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arXiv:0802.1618 · Physical Review A

Coupling of electronic and motional dynamics in a cold-atom optical lattice

Hashem Zoubi, Helmut Ritsch

Published Feb 9, 2009• 8 citations
arXivHTMLPDF

Abstract

We study the coupling of resonant electronic excitations to vibrational center-of-mass motion of ultracold atoms in an optical lattice, when ground- and excited-state optical potentials differ. On-site excitation-vibration coupling can be approximately treated by renormalizing the effective transition energy, which appears, e.g., in lattice clock setups. In addition the dipole-dipole coupling between neighboring sites mediates emission and absorption of vibrational quanta in conjunction with optical transitions. This mechanism for excitation of vibrations can lead to significant heating of the lattice atoms motion during resonant light interaction. We calculate estimates of the corresponding parameters for a gas in the Mott-insulator state from a perturbation expansion in small atomic displacements.

DOI
10.1103/physreva.79.023411

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We study the coupling of resonant electronic excitations to vibrational center-of-mass motion of ultracold atoms in an optical lattice, when ground- and excited-state optical potentials differ. On-site excitation-vibration coupling can be approximately treated by renormalizing the effective transition energy, which appears, e.g., in lattice clock setups. In addition the dipole-dipole coupling between neighboring sites mediates emission and absorption of vibrational quanta in conjunction with optical transitions. This mechanism for excitation of vibrations can lead to significant heating of the lattice atoms motion during resonant light interaction. We calculate estimates of the corresponding parameters for a gas in the Mott-insulator state from a perturbation expansion in small atomic displacements.
This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e.g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.
We form a 1D optical lattices for Cs atoms using light tuned a few thousand linewidths below the 6S1/2(F equals 4) yields 6P3/2(F' equals 5) transition at 852 nm. In this far-off- resonance lattice the time scale for damping of motional coherences and kinetic energy can be orders of magnitude longer than the vibrational oscillation period for atoms trapped in the lattice potential wells. Atoms are loaded directly into deeply bound states, by adiabatic transfer from a superimposed, near-resonance optical lattice. This yields a mean vibrational excitation n approximately equals 0.3, and localization (Delta) z approximately (lambda) /20 deep in the Lamb-Dicke regime. Light scattering subsequently heats the atoms, but the initial rate is only of order 10-3 vibrational quanta per oscillation period. Low vibrational excitation, localization in the Lamb-Dicke regime and low heating rates make these atoms good candidates for resolved- sideband Raman cooling, and for the generation and study of non-classical states of center-of-mass motion. We propose a scheme for resolved-sideband Raman cooling and quantum state preparation; the scheme employs Raman coupling between magnetic sublevels induced by the lattice light field itself.
We study the resonant electronic excitation dynamics for ultracold atoms trapped in a deep optical lattice prepared in a Mott-insulator state. Excitons in these artificial crystals are similar to Frenkel excitons in noble atom or molecular crystals. They appear when the atomic excited state linewidth is smaller than the exciton bandwidth generated by dipole-dipole coupling. When the atoms are placed within a cavity the electronic excitations and the quantized cavity mode get coupled. In the collective strong coupling regime excitations form two branches of cavity polaritons with Rabi splitting larger than the atomic and the cavity linewidth. To demonstrate their properties we calculate the transmission, reflection, and absorption spectra for an incident weak probe field, which show resonances at the polariton frequencies.
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.
We compute the near-resonant dipole-dipole interaction between atoms in a three-dimensional optical lattice. After a general derivation, we concentrate specifically on the case of a J=1/2\ensuremath{\rightarrow}J=3/2 off-resonant transition, in which case the excited electronic states can be adiabatically eliminated. We present in detail the spatial dependence of the resulting effective dipole-dipole potential, and discuss the physical origin of its anisotropy. In addition to impacting the center-of-mass motion of the atoms, the effective dipole-dipole potential can induce electronic transitions within one or both atoms. The symmetries of the matrix elements corresponding to these various mechanisms are also commented upon. \textcopyright{} 1996 The American Physical Society.
Photoexcited states are relaxed by transferring energy to the environments. In order to study which coupling allows fast energy transfer to lattice vibrations in correlated electron systems, we calculate the time evolutions of the kinetic energies of different types and frequencies of lattice vibrations. The one-dimensional half-filled Hubbard model is augmented with electron-lattice couplings that modulate transfer integrals, site energies, and Coulomb repulsion strengths. The time-dependent Schr\"odinger equation is solved for exact many-electron wave functions, and the classical equation of motion for the lattice displacements. In order to transfer energy to classical lattice vibrations that modulate transfer integrals or site energies, the translational invariance must be broken to give optical activity to an electronic excitation with wave number $\ensuremath{\pi}$ and to these lattice vibrations. On the other hand, a certain amount of energy is always transferred to lattice vibrations that modulate Coulomb repulsion strengths, irrespective of the symmetry of the ground state, as long as the corresponding electron-lattice couplings are present. In strongly correlated electron systems, these couplings can be strong, although they are usually insignificant because their effects on the equilibrium properties can be absorbed into redefinition of Coulomb repulsion strengths. We will discuss competition or collaboration between energy-transfer pathways through different types of electron-lattice couplings.