Nonlinear relaxation and fluctuations of damped quantum systems

Roy J. Glauber, Vladimir I. Man’ko

Mario F. Gely, Adrián Sanz Mora, Shun Yanai +3 more

Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or superconducting resonators, the origin of nonlinear damping is sometimes unclear. This presents a problem, as the damping rate is a key figure of merit in the application of these systems to extremely precise sensors or quantum computers. Through measurements of a superconducting resonator, we show that from the interplay of quantum fluctuations and the nonlinearity of a Josephson junction emerges a power-dependence in the resonator response which closely resembles nonlinear damping. The phenomenon can be understood and visualized through the flow of quasi-probability in phase space where it reveals itself as dephasing. Crucially, the effect is not restricted to superconducting circuits: we expect that quantum fluctuations or other sources of noise give rise to apparent nonlinear damping in systems with a similar conservative nonlinearity, such as nano-mechanical oscillators or even macroscopic systems.

R. Tanaś

K. W. Becker

Mario F. Gely, Adrián Sanz Mora, Shun Yanai +3 more

Nonlinear damping, a force of friction that depends on the amplitude of motion, plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or superconducting resonators, the origin of nonlinear damping is sometimes unclear. This presents a problem, as the damping rate is a key figure of merit in the application of these systems to extremely precise sensors or quantum computers. Through measurements of a superconducting circuit, we show that nonlinear damping can emerge as a direct consequence of quantum fluctuations and the conservative nonlinearity of a Josephson junction. The phenomenon can be understood and visualized through the flow of quasi-probability in phase space, and accurately describes our experimental observations. Crucially, the effect is not restricted to superconducting circuits: we expect that quantum fluctuations or other sources of noise give rise to nonlinear damping in other systems with a similar conservative nonlinearity, such as nano-mechanical oscillators or even macroscopic systems.

Yuh‐Jen Cheng

A quantum Langevin equation is derived to describe the relaxation dynamics of a magnetic moment in a static magnetic field and radiative reservoir. The damping and fluctuation forces are derived from the radiative interaction between magnetic moment and surrounding reservoir. Through the use of a symmetrized interaction Hamiltonian, the damping force is identified due to the combination of radiation self-reaction and reservoir fluctuations. The radiation self-reaction is a quantum version of its classical counterpart, whereas the reservoir fluctuations are solely a quantum effect resulting from the quantization of the electromagnetic field. The relative magnitude between these two effects changes during the relaxation process. This equation shows that the relative magnitude of the quantum correction to the classical Landau-Lifshitz description is inversely proportional to the system angular momentum quantum number.