Representation of the evolution operator via membrane amplitudes

Mikhail Karasev

Andrzej Posiewnik

Ye‐Hong Chen, Zhi‐Cheng Shi, Jie Song +1 more

In this paper, by invariant-based inverse engineering, we design classical driving fields to transfer quantum fluctuations between two suspended membranes in an optomechanical cavity system. The transfer can be quickly attained through a nonadiabatic evolution path determined by a so-called dynamical invariant. Such an evolution path allows one to optimize the occupancies of the unstable ``intermediate'' states; thus, the influence of cavity decays can be suppressed. Numerical simulation demonstrates that a perfect fluctuation transfer between two membranes can be rapidly achieved in one step, and the transfer is robust to both the amplitude noises and cavity decays.

Xianfeng Chen, Li-Li Hou

We set up the fermionic thermal entangled state approach to address Fermi operator master equations for the amplitude- and phase-decay processes and find the explicit Kraus operator-sum representations (KOSR) describing time-evolution of Fermi systems. As an application of KOSR, the evolution law of the two-level atomic system interacting with a photon field in these two decay processes is analytically derived, which shows that the interaction system has a quantum jump as a result of dissipation, but it always remains unchanged in the phase-decay process.

T. Yu. Mikhaîlova, Vladimir I. Pupyshev

Yuri Ozhigov

A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A basic state of simulated system is treated as a collision of the two corresponding amplitude quanta, that gives the quantum statistics of measurements. The movement of the external membrane of the bubble corresponds to the classical dynamics of the simulated system. Measurements are treated as the membrane perforations and they are completely determined by initial conditions. An identity of particles and an entanglement is simulated by the membranes touching. The required memory grows linearly where the number of particles increases, but entangled states of the big number of particles can be simulated. The method can be used for a visualization of quantum dynamics.