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## Spontaneous generation of quantum entanglement between many atoms

In a recent paper published in the journal Physical Review Letters, our colleague Ivor Krešić described a new method of generating quantum entanglement between ultracold atoms, based on self-organization in optical resonators laser-pumped to a state out of thermodynamic equilibrium. In addition to revealing a previously unexplored connection between self-organization and quantum entanglement, this discovery also offers an opportunity to improve existing techniques for creating correlated atomic pairs.

**Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms**

Ivor Krešić, Gordon R. M. Robb, Gian-Luca Oppo, Thorsten Ackemann

Physical Review Letters **131**, 163602 (2023)

DOI: 10.1103/PhysRevLett.131.163602

Self-organization of ultracold atoms in optical resonators is often used for quantum simulations of phenomena relevant to the physics of many-particle systems, such as the Dicke phase transition or supersolidity. Experimental results in this area can usually be explained theoretically in the mean-field approximation, where quantum correlations between atomic degrees of freedom are neglected. In this work, using a fully quantum description, it was theoretically demonstrated how, in configurations where the physics of self-organization is described by Hamiltonians possessing continuous translational symmetry, spontaneous generation of multiparticle quantum entanglement atomic in momentum states is possible. Two theoretical models were studied, one based on light-mediated interaction of ultracold atoms placed in a ring resonator, and the other based on direct collisions between ultracold atoms in an oscillating magnetic field. Numerical calculations show that this method could potentially be very effective in generating quantum entangled atoms even in so-called “bad resonators”. The discovery opens the door to many exciting applications in quantum metrology, simulations and computing, not only using atomic condensates, but other types of dipole particle ensembles as well.

*Figure 1. Generation of multiparticle quantum entanglement with two modes of atomic momentum using self-organization. (a) The “spin” probability distribution of this quantum entangled state appears on the Bloch sphere as a thin ribbon around the equatorial plane, where the J _{i} operators are given in the Schwinger representation. Stronger quantum entanglement is present in states with a larger J_{eff} radius and smaller width of the band. During the quantum evolution of ultracold atoms in a resonator pumped by a laser above the critical intensity, (b) the width of the band grows more slowly than (c) the mean value of the radius, and for a certain duration of pumping the atomic system is in a highly quantum entangled (“Dicke-squeezed”) state.*