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Register a new userMagnetic interactions of cold atoms with anisotropic conductors
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T. David
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We analyze atom-surface magnetic interactions on atom chips where the magnetic trapping potentials are produced by current carrying wires made of electrically anisotropic materials. We discuss a theory for time dependent fluctuations of the magnetic potential, arising from thermal noise originating from the surface. It is shown that using materials with a large electrical anisotropy results in a considerable reduction of heating and decoherence rates of ultra-cold atoms trapped near the surface, of up to several orders of magnitude. The trap loss rate due to spin flips is expected to be significantly reduced upon cooling the surface to low temperatures. In addition, the electrical anisotropy significantly suppresses the amplitude of static spatial potential corrugations due to current scattering within imperfect wires. Also the shape of the corrugation pattern depends on the electrical anisotropy: the preferred angle of the scattered current wave fronts can be varied over a wide range. Materials, fabrication, and experimental issues are discussed, and specific candidate materials are suggested.
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This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su-Schrieffer-Heeger model, the Hofstadter-Harper model, the Haldane model and the Kane-Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.
When an electron or hole is in a conduction band of a crystal, it can be very different from 2, depending upon the crystalline anisotropy and the direction of the applied magnetic induction ${bf B}$. In fact, it can even be 0! To demonstrate this quantitatively, the Dirac equation is extended for a relativistic electron or hole in an orthorhombically-anisotropic conduction band with effective masses $m_j$ for $j=1,2,3$ with geometric mean $m_g=(m_1m_2m_3)^{1/3}$. The appropriate Foldy-Wouthuysen transformations are extended to evaluate the non-relativistic Hamiltonian to $O({rm m}c^2)^{-4}$, where ${rm m}c^2$ is the particles Einstein rest energy. For ${bf B}||hat{bf e}_{mu}$, the Zeeman $g_{mu}$ factor is $2{rm m}sqrt{m_{mu}}/m_g^{3/2} + O({rm m}c^2)^{-2}$. While propagating in a two-dimensional (2D) conduction band with $m_3gg m_1,m_2$, $g_{||}<<2$, consistent with recent measurements of the temperature $T$ dependence of the parallel upper critical induction $B_{c2,||}(T)$ in superconducting monolayer NbSe$_2$ and in twisted bilayer graphene. While a particle is in its conduction band of an atomically thin one-dimensional metallic chain along $hat{bf e}_{mu}$, $g<<2$ for all ${bf B}={bf abla}times{bf A}$ directions and vanishingly small for ${bf B}||hat{bf e}_{mu}$. The quantum spin Hall Hamiltonian for 2D metals with $m_1=m_2=m_{||}$ is $K[{bf E}times({bf p}-q{bf A})]_{perp}sigma_{perp}+O({rm m}c^2)^{-4}$, where ${bf E}$ and ${bf p}-q{bf A}$ are the planar electric field and gauge-invariant momentum, $q=mp|e|$ is the particles charge, $sigma_{perp}$ is the Pauli matrix normal to the layer, $K=pmmu_B/(2m_{||}c^2)$, and $mu_B$ is the Bohr magneton.
We present a general theory of current deviations in straight current carrying wires with random imperfections, which quantitatively explains the recent observations of organized patterns of magnetic field corrugations above micron-scale evaporated wires. These patterns originate from the most efficient electron scattering by Fourier components of the wire imperfections with wavefronts along the $pm 45^{circ}$ direction. We show that long range effects of surface or bulk corrugations are suppressed for narrow wires or wires having an electrically anisotropic resistivity.
In two dimensions, a system of self-gravitating particles collapses and forms a singularity in finite time below a critical temperature $T_c$. We investigate experimentally a quasi two-dimensional cloud of cold neutral atoms in interaction with two pairs of perpendicular counter-propagating quasi-resonant laser beams, in order to look for a signature of this ideal phase transition: indeed, the radiation pressure forces exerted by the laser beams can be viewed as an anisotropic, and non-potential, generalization of two-dimensional self-gravity. We first show that our experiment operates in a parameter range which should be suitable to observe the collapse transition. However, the experiment unveils only a moderate compression instead of a phase transition between the two phases. A three-dimensional numerical simulation shows that both the finite small thickness of the cloud, which induces a competition between the effective gravity force and the repulsive force due to multiple scattering, and the atomic losses due to heating in the third dimension, contribute to smearing the transition.
Two-dimensional ($p_{x}+ip_{y}$) superfluids/superconductors offer a playground for studying intriguing physics such as quantum teleportation, non-Abelian statistics, and topological quantum computation. Creating such a superfluid in cold fermionic atom optical traps using p-wave Feshbach resonance is turning out to be challenging. Here we propose a method to create a $p_{x}+ip_{y}$ superfluid directly from an s-wave interaction making use of a topological Berry phase, which can be artificially generated. We discuss ways to detect the spontaneous Hall mass current, which acts as a diagnostic for the chiral p-wave superfluid.
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