Creating State-Dependent Lattices for Ultracold Fermions by Magnetic Gradient Modulation

Gregor Jotzu, Michael Messer, Frederik Görg, Daniel Greif, Rémi Desbuquois, and Tilman Esslinger

Phys. Rev. Lett. 115, 073002 – Published 13 August 2015

Abstract

We demonstrate a versatile method for creating state-dependent optical lattices by applying a magnetic field gradient modulated in time. This allows for tuning the relative amplitude and sign of the tunneling for different internal states. We observe substantially different momentum distributions depending on the spin state of fermionic ${}^{40}K$ atoms. Using dipole oscillations, we probe the spin-dependent band structure and find good agreement with theory. In situ expansion dynamics demonstrate that one state can be completely localized while others remain itinerant. A systematic study shows negligible heating and lifetimes of several seconds in the Hubbard regime.

Received 21 April 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.073002

Authors & Affiliations

Gregor Jotzu, Michael Messer, Frederik Görg, Daniel Greif, Rémi Desbuquois, and Tilman Esslinger

Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland

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Vol. 115, Iss. 7 — 14 August 2015

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Images

Figure 1
(a) Magnetic moments of the $F = 9 / 2$ hyperfine manifold of ${}^{40}K$ as a function of the external field. Blue, red, and green denote the $| m_{F} = - 9 / 2 ⟩$ , $| - 5 / 2 ⟩$ , and $| - 1 / 2 ⟩$ sublevels throughout. (b) The effective energy bands in quasimomentum space are given by the time average of the “shaken” bands. As the force depends on the internal state, so does the effective band. (c) A cloud of ${}^{40}K$ (blue) is trapped in a retroreflected laser beam. An oscillating current $I (τ)$ in a single coil creates the oscillating gradient $\partial_{x} | B |$ . The uniform external field $B_{ext}$ is provided by additional coils.
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Figure 2
Fermions in spin-dependent bands. (a) Quasimomentum distribution in the lattice, summed over $q_{y}$ and $q_{z}$ , as a function of gradient modulation amplitude for the $| - 9 / 2 ⟩$ (left) and $| - 5 / 2 ⟩$ (right) state. The effective band structures for each spin state are shown as diagrams for $κ_{- 9 / 2} = 0$ , 1.2, 2.4, and 3.0. (b) Second moment of the distributions [38]. Blue circles (red diamonds) denote $| - 9 / 2 ⟩$ ( $| - 5 / 2 ⟩$ ) atoms. Data show mean $\pm$ s.d. of five measurements. (c) Dipole oscillations in the spin-dependent bands (illustrated in the inset) show how the tunneling is renormalized for each spin, relative to the oscillations without modulation (which have frequency $ν_{0}$ ). The oscillation frequency squared is proportional to the tunneling and is determined from fits to at least 60 measurements of the time-dependent quasimomentum peak position. Error bars show the fit uncertainty and solid lines the Bessel functions for each spin, calculated without free parameters. The star indicates $| - 9 / 2 ⟩$ atoms without a lattice. (d) Tunneling ratio of the two spins as a function of modulation amplitude.
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Figure 3
Spin-dependent expansion dynamics for $κ_{- 9 / 2} = 2.41 (4)$ . (a) While the effective tunneling for the $| - 9 / 2 ⟩$ atoms is suppressed, atoms in other states are still itinerant and the cloud expands. (b) Gaussian width $w_{x}$ of the real-space density distribution [38] of spin-polarized noninteracting $| - 9 / 2 ⟩$ (blue circles), $| - 5 / 2 ⟩$ (red diamonds), and $| - 1 / 2 ⟩$ (green squares) atoms, compared to their initial values. (c) Expansion of a repulsively interacting mixture of $| - 9 / 2 ⟩$ and $| - 5 / 2 ⟩$ atoms. Data show mean $\pm$ s.d. of five (b) or nine (c) measurements. Solid lines are linear fits.
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Figure 4
Heating measurements. (a) Schematic of the ramp protocol. (b) Temperature after the full ramp ( $τ_{W} = 0$ ), heating rates and lifetimes as a function of modulation amplitude. Grey circles (orange diamonds) indicate a lattice with tunneling $t = h \times 174 Hz$ (67 Hz). The line (shaded region) shows the results (error bars) in the dipole trap without the optical lattice and gradient modulation. (c) Same quantities measured as a function of modulation frequency, for $κ_{- 9 / 2} = 1.0$ . Zero frequency indicates no modulation. Data and error bars are mean $\pm$ s.d. of ten measurements (upper panels), or the results of linear (center) or exponential (lower) fits to the temperature and atom number versus $τ_{W}$ .
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