Efimov trimers are unique three-body quantum states emerging near two-atom Feshbach resonances. Their existence is a consequence of the universal three-body interactions arising from the long-range behavior of the two-body interaction potential. The strength of this interaction is tuned using a magnetic field-dependent Feshbach resonance, characterized by the scattering length *a*. As *a* approaches infinity, Efimov states are formed. However, the character of the Feshbach resonance (broad or narrow) significantly influences the three-body physics. Broad resonances, observed in atoms like ⁸⁷Rb and ¹³³Cs, exhibit a universal repulsive wall near *R ≈ 2r_vdw* (where *R* is the hyperradius and *r_vdw* is the van der Waals length), leading to the ground Efimov state dissociating at *a* ≈ −9.73*r_vdw*. Narrow resonances, with a dimensionless strength parameter *s_res* << 1, introduce an additional length scale *r₂ ≈ 2a/s_res*, affecting the three-body interactions. While previous observations of ⁷Li (possessing narrow resonances) seemed consistent with broad-resonance behavior, this study challenges that understanding. This research aims to explore the behavior of the Efimov state in ⁷Li atoms near the atom-dimer threshold using a novel coherent spectroscopy technique. The study's importance lies in resolving the discrepancy between expectations based on the universality observed in broad resonances and the experimental findings in ⁷Li. Understanding the behavior of Efimov states in narrow resonances is crucial for advancing our knowledge of universal few-body physics and resolving inconsistencies in previous observations concerning ⁷Li atoms.

Extensive research has been conducted on the Efimov effect, focusing primarily on systems with broad Feshbach resonances. Studies using ¹³³Cs and ⁸⁷Rb have confirmed the universal behavior predicted by theory, observing the log-periodic series of bound Efimov states and their dissociation at a specific value of the scattering length. These studies established the concept of van der Waals universality, where the three-body interaction potential features a universal repulsive wall preventing atoms from probing small hyperradii. However, theoretical work has predicted deviations from this universality for narrow Feshbach resonances. These deviations stem from the emergence of an additional length scale *r₂* related to the resonance strength, modifying the three-body potential. Recent experimental work has started to explore these deviations in intermediate-strength resonances, finding slight differences from the predictions of van der Waals universality. However, the specific case of ⁷Li, which possesses particularly narrow Feshbach resonances, remained a puzzle due to the apparent agreement with broad-resonance observations. This paper addresses this gap in our understanding.

This research utilizes a novel coherent spectroscopy technique, referred to as the Dimer-Trimer Superposition (DITRIS) interferometer, to study the Efimov state in ⁷Li atoms. Unlike traditional methods relying on inelastic losses, the DITRIS interferometer employs high-resolution coherent spectroscopy to measure the energy difference between the Efimov trimer and the atom-dimer state. A double-pulse sequence is used to generate a superposition state of dimers and trimers. The first pulse creates the superposition, and the second pulse dissociates these states. The accumulated phase difference between these states, during a variable free evolution time, is then measured. This allows for precise measurement of the trimer binding energy relative to the atom-dimer threshold. The frequency of oscillations in the number of free atoms as a function of the free evolution time is directly proportional to the energy difference *E_T - E_D*. This method overcomes limitations of traditional rf association and loss spectroscopy, which fail in the energy regime where the trimer and dimer are closely spaced. The pulse duration must be short enough to cover the energy difference between the trimer and the dimer, but long enough to get a detectable signal, hence a 10 µs pulse is used, modeled as a specific function for optimization. The scattering length is tuned by varying the magnetic field near the 894 G Feshbach resonance of ⁷Li, where *s_res ≈ 0.493*. The experimental setup involves standard laser cooling and evaporation techniques to produce a cold gas of ⁷Li atoms. Absorption imaging detects the number of free atoms. Data analysis involves a three-parameter fit inspired by Fourier transforms to extract the dominant oscillation frequencies from the interferometer signals. Accurate calibration of the scattering length is achieved using the dimer binding energy measured during data acquisition. Theoretical analysis involves numerical calculations using the adiabatic hyperspherical representation to compute the three-body interaction potential and the Efimov state energy. A two-channel interaction model with variable *s_res* provides insight into the difference between broad and narrow resonances. A more realistic multichannel model that accounts for interactions in ⁷Li is then employed for a more quantitative comparison with the experimental data. This multichannel model uses a weighted cross-section difference to characterize the existence of the Efimov state above the atom-dimer threshold by comparing the ⁷Li atom-dimer elastic cross-section to a broad-resonance system with the same atom-dimer scattering length. The difference should display an enhancement when the collision energy matches the ⁷Li Efimov state energy.

The key findings of this research are: 1. **Observation of a Metastable Efimov Trimer Above the Atom-Dimer Threshold:** Contrary to expectations based on van der Waals universality, the experiment observed an Efimov trimer state in ⁷Li that persists above the atom-dimer threshold. This metastable state exhibits coherence times significantly exceeding its estimated lifetime. 2. **Reshaping of Three-Body Interactions for Narrow Resonances:** Theoretical calculations reveal a fundamental reshaping of the three-body interaction potential for narrow Feshbach resonances. Unlike the universal repulsive wall observed in broad resonances, narrow resonances develop a double-well structure with a repulsive barrier at larger hyperradii (*R ≥ 4r_vdw*). This barrier stabilizes the Efimov state above the atom-dimer threshold. 3. **Confirmation by Multichannel Calculations:** The theoretical multichannel calculations, using a more realistic model of ⁷Li interactions, qualitatively reproduce the experimental observation of the Efimov state above the threshold. This confirms that the repulsive barrier is the underlying mechanism responsible for the metastable state. 4. **Experimental Sensitivity and Precision:** The DITRIS interferometer successfully measures the Efimov state binding energy with high precision, revealing subtle details of the energy spectrum near the threshold that are inaccessible to traditional methods. The high precision also allowed for the detection of the metastable Efimov trimer above the threshold, demonstrating the power and capability of this novel technique. 5. **Significant Deviation from van der Waals Universality:** The experimental and theoretical results conclusively demonstrate a significant deviation from the universality observed in systems with broad Feshbach resonances, highlighting the importance of considering the resonance width when studying Efimov physics.

The findings of this research address the long-standing question of the behavior of Efimov states in systems with narrow Feshbach resonances, particularly ⁷Li. The experimental observation of a metastable Efimov trimer above the atom-dimer threshold, combined with the theoretical explanation involving a reshaped three-body potential with a repulsive barrier, directly challenges the prevailing van der Waals universality paradigm. This work reveals that the resonance width significantly impacts Efimov physics, leading to deviations from the universality previously observed in systems with broad resonances. The surprisingly long coherence times observed for this metastable trimer raise questions about the role of coherence in stabilizing few-body states. The reshaped three-body potential offers new insights into the behavior of ultracold atoms near narrow resonances. The combination of experimental and theoretical work presented makes a strong case for re-evaluating the existing universality models in systems with narrow resonances.

This study presents conclusive evidence for a reshaped three-body interaction in systems with narrow Feshbach resonances, leading to the observation of a metastable Efimov state above the atom-dimer threshold. This contrasts sharply with the behavior observed in systems with broad resonances. The results highlight the limitations of van der Waals universality for narrow resonance systems. Future research could investigate the lifetime of this metastable state and explore the potential for exploiting the reshaped three-body interaction for quantum control of few-body systems. The development and successful application of the DITRIS interferometer, offering a new method for high precision measurements in this domain, provides a powerful tool for future exploration of few-body physics.

The theoretical models employed, while providing valuable insights, involve approximations due to the complexity of multichannel interactions in ⁷Li. These approximations may influence the quantitative agreement between theory and experiment. The study focuses on a specific Feshbach resonance in ⁷Li; further investigation is needed to determine the extent to which these findings generalize to other narrow resonances in different atomic species. Finally, while the DITRIS interferometer demonstrates high precision in energy measurements, a comprehensive investigation of the trimer lifetime remains a subject for future research, as the current study focuses primarily on energy level determination and only makes a preliminary observation about the state lifetime.