arXiv subjects

M. Schlosser

Publications and source records attributed to M. Schlosser.

5 recordsLinked to original sources

arXiv2010

Coherent Transport of Atomic Quantum States in a Scalable Shift Register

We demonstrate the coherent transport of two-dimensional (2D) arrays of small ensembles of neutral atoms in a shift register architecture based on 2D arrays of microlenses. We show the scalability of the transport process by presenting the repeated hand-over of atoms from site to site. We prove the conservation of coherence during transport, reloading, and a full shift register cycle. This shows that the fundamental shift sequence can be cascaded and thus scaled to complex and versatile 2D architectures for atom-based quantum information processing, quantum simulation, and the investigation of quantum degenerate gases.

quant-ph↗

arXiv2010

Experimental observation of magic-wavelength behavior in optical lattice-trapped $^{87}$Rb

We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped $^{87}$Rb atoms. Recent progress in metrology exploits so-called "magic wavelengths," whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically-trapped neutral atoms.

cond-mat.quant-gas↗

arXiv2000

Elementary derivations of identities for bilateral basic hypergeometric series

We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof ("A simple proof of Bailey's very-well-poised 6-psi-6 summation", Proc. Amer. Math. Soc., to appear) of Bailey's very-well-poised 6-psi-6 summation. Using a similar but different method, we now give elementary derivations of some transformations for bilateral basic hypergeometric series. In particular, these include M. Jackson's very-well-poised 8-psi-8 transformation, a very-well-poised 10-psi-10 transformation, by induction, Slater's general transformation for very-well-poised 2r-psi-2r series, and Slater's transformation for general r-psi-r series. Finally, we derive some new transformations for bilateral basic hypergeometric series of Chu-Gasper-Karlsson-Minton-type.

math.CA↗

arXiv2000

A simple proof of Bailey's very-well-poised 6-psi-6 summation

We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation. Similarly, we apply Rogers' nonterminating 6-phi-5 summation and elementary series manipulations to give a simple proof of Bailey's very-well-poised 6-psi-6 summation. Our method of proof extends M. Jackson's first elementary proof of Ramanujan's 1-psi-1 summation.

math.CA↗

arXiv2000

A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series

In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of Ramanujan's 1-psi-1 summation theorem. From this new A_n 1-psi-1 summation and from an A_n 1-psi-1 summation of Gustafson we deduce two lemmas for deriving simple A_n generalizations of bilateral basic hypergeometric series identities. These lemmas are closely related to the Macdonald identities for A_n. As samples for possible applications of these lemmas, we provide several A_n extensions of Bailey's 2-psi-2 transformations, and several A_n extensions of a particular 2-psi-2 summation.

math.CA↗