Coherent frequency doubling in nonlinear nonhomogeneous elements

Natalia Korolkova, A. S. Chirkin

Kōichi Shimoda

Uditnarayan Kouskiya, Caglar Oskay

This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models. The approach leverages the potential energy structure of hyperelasticity and employs a hybrid quantum classical framework in which the energy functional is evaluated using parameterized quantum circuits and optimized through classical routines. To enable a hybrid (classical quantum implementation), polynomial approximations of the nonlinear terms in strain energy density are introduced, yielding a representation compatible with variational quantum algorithms. The methodology is demonstrated on a special case of the NeoHookean material model in a one dimensional setting using finite element discretizations with first and second order shape functions and nonhomogeneous boundary conditions. Numerical experiments investigate the influence of the polynomial approximation order on the accuracy and efficiency of the proposed approach, illustrating its feasibility for near-term quantum devices.

Rüdiger Schack, Andreas Sizmann, Axel Schenzle

We present a theoretical investigation of the potential for squeezing of a doubly resonant cavity that contains a laser medium as well as a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity. If the lasing mode is coupled to its second harmonic, i.e., for a self-frequency-doubling laser, we find more than 60% squeezing in the up-converted mode outside the cavity. In the opposite case of a ``self-down-converting laser,'' i.e., when the lasing mode is coupled to its subharmonic, a perfectly squeezed vacuum in the down-converted mode develops into a less squeezed state with a nonvanishing coherent amplitude as the pump rate is increased. Our analysis extends beyond the first stable regime of the classical dynamics and compares results for different laser models.

Kōichi Shimoda

Anatol Rotaru, V. Z. Tronchu

Much attention is being paid of late to the study of cooperative processes in the exciton region of the spectrum. Previously, using generalized Keldysh equations that describe coherent excitons and photons that are weakly nonhomogeneous in space and in time, the theory of optical bistability (OB) was developed in the exciton region of the spectrum, and optical switchover between branches of optical-bistability loop was investigated. The paper presents a theoretical investigation of regular and chaotic self-pulsations in a CuCl crystal with the participation of coherent excitons and biexcitons. We proposed the method of chaotic self-pulsation breakdown in the system of coherent excitons and biexcitons. The method consists in action of external periodical turbulence (Y/spl tilde/=Y+/spl alpha/ sin(/spl omega//spl tau/)) upon a stochastic system. The range of amplitude values and frequencies of an external harmonic pump were found at which the chaotic oscillation regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle.