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Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

Hirokazu Miyake, Georgios A. Siviloglou, Colin J. Kennedy +2 more

We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.

arXiv:1308.1431Physical Review LettersOct 28, 20131,151 citations

Realization of the Harper Hamiltonian with Ultracold Atoms in Optical Lattices

Hirokazu Miyake, Georgios A. Siviloglou, Colin J. Kennedy +2 more

We experimentally realized the Harper Hamiltonian with charge neutral, ultracold atoms in optical lattices using laser-assisted tunneling and a potential energy gradient. The energy spectrum of this Hamiltonian is the fractal Hofstadter butterfly.

Jan 1, 20140 citations

Realizing the Harper Hamiltonian and Spin-Orbit Coupling with Laser-Assisted Tunneling in an Optical Lattice

Colin J. Kennedy, Hirokazu Miyake, William Cody Burton +3 more

Bulletin of the American Physical SocietyJun 5, 20140 citations

Publisher’s Note: Experimental observation of magic-wavelength behavior of Rb87 atoms in an optical lattice [Phys. Rev. A81, 031611 (2010)]

Nathan E. Lundblad, Malte Schlosser, J. V. Porto

Physical Review AApr 27, 20105 citations

Synthetic magnetic fields for atoms and photons

Tena Dubček, Colin J. Kennedy, Ling Lü +6 more

We present our recent results in the rapidly developing field of synthetic magnetic fields for atoms and photons, in optical lattices and photonic structures, respectively. First, we show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three- dimensional optical lattices [1]. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions [1], which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected 'Fermi arc' surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well-within experimental reach with an extension of techniques recently used in ultracold gases [2]. We also present a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices [2]. The synthetic fields emerge from the nontrivial phases of the resulting tunneling matrix elements. The scheme is straightforward to implement at optical frequencies in optically induced one- and two- dimensional dielectric photonic lattices. We propose the implementation of the Harper- Hofstadter Hamiltonian in these photonic lattices [2]. [1] Dubcek et al., Phys. Rev. Lett. 114, 225301 (2015). [2] Dubcek et al., New Journal of Phys., New J. Phys. 17, 125002 (2015).We present our recent results in the rapidly developing field of synthetic magnetic fields for atoms and photons, in optical lattices and photonic structures, respectively. First, we show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three- dimensional optical lattices [1]. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions [1], which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected 'Fermi arc' surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well-within experimental reach with an extension of techniques recently used in ultracold gases [2]. We also present a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices [2]. The synthetic fields emerge from the nontrivial phases of the resulting tunneling matrix elements. The scheme is straightforward to implement at optical frequencies in optically induced one- and two- dimensional dielectric photonic lattices. We propose the implementation of the Harper- Hofstadter Hamiltonian in these photonic lattices [2]. [1] Dubcek et al., Phys. Rev. Lett. 114, 225301 (2015). [2] Dubcek et al., New Journal of Phys., New J. Phys. 17, 125002 (2015).

Oct 28, 20160 citations

Realization of the Harper Hamiltonian with Artificial Gauge Fields in Optical Lattices

Hirokazu Miyake, Georgios A. Siviloglou, Colin J. Kennedy +2 more

Bulletin of the American Physical SocietyMar 6, 20140 citations

Publisher’s Note: Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices [Phys. Rev. Lett.111, 185302 (2013)]

Abstract

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Publisher’s Note: Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices [Phys. Rev. Lett.111, 185302 (2013)]

Abstract

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