Coherent States for a Bosonic System with a Finite Number of Degrees of Freedom

A. M. Perelomov

J. Fransson, B. C. Sanders, A. P. Sowa

We investigate the concept of macroscopically distinguishable superpositions within an infinite array of boson sites. Our approach is rigorous within the frame of Hilbert space theory. In this context, it is natural to differentiate between states -- and corresponding dynamics -- that involve only finitely many degrees of freedom, referred to as local, and those that are inherently nonlocal. Previous studies have shown that such systems can support nonlocal coherent states (NCS). In this work, we demonstrate that NCS can dynamically evolve into nonlocal cat states under the influence of a nonlocal Hamiltonian -- specifically, the square of the total number operator. Crucially, the resulting dynamics cannot be decomposed into local factors. Furthermore, we explore broader mathematical implications of these phenomena within the framework of generalized bosons. Our findings highlight that the concepts of coherent states and nonlocal cat states are not inherently bound together; rather, their fusion is a distinctive feature of standard bosons. Finally, we propose that if the generalized boson framework can be physically realized in engineered quantum systems, the phenomena described here may hold significant relevance for both physics and materials science.

A. M. Perelomov

Monique Combescure, Didier Robert

S. Braun, J. P. Ronzheimer, Michael Schreiber +4 more

Absolute temperature is usually bound to be positive. Under special conditions, however, negative temperatures-in which high-energy states are more occupied than low-energy states-are also possible. Such states have been demonstrated in localized systems with finite, discrete spectra. Here, we prepared a negative temperature state for motional degrees of freedom. By tailoring the Bose-Hubbard Hamiltonian, we created an attractively interacting ensemble of ultracold bosons at negative temperature that is stable against collapse for arbitrary atom numbers. The quasimomentum distribution develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Negative temperatures imply negative pressures and open up new parameter regimes for cold atoms, enabling fundamentally new many-body states.

Gregory G. Athanasiu, Emmanuel G. Floratos