating a sharp boundary for the two-component region. The cooling efficiency is assessed through extensive finite-temperature Lanczos calculations. The results lay the foundation for quantum simulations of two-dimensional systems of Hubbard or Heisenberg type, offering crucial insights into intriguing low-temperature phenomena in condensed-matter physics.
Accessing new regimes in quantum simulation requires the development of new techniques for quantum state preparation. We demonstrate the quantum state engineering of a strongly correlated many-body state of the two-component repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an ultralow entropy doublon band insulator created through entropy redistribution. After isolating the band insulator, we change the underlying potential to expand it into a half-filled system. The final many-body state realized shows strong antiferromagnetic correlations and a temperature below the exchange energy. We observe an increase in entropy, which we find is likely caused by the many-body physics in the last step of the scheme. This technique is promising for low-temperature studies of cold-atom-based lattice models.
At present, there is considerable interest in using atomic fermions in optical lattices to emulate the mathematical models that have been used to study strongly correlated electronic systems. Some of these models, such as the 2-dimensional fermion Hubbard model, are notoriously difficult to solve, and their key properties remain controversial despite decades of studies. It is hoped that the emulation experiments will shed light on some of these long-standing problems. A successful emulation, however, requires reaching temperatures as low as 10(-12) K and beyond, with entropy per particle far lower than what can be achieved today. Achieving such low-entropy states is an essential step and a grand challenge of the whole emulation enterprise. In this article, we point out a method to literally squeeze the entropy out from a Fermi gas into a surrounding Bose-Einstein condensed gas, which acts as a heat reservoir. This method allows one to reduce the entropy per particle of a lattice Fermi gas to a few percent of the lowest value obtainable today.
The present thesis is devoted to the study of physical phenomena emerging from strong correlations in strongly interacting quantum many-body systems with several components. Hubbard models are widely used as minimal models which take into account the interactions between particles and they have been studied in relation to phenomena such as Mott localization, unconventional superconductivity, quantum magnetism and many others. All of these striking phenomena share their origin from the strong correlations among fermions induced by their mutual interactions. Furthermore, condensed matter models are usually realized only in an approximate fashion in actual solid-state systems, making the situation all the more puzzling and hard to be treated analytically or numerically. Therefore, a great effort has been performed to simulate Hubbard models in a system of atoms cooled down to ultra low temperatures and trapped in optical lattices. The most peculiar feature of cold atoms experiments consists in the possibility of tuning relevant physical parameters of the systems, as the density or the interactions among atoms, using laser and/or magnetic fields. This paved the way to the observation of fundamental quantum states of matter as the weakly interacting Bose-Einstein condensate, the super fluid to Mott insulator transition, the super fluid BEC-BCS crossover, the Mott transition in systems of composite fermions and so on. Hence, it is considered of great interest establishing connections between the quantum simulations cold atomic toolbox and systems realized in solid-state physics...
Over the past few decades, quantum simulation with ultracold atoms in optical lattices has proven to be a useful tool for understanding many-body Hamiltonians.One of its primary directions is the experimental study of the Fermi Hubbard Model (FHM), which aims to capture the fundamental properties of cuprate superconductors and has produced a wide range of intriguing phenomena, including the metal-to-Mott insulator transition, antiferromagnetism, strange metallicity, pseudogap physics, and is frequently used in the study of superconductivity. In recent years, new kinds of quantum simulators have emerged, and in particular we focus on two of them: 1) quantum simulators that study high symmetry fermions in optical lattices, and 2) optical tweezer arrays which provide a bottom-up approach to engineering the FHM. The first class of emerging quantum simulators utilizes alkaline-earth-like atoms (AEA’s) – which have large nuclear spin I (such as 173Yb and 87Sr) – to engineer the SU(N = 2I +1) symmetric FHM, where N = 2,..., 10. The second class corresponds to quantum simulators based on optical tweezer arrays which combine deterministic single tweezer ground state loading and tunneling coupled sites. Both classes of quantum simulators are interesting on their own. For example, the SU(N) FHM is generating a lot of interest due to its connections to multiorbital solid state systems and theoretical predictions of rich phase diagrams which exhibit exotic phases of matter, including unusual ones like spin liquids. On the other hand, optical tweezer arrays have gained a lot of attention since they can be used to study arbitrary geometries and access very low-entropy samples. This thesis reports on the numerical study of both quantum simulation architectures. Results of the SU(N) FHM at finite temperature, for different fillings and interaction strengths that span the non-interacting to the strongly interacting limit are obtained using Determinant Quantum Monte Carlo, Exact Diagonalization, and Numerical Linked Cluster Expansion. In particular, we focus on how thermodynamic and magnetic observables, such as the number of on-site pairs, energy, entropy, spin correlations, and structure factors depend on N, the interaction strength U/t, temperature T/t, and the anisotropy of tunneling rates. Our results demonstrate that in a homogeneous square lattice with one particle per site on average, thermodynamic observables as a function of temperature obey a universal scaling with N, and that short-range antiferromagnetic correlations are stronger for larger N and in lower dimensions. In addition, we present theory-experiment comparisons where possible, where we perform thermometry and provide a precise characterization of the equation of state of the SU(N) FHM. Our results emerge as a tool to perform thermometry in experiments from theory-experiment comparison and also provide guidance for future experiments with AEAs in optical lattices. Additionally, we present calculations using numerically precise discrete variable representation methods for two-dimensional stroboscopic tweezer arrays and compare the outcomes with experimental data. We quantify the effects of stroboscopic potentials on Hubbard parameters like the interaction strength U and the tunneling t in optical tweezer arrays and illustrate how heating from the stroboscopic potential relies on strobe frequency. Our calculations enable evaluation and optimization of two-dimensional tweezer array experiments. An important milestone of the results of this thesis corresponds to the record temperatures and entropies achieved with these quantum simulation architectures: 1) the coldest fermions ever created in nature in absolute temperature and in cold atoms, and 2) the lowest entropy per particle fermions ever created, albeit in a so-far small system.
We propose and analyze a method for preparing low entropy many-body states in isolated quantum optical systems of atoms, ions, and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a "conformal cooling quench" remove sufficient entropy within experimentally accessible timescales? Finite-temperature, time-dependent matrix product state calculations reveal that even moderately sized bath regions can remove enough energy and entropy density to expose coherent low-temperature physics. The protocol is particularly natural in systems with long-range interactions, such as lattice-trapped polar molecules and Rydberg-excited atoms, where the magnitude of the Hamiltonian scales directly with the interparticle spacing. To this end, we propose simple, near-term implementations of conformal cooling quenches in systems of atoms or molecules, where signatures of low-temperature phases may be observed.
A major focus in condensed matter physics is to study the origin of exotic quantum phases such as coexistent and inhomogeneous phases, quantum criticality, and secondary ordered phases close to quantum critical points. Exotic phenomena in strongly correlated systems occur due to competing complex interactions of spin, charge, lattice, and orbital degrees of freedom. Complex quantum phases in strongly correlated systems are challenging, but they might be very useful due to their possible functionality to make advance devices. In order to understand, utilize, and optimize such behaviors, we need to improve our understanding of these systems. Studies in cold atom systems are of interest since cold atom experiments provide a control on model parameters. In this thesis, we use novel analytical and computational techniques to treat strongly interacting bosonic systems. Taking advantage of the very versatile quantum Monte Carlo Stochastic Green Function algorithm, we studied several interesting problems. First, we explore a recently developed new confining method for cold atoms on optical lattices. Atoms are confined via a hopping integral that decreases as a function of the distance from the center of the lattice. This method might lead to lower temperatures than existing diagonal confinement methods. Next, we study the ground state phase diagram of interacting bosons on a ring-shape lattice with a region of weak hopping integrals. The model, an extension of the well known Bose-Hubbard model, develops a novel local Mott phase in addition to the usual Mott and superfluid phases in the homogeneous system. This might provide a new insight to the description of atomtronics applications. Finally, we study the two species Bose Hubbard model in a two-dimensional lattice. This model presents novel phases due to the complexity associated with multiple species. Its phase diagram shows ordered and coexistence phases including a ferromagnetic phase separated phase with high entropy. This phase might be accessible experimentally. The novel phases found from our studies are linked to experiments on ultra-cold atoms trapped by laser beams.