Ultracold atomic and molecular systems provide a useful platform for understanding quantum many-body physics. Recent progresses in AMO experiments enable access to systems exhibiting long-range interactions, opening a window for exploring the interplay between long-range interactions and dissipation. In this thesis, I develop theoretical approaches to study non-equilibrium dynamics in systems where such interplay is crucial.I first focus on a system of KRb molecules, where dipolar interactions and fast chemical reactions coexist. Using a classical kinetic theory and Monte Carlo methods, I study the evaporative cooling in a quasi-two-dimensional trap, and develop a protocol to reach quantum degeneracy. I also study the case where molecules are loaded into an optical lattice, and show that the strong dissipation induces a quantum Zeno effect, which suppresses the molecule loss. The analysis requires including multiple bands to explain recent experimental measurements, and can be used to determine the molecular filling fraction.I also investigate a system of radiating atoms, which experience long-range elastic and dissipative interactions. I explore the collective behavior of atoms and the role of atomic motion. The model is validated by comparison with a recent light scattering experiment using Sr atoms. I also show that incoherently pumped dipoles can undergo a dynamical phase transition to synchronization, and study its signature in the quantum regime.
Ultracold atomic and molecular systems provide a useful platform for understanding quantum many-body physics. Recent progresses in AMO experiments enable access to systems exhibiting long-range interactions, opening a window for exploring the interplay between long-range interactions and dissipation. In this thesis, I develop theoretical approaches to study non-equilibrium dynamics in systems where such interplay is crucial.I first focus on a system of KRb molecules, where dipolar interactions and fast chemical reactions coexist. Using a classical kinetic theory and Monte Carlo methods, I study the evaporative cooling in a quasi-two-dimensional trap, and develop a protocol to reach quantum degeneracy. I also study the case where molecules are loaded into an optical lattice, and show that the strong dissipation induces a quantum Zeno effect, which suppresses the molecule loss. The analysis requires including multiple bands to explain recent experimental measurements, and can be used to determine the molecular filling fraction.I also investigate a system of radiating atoms, which experience long-range elastic and dissipative interactions. I explore the collective behavior of atoms and the role of atomic motion. The model is validated by comparison with a recent light scattering experiment using Sr atoms. I also show that incoherently pumped dipoles can undergo a dynamical phase transition to synchronization, and study its signature in the quantum regime.
Remarkable experimental progress and theoretical advancements in the study of strongly corre- lated systems have opened up new doors towards a better understanding of interesting states of matter. Such states could possibly be used to develop novel technological applications based on the principles of quantum mechanics. In recent years, the investigation of both complex solid state and ultracold atom systems has lead to a number of fascinating discoveries with regards to their non-equilibrium properties. One route to probe non-equilibrium physics is to consider the evolution of open systems defined by the coupling to an external environment introducing dissipation. Engineering the environment according to predefined requirements can then be used to dynamically prepare states which are difficult to access otherwise. This thesis explores the dynamics of many-body open quantum systems aiming at under- standing the effects resulting from the interplay of kinetic motion, interactions and dissipation in different physical settings. First, we build upon recent developments concerning the coupling of ultracold atoms to optical resonators which are subject to photon losses. We show how the dissipation can trigger an attractor dynamics towards a topologically non-trivial steady state that is robust against perturbations. The numerically obtained full open system evolution en- ables us to not only characterize in detail the steady state but also to analyze the features of the approaching dynamics. Second, we study the propagation of two-time correlation functions in interacting quantum spin-1/2 chains in contact with an environment causing dephasing. Pro- vided with the numerically exact full time-evolution, we identify an algebraic scaling regime where time-translation invariance breaks down and uncover the emergence of aging dynam- ics. Finally, we study a system of interacting fermionic atoms in a one-dimensional lattice with particle loss at the central site. There we report on the dissipation-induced deceleration of the non-equilibrium dynamics known as the quantum Zeno effect. As in the majority of cases quantum many-body systems are not solvable analytically, another central aspect of this thesis deals with adapting numerical methods based on matrix product state algorithms to investigate open quantum systems dynamics.
Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task.\nIn this thesis, we emphasize how the unique features of particular atomic and molecular sys- tems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline- earth atoms. In particular, we show how groundstate properties--for instance anomalous mass enhancement--can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.
Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.
Quantum optics and ultracold gases are established fields, but they almost do not overlap: the quantum nature of light is typically neglected in works on ultracold atoms. In our work the quantumness of both light and ultracold matter plays a key role. First, we show that light is a quantum nondemolition (QND) probe of many-body phases: they can be distinguished by correlations and full distribution functions (we consider bosons, fermions, and dipolar molecules). Light is not only sensitive to densities, but also to the matter-field interference. Second, we prove that the measurement backaction constitutes a novel source of competitions in many-body systems, especially, for non-QND cases. This leads to a plethora of new phenomena: oscillations of multipartite entangled modes, protection and break-up of fermion pairs, antiferromagnetic orders, long-range pair tunnelling and entanglement beyond Hubbard models. We prove that feedback control induces phase transitions and tunes their universality class. Third, the quantization of trapping potential (quantum optical lattices) leads to novel phases, including both density orders (supersolids, density waves) and bond orders of matter fields (superfluid and supersolid dimers, trimers). Results beyond ultracold atoms include: We extend the paradigm of feedback control from the state control to control of phase transitions. We present the measurement backaction as a novel source of competitions in many-body physics. We merge quantum Zeno dynamics and non-Hermitian physics and show a novel type of Zeno phenomena with Raman transitions beyond Zeno dynamics. We propose quantum simulators based on collective light-matter interaction. Our models can be applied to arrays of other systems (qubits). In general, quantum measurements and feedback produce new phenomena untypical to both closed unitary systems and open dissipative ones in many-body physics.
This thesis reports on the construction of a novel experimental apparatus to create an ultracold sample of chemical stable 23Na40K polar molecules at their absolute ground states. The long range nature of the dipolar interactions between the ground state molecules, is expected to facilitate to observe new quantum many-body states and to simulate prototypical lattice spin models for exploring quantum magnetism and high Tc superconductivity. The experimental procedures are presented in this thesis including: trapping and cooling 23Na and $ ^{40}\rm{K}$ atoms to quantum degeneracy, associating weakly bound state molecules with Feshbach resonances, and transferring the Feshbach molecules to the rovibrational ground states via stimulated Raman adiabatic passage. As a result, successful transfer has been demonstrated in our experiment with a single-path transfer efficiency ≃60% via a hyperfine non-resolved intermediate state ∣d3Π,ν=5,J=1,Ω=1⟩. In addition, a perturbative theoretical study on the Fermi liquid properties of a single-component weakly-interacting two dimensional dipolar fermions with dipole moments d oriented perpendicularly to the plane of their translational motion is presented in the thesis. When the dipole moments are tilted with respect to the translational plane, the effect of anisotropic interaction appears, and collective excitations in the collisionless regime are studied in this configuration. Furthermore, stable dilute supersolid states with two-dimensional bosonic dipoles are predicted to exist with an additional three-body repulsive contact interaction. These novel quantum effects should be accessible experimentally once the NaK ground state molecules reach quantum degeneracy by further evaporative cooling.
The scientific interface between atomic, molecular and optical (AMO) physics, condensed matter, and quantum information science has recently led to the development of new insights and tools that bridge the gap between macroscopic quantum behavior and detailed microscopic intuition. While the dialogue between these fields has sharpened our understanding of quantum theory, it has also raised a bevy of new questions regarding the out-of-equilibrium dynamics and control of many-body systems. This thesis is motivated by experimental advances that make it possible to produce and probe isolated, strongly interacting ensembles of disordered particles, as found in systems ranging from trapped ions and Rydberg atoms to ultracold polar molecules and spin defects in the solid state. The presence of strong interactions in these systems underlies their potential for exploring correlated many-body physics and this thesis presents recent results on realizing fractionalization and localization. From a complementary perspective, the controlled manipulation of individual quanta can also enable the bottom-up construction of quantum devices. To this end, this thesis also describes blueprints for a room-temperature quantum computer, quantum credit cards and nanoscale quantum thermometry.