Phase-Stable Free-Space Optical Lattices for Trapped Ions

C. T. Schmiegelow, H. Kaufmann, T. Ruster, J. Schulz, V. Kaushal, M. Hettrich, F. Schmidt-Kaler, and U. G. Poschinger

Phys. Rev. Lett. 116, 033002 – Published 21 January 2016

Abstract

We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, and we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mechanisms. Finally, we employ lattice-induced phase shifts for inferring the variation of the ion position over the $157 μ m$ range along the trap axis at accuracies of better than 6 nm.

Received 21 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.033002

Physics Subject Headings (PhySH)

Atom & ion trapping & guiding Cold gases in optical lattices

Atomic, Molecular & Optical

Authors & Affiliations

C. T. Schmiegelow, H. Kaufmann, T. Ruster, J. Schulz, V. Kaushal, M. Hettrich, F. Schmidt-Kaler, and U. G. Poschinger^*

Institut für Physik, Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany

^*poschin@uni-mainz.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 116, Iss. 3 — 22 January 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Realization of phase-stable standing waves for trapped ions. (a) An ion trapped in a segmented Paul trap [24] is exposed to two laser beams with polarizations $ϵ_{x, y}$ generating an interference pattern of alternating $lin ⊥ lin$ polarization. The ion is trapped by applying a voltage on the center segment (yellow), kicked by sudden voltage changes in the neighboring segments (dark yellow), and shifted along the trap axis by changing the voltage at the next-nearest-neighbor trap segments (orange). (b) Sketch of the interferometer comprised of the two laser beams, controlled by acousto-optical modulators (AOMs), and the trapped ion. (c) Relevant energy levels of ${}^{40}{Ca}^{+}$ . The lattice beams off-resonantly drive the $S_{1 / 2} \leftrightarrow P_{1 / 2}$ transition, inducing a position-dependent ac-Stark shift of the ground state sublevels.
Reuse & Permissions
Figure 2
Coherent combination of spin-dependent optical and electrical displacement operations. (a) Phase-space picture of the optical kicks (red or blue) and electrical kicks (orange arrows). The direction of the optical kick is given by the spin, while the direction $θ$ of the electrical kick is determined by the delay time. The resulting oscillator displacement $α$ is indicated by the red ( $| ↓ ⟩$ ) and blue ( $| ↑ ⟩$ ) dots and dashed lines, tracing out the respective circles upon variation of $θ$ . (b) Measured oscillator displacement $| α |$ after the electrical kick versus delay between optical and electrical kick for both spin initializations (blue squares, $| ↑ ⟩$ ; red circles, $| ↓ ⟩$ ). Solid curves are fits to Eq. (3). The signals for opposite spin initializations are out of phase by $π (1.02 \pm 0.04)$ . (c) Same data, shown in polar phase-space coordinates.
Reuse & Permissions
Figure 3
Temporal phase evolution of a spin superposition state in the phase-stabilized SW. (a) Spin-echo signal $S (z, t)$ versus exposure time $t$ for an ion cooled close to the motional ground state. We probe at an antinode (red), a node (blue), and halfway between (magenta). The solid lines are fits to Eq. (4). We infer a mean phonon number of $\bar{n} = 0.4 (2)$ and rms phase fluctuations of $Δ ϕ = 0.048 (3) π$ . (b) Data without ground state cooling. For the fit, we use $Δ ϕ$ obtained from the sideband-cooled data and infer a mean phonon number $\bar{n} = 28 (3)$ .
Reuse & Permissions
Figure 4
(a) Small panels: Spin-echo signal versus shift voltage for resolved scans (blue) in steps of 1.2 mV resolving the SW oscillations. Large panel: Same signal (red) for a step of 18 mV, leading to position steps larger than the SW period, which gives rise to aliasing. The aliased data is also shown in the small panels (red). All fits shown in black pertain to Eq. (6) in conjunction with fifth order polynomial $z_{eq} (V_{shift})$ . The variation of the period is due to the inhomogeneity of the electric field generated by the shift and trap electrodes. (b) Variation of $z_{eq}$ with respect to $V_{shift}$ , i.e., $z_{eq}^{'} (V_{shift})$ , as inferred from the resolved scans (blue dots), the fit of $z (V_{shift})$ to these (dashed blue line), and the fit to the aliased data (solid black line). The dot-dashed magenta curve corresponds to the equilibrium positions as obtained from electrostatic simulations of the trap structure.
Reuse & Permissions

Physical Review Letters