Quantum Properties of a Macroscopic Oscillator

Yuri S. Kivshar, Tristram J. Alexander, Sergei K. Turitsyn

A. Metelmann

R. W. Hayward

Tobias Nadolny, Christoph Bruder

We theoretically describe macroscopic quantum synchronization effects occurring in a network of all-to-all coupled quantum limit-cycle oscillators. The coupling causes a transition to synchronization as indicated by the presence of global phase coherence. We demonstrate that the microscopic quantum properties of the oscillators qualitatively shape the synchronization behavior in a macroscopically large network. Specifically, they result in a blockade of collective synchronization that is not expected for classical oscillators. Additionally, the macroscopic ensemble shows emergent behavior not present at the level of two coupled quantum oscillators.

Liang Mai

Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q -deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q -deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q -deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1 ,1) Lie algebra or q -deformed quantum algebra also have such properties.

D. Goderis, André F. Verbeure, P. Vets

The theory of fluctuations for a quantum lattice system is rigorously defined. The property of stability of equilibrium states against macroscopic fluctuations is formulated and small oscillations around equilibrium are studied.