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Quantum control of dynamics of quasiparticles in periodic and disordered lattice potentials

Xiang, Ping

Published Jan 1, 2014• 2 citations
Publisher

Abstract

This thesis describes research on controlling the dynamics of quasiparticles in periodic and disordered lattice potentials. Working with model systems of arrays of atoms and molecules trapped in optical lattices, I focus on, but not limited to, the rotational excitons of polar molecules and propose to use external fields to control the binding and propagation of quasiparticles. First, we study the binding of rotational excitons in a periodic potential. We show that non-linear interactions of such excitons can be controlled by an electric field. The exciton-exciton interactions can be tuned to induce exciton pairing, leading to the formation of biexcitons and three-body bound states of excitons. In addition, we propose a non-optical way to create biexcitons by splitting a high-energy exciton into two low-energy excitons. Second, we present schemes to control the propagation of a collective excited state in ordered and disordered aggregates of coupled particles. We demonstrate that the dynamics of these excitations can be controlled by applying a transient external potential which modifies the phase of the quantum states of the individual particles. The method is based on an interplay of adiabatic and sudden time scales in the quantum evolution of the many-body states. We show that specific phase transformations can be used to accelerate or decelerate quantum energy transfer and spatially focus delocalized excitations onto different parts of arrays of quantum particles. For the model systems of atoms and molecules trapped in an optical lattice, we consider possible experimental implementations of the proposed technique and study the effect of disorder, due to the presence of impurities, on its fidelity. We further show that the proposed technique can allow control of energy transfer in completely disordered systems. Finally, in an effort to refine the theoretical tools to study dynamics of quasiparticles, I extend calculations of lattice Green's functions to disordered systems. We develop a generic algorithm that can be easily adapted to systems with long-range interactions and high dimensionalities. As an application of the method, we propose to use the Green's function to study the tunneling of biexciton states through impurities.

DOI
10.14288/1.0165942

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•Jan 1, 2008•0 citations
This thesis describes research on controlling the dynamics of quasiparticles in periodic and disordered lattice potentials. Working with model systems of arrays of atoms and molecules trapped in optical lattices, I focus on, but not limited to, the rotational excitons of polar molecules and propose to use external fields to control the binding and propagation of quasiparticles. First, we study the binding of rotational excitons in a periodic potential. We show that non-linear interactions of such excitons can be controlled by an electric field. The exciton-exciton interactions can be tuned to induce exciton pairing, leading to the formation of biexcitons and three-body bound states of excitons. In addition, we propose a non-optical way to create biexcitons by splitting a high-energy exciton into two low-energy excitons. Second, we present schemes to control the propagation of a collective excited state in ordered and disordered aggregates of coupled particles. We demonstrate that the dynamics of these excitations can be controlled by applying a transient external potential which modifies the phase of the quantum states of the individual particles. The method is based on an interplay of adiabatic and sudden time scales in the quantum evolution of the many-body states. We show that specific phase transformations can be used to accelerate or decelerate quantum energy transfer and spatially focus delocalized excitations onto different parts of arrays of quantum particles. For the model systems of atoms and molecules trapped in an optical lattice, we consider possible experimental implementations of the proposed technique and study the effect of disorder, due to the presence of impurities, on its fidelity. We further show that the proposed technique can allow control of energy transfer in completely disordered systems. Finally, in an effort to refine the theoretical tools to study dynamics of quasiparticles, I extend calculations of lattice Green's functions to disordered systems. We develop a generic algorithm that can be easily adapted to systems with long-range interactions and high dimensionalities. As an application of the method, we propose to use the Green's function to study the tunneling of biexciton states through impurities.
An elementary excitation in an aggregate of coupled particles generates a collective excited state. We show that the dynamics of these excitations can be controlled by applying a transient external potential which modifies the phase of the quantum states of the individual particles. The method is based on an interplay of adiabatic and sudden time scales in the quantum evolution of the many-body states. We show that specific phase transformations can be used to accelerate or decelerate quantum energy transfer and spatially focus delocalized excitations onto different parts of arrays of quantum particles. We consider possible experimental implementations of the proposed technique and study the effect of disorder due to the presence of impurities on its fidelity. We further show that the proposed technique can allow control of energy transfer in completely disordered systems.
Rotational excitation of polar molecules trapped in an optical lattice gives rise to rotational excitons. Here we show that nonlinear interactions of such excitons can be controlled by an electric field. The exciton-exciton interactions can be tuned to induce exciton pairing, leading to the formation of biexcitons. Tunable nonlinear interactions between excitons can be used for many applications ranging from the controlled preparation of entangled quasiparticles to the study of polaron interactions and the effects of nonlinear interactions on quantum energy transport in molecular aggregates.
Ultracold polar molecules trapped on an optical lattice is a many-body system that, under appropriate conditions, may support collective excitations reminiscent of excitons in solid state crystals. Here, we discuss the rotational excitations of molecules on an optical lattice leading to rotational Frenkel excitons. Apart from solid hydrogen, there is no other natural system that exhibits rotational excitons. The rotational excitons have unique properties that can be exploited for tuning non-linear exciton interactions and exciton-impurity scattering by applying an external electric field. We show that this can be used to explore the competing role of the dynamical and kinematic exciton-exciton interactions in excitonic energy transfer and to study quantum localization in a dynamically tunable disordered potential. The rotational excitons can also be used as a basis for quantum simulation of condensed matter models that cannot be realized with ultracold atoms. As an example, we discuss the possibility of engineering the Holstein model with polar molecules on an optical lattice.
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
We show that a two-species mixture of polar molecules trapped on an optical lattice gives rise to a system of rotational excitons in the presence of tunable impurities. The exciton-impurity interactions can be controlled by an external electric field, which can be exploited for quantum simulation of localization phenomena in disordered media. We demonstrate that an external electric field can be used to induce resonant enhancement of the exciton-impurity scattering cross sections and delocalization of excitonic states in a correlated one-dimensional disorder potential.
Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations between the spin of adjacent atoms are realisable with optical lattices forming arrays of double-well potentials. We study the creation of a lattice containing a spin-encoded Bell-pair in each double-well, and show that resilient, highly-entangled many-body states are realisable using lattice manipulations. We show that the creation of cluster-like states encoded on Bell-pairs can be achieved using these systems, and we provide measurement networks that allow the execution of quantum algorithms while maintaining intact the resilience of the system. Finally, we investigate the possibility to create a diatomic molecular state and simulate Fermi systems via the excitation to Rydberg levels of ground-state atoms trapped in optical lattices. We develop a method based on symbolical manipulations to compute the interaction parameters between highly-excited electrons, and evaluate them for different electronic configurations. We use these parameters to investigate the existence of diatomic molecular states with equilibrium distances comparable to typical lattice spacings. Considering the possibility to excite atoms trapped in an optical lattice to Rydberg levels such that the electronic cloud of neighbouring atoms overlap, we propose a model describing their interactions and compute its parameters. If such systems were realised, they would allow the simulation of Fermi systems at a temperature much below the Fermi temperature, thus enabling the observation of quantum phenomena hitherto inaccessible with current technology.