Second-Scale Coherence Measured at the Quantum Projection Noise Limit with Hundreds of Molecular Ions

Yan Zhou, Yuval Shagam, William B. Cairncross, Kia Boon Ng, Tanya S. Roussy, Tanner Grogan, Kevin Boyce, Antonio Vigil, Madeline Pettine, Tanya Zelevinsky, Jun Ye, and Eric A. Cornell

Phys. Rev. Lett. 124, 053201 – Published 4 February 2020

Abstract

Cold molecules provide an excellent platform for quantum information, cold chemistry, and precision measurement. Certain molecules have enhanced sensitivity to beyond standard model physics, such as the electron’s electric dipole moment ( $e EDM$ ). Molecular ions are easily trappable and are therefore particularly attractive for precision measurements where sensitivity scales with interrogation time. Here, we demonstrate a spin precession measurement with second-scale coherence at the quantum projection noise (QPN) limit with hundreds of trapped molecular ions, chosen for their sensitivity to the $e EDM$ rather than their amenability to state control and readout. Orientation-resolved resonant photodissociation allows us to simultaneously measure two quantum states with opposite $e EDM$ sensitivity, reaching the QPN limit and fully exploiting the high count rate and long coherence.

Received 17 October 2019
Accepted 16 December 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.053201

Physics Subject Headings (PhySH)

Baryogenesis & leptogenesis Cold and ultracold molecules Molecule trapping & guiding Optical pumping Photodissociation Relativistic & quantum electrodynamic effects in atoms, molecules,& ions

Molecules Trapped ions

CP violation Electric moment

Precision measurements

Atomic, Molecular & OpticalParticles & Fields

Authors & Affiliations

Yan Zhou^1,*,†, Yuval Shagam ^1,*,‡, William B. Cairncross¹, Kia Boon Ng¹, Tanya S. Roussy¹, Tanner Grogan¹, Kevin Boyce¹, Antonio Vigil¹, Madeline Pettine ¹, Tanya Zelevinsky ², Jun Ye ¹, and Eric A. Cornell¹

¹JILA, NIST, and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
²Department of Physics, Columbia University, New York, New York 10027-5255, USA

^*These authors contributed equally to this work.
^†Corresponding author. yan.zhou@jila.colorado.edu
^‡Corresponding author. yuval.shagam@jila.colorado.edu

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Vol. 124, Iss. 5 — 7 February 2020

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Images

Figure 1
Molecules are prepared in two oriented states. Upon dissociation, the photofragments are ejected in the direction of the molecular orientation and kicked out toward an imaging detector. The 2D image of ${Hf}^{+}$ ions after ${HfF}^{+}$ dissociation is pictured. The quantization axis is defined by the applied electric field $\vec{ϵ}$ . $Δ E_{Stark}$ is the energy difference between the molecular orientations.
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Figure 2
Preparation of the initial quantum state and orientation-selective photofragmentation of ${HfF}^{+}$ and ${ThF}^{+}$ . (a) We use circularly polarized light via an $Ω = 0^{-}$ electronic state to pump to the fully stretched $m_{F}$ states of the lowest rovibrational state of ${{}^{3}Δ}_{1}$ . (b) After the spin precession sequence, we project the fully stretched $m_{F}$ states by depletion of the other stretched states. This is done with a circularly polarized excitation to the $Ω = 0^{+}$ from which the possibility of decay back to ${{}^{3}Δ}_{1}$ is small. Additional molecular species specific optical and microwave fields provide rotational and vibrational cooling (see Supplemental Material [25]). This is followed by two-color photodissociation of the $e EDM$ -sensitive ${{}^{3}Δ}_{1}$ states, where the product of $m_{F}$ and $Ω$ determines the molecular orientation. The first REMPD photon excites the molecules to the fully stretched bound intermediate state $| Ω_{i} = 2 ⟩$ , which maintains their orientation. The second REMPD photon couples the intermediate state to the continuum states, resulting in oriented photofragments, ${Hf}^{+}$ or ${Th}^{+}$ and F atoms, and determines the kinetic energy (KE). The metallic ions from each molecular orientation are individually mapped onto an imaging detector with the resulting 1D distributions. Their orientation contrasts $C_{D}$ (defined in the Supplemental Material [25]) are 78% and 67%, respectively.
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Figure 3
Demonstration of a differential measurement at the QPN limit. (Upper) Spin precessions of the upper and lower doublets [Eqs. (1) and (2)], which have $\sim 0.6 Hz$ frequency difference caused by different magnetic moments. (Lower) The scatter in $Δ ℘$ . From the scatter of $℘_{u}$ and $℘_{l}$ determined independently, we would anticipate $σ_{Δ ℘}$ (blue diamonds) to be 5 times above the QPN limit (dotted line). With normalization by each cycle’s ion production noise (orange circles), $σ_{Δ ℘}$ is still more than 2 times the QPN limit. By extracting $Δ ℘$ with simultaneous orientation-selective detection (green squares), we completely eliminate all common-mode noise to bring $σ_{Δ ℘}$ close to the QPN limit when the fringes of the upper and lower doublets are in phase. Spin precession phase noise dominates the out-of-phase measurements ( $\sim 745 ms$ ). At early times ( $\sim 5 ms$ ), dips in $σ_{Δ ℘}$ are observed at maximum or minimum polarizations [Eq. (3)]. Vertical dashed lines mark the zero crossings when the spin precessions are in phase, while dash-dotted lines mark them for the out-of-phase case.
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