Quasi-periodically driven quantum parametric oscillators have been the subject of several recent investigations. Here we show that for such oscillators, the instability zones of the mean position and variance (alternatively the mean energy) for a time developing wave packet are identical for the strongest resonance in the three-dimensional parameter space of the quasi-periodic modulation as it is for the two-dimensional parameter space of the periodic modulations.
For a particle in a box, the operator $- i partial_x$ is not Hermitean. We provide an alternative construction of a momentum operator $p = p_R + i p_I$, which has a Hermitean component $p_R$ that can be extended to a self-adjoint operator, as well as an anti-Hermitean component $i p_I$. This leads to a description of momentum measurements performed on a particle that is strictly limited to the interior of a box.
The quantum stochastic Schroedinger equation or Hudson-Parthasareathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of output fields. An important feature of such an equation is that it allows to treat not only absorption and emission of quanta, but also scattering processes, which however had very few applications in physical modelling. Moreover, recent developments have shown that also some non-Markovian dynamics can be generated by suitable choices of the state of the quantum noises involved in the HP-equation. This paper is devoted to an application involving these two features, non-Markovianity and scattering process. We consider a micro-mirror mounted on a vibrating structure and reflecting a laser beam, a process giving rise to a radiation-pressure force on the mirror. We show that this process needs the scattering part of the HP-equation to be described. On the other side, non-Markovianity is introduced by the dissipation due to the interaction with some thermal environment which we represent by a phonon field, with a nearly arbitrary excitation spectrum, and by the introduction of phase noise in the laser beam. Finally, we study the full power spectrum of the reflected light and we show how the laser beam can be used as a temperature probe.
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light modes has enabled, for example, the preparation of squeezed states of light and generation of entangled photon pairs. While strong nonlinear interaction between the modes has been realized in circuit QED systems, achieving significant interaction strength on the level of single quanta in other physical systems remains a challenge. Here we experimentally demonstrate such interaction that is equivalent to photon up- and down-conversion using normal modes of motion in a system of two Yb ions. The nonlinearity is induced by the intrinsic anharmonicity of the Coulomb interaction between the ions and can be used to simulate fully quantum operation of a degenerate optical parametric oscillator. We exploit this interaction to directly measure the parity and Wigner functions of ion motional states. The nonlinear coupling, combined with near perfect control of internal and motional states of trapped ions, can be applied to quantum computing, quantum thermodynamics, and even shed some light on the quantum information aspects of Hawking radiation.
Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators. Nonetheless, in the last decade opto-mechanical experiments have actualized macroscopic mechanical oscillators exhibiting such non-classical properties. A key indicator is the asymmetry in the strength of the motional sidebands generated in an electromagnetic field that measures interferometrically the oscillator position. This asymmetry is a footprint of the quantum motion of the oscillator, being originated by the non-commutativity between its ladder operators. A further step on the path highlighting the quantum physics of macroscopic systems is the realization of strongly non-classical states and the consequent observation of a distinct quantum behavior. Here we extend indeed the analysis to a squeezed state of a macroscopic mechanical oscillator embedded in an optical cavity, produced by parametric effect originated by a suitable combination of optical fields. The motional sidebands assume a peculiar shape, related to the modified system dynamics, with asymmetric features revealing and quantifying the quantum component of the squeezed oscillator motion.
In this paper we review the basic results concerning the Wigner transform and then we completely solve the quantum forced harmonic/inverted oscillator in such a framework; eventually, the tunnel effect for the forced inverted oscillator is discussed.
Subhadip Biswas
,Pratyusha Chowdhury
,Jayanta K Bhattacharjee
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(2019)
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"Instability Zones in the Dynamics of a Quantum Mechanical Quasiperiodic Parametric Oscillator"
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Subhadip Biswas
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