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New mechanisms for external field control of microscopic interactions in ultracold gases

Zhiying Li

Published Jan 1, 2009• 0 citations
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Abstract

This Thesis describes new mechanisms for controlling elastic and inelastic collisions of ultracold atoms and molecules with static electromagnetic and laser fields. The dynamical properties of ultracold atoms are usually tuned in experiments by applying an external magnetic field to induce a Feshbach resonance. The work presented in this Thesis demonstrates the possibility of inducing and manipulating Feshbach resonances with electric fields. We discuss in detail the mechanisms of electric-field-induced resonances in ultracold mixtures of alkali metal atoms and demonstrate that electric fields may shift and split the magnetic resonances. We show that electric fields may spin up the collision complex of ultracold atoms and induce anisotropic scattering which may be exploited in experiments on many-body dynamics of ultracold gaseous mixtures. The mechanisms of electric-field-induced resonances described in this Thesis allow for two-dimensional control of inter-particle interactions, leading to total control over ultracold gases. To guide future experiments, we generate accurate interaction potentials for ultracold Li--Rb mixtures by fitting positions and widths of experimentally measured Feshbach resonances. Ultracold atomic and molecular gases can be confined by laser fields in one or two dimensions which produces an optical lattice of ultracold particles. We develop a multichannel scattering theory for collisions of atoms and molecules in two dimensions and explore the effects of the confining laser potential on inelastic and reactive collisions of ultracold atoms and molecules in a 1D optical lattice. We show that ultracold collisions can be controlled in a quasi-2D geometry by varying the orientation of a magnetic field with respect to the confinement plane normal and demonstrate that the threshold energy dependence of cross sections for inelastic collisions in an optical lattice can be tuned by varying the confining potential and the magnetic field. Our results show that applying laser confinement in one dimension may stabilize ultracold systems with large scattering lengths, which may open up interesting opportunities for studies of ultracold controlled chemistry and might lead to a new research direction of ultracold chemistry in restricted geometries.

DOI
10.14288/1.0061165

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This Thesis describes new mechanisms for controlling elastic and inelastic collisions of ultracold atoms and molecules with static electromagnetic and laser fields. The dynamical properties of ultracold atoms are usually tuned in experiments by applying an external magnetic field to induce a Feshbach resonance. The work presented in this Thesis demonstrates the possibility of inducing and manipulating Feshbach resonances with electric fields. We discuss in detail the mechanisms of electric-field-induced resonances in ultracold mixtures of alkali metal atoms and demonstrate that electric fields may shift and split the magnetic resonances. We show that electric fields may spin up the collision complex of ultracold atoms and induce anisotropic scattering which may be exploited in experiments on many-body dynamics of ultracold gaseous mixtures. The mechanisms of electric-field-induced resonances described in this Thesis allow for two-dimensional control of inter-particle interactions, leading to total control over ultracold gases. To guide future experiments, we generate accurate interaction potentials for ultracold Li--Rb mixtures by fitting positions and widths of experimentally measured Feshbach resonances. Ultracold atomic and molecular gases can be confined by laser fields in one or two dimensions which produces an optical lattice of ultracold particles. We develop a multichannel scattering theory for collisions of atoms and molecules in two dimensions and explore the effects of the confining laser potential on inelastic and reactive collisions of ultracold atoms and molecules in a 1D optical lattice. We show that ultracold collisions can be controlled in a quasi-2D geometry by varying the orientation of a magnetic field with respect to the confinement plane normal and demonstrate that the threshold energy dependence of cross sections for inelastic collisions in an optical lattice can be tuned by varying the confining potential and the magnetic field. Our results show that applying laser confinement in one dimension may stabilize ultracold systems with large scattering lengths, which may open up interesting opportunities for studies of ultracold controlled chemistry and might lead to a new research direction of ultracold chemistry in restricted geometries.
The research field of cold and ultracold atoms and molecules is rapidly growing and expanding into different areas of research such as quantum information science and condensed matter physics. The success of this field is due to the possibility of precisely controlling and manipulating atoms and molecules at low temperatures. The progress in this field relies on the development of new methods for controlling collisional dynamics and interactions of particles with electromagnetic fields. This Thesis describes research on modification of the collisional dynamics of ultracold atoms and molecules by external laser and microwave fields as well as new methods for the detection of weak electromagnetic fields. First, we study the scattering of atoms and molecules confined in a 2D geometry by optical lattices. In particular we develop a theory for scattering in 2D and derive the equations for the threshold dependence of the collision cross sections. We show that inelastic processes and chemical reactions can be suppressed under strong confinement in one dimension and can be controlled by varying the orientation of the external field with respect to the plane of confinement. Next, we present a rigorous theory of low-temperature molecular collisions in the presence of a microwave field. The microwave field can theoretically be used to trap and control polar molecules. The molecular collisions may lead to trap loss and decoherence. We develop a rigorous quantum theory for molecular scattering in the presence of microwave fields. We study inelastic, spin-changing molecular collisions and Feshbach resonances in the presence of microwave fields. We demonstrate that inelastic collisions accompanied by absorption of microwave photons can be significant. The detection of weak electromagnetic fields is very important for various applications ranging from fundamental measurements to biomagnetic imaging, and for tests of microwave chips. We present a method for the detection of weak electromagnetic fields in a wide range of frequencies from sub-kHz to THz with ultracold polar molecules. We show that using ultracold molecules one can achieve the sensitivity of two orders of magnitude larger than with a similar method based on ultracold Rb atoms.
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.
We present a detailed analysis of Feshbach resonances in ultracold collisions of Li and Cs atoms in the presence of superimposed electric and magnetic fields. We show that electric fields induce resonances through couplings between the sss- and ppp-wave scattering channels and modify the scattering length to a great extent. Electric-field-induced resonances lead to the anisotropy of ultracold scattering and provide the diagnostics for magnetic ppp-wave resonances in ultracold gases. We show that the electric field couplings may shift the positions of sss-wave magnetic resonances, thereby making the electric field control of ultracold atoms possible even far away from ppp-wave resonances. Finally, we demonstrate that electric fields may rotate and spin up the collision complex of ultracold atoms at substantial rates.
We present a detailed analysis of Feshbach resonances in ultracold collisions of Li and Cs atoms in the presence of superimposed electric and magnetic fields. We show that electric fields induce resonances through couplings between the sss- and ppp-wave scattering channels and modify the scattering length to a great extent. Electric-field-induced resonances lead to the anisotropy of ultracold scattering and provide the diagnostics for magnetic ppp-wave resonances in ultracold gases. We show that the electric field couplings may shift the positions of sss-wave magnetic resonances, thereby making the electric field control of ultracold atoms possible even far away from ppp-wave resonances. Finally, we demonstrate that electric fields may rotate and spin up the collision complex of ultracold atoms at substantial rates.
The effects of combined external electric and magnetic fields on elastic collisions in ultracold Li-Rb mixtures are studied using recently obtained experimentally verified potentials. Our analysis provides both quantitative predictions for and a detailed physical interpretation of the phenomena arising from electric-field-induced interactions. It is shown that the electric field shifts the positions of intrinsic magnetic Feshbach resonances, generates copies of resonances previously restricted to a particular partial-wave collision to other partial-wave channels, and splits Feshbach resonances into multiple resonances for states of nonzero angular momenta. It was recently observed that the magnetic dipole-dipole interaction can also lift the degeneracy of a ppp-wave state splitting of the associated ppp-wave Feshbach resonance into two distinct resonances at different magnetic fields. Our work shows that the splitting of the resonances produced by an applied electric field is more than 1 order of magnitude larger. This phenomenon offers a complementary way to produce and tune an anisotropic interaction and to study its effect on the many-body physics of heteronuclear atomic gases.
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to ε/ℏω0\sqrt{ε/\hbar ω_0}ε/ℏω0​​, where εεε is the kinetic energy and ω0ω_0ω0​ is the oscillation frequency of the trapped particles in the confinement potential.