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This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second…
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises…
We analytically tackle opto-vibronic interactions in molecular systems driven by either classical or quantum light fields. In particular, we examine a simple model of molecules with two relevant electronic levels, characterized by potential…
Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases,…
Optomagnetics emerges as a growing field of research cross-linking optics, magnetism and material science. Here, we provide a microscopic quantum mechanical and a macroscopic classical models to describe optomagnetic effects from nonlinear…
Intense light-matter interaction largely relies on the use of high-power light sources, creating fields comparable to, or even stronger than, the field keeping the electrons bound in atoms. Under such conditions, the interaction induces…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
In this paper, to study the effects of a nonlinear medium on the atom-field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as the our nonlinear optical phenomena and with the…
Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and…
Several optomechanics experiments are now entering the highly sought nonlinear regime where optomechanical interactions are large even for low light levels. Within this regime, new quantum phenomena and improved performance may be achieved,…
We consider theoretically the optomechanical interaction of several mechanical modes with a single quantized cavity field mode for linear and quadratic coupling. We focus specifically on situations where the optical dissipation is the…
Cavity optomechanics has proven to be a field of research rich with possibilities for studying motional cooling, squeezing, quantum entanglement and metrology in solid state systems. While to date most studies have focused on the modulation…
The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion…
Quantum optomechanical system serves as an interface for coupling between photons and phonons due to mechanical oscillations. We used the Heisenberg-Langevin approach under Markovian white noise approximation to study a quadratically…
Nonlinear interactions between single quantum particles are at the heart of any quantum information system, including analog quantum simulation and fault-tolerant quantum computing. This remains a particularly difficult problem for photonic…
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective…
The inherently nonlinear interaction between light and motion in cavity optomechanical systems has experimentally been studied in a linearized description in all except highly driven cases. Here we demonstrate a nanoscale optomechanical…
This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now…
In this paper, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of…