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Parity-doublet spin interactions in ultracold polyatomic molecules

This study demonstrates the observation and control of resonant dipolar exchange interactions in laser-cooled CaOH molecules encoded in parity-doublet states, utilizing Floquet engineering to suppress many-body dephasing and establish a coherent, programmable platform for entanglement-enhanced precision measurements of fundamental physics.

Original authors: John Doyle, Junheng Tao, Paige Robichaud, Christian Hallas, Giseok Lee

Published 2026-08-28

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CC BY 4.0

Original authors: John Doyle, Junheng Tao, Paige Robichaud, Christian Hallas, Giseok Lee

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Molecules are often thought of as simple building blocks, but in the world of quantum physics, they are intricate instruments capable of revealing the deepest secrets of the universe. Scientists use them to hunt for tiny violations of symmetry—subtle breaks in the laws of nature that could explain why the universe is made of matter rather than antimatter. To do this, researchers look for specific pairs of energy states within a molecule that are nearly identical but have opposite "handedness," known as parity. These pairs are incredibly sensitive to external forces, acting like fine-tuned sensors. However, to get the most precise readings possible, scientists need to move beyond looking at single molecules one by one. They need to create a large group of molecules that act together as a single, entangled unit. The challenge has been that getting these molecules to interact without destroying their delicate quantum states has been difficult, especially when they are moving around freely in a trap.

A team of researchers at Harvard University has now taken a major step toward solving this problem by demonstrating how to control the interactions between ultracold polyatomic molecules. They worked with calcium hydroxide molecules, cooling them down to a temperature of 60 microkelvin and trapping them in a small volume created by intersecting laser beams. Inside this trap, the molecules were prepared in a special state where they could exist in two slightly different energy configurations, which the researchers treated as the "up" and "down" states of a tiny quantum spin. Because these two states are so similar yet have opposite parity, they can exchange energy with one another through a long-range force called a dipolar interaction, effectively talking to each other across the trap.

The researchers observed two clear signs that these molecules were interacting. First, they noticed that when they prepared the molecules in a specific superposition of states, the clarity of their collective signal faded faster as they added more molecules to the trap. This fading, or dephasing, happened because the molecules were moving around and experiencing slightly different interactions depending on where they were, creating a spread of effects that scrambled their timing. Second, they prepared the molecules with a specific imbalance between the "up" and "down" states and watched the entire group rotate or precess in a way that depended directly on how many molecules were present and how they were initially balanced. These observations confirmed that the molecules were engaging in a resonant exchange of energy, behaving like a collection of tiny magnets influencing one another.

To prove that this behavior was exactly what they expected, the team used a sophisticated computer model that simulated the random motion of the molecules and their interactions. The model, which relied on independently measured properties of the trap and the molecules, predicted the rate at which the signal would fade and the speed of the rotation with high accuracy. This agreement between the real experiment and the simulation confirmed that the researchers had successfully isolated and controlled the resonant dipolar exchange interaction within the very same states used for precision sensing.

Having established that they could control these interactions, the team then asked if they could use this control to protect the molecules from the very dephasing that was causing the signal to fade. They realized that if they could make the interaction between the molecules perfectly symmetric, the disorder caused by their random motion would no longer destroy their collective coherence. To achieve this, they used a technique called Floquet engineering, which involves rapidly switching the orientation of the molecules' spin states using precise radio-frequency pulses. By carefully timing these switches, they could effectively average out the different types of interactions, creating a new, engineered environment where the molecules behaved as if they were interacting in a perfectly symmetric way.

When they tested this engineered environment, they found that the collective signal remained stable for much longer, even though the molecules were still moving around and the individual interactions between them were still disordered. This demonstrated that by tuning the symmetry of the interaction, they could create a protected regime where the molecules could stay entangled and coherent. This finding is significant because it shows a path forward for using dense groups of molecules to create entangled states that are robust against the noise of their own motion. It transforms the parity-doublet states from simple, long-lived probes into a programmable resource that can be used to generate and protect the complex quantum correlations needed for the next generation of fundamental physics experiments.

Technical Summary: Parity-Doublet Spin Interactions in Ultracold Polyatomic Molecules

Problem and Motivation
Precision measurements searching for physics beyond the Standard Model (BSM), such as the electron electric dipole moment (eEDM), rely on the internal structure of molecules to amplify symmetry-violating effects. Parity-doublet states in linear polyatomic molecules are particularly valuable because they allow for large molecular polarization with weak electric fields while enabling co-magnetometry to suppress systematic errors. However, current precision measurements using these states have largely relied on independent, non-interacting molecules. To achieve entanglement-enhanced precision, it is necessary to establish coherent interactions between molecules within the same metrologically important manifold. While ultracold diatomic molecules have been used to simulate spin models, polyatomic molecules offer a richer structure with natural parity-doublets compatible with laser cooling, yet their coherent many-body interactions within the sensing manifold had not been demonstrated.

Methodology
The authors utilized laser-cooled CaOH molecules confined in a crossed optical dipole trap (cODT) at a temperature of $T = 60$ $\mu$ K. The experimental system encodes a pseudo-spin in the $\ell$ -type parity-doublet states of the $\tilde{X}^2\Sigma^+(010)$ vibrational bending mode. The two-level system consists of stretched hyperfine states with opposite parity: $|\uparrow\rangle \equiv |N=1, J=3/2, F=2, m_F=2, p=+\rangle$ and $|\downarrow\rangle \equiv |N=1, J=3/2, F=2, m_F=2, p=-\rangle$ . These states share nearly identical angular momentum quantum numbers, minimizing differential magnetic and optical shifts, while possessing a large transition electric dipole moment ( $d_{\uparrow\downarrow} = 0.73$ D).

In the absence of a static electric field, the parity-doublet splitting is small, and the transition dipole moment enables resonant dipolar exchange interactions described by an XY spin Hamiltonian. The molecules undergo thermal itinerant motion, sampling spatially disordered, long-range exchange couplings. The researchers employed:

State Preparation: Optical and microwave pumping combined with an RF adiabatic sweep to prepare molecules in specific parity-doublet states.
Coherence Control: Dynamical decoupling sequences (XY16) to suppress single-particle decoherence from trap shifts, extending coherence times significantly beyond the radiative lifetime.
Interaction Probing: Ramsey pulse sequences to measure density-dependent contrast decay and spin-projection-dependent mean-field precession.
Floquet Engineering: Global $\pi/2$ frame rotations applied during interaction intervals to synthesize effective XXZ Hamiltonians with tunable anisotropy ( $\Delta$ ), aiming to reach the SU(2)-symmetric Heisenberg limit.
Modeling: A discrete truncated Wigner approximation (DTWA) using independently calibrated experimental parameters (trap frequencies, temperature, molecule number) to simulate the many-body dynamics.

Key Results

Observation of Resonant Dipolar Exchange: The team observed two complementary signatures of interactions within the parity-doublet manifold:
- Density-Dependent Dephasing: A rapid collective spin decay (Ramsey contrast loss) that scales with molecular density, attributed to the spread of interaction-induced phases across the ensemble.
- Mean-Field Precession: A spin-projection-dependent precession rate that scales linearly with density and reverses sign when the population imbalance ( $\langle S_z \rangle$ ) is reversed. This confirms a one-axis-twisting (OAT) interaction mechanism.
  Both observables were quantitatively well-described by the DTWA model without adjustable parameters.
Symmetry-Protected Coherence: By Floquet engineering the interaction anisotropy, the authors tuned the system from the native XY limit ( $\Delta=0$ ) toward the isotropic Heisenberg point ( $\Delta=1$ ). They observed a strong suppression of many-body dephasing near the SU(2)-symmetric point. In this regime, the collective spin is protected against exchange-induced dephasing despite the spatial disorder of the couplings, a phenomenon confirmed by DTWA snapshots showing the preservation of the fully polarized collective-spin state.
Characterization of the Spin Hamiltonian: The experiments successfully characterized the system as an itinerant XY spin model that can be programmatically tuned to an XXZ model. The mean-field shift was identified as $-2\chi\langle S_z \rangle S_z$ , where $\chi$ scales with density.

Significance and Claims
The paper establishes parity-doublet states as a coherent, interacting, and programmable molecular degree of freedom. The primary significance lies in connecting the polyatomic precision-measurement platform with dipolar many-body physics. By demonstrating that interactions can be controlled within the sensing manifold, the work opens a route to generating entanglement-enhanced tests of fundamental physics. Specifically, the identification of a protected regime near the Heisenberg point suggests a pathway to mitigate interaction-induced coherence penalties in dense molecular ensembles, which is crucial for spin squeezing and high-sensitivity measurements. The authors posit that these capabilities transform parity-doublets from single-particle probes into resources for quantum many-body physics and quantum sensing, potentially enabling protocols to generate and protect entangled states for future BSM searches.

Technical Summary: Parity-Doublet Spin Interactions in Ultracold Polyatomic Molecules

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