3D Sisyphus Cooling of Trapped Ions

S. Ejtemaee and P. C. Haljan

Phys. Rev. Lett. 119, 043001 – Published 25 July 2017

Abstract

Using a laser polarization gradient, we realize 3D Sisyphus cooling of ${}^{171}{Yb}^{+}$ ions confined in and near the Lamb-Dicke regime in a linear Paul trap. The cooling rate and final mean motional energy of a single ion are characterized as a function of laser intensity and compared to semiclassical and quantum simulations. Sisyphus cooling is also applied to a linear string of four ions to obtain a mean energy of 1–3 quanta for all vibrational modes, an approximately order of magnitude reduction below Doppler cooled energies. This is used to enable subsequent, efficient sideband laser cooling.

Received 1 March 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.043001

Physics Subject Headings (PhySH)

Cold atoms & matter waves Cooling & trapping Trapped ions

Atom & ion cooling

Atomic, Molecular & Optical

Authors & Affiliations

S. Ejtemaee and P. C. Haljan^*

Department of Physics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada

^*Corresponding author. phaljan@sfu.ca

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Issue

Vol. 119, Iss. 4 — 28 July 2017

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Images

Figure 1
(a) Relevant energy levels of ${}^{171}{Yb}^{+}$ for Sisyphus cooling. (b) An example of a single-ion Sisyphus cooling event from optical pumping between shifted harmonic trapping potentials associated with two effective sublevels of the ${{}^{2}S}_{1 / 2} | F = 1 ⟩$ ground state. The shift in potentials is due to dipole forces from the 1D polarization gradient shown, which is formed by counterpropagating, linearly polarized Sisyphus beams in a transverse magnetic field. (c) Laser beam configuration: Double-pass acousto-optic modulators (AOMs) are used to control the power and frequency of the Sisyphus beams, which enter the vacuum chamber and trap from the north and south sides. Perpendicular Raman beams entering from the east and south are used to probe ion motion in the axial ( $\hat{z}$ ) trap direction; west and south beams are used for the transverse ( $\hat{x}$ and $\hat{y}$ ) directions. Shown at right are the axial and transverse Raman wave vector directions overlaid on the principal axes of the trap.
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Figure 2
(a) Experiment sequence for assessing Sisyphus cooling of a single trapped ion. Each step of the $N_{c}$ -pulse Sisyphus sequence involves a cooling pulse and a reset (i.e., repump) to the $| ↑ ⟩$ state using optical pumping (OP) and microwave pulses. (b)–(e) Raman carrier Rabi oscillations in the (b)–(c) transverse and (d)–(e) axial directions with cooling times of [(b),(d)] $10 \times 0.1$ and [(c),(e)] $80 \times 0.1 ms$ . Gray lines are the measured probability $P_{↑}$ of obtaining $| ↑ ⟩$ averaged over 50 runs per time value. Red and blue lines are fits to extract $\bar{n}$ . (f) Cooling dynamics for transverse (red) and axial (blue) directions at $s_{0} = 11$ . Error bars are statistical uncertainties from fits. Dashed lines are exponential fits used to extract the cooling rate. Only points with $\bar{n} \leq 15$ are considered to omit the initial cooling dynamics.
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Figure 3
Sisyphus cooling rate $Γ_{c}$ (top) and steady-state mean phonon number ${\bar{n}}_{s s}$ (bottom) as a function of a single-beam saturation parameter $s_{0}$ for the transverse direction (left) and axial direction (right). Panels include experimental data (black filled circles) and predictions from 1D (dashed blue line) and 3D (solid blue line) semiclassical simulations, and 1D quantum simulations with initial $n_{i} = 8$ Fock state (dotted red line) and initial $\bar{n} = 22$ thermal state (red circles). Semiclassical simulations average over 1000 Monte Carlo runs. Quantum simulations average over 40 (80) runs for Fock (thermal) initial states. Vertical error bars for data are statistical uncertainties from fits, and horizontal error bars account for calibration uncertainty and drifts in laser intensity. In (b), error bars for the quantum simulation with the thermal initial state are bootstrap uncertainties. Shaded error bands and error bars for quantum simulations in (c) and (d) show the standard deviation of fluctuations at the steady state.
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Figure 4
(a) Raman Rabi oscillations on the first red sideband transition for the $y$ -zigzag vibrational mode ( $ω / 2 π = 0.48 MHz$ ) in a Sisyphus-cooled linear string of four ${}^{171}{Yb}^{+}$ ions. The initial internal state is either $| ↓, ↓, ↓, ↓ ⟩$ (red) or $| ↑, ↑, ↑, ↑ ⟩$ (blue). Vertical scale proportional to the number of ions in $| ↑ ⟩$ averaged over 50 runs. Black lines are a combined fit to extract ${\bar{n}}_{s s} = 2.0$ and include approximate models for optical pumping and contrast loss for red and blue curves, respectively. (b) Mean phonon number for all four-ion vibrational modes following Sisyphus cooling at $s_{0} = 15$ . Trap frequencies ${0.84, 0.87, 0.34} MHz$ . Dashed line shows $ω^{- 1}$ scaling for reference. (c) Same mode as (a) but Sisyphus then sideband cooled ( $\bar{n} \leq 0.05$ from fit).
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