Parity-Doublet Coherence Times in Optically Trapped Polyatomic Molecules

TL;DR

Parity-doublet states in linear triatomic molecules offer near-degenerate, parity-opposite levels that are promising for robust quantum information processing and precision measurements. The authors trap CaOH in an optical dipole trap, prepare parity-doublet qubits in the bending-mode and perform Ramsey measurements, achieving a bare coherence time of $T_2^* = 0.8(2)$ s and extending to $T_2^* > 2.9$ s with a spin-echo by cancelling ambient fields and suppressing trap-induced shifts. They characterize the rotational Stark sensitivity and parity-dependent trap shifts, showing that trap light shifts dominate decoherence but can be mitigated by a magic polarization angle or by tuning to a magic wavelength. These long coherence times enable scalable quantum simulations and entangling operations in optical tweezer arrays of polyatomic molecules and bolster prospects for precision searches for BSM physics.

Abstract

Polyatomic molecules provide complex internal structures that are ideal for applications in quantum information science, quantum simulation, and precision searches for physics beyond the Standard Model. A key feature of polyatomic molecules is the presence of parity-doublet states. These structures, which generically arise from the rotational and vibrational degrees of freedom afforded by polyatomic molecules, are a powerful feature to pursue these diverse quantum science applications. Linear triatomic molecules contain $\ell$-type parity doublet states, which are predicted to exhibit robust coherence properties. We optically trap CaOH molecules, prepare them in $\ell$-type parity-doublet states, and realize a bare qubit coherence time of $T_2^* = 0.8(2)$ s. We suppress differential Stark shifts by employing molecular spectroscopy to cancel ambient electric fields, and characterize parity-dependent trap shifts, which are found to limit the coherence time. The parity-doublet coherence times achieved in this work are a defining milestone for the use of polyatomic molecules in quantum science.

Figures (6)

• Figure 1: a. A visual depiction of the vibrational bending mode of the molecule. The projection of the vibrational angular momentum onto the internuclear axis is given by $\ell$. b. $N=1$ and $N=2$ rotational state structure in the $\tilde{X}(010)$ vibronic state of CaOH, containing parity doublet states. The degeneracy between parity doublet states is split by Coriolis interactions which separate in-plane and out-of-plane vibrations, where $\ket{\pm} = \frac{1}{\sqrt{2}}\left(\ket{\ell}\pm(-1)^{N-\ell}\ket{-\ell}\right)$. The qubit states examined in this work are fully stretched states labeled $\ket{1+}$ and $\ket{1-}$ in $N=1$ and $\ket{2+}$ and $\ket{2-}$ in $N=2$.
• Figure 2: a. Coherence time of parity-doublet states in $N=1$. In the Ramsey measurement, two $\pi/2$ RF pulses are separated by a variable hold duration. We detune the RF frequency by 1 kHz, which allows us to measure over a period of 1 ms to extract the contrast of a full precession around the Bloch sphere. Decay of the contrast is fit to an exponential decoherence model to determine the coherence time, which we find to be $T_2^* = 0.8(2)~\text{s}$. With spin echo, the coherence time is determined to be $>$$2.9$ s at the $95\%$ confidence level. The error reported comes from bootstrapped samples of the data. b. Three examples of the Ramsey measurement are shown below the coherence decay plot for free precessions $\tau$ of 1 ms, 300 ms, and 600 ms, normalized to the measured fringe contrast at 1 ms. Error bars represent $68\%$ confidence intervals.
• Figure 3: Decoherence rate dependence on electric field. We measure the Ramsey coherence time of parity-doublets in the $N=1$ and $N=2$ rotational states in several electric field environments. The decoherence rates shown are corrected for by the decoherence rate at zero applied field, which is limited by trap shifts. Due to the quadratic Stark shift, the decoherence dependence is fit to a line, as it reflects variation in the Stark shift. The ratio of the fitted slopes for $N=1$ and $N=2$ is 7(1), which is in agreement with our predicted value of 6.75 arising from the frequency splitting and dipole moment of the states. See the Supplemental Material for more details Supplemental. Error bars represent $68\%$ confidence intervals.
• Figure 4: Decoherence rate dependence on trap depth. The decay in contrast for the Ramsey sequence is measured at several trap depths for $\ket{1+}$ and $\ket{1-}$. The temperature of the molecules during the Ramsey measurement is dependent on the trap depth as a result of adiabatic cooling and scales as $\propto\sqrt{U_0}$. The sensitivity of the decoherence rate to trap depth is numerically fit to a model which accounts for the spread of light intensities sampled by the molecules and the trap shift dependence (see Supplemental Material Supplemental). Inset: Magic angle scan. We measure the Ramsey contrast after $\tau = 0.45$ s as a function of trap polarization angle. The data shown here is for a trap depth of $U_0\sim40~\text{\textmu K}$. There is a calibration offset of the angle of up to 0.2°. Error bars represent $68\%$ confidence intervals.
• Figure S1: Experimental sequence used in this work to determine the coherence time for $N=1$ parity-doublet states, as read left to right. Pushout pulses use resonant mainline light to deplete all molecules in negative parity ground states.