A macroscopic oscillator goes and stays quantum

Vladimir B. Braginskii, V. S. Nazarenko

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

Gesualdo Delfino A

We previously showed that a quantum quench in a one-dimensional translation invariant system produces undamped oscillations of a local observable when the post-quench state includes a single-quasiparticle mode and the observable couples to that mode [J. Phys. A 47 (2014) 402001]. Here we consider quenches that break initial translation invariance. Focusing on quenches performed only on an interval of the whole system, we analytically determine the time evolution of local observables, which occurs inside a truncated light cone spreading away from the quenched interval as time increases. If the quench excites a single-quasiparticle mode, oscillations with the frequency of the quasiparticle mass stay undamped until a time increasing with the length of the quenched interval, before eventually decaying as t−1/2. The translation invariant case with no damping is recovered as the length of the interval goes to infinity.

KENICHI KONISHI, GIAMPIERO PAFFUTI

It is proven that the energy of a quantum mechanical harmonic oscillator with a generically time-dependent but cyclic frequency, ω(t0) = ω(0), cannot decrease on an average if the system is originally in a stationary state, after the system goes through a full cycle. The energy exchange always takes place in the direction from the macroscopic system (environment) to the quantum microscopic system.

R. W. Hayward

Caterina Foti, Alessandro Cuccoli, Paola Verrucchi

We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic; the problem is related to the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. The aim of the work is to understand (1) if, (2) to what extent, and possibly (3) how the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-$\frac{1}{2}$ particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin $S$ constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-$S$ limit. We find an insightful expression for the propagator of the whole system, where we identify an effective ``back-action'' term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.