Adiabatic results in quantum theory and quantum-classical coupling

Kurt O. Friedrichs

Yang Liu, Y. N. Zhang, H. D. Liu +1 more

It is known that the dynamics and geometric phase of a quantum system can be simulated by classical coupled oscillators using the quantum−classical mapping method without loss of physics. In this work, we show that this method can also be used to simulate the schemes of quantum shortcuts to adiabaticity, which can quickly achieve the adiabatic effect through a non-adiabatic process. By mapping quantum systems by classical oscillators, two schemes, Berry’s “transitionless quantum driving” and the Lewis−Riesenfeld invariant method, are simulated by a corresponding transitionless classical driving method, which keeps adiabatic phase trajectories and acquires Hannay’s angle and the classical Lewis−Riesenfeld invariant method by manipulating the configurations of classical coupled oscillators. The classical shortcuts to adiabaticity for the two coupled classical oscillators, which is the classical version of a spin-1/2 in a magnetic field, is employed to illustrate our results and compared with quantum shortcuts-to-adiabaticity methods.

Soumya Bera, Serge Florens, Harold U. Baranger +3 more

The coupling of a qubit to a macroscopic reservoir plays a fundamental role in understanding the complex transition from the quantum to the classical world. Considering a harmonic environment, we use both intuitive arguments and numerical many-body quantum tomography to study the structure of the complete wavefunction arising in the strong-coupling regime, reached for intense qubit-environment interaction. The resulting strongly-correlated many-body ground state is built from quantum superpositions of adiabatic (polaron-like) and non-adiabatic (antipolaron-like) contributions from the bath of quantum oscillators. The emerging Schrödinger cat environmental wavefunctions can be described quantitatively via simple variational coherent states. In contrast to qubit-environment entanglement, we show that non-classicality and entanglement among the modes in the reservoir are crucial for the stabilization of qubit superpositions in regimes where standard theories predict an effectively classical spin.

Michael Berry

V. S. Buslaev, E. A. Grinina

O. S. Barišić

The polaron formation is investigated in the intermediate regime of the Holstein model by using an exact diagonalization technique for the one-dimensional infinite lattice. The numerical results for the electron and phonon propagators are compared with the nonadiabatic weak- and strong-coupling perturbation theories, as well as with the harmonic adiabatic approximation. A qualitative explanation of the crossover regime between the self-trapped and free-particle-like behaviors, not well-understood previously, is proposed. It is shown that a fine balance of nonadiabatic and adiabatic contributions determines the motion of small polarons, making them light. A comprehensive analysis of spatially and temporally resolved low-frequency lattice correlations that characterize the translationally invariant polaron states is derived. Various behaviors of the polaronic deformation field, ranging from classical adiabatic for strong couplings to quantum nonadiabatic for weak couplings, are discussed.