Dynamic theory of driven multilevel dissipative quantum systems

Zhongyuan Zhou, Shih‐I Chu, Siyuan Han

A theory on the dynamics of a driven dissipative multilevel quantum system is applied to investigate relaxation and decoherence induced by an external circuit of a resonantly driven SQUID flux qubit. It is shown that in the case of weak field and weak damping the numerical and analytical results are in excellent agreement. It is also shown that the SQUID qubit can be optimized by varying external circuit parameters.

Ilya Prigogine

Yulia E. Shchadilova, Mor M. Roses, Emanuele G. Dalla Torre +2 more

We present a fermionic description of nonequilibrium multilevel systems. Our approach uses the Keldysh path-integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on the Majorana fermion representation of spin-1/2 models which follows earlier applications in the context of spin and Kondo systems. We apply this formalism to problems of increasing complexity: a dissipative two-level system, a driven-dissipative multilevel atom, and a generalized Dicke model describing many multilevel atoms coupled to a single cavity. We compare our theoretical predictions with recent QED experiments and point out the features of a counterlasing transition. Our technique provides a convenient and powerful framework for analyzing driven-dissipative quantum systems, complementary to other approaches based on the solution of Lindblad master equations.

Kang Shen, Xiangming Hu, Fei Wang

Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural route beyond periodic order, enabling dissipative time quasicrystals without externally imposed quasiperiodic driving. We consider a collectively driven-dissipative four-level ensemble with two degenerate excited states and two degenerate ground states. In the thermodynamic limit, the exact mean-field dynamics reduces to an irrational flow on a two-dimensional torus, yielding quasiperiodic order parameters with discrete spectra generated by two incommensurate fundamental frequencies. Vanishing maximal Lyapunov exponents demonstrate that the nonlinear self-consistent dynamics remains nonchaotic. Our results establish a minimal interference-induced mechanism for time-quasiperiodic order and open a route toward higher-dimensional quasiperiodic dynamics in multilevel systems.