Quantum non-linear oscillations

Matteo Simoni, Ivan Rojkov, M. Mazzanti +7 more

Non-linearities are a key feature allowing non-classical control of quantum harmonic oscillators. However, when non-linearities are strong, designing protocols for control is often difficult, placing a barrier to exploiting these properties fully. Here, using a single trapped-ion oscillator operated in the strongly non-linear regime of the atom-light interaction, we show how to generate localized multi (2, 3, 4, and 5)-component Schrödinger's cat manifolds using a novel form of non-linear reservoir engineering. We then specifically select Hamiltonians which allow us to perform measurements on these state manifolds. To our knowledge, our work is the first experimental use of such high order non-linear processes for control of non-classical states of a quantum harmonic oscillator, opening up a new toolbox which can be applied to bosonic quantum error correction, computation, and sensing.

F. Suekane

Andrey G. Grozin

Gabriel González Contreras

Overdamping is a regime in which friction is sufficiently large that the motion either decays to its equilibrium position or it crosses the equilibrium position exactly once before returning monotonically towards the equilibrium position. The phenomena of overdamping has been studied classically and quantum mechanically only for the case of the linear damped harmonic oscillator. Here we study the classical and quantum dynamics of a family of over-damped non linear systems. The main objective of this paper is to find a Lagrangian and Hamiltonian framework to study over-damped non linear systems and to show that a quantum mechanical description can be developed in the momentum representation. Our results reduce to the well known solution of the linear damped harmonic oscillator when the non linear part is set to zero.

F. Suekane

Alexander E. Kozhekin, V. I. Rupasov

The interaction of a quantized electromagnetic field with a non-linear oscillator is described by a model which is analogous to the Dicke model. The exact two-particle eigenstates of the 'oscillator+field' system are obtained and these states are used to solve the problem of spontaneous decay of a twofold excited state of a non-linear oscillator. The shape of radiation lines and the 'linear oscillator' paradox are discussed. The authors also hope the exact solution of the problem will be useful for investigations of two-photon correlations in a non-linear medium for all cases when multiphoton correlations are insignificant.