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arXiv:1208.0363 · Annual review of cold atoms and molecules

ROTATIONAL EXCITATIONS OF POLAR MOLECULES ON AN OPTICAL LATTICE: FROM NOVEL EXCITON PHYSICS TO QUANTUM SIMULATION OF NEW LATTICE MODELS

Marina Litinskaya, Roman V. Krems

Published Jan 27, 2013• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/9789814440400_0002

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Bulletin of the American Physical Society•Jan 21, 2015•0 citations
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.
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.
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.
We show that an ensemble of polar molecules trapped in an optical lattice can be considered as a controllable open quantum system. The coupling between collective rotational excitations and the motion of the molecules in the lattice potential can be controlled by varying the strength and orientation of an external dc electric field as well as the intensity of the trapping laser. The system can be described by a generalized Holstein Hamiltonian with tunable parameters and can be used as a quantum simulator of excitation energy transfer and polaron phenomena. We show that the character of excitation energy transfer can be modified by tuning experimental parameters.
Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.
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.
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t∼1t \sim 1t∼1 sec. For 3D lattices with 555555 sites in each dimension and vacancy concentration $ 90~\%$, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2. Our results raise a general question whether quantum particles with long-range tunnelling can undergo quantum localization in 3D lattices with substitutional disorder.