Rotational Coherence Times of Polar Molecules in Optical Tweezers

Sean Burchesky, Loïc Anderegg, Yicheng Bao, Scarlett S. Yu, Eunmi Chae, Wolfgang Ketterle, Kang-Kuen Ni, and John M. Doyle

Phys. Rev. Lett. 127, 123202 – Published 17 September 2021

Abstract

Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7) ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a “magic” angle. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.

Received 3 June 2021
Accepted 19 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.123202

Physics Subject Headings (PhySH)

Coherent control

Atomic, Molecular & Optical

Authors & Affiliations

Sean Burchesky^1,2,*, Loïc Anderegg ^1,2, Yicheng Bao^1,2, Scarlett S. Yu^1,2, Eunmi Chae³, Wolfgang Ketterle ^2,4, Kang-Kuen Ni^1,2,5, and John M. Doyle^1,2

¹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
²Harvard-MIT Center for Ultracold Atoms, Cambridge, Massachusetts 02138, USA
³Department of Physics, Korea University, Seongbuk-gu, Seoul 02841, South Korea
⁴Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁵Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

^*Corresponding author. burchesky@g.harvard.edu

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Vol. 127, Iss. 12 — 17 September 2021

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Images

Figure 1
CaF structure. (a) The $X$ -state level structure of CaF. Quantum numbers $N$ , $J$ , and $F$ denote rotation, electron $spin + rotation$ , and total angular momentum, respectively. The lower and upper qubit states are labeled $| 0 ⟩$ and $| 1 ⟩$ . (b) The Ramsey pulse sequence uses a $10 μ s$ $π / 2$ pulse to create a coherent superposition of $| 0 ⟩$ and $| 1 ⟩$ states. The Bloch vector precesses, accumulating phase until the second $π / 2$ pulse with a phase shift ( $ϕ$ ) rotates the Bloch vector back into the measurement basis prior to imaging the $N = 1$ population. (c) The tweezer light polarization and applied magnetic field lie in the plane perpendicular to the $k$ vector of the tweezer light.
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Figure 2
Coherence time. (a),(b) During the Ramsey and spin-echo pulse sequences, we scan the phase ( $ϕ$ ) of the second $π / 2$ pulse for a fixed precession time. The projection of the wave function on $| 1 ⟩$ oscillates as a function of $ϕ$ , which is measured by imaging the population in $| 1 ⟩$ . (c) The contrast is fit for several precession times. We extract the decay of the contrast using a Gaussian $C (t) = e^{- t^{2} / T_{c}^{2}}$ model, producing $1 / e$ -coherence times of $T_{2}^{*} = 93 (7) ms$ and $T_{2} = 470 (40) ms$ for the Ramsey and spin-echo pulse sequence, respectively.
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Figure 3
Magic angle. (a) We measure the contrast at a fixed precession time of 30 ms and scan the polarization angle between the applied magnetic field and tweezer polarization. Two $θ_{m}$ ’s appear on either side of 90°, split by $25 (4) °$ . The inset shows a fine scan of the magic angle centered around 103° with a precession time of 60 ms. A Gaussian fit is used to determine the center. (b) The differential light shift as a function of intensity is initially increasing linearly but then curves down resulting in a zero-slope region that is first-order insensitive to changes in intensity. Tuning $θ_{m}$ moves the zero-slope region near the tweezer intensity of $130 kW / {cm}^{2}$ (vertical line), where the coherence time is maximized. (c) The slope of the light shift (differential polarizability), calculated for a magnetic field of 1.6 gauss, has two zero crossings ( $θ_{m}$ ) as a function of angle. Thermal averaging of the light intensity sampled by the molecules in the tweezer shifts and broadens the magic angle, as explained in the text.
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Figure 4
Temperature scaling. (a) We measure the decay of contrast for a Ramsey pulse sequence at several different temperatures. The initial temperature is adjusted between 40 and $120 μ K$ ; then, the trap is ramped down to $26 μ K$ , resulting in adiabatic cooling of the molecules to the temperatures listed in the plot. (b) The decoherence rate ( $1 / T_{2}^{*}$ ) as a function of temperature is plotted. The purple curve is the result of a Monte Carlo simulation with an overall scale factor.
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