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International Journal of Modern Physics A

2D MATTER WAVES GUIDED IN VAN DER WAALS POTENTIALS OF DIELECTRIC SURFACES

WELITON M. SOARES, Thierry Passerat de Silans, Marcos Oriá, Martine Chevrollier

Published Apr 9, 2009• 1 citation
Publisher

Abstract

The dipolar interaction between neutral atoms and non-resonant surfaces results in attractive potentials.We describe here techniques to probe these interactions, particulary focussing in mechanisms to selectively prepare adsorption quantum states. The control of the external degrees of freedom of atoms very close to a surface allows one, in the one hand, to get values for the parameters of the potentials between neutral atoms and solid surfaces and, on the other hand, to develop schemes to explore matter behavior at low dimensionality. As an application for the 2D confined atomic matter-wave we consider Bloch oscillation for atoms in a periodic surface potential.

DOI
10.1142/s0217751x09045340

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The dipolar interaction between neutral atoms and non-resonant surfaces results in attractive potentials.We describe here techniques to probe these interactions, particulary focussing in mechanisms to selectively prepare adsorption quantum states. The control of the external degrees of freedom of atoms very close to a surface allows one, in the one hand, to get values for the parameters of the potentials between neutral atoms and solid surfaces and, on the other hand, to develop schemes to explore matter behavior at low dimensionality. As an application for the 2D confined atomic matter-wave we consider Bloch oscillation for atoms in a periodic surface potential.
Summary form only given. In atom optics, techniques were proposed to confine atoms in 2D waveguides utilizing light potentials or static magnetic fields on surfaces. For atoms close to the surface at distances shorter than the optical wavelength, the atoms-surface van der Waals interaction is inevitable and represents a complicating factor for these experiments. Here we propose to confine neutral atoms directly in a particular state of a surface potential well thanks to a laser induced Raman transfer connecting optical transitions of free cold atoms to the surface bound states. We numerically solve the 1D Schrodinger equation for cesium atom parameters. To populate the atom-surface long range states we consider cold Cs atoms near a dielectric surface interacting simultaneously with two resonant lasers.
We discuss how the presence of two-dimensional (2D) materials, such as graphene, can significantly affect two intrinsically quantum phenomena that have traditionally served as probes of the fundamental van der Waals (VDW) interaction. First, we show theoretically that Quantum Reflection (QR) of slow atoms off attractive VDW potential tails (due to interactions with 2D materials) is very strongly dependent on material characteristics (such as band structure, doping and screening level, etc). Secondly, we analyze manifestations of such 2D effects for many atoms forming a confined Bose-Einstein condensate (BEC) placed near 2D materials, which in turn makes the BEC frequency sensitive to the interface. In both cases we find that relatively small 2D material changes (either by external factors such as strain or doping, or by using gapped 2D materials instead of graphene) can have a profound effect on the above phenomena. In particular, Quantum Reflection at a given energy can experience a significant enhancement or supression (relative to conventionally used bulk materials) making 2D quantum materials an attractive playground for the study of many-body phenomena at the interface of atomic and solid state physics. *This work received support under NASA grant number 80NSSC19M0143.
The experimental achievement of Bose-Einstein condensation and Fermi degeneracy with ultracold gases boosted tremendous progresses both in theoretical methods and in the development of new experimental tools. Among them, intriguing possibilities have been opened by the implementation of optical lattices: periodic potentials for neutral atoms created by interfering laser beams. Degenerate gases in optical lattices can be forced in highly anisotropic traps, reducing the effective dimensionality of the system. From a fundamental point of view, the behavior of matter waves in reduced dimensions sheds light on the intimate properties of interparticle interactions. Furthermore, such reduced-dimensional systems can be engineered to quantum-simulate fasci- nating solid state systems, like bidimensional crystals, in a clean and controllable environment. Motivated by the exciting perspectives of this field, we devote this Thesis to the theoretical study of two systems where matter waves propagate in reduced dimensions. The long-range and anisotropic character of the dipole-dipole interaction critically affects the behavior of dipolar quantum gases. The continuous experimental progresses in this flourishing field might lead very soon to the creation of degenerate dipolar gases in optical potentials. In the first part of this Thesis, we investigate the emergence of a single dipolar-induced resonance in the two-body scattering process in quasi-one dimensional geometries. We develop a two-channel approach to describe such a resonance in a highly elongated cigar-shaped harmonic trap, which approximates the single site of a quasi-one-dimensional optical lattice. At this stage, we develop a novel atom-dimer extended Bose-Hubbard model for dipolar bosons in this quasi-one-dimensional optical lattice. Hence we investigate the T = 0 phase diagram of the model by exact diagonalization of a small-sized system, highlighting the effects of the dipolar-induced resonance on the many-body behavior in the lattice. In the second part of the Thesis, we present a general scheme to realize cold-atom quantum simulators of bidimensional atomic crystals, based on the possibility to independently trap two different atomic species. The first one constitutes a two-dimensional matter wave which interacts only with the atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach, we investigate the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagomeÌ ) lattices, studying both ideal periodic systems and experimental- sized, eventually disordered, ones. The features of the artificial atomic crystal critically depend on the two-body interspecies interaction strength, which is shown to be widely tunable via 0D-2D mixed-dimensional resonances. Keywords: matter waves, reduced dimensions, dipolar-induced resonances, mixed-dimensional resonances, extended Bose-Hubbard model, atomic artificial crystals.
van der Waals interactions between atoms and dielectric surfaces are reinvestigated. To describe the nonretarded interaction potential between a dispersive dielectric surface and an atom in an arbitrary internal energy state, we derive a general expression in terms of an integral, over real frequency, of the combined atom and surface polarizabilities. It is shown that, for excited atoms, the expression is equivalent to the one obtained by Wylie and Sipe [Phys. Rev. A 32, 2030 (1985)]. We thus demonstrate how to extend this approach to excited atoms interacting with birefringent dielectrics. For isotropic dielectrics, a method of integration in closed form allows us to derive an approximate formula for the van der Waals interaction constant in terms of resonance frequencies and oscillator strengths of both the atom and the dielectric. Frequency-dependent ``dielectric reflection'' coefficients are introduced for virtual atomic dipole couplings either in absorption or in emission. In absorption, the reflection coefficient is always positive and smaller than unity. In emission, it may take arbitrary values, positive or negative (corresponding to van der Waals repulsion). Such a behavior is shown to be related to resonant excitation exchange between the atomic system and the dielectric medium, when an atomic transition frequency gets in resonance with a dielectric absorption band. Numerical calculations performed for the cesium-sapphire system are shown to be in good agreement with data obtained by selective-reflection spectroscopy. Finally, experimental tests of the birefringent character of the sapphire response are discussed.
The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson's spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.