Interactions between quantum particles can give rise to behaviors greater than the sum of their parts. The low-dimensional cold atomic framework provides a unique platform with exquisite control and enhanced correlations to develop a deeper understanding of such quantum phenomena, with promise for emerging technologies. In this thesis, I study novel quantum many-body physics in spinor gases trapped in optical lattices and develop efficient theoretical tools for such investigations. My work illustrates the central role of spin and charge degrees of freedom for comprehending and manipulating intricate quantum behaviors. With a broad goal of understanding the emergent physics in strongly correlated many-body systems, in Chapter 2, I investigate the two-component coupled Bose gas. An unprecedented phase emerges from the coupling of two components in the nearest-neighbor sites via a resonant two-photon Raman transition. Furthermore, coupling provides a novel tuning knob for the controlled manipulation of spin phases. Probing for behaviors away from the Mott state, the limitations of existing theoretical approaches are exposed. To address this, in Chapter 3, I develop a powerful theoretical framework for the unrestricted study of strongly correlated systems, valid even for large spin systems. This generalized effective spin-chain (GESC) formalism has numerous advantages: elegant mathematical form, computationally efficient parameterization, generalized for arbitrary spin and statistics, and universality: not limited to lattice systems. Importantly, leveraging a spin–charge separated form, it provides a unique vantage into system behaviors originating from quantum fluctuations. Motivated by the immense potential of anyons in cold atomic setups, in Chapter 4, I investigate the combined effect of fractional statistics and the presence of multiple components on their ground state and dynamical properties. This reveals the potential of statistical-phase-induced transition between different system phenomena. The GESC formalism is extended to consider anyons and used to obtain insights into the origin of exchange-phase-dependent and independent behavior. I demonstrate the versatility of the GESC formalism, in Chapter 5, to Bose–Fermi mixtures, beyond one-dimensional systems, and to consider long-range interactions. In doing so, avenues are provided for leveraging the immense utility of this formalism in exploring the novel physics such systems have to offer.
Interactions between quantum particles can give rise to behaviors greater than the sum of their parts. The low-dimensional cold atomic framework provides a unique platform with exquisite control and enhanced correlations to develop a deeper understanding of such quantum phenomena, with promise for emerging technologies. In this thesis, I study novel quantum many-body physics in spinor gases trapped in optical lattices and develop efficient theoretical tools for such investigations. My work illustrates the central role of spin and charge degrees of freedom for comprehending and manipulating intricate quantum behaviors. With a broad goal of understanding the emergent physics in strongly correlated many-body systems, in Chapter 2, I investigate the two-component coupled Bose gas. An unprecedented phase emerges from the coupling of two components in the nearest-neighbor sites via a resonant two-photon Raman transition. Furthermore, coupling provides a novel tuning knob for the controlled manipulation of spin phases. Probing for behaviors away from the Mott state, the limitations of existing theoretical approaches are exposed. To address this, in Chapter 3, I develop a powerful theoretical framework for the unrestricted study of strongly correlated systems, valid even for large spin systems. This generalized effective spin-chain (GESC) formalism has numerous advantages: elegant mathematical form, computationally efficient parameterization, generalized for arbitrary spin and statistics, and universality: not limited to lattice systems. Importantly, leveraging a spin–charge separated form, it provides a unique vantage into system behaviors originating from quantum fluctuations. Motivated by the immense potential of anyons in cold atomic setups, in Chapter 4, I investigate the combined effect of fractional statistics and the presence of multiple components on their ground state and dynamical properties. This reveals the potential of statistical-phase-induced transition between different system phenomena. The GESC formalism is extended to consider anyons and used to obtain insights into the origin of exchange-phase-dependent and independent behavior. I demonstrate the versatility of the GESC formalism, in Chapter 5, to Bose–Fermi mixtures, beyond one-dimensional systems, and to consider long-range interactions. In doing so, avenues are provided for leveraging the immense utility of this formalism in exploring the novel physics such systems have to offer.
This thesis is devoted to exploit strong correlations among ultracold atoms in order to create novel, exotic quantum states. In the first two chapters, we devise dynamical out-of-equilibrium preparation schemes which lead to intriguing final states. First of all, we propose to create the elusive supersolid state via a quantum quench protocol. Supersolids – quantum hybrids exhibiting both superflow and solidity – have been envisioned long ago, but have not been demonstrated in experiment so far. Our proposal to create a supersolid state is perfectly accessible with current technology and may clear the way to the experimental observation of supersolidity. Another out-of-equilibrium preparation scheme is discussed in the second chapter, giving rise to novel Cooper pairs of bosons. Ordinarily, Cooper pairs are composed of fermions – not so in our setup! We show that a Mott state of local bosonic Bell pairs can evolve into a Cooper-paired state of bosons, where the size of the pairs becomes macroscopic. This state can be prepared via a quick, diabatic ramp from the Mott into the superfluid regime. Furthermore, we propose to use bosons featuring conditional-hopping amplitudes in order to create Abelian anyons in one-dimensional optical lattices. We derive an exact mapping between anyons and bosons via a “fractional” Jordan-Wigner transformation. We suggest to employ a laser-assisted tunneling scheme to establish the many-particle state of “conditional-hopping bosons”, thus realizing a gas of Abelian anyons. The fractional statistics phase can be directly tuned by the lasers. The realization of non-Abelian anyons would be especially delightful, due to their significance in topological quantum computation schemes. We propose to employ strongly correlated bosons in one-dimensional optical lattices to create the Pfaffian state – which is known to host non-Abelian anyons as elementary excitations. In this setup, three-body correlations are required to dominate the system, which we model by on-site interactions of atoms with diatomic molecules. Finally, we use strong correlations in one-dimensional systems to create the effect of spin-charge separation, as formulated theoretically first in 1968. For a model of two-component bosons we compute the effective mass of a spin-flip excitation via Bethe Ansatz. In the strongly correlated regime, we show that the effective mass reaches the total mass of all particles in the system. The spin wave thus travels much more slowly than the density wave, giving rise to a strong spin-charge separation.
The interplay between spin and motional degrees of freedom in interacting electron systems has been a long-standing research topic in condensed matter physics. Interactions can modify the behavior of individual electrons and give rise to emergent collective phenomena such as superconductivity and colossal magnetoresistance. Theoretical understanding of non-equilibrium dynamics in interacting fermionic matter is limited, however, and many open questions remain. Ultracold atomic Fermi gases, with precisely controllable parameters, offer an outstanding opportunity to investigate the emergence of collective behavior in out-of-equilibrium settings. In this thesis we will describe how an optical lattice clock operated with neutral Fermionic atoms can be turned into a quantum simulator of charged particles in a strong magnetic field. We will then discuss the counterintuitive notion that weak interactions in a Fermi gas can lead to large scale collective behavior and global correlations. These ideas are being tested experimentally at JILA and the University of Toronto. We also investigate in detail the so-called spin model approximation which is used extensively throughout this thesis.
Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin, which have Feshbach-induced spin-dependent interactions, to produce a quantum dimer model. I propose an experiment to detect the ground state in this system. In a final project, I develop tools to simulate the dynamics of fermionic superfluids in which fermions interact via a short-range interaction.
Ultra-cold quantum gases subjected to light-induced synthetic gauge potentials have become an emergent field of theoretical and experimental studies. Because of the novel application of two-photon Raman transitions, ultra-cold neutral atoms behave like charged particles in magnetic field. The Raman coupling naturally gives rise to an effective spin-orbit interaction which couples the atom’s center-of-mass motion to its selected pseudo-spin degrees of freedom. Combined with unprecedented controllability of interactions, geometry, disorder strength, spectroscopy, and high resolution measurement of momentum distribution, etc., we are truly in an exciting era of ful- filling and going beyond Richard Feynman’s vision of realizing quantum simulators to better understand the quantum mechanical nature of the universe, manifested immensely in the ultra-cold regimes. In this dissertation, we present a collection of theoretical progresses made by the doctoral candidate and his colleagues and collaborators. From the past few years of work, we mainly address three aspects of the synthetic spin-orbit and light field induced coupling in ultracold quantum gases: a) The ground-state physics of single- particle system, two-body bound states, and many-body systems, all of which are subjected to spin-orbit coupling originated from synthetic gauge potentials; b) The symmetry breaking, topological phase transition and quench dynamics, which are conveniently offered by the realized experimental setup; c) The proposal and impli- cations of light field induced dynamical spin-orbit coupling for atoms inside optical cavity. Our work represents an important advancement of theoretical understanding to the active research frontier of ultra-cold atom physics with spin-orbit coupling.
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.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].