Many-Body Systems

Simon Tölle, H.‐W. Hammer, Bernard Ch. Metsch

Few-body systems with resonant short-range interactions display universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry. Similar universal properties appear in 4-body and possibly higher-body systems as well. We set up an effective theory for few-body systems in a harmonic trap and study the modification of universal physics for 3- and 4-particle systems in external confinement. In particular, we focus on systems where the Efimov effect can occur and investigate the dependence of the 4-body spectrum on the experimental tuning parameters.

Umberto Lombardo, G. Giuliani, Yifei Niu

Lorenzo Contessi, Johannes Kirscher, Manuel Pavón Valderrama

We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a {\it unitary graph} in which the vertices represent distinguishable particles and the edges resonant 2-body interactions. Few-body systems whose unitary graph is connected will collapse unless a repulsive 3-body interaction is included. We find two categories of graphs, distinguished by the kind of 3-body repulsion necessary to stabilize the associated system. Each category is characterized by whether the graph contains a loop or not: for tree-like graphs (graphs containing a loop) the 3-body force renormalizing them is the same as in the 3-body system with two (three) resonant interactions. We show numerically that this conjecture is correct for the 4-body case as well as for a few 5-body configurations. We explain this result in the 4-body sector qualitatively by imposing Bethe-Peierls boundary conditions on the pertinent Faddeev-Yakubovsky~decomposition of the wave function.

Zheng-Yuan Zhang, Tianyi Zhang, Zong-Kai Liu +2 more

The interaction of many-body quantum system is a critical problem to be solved in the field of quantum information science. Rydberg atoms have large dipole moment, enabling them to interact with others in a long range, thereby offering us a powerful tool for studying many-body quantum physics. Meanwhile, atoms in the ground state are stable, which makes it easy to manipulate them. Therefore, Rydberg-atom many-body system is an ideal platform for studying the interaction of many-body quantum system. Studies of Rydberg-atom many-body system may contribute to understanding the properties of many-body system and putting the interaction of many-body quantum system into practical applications. In this review, we introduce some studies of properties of interaction of Rydberg-atom many-body system, including the Rydberg excitation blockade, the variation of Rabi frequencies of the many-body system and special spatial distribution of Rydberg atoms in a many-body system. Firstly, the Rydberg excitation blockade, the most important property in the Rydberg-atom many-body system, indicates that atoms’ excitation will be suppressed in a certain range around one Rydberg excitation because the interaction between the Rydberg excitation and atoms leads the energy level to shift so that atoms cannot be excited by the same pulse. Secondly, there is a collective Rabi frequency in the system, which is proportional to the square of the number of atoms in the suppressed area. And additionally, because of the Rydberg blockade effect, Rydberg excitations in the ensemble cannot be at casual positions but a regular distribution is formed. Besides the studies of properties, several researches on the applications of interaction of Rydberg-atom many-body system are introduced, including single-photon source, quantum storage, single-atom imaging, quantum simulation, etc. These applications contribute to the development of quantum community and quantum computing, which may bring us a quantum-technology time. Finally, we discuss the future development of Rydberg-atom many-body system and its further applications. Further development includes the development of many-body system with a larger number of atoms, the development of many-body system of atoms with more than one electron, and some other specific subjects based on many-system, such as Rydberg dimer and topological phase. Also some promising applications such as in studying optimization problem by quantum annealing, may become true.

Luca Salasnich