A variational principle for oscillators coupled to a two-level system

Marc Vanhimbeeck, Hans A. De Raedt, D. Schoemaker

Symmetrized Trotter approximations to ${e}^{\mathrm{\ensuremath{-}}\ensuremath{\beta}H}$ are employed to compute the low-energy eigenstates of a two-level system linearly coupled to a harmonic oscillator. At high coupling strengths the ground state is nearly doubly degenerate and the projectors become very inefficient. It is demonstrated that the projection technique in combination with the variational principle yields a new efficient method to calculate simultaneously all nearly degenerate eigenvalues and eigenstates. The dynamic properties of the system in the ground state are studied by evaluating the time- and frequency-dependent correlation functions. Depending on the ratio of the tunneling frequency relative to the oscillator frequency, the system behaves differently under increasing coupling strength.

裕也 中尾, Hiroya Nakao

H.H. Rosenbrock

Myung-Joong Hwang, Mahn‐Soo Choi

The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.

Jerry Goodisman

M. Grigorescu

The evolution of a quantum particle interacting with a classical system is described by a generalized variational principle. The dynamical variable is a quantum state vector which includes the classical action as a phase factor, and the common time is treated as a collective variable. Combined with the model of bilinear coupling, the variational principle is applied to the problem of a quantum system in a thermal environment. It is shown that the statistical ensemble of Brownian state vectors is described by the solution of a nonlinear quantum Fokker-Planck equation for the density matrix. Exact solutions of this equation are obtained for the case of a two-level system, considering both stationary and nonstationary initial states.