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arXiv:1010.1782 · Physical Review A

Tunable Holstein model with cold polar molecules

Felipe Herrera, Roman V. Krems

Published Nov 9, 2011• 61 citations
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Abstract

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.

DOI
10.1103/physreva.84.051401

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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.

•Jan 1, 2014•2 citations
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 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 determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. We then show that ultracold molecules trapped in optical lattices can be used as a quantum simulator to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with external electric fields. The parameters of current experiments place them in the region where one of the transitions occurs. We also propose a scheme to measure the polaron dispersion using stimulated Raman spectroscopy.
Ultracold molecules are expected to find applications in cold chemistry, quantum phases, precision measurements and quantum information. In this thesis three novel applications of cold molecules are studied. First the thesis presents a general method for coherent control of collisions between non-identical particles. It is shown that by preparing two alkali-metal atoms in a superposition of hyperfine states, the elastic-to-inelastic cross section ratio can be manipulated at ultracold temperatures by tuning laser parameters in the presence of a magnetic field. The static field is needed to induce quantum interference between scattering states. Extensions of this scheme for ultracold molecular reactive scattering are discussed. Second, the thesis describes rotational excitons and polarons in molecular ensembles trapped in optical lattices. Rotational excitons can be manipulated using static electric and magnetic fields. For a one-dimensional molecular array with substitutional impurities any localized exciton state can be delocalized by applying a suitable electric field. The electric field induces correlations between diagonal and off-diagonal disorder. It is also shown that the translational motion of polar molecules in an optical lattice can lead to phonons. The lattice dynamics and the phonon spectrum depend on the strength and orientation of a static electric field. An array of polar molecules in an optical lattice can be described by generalized polaron model with tunable parameters including diagonal and off-diagonal exciton-phonon interactions. It is shown that in a strong electric field the system is described by a generalized Holstein model, and at weak electric fields by the Su-Schrieffer-Heeger (SSH) model. The possibility of observing a sharp polaron transition in the SSH model using polar alkali-metal dimers is discussed. Finally, the thesis presents a method to generate entanglement of polar molecules using strong off-resonant laser pulses. Bipartite entanglement between alkali-metal dimers separated by hundreds of nanometers can be generated. Maximally entangled states can be prepared by tuning the pulse intensity and duration. A scheme is proposed to observe the violation of Bell’s inequality based on molecular orientation correlation measurements. It is shown that using a combination of microwave and off-resonant optical pulses, arbitrary tripartite and many-particle states can be prepared.
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.