Researchers Calculate Resonant State of Four Atoms Appearing in Cold Atom Scattering

Scientists have long predicted the existence of weakly bound, four-boson systems, and a new study details the properties of the second excited state of the helium-4 tetramer. A. Deltuva, undertaking this research independently, presents rigorous calculations of atom-trimer scattering using a momentum-space transition operator framework with realistic interatomic potentials. This work is significant because it identifies a resonant behaviour below the excited trimer threshold, despite sizable non-resonant contributions, and accurately determines the position and width of this elusive state, highlighting the importance of finite-range effects in understanding these universal systems.

Scientists have uncovered a previously uncalculated resonant state within the complex interactions of cold helium atoms, pushing the boundaries of understanding in few-body quantum physics. This work details the properties of the second excited state of a tetramer, a cluster of four helium-4 atoms, which exists not as a stable, bound entity but as a fleeting resonance in the atom-trimer scattering process. The study builds upon the established framework of Efimov physics, which predicts the existence of an infinite series of weakly bound states in systems of identical bosons like helium-4, while focusing on a state previously elusive due to its higher energy and proximity to the atom scattering threshold. The research rigorously calculates this behaviour using a momentum-space transition operator framework, employing two realistic interatomic potentials to model the delicate balance of attractive and repulsive forces between the atoms. This approach was selected to accurately model the complex interactions between cold atoms, particularly the weakly attractive van der Waals tail and strong short-distance repulsion inherent in helium interactions, which pose significant challenges for numerical solutions. To overcome difficulties associated with spatially extended states and strong short-range repulsion, a “softening and extrapolation” method was implemented, gradually reducing the strength of the short-range repulsion, enabling accurate solutions of the dynamical equations, followed by extrapolation of the results back to the original potential. By meticulously calculating the phase shift and cross section of atom-trimer scattering, the team identified a resonant behaviour below the excited trimer threshold, signifying the temporary formation of the second excited tetramer. The position and width of this resonant state were determined, revealing significant finite-range effects, meaning the size and shape of the atoms play a crucial role in its properties. These findings not only complete the picture of the helium-4 tetramer energy levels but also provide valuable insights into the behaviour of ultracold atomic gases and the broader field of few-body quantum systems. Solving the four-body equations in momentum space allows for the determination of both tetramer binding energies and atom-trimer scattering lengths, providing a comprehensive understanding of the system’s behaviour. Calculations reveal dimer and trimer binding energies crucial for understanding four-atom interactions in cold helium systems. Using the LM2M2 potential, the dimer binding energy is 1.6125 milliKelvin, while the excited trimer exhibits a binding energy of 2.646 milliKelvin, and the ground trimer reaches 131.58 milliKelvin. Employing the more recent PCJS potential, these values shift to 1.3094 milliKelvin for the dimer, 2.277 milliKelvin for the excited trimer, and 126.30 milliKelvin for the ground trimer. A further calculation with the LM2M2 potential, restricted to lower angular momenta (lx, ly ≤8), yields a dimer binding energy of 1.3094 milliKelvin, an excited trimer binding energy of 2.278 milliKelvin, and a ground trimer binding energy of 126.50 milliKelvin. These subtle differences between the potentials highlight the sensitivity of the results to the precise form of the interatomic interaction. Scientists have long sought to understand the subtle interplay of forces governing collections of ultracold atoms, and this work represents a step forward in that endeavour, demonstrating a refined ability to predict the behaviour of these systems as they approach the threshold of binding and unbinding. The challenge isn’t simply calculating the numbers, but understanding how universal predictions, those based on idealized conditions, are modified by the messy reality of interatomic potentials. This research clarifies the extent to which these ‘finite-range effects’ distort the behaviour of tetramers, specifically the second excited state, with the finding that the predicted resonance width is noticeably broadened by these effects. It suggests that observing this state in real experiments will require even greater precision than previously anticipated, but also provides a benchmark for interpreting experimental data. The implications extend beyond helium, offering insights applicable to other weakly bound systems and potentially informing our understanding of more complex phenomena like neutron stars. However, the reliance on specific interatomic potentials introduces a degree of model dependence; while the comparison between two potentials reveals reasonable consistency, further investigation with a wider range of models is needed to establish the robustness of these findings. Future work might focus on extending these calculations to larger numbers of atoms, or exploring the influence of external fields on these fragile states, ultimately aiming to bridge the gap between theoretical prediction and experimental control, paving the way for novel quantum technologies based on these exquisitely balanced systems.