Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices

Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices

7 Sep 2013 | M. Aidelsburger1,2, M. Atala1,2, M. Lohse1,2, J. T. Barreiro1,2, B. Paredes3 and I. Bloch1,2
The authors demonstrate the experimental realization of an optical lattice that generates large, tunable artificial magnetic fields using ultracold atoms. By employing laser-assisted tunneling in a tilted optical potential, they engineer spatially dependent complex tunneling amplitudes, causing atoms hopping in the lattice to accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. This setup allows for the observation of cyclotron orbits of atoms on lattice plaquettes, revealing a system described by the Hofstadter model. Additionally, the system naturally realizes the time-reversal symmetric Hamiltonian underlying the quantum spin Hall effect, where two atomic spin states with opposite magnetic moments experience opposite directions of the magnetic field. The experimental setup involves a 3D optical lattice with a magnetic field gradient along one axis, creating a linear potential with an energy offset between neighboring sites depending on the atomic spin state. The authors show that the system can be tuned to achieve a uniform effective flux of Φ = π/2 per plaquette, and they demonstrate the uniformity of the magnetic field by performing measurements in plaquettes shifted by one lattice constant. They also measure the particle current perpendicular to the initial motion as a function of spin imbalance, showing a linear dependence and a reversal of sign when flipping the spin. This work opens the path to explore topological phases of matter, including quantum Hall and $Z_2$ topological insulators, and the fractal band structure of the Hofstadter butterfly.The authors demonstrate the experimental realization of an optical lattice that generates large, tunable artificial magnetic fields using ultracold atoms. By employing laser-assisted tunneling in a tilted optical potential, they engineer spatially dependent complex tunneling amplitudes, causing atoms hopping in the lattice to accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. This setup allows for the observation of cyclotron orbits of atoms on lattice plaquettes, revealing a system described by the Hofstadter model. Additionally, the system naturally realizes the time-reversal symmetric Hamiltonian underlying the quantum spin Hall effect, where two atomic spin states with opposite magnetic moments experience opposite directions of the magnetic field. The experimental setup involves a 3D optical lattice with a magnetic field gradient along one axis, creating a linear potential with an energy offset between neighboring sites depending on the atomic spin state. The authors show that the system can be tuned to achieve a uniform effective flux of Φ = π/2 per plaquette, and they demonstrate the uniformity of the magnetic field by performing measurements in plaquettes shifted by one lattice constant. They also measure the particle current perpendicular to the initial motion as a function of spin imbalance, showing a linear dependence and a reversal of sign when flipping the spin. This work opens the path to explore topological phases of matter, including quantum Hall and $Z_2$ topological insulators, and the fractal band structure of the Hofstadter butterfly.
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