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Bulletin of the American Physical Society

Interference Signatures of Abelian and Non-Abelian Aharonov-Bohm effect on Neutral Atoms in Optical Lattices

Mingxia Huo, Wei Nie, David A. W. Hutchinson, L. C. Kwek

Published Mar 19, 2013• 0 citations
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Abstract

Ming-Xia Huo, Nie Wei, David A.W. Hutchinson, 2 and Leong Chuan Kwek 3 Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616

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Ming-Xia Huo, Nie Wei, David A.W. Hutchinson, 2 and Leong Chuan Kwek 3 Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616
Hong-Yi Su, Jing-Ling Chen∗,1, 2 Fu-Lin Zhang †,3 Chunfeng Wu, Zhen-Peng Xu, Mile Gu, Sai Vinjanampathy, and L. C. Kwek 5 Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 Physics Department, School of Science, Tianjin University, Tianjin 300072, China Pillar of Engineering Product Development, Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682 National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616 (Dated: January 13, 2015)
Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 andNational Institute of Education and Institute of Advanced Studies,Nanyang Technological University, 1 Nanyang Walk, Singapore 637616(Dated: January 11, 2014)We study an experimentally feasible qubit system employing neutral currents. Our system is based on bosoniccold atoms trapped in ring-shaped optical lattice potentials. The lattice makes the system strictly one dimen-sional and it provides the infrastructure to realize a tunable ring-ring interaction. By breaking the Galileaninvariance we demonstrate how atomic currents through the lattice provide a realization of a qubit. We breakthe Galilean invariance either by artificially creating a phase slip in a single ring, or by considering two ho-mogeneous ring lattices, coupled by tunneling interaction. The Hamiltonian of the system effectively leads toa washboard potential in the phase representation, tilted by the applied ’flux’. The single qubit infrastructureis experimentally investigated with tailored optical potentials. An experimentally feasible scheme of the two-ring-qubit is discussed. In this case, the dynamics is demonstrated to show macroscopic quantum self trapping.Time-of-flight expansion maps the pattern of atomic currents into detectable atomic density distributions. Basedon our analysis, we provide viable protocols to initialize, address, and read-out the qubit.
We study lower bounds for quantum distributed computing, where a set of nodes (representing quantum computers) interconnected by an underlying network consisting of (bandwidth-restricted) links, communicate using quantum communication. Nodes have unlimited computational power and may share an unlimited number of entangled qubits. Our main contribution is a simple uniform technique for proving lower bounds for quantum distributed algorithms. In particular, we identify a new quantum communication model called the Server model which provides a connection between distributed algorithms and communication complexity: it is strong enough to capture the hardness of several distributed computing problems, while weak enough that several hard problems in two-party communication complexity remain hard; to this end, we identify a set of communication complexity techniques that can be carried over to the Server model, namely techniques based on nonlocal games. We show that these techniques serve as a fundamental tool in proving lower bounds in quantum distributed computing. The new techniques help us to prove several non-trivial quantum distributed lower bounds (which are the first-known quantum bounds for fundamental global problems such as minimum spanning tree, shortest paths etc.), some of which are new even in the classical setting. First, it allows us to show that all previous classical lower bounds of more than twenty verification and optimization graph problems in [Das Sarma et al., STOC 11] also hold in the quantum setting. Many of these bounds are tight, implying a large class of problems that do not gain an advantage from quantum effects. Our results also imply the following new results in the classical communication models: (1) the first randomized lower bounds for Hamiltonian cycle and spanning tree verification problems in both the distributed computing and the communication complexity model, answering the open problem of Das Sarma et al. and subsuming many bounds in [Babai, Frankl, and Simon, FOCS 96], and (2) the first lower bound that is tight for all weight aspect ratios, matching previous upper bounds of [Elkin, STOC 04]. Submitted for a Regular Presentation. The full version of this paper can be found as [15] at http://arxiv.org/abs/1207.5211. ∗Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. E-mail: elkinm@cs.bgu.ac.il. †Division of Mathematical Sciences, Nanyang Technological University, Singapore 637371 & Centre for Quantum Technologies, National University of Singapore, Singapore 117543. E-mail: hklauck@gmail.com. Research at the Centre for Quantum Technologies is funded by the Singapore Ministry of Education and the National Research Foundation. ‡Division of Mathematical Sciences, Nanyang Technological University, Singapore 637371. Work partially done while at University of Vienna, Austria. E-mail: danupon@gmail.com. §Division of Mathematical Sciences, Nanyang Technological University, Singapore 637371 & Department of Computer Science, Brown University, Providence, RI 02912, USA. E-mail: gopalpandurangan@gmail.com. Supported in part by the following research grants: Nanyang Technological University grant M58110000, Singapore MOE Academic Research Fund (AcRF) Tier 2 grant MOE2010-T2-2-082, and a grant from the US-Israeli Binational Science Foundation (BSF).