We experimentally study the effect of a slight nonorthogonality in a two-dimensional optical lattice onto resolved-sideband Raman cooling. We find that when the trap frequencies of the two lattice directions are equal, the trap frequencies of the combined potential exhibit an avoided crossing and the corresponding eigenmodes are rotated by ${45}^{\ensuremath{\circ}}$ relative to the lattice beams. Hence, tuning the trap frequencies makes it possible to rotate the eigenmodes such that both eigenmodes have a large projection onto any desired direction in the lattice plane, in particular, onto the direction along which Raman cooling works. Using this, we achieve two-dimensional Raman ground-state cooling in a geometry where this would be impossible, if the eigenmodes were not rotated. Our experiment is performed with a single atom inside an optical resonator but this is inessential and the scheme is expected to work equally well in other situations.We experimentally study the effect of a slight nonorthogonality in a two-dimensional optical lattice onto resolved-sideband Raman cooling. We find that when the trap frequencies of the two lattice directions are equal, the trap frequencies of the combined potential exhibit an avoided crossing and the corresponding eigenmodes are rotated by ${45}^{\ensuremath{\circ}}$ relative to the lattice beams. Hence, tuning the trap frequencies makes it possible to rotate the eigenmodes such that both eigenmodes have a large projection onto any desired direction in the lattice plane, in particular, onto the direction along which Raman cooling works. Using this, we achieve two-dimensional Raman ground-state cooling in a geometry where this would be impossible, if the eigenmodes were not rotated. Our experiment is performed with a single atom inside an optical resonator but this is inessential and the scheme is expected to work equally well in other situations.

arXiv:1804.06155Physical Review AJul 2, 20185 citations

Two-dimensional electronic spectroscopy

John D. Hybl, Allison W. Albrecht, Sarah M. Gallagher Faeder +1 more

Chemical Physics LettersNov 1, 1998436 citations

Electronic states in two-dimensional interacting systems

Жуков Леонид Евгеньевич

Nov 1, 19980 citations

Statistical Mechanics of Monolayers of Bose and Fermi Atoms Adsorbed on Crystalline Surfaces

J. G. Dash, Michael Bretz

We have calculated the heat capacity and entropy of Bose and Fermi atoms adsorbed on crystalline surfaces at low temperatures. The treatment is quantum mechanical at the outset, the influence of tunneling of atoms between adsorption sites being discussed in detail. It is shown by general qualitative arguments that the energy spectrum of a low-coverage monolayer contains a low-lying tunneling band of translational surface states. The finite energy width of the tunneling band ensures that the monolayer entropy due to the distribution of particles among the translational states will vanish at 0\ifmmode^\circ\else\textdegree\fi{}K. This entropy is shown to be equivalent to the configuration entropy at relatively high temperatures and therefore demonstrates the manner in which the configuration entropy is removed at 0\ifmmode^\circ\else\textdegree\fi{}K. At higher temperatures, particles become excited to higher bands which may be separated from the tunneling band by an energy gap. Quantum-statistical properties of non-interacting bosons and fermions in a two-band model are analyzed in terms of the number of adsorption sites, the tunneling band width, and the interband energy gap. When the interband gap is larger than the tunneling band width, the monolayer heat capacity displays two distinct peaks, at temperatures $\mathrm{kT}$ characteristic of the interband energy gap and of the tunneling band width. The heat capacity approaches ideal two-dimensional gas behavior at zero interband gap. The systems are studied over a range of other parameters, including the ratios of densities of states in the two bands and the number of atoms adsorbed on the surface. A qualitative discussion is given of the influence of interactions among the adsorbed atoms, and of their modifications by the substrate. The relevance of the theory to current experiments on helium monolayers is discussed.We have calculated the heat capacity and entropy of Bose and Fermi atoms adsorbed on crystalline surfaces at low temperatures. The treatment is quantum mechanical at the outset, the influence of tunneling of atoms between adsorption sites being discussed in detail. It is shown by general qualitative arguments that the energy spectrum of a low-coverage monolayer contains a low-lying tunneling band of translational surface states. The finite energy width of the tunneling band ensures that the monolayer entropy due to the distribution of particles among the translational states will vanish at 0\ifmmode^\circ\else\textdegree\fi{}K. This entropy is shown to be equivalent to the configuration entropy at relatively high temperatures and therefore demonstrates the manner in which the configuration entropy is removed at 0\ifmmode^\circ\else\textdegree\fi{}K. At higher temperatures, particles become excited to higher bands which may be separated from the tunneling band by an energy gap. Quantum-statistical properties of non-interacting bosons and fermions in a two-band model are analyzed in terms of the number of adsorption sites, the tunneling band width, and the interband energy gap. When the interband gap is larger than the tunneling band width, the monolayer heat capacity displays two distinct peaks, at temperatures $\mathrm{kT}$ characteristic of the interband energy gap and of the tunneling band width. The heat capacity approaches ideal two-dimensional gas behavior at zero interband gap. The systems are studied over a range of other parameters, including the ratios of densities of states in the two bands and the number of atoms adsorbed on the surface. A qualitative discussion is given of the influence of interactions among the adsorbed atoms, and of their modifications by the substrate. The relevance of the theory to current experiments on helium monolayers is discussed.

Physical ReviewOct 5, 196830 citations

Coupled Two-Dimensional Atomic Oscillation in an Anharmonic Trap

胡栋, 牛临潇, 张家华 +3 more

Chinese Physics LettersJan 1, 20170 citations

Cooperative ordering in lattices of interacting two-level dipoles

Robert J. Bettles, S. A. Gardiner, Charles S. Adams

We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the single resonant dipole case, and with a modified lifetime, due to the interactions between dipoles. Of particular interest is the kagome lattice, where the semiregular geometry permits simultaneous excitation of two dominant modes, one strongly subradiant, leading to an electromagnetically induced transparencylike interference in a two-level system. The interfering modes are associated with ferroelectric and antiferroelectric ordering in alternate lattice rows with long-range interactions.We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the single resonant dipole case, and with a modified lifetime, due to the interactions between dipoles. Of particular interest is the kagome lattice, where the semiregular geometry permits simultaneous excitation of two dominant modes, one strongly subradiant, leading to an electromagnetically induced transparencylike interference in a two-level system. The interfering modes are associated with ferroelectric and antiferroelectric ordering in alternate lattice rows with long-range interactions.

arXiv:1410.4776Physical Review ADec 14, 201598 citations

\mathrm{kT}

characteristic of the interband energy gap and of the tunneling band width. The heat capacity approaches ideal two-dimensional gas behavior at zero interband gap. The systems are studied over a range of other parameters, including the ratios of densities of states in the two bands and the number of atoms adsorbed on the surface. A qualitative discussion is given of the influence of interactions among the adsorbed atoms, and of their modifications by the substrate. The relevance of the theory to current experiments on helium monolayers is discussed.