Coherent states of the Laguerre-Gauss modes.

Large quantum photonic systems hold promise for surpassing classical computational limits, yet their state preparation remains a challenge. We propose an alternative approach to study multiparticle dynamics by mapping the excitation mode of these systems to physical properties of the Laguerre-Gauss modes. We construct coherent states establishing a direct link between excitation number dynamics and the evolution of the Laguerre-Gauss modes.

Optical coupling control of isolated mechanical resonators.

We present a Hamiltonian model describing two pairs of mechanical and optical modes under standard optomechanical interaction. The vibrational modes are mechanically isolated from each other and the optical modes couple evanescently. We recover the ranges for variables of interest, such as mechanical and optical resonant frequencies and naked coupling strengths, using a finite element model for a standard experimental realization.

A quadratic time-dependent quantum harmonic oscillator.

We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set-mass, frequency, driving strength, and parametric pumping-is time-dependent. Our unitary-transformation-based approach provides a solution to our general quadratic time-dependent quantum harmonic model. As an example, we show an analytic solution to the periodically driven quantum harmonic oscillator without the rotating wave approximation; it works for any given detuning and coupling strength regime.

Non-local scattering control in coupled resonator networks.

We demonstrate scattering control of Gaussian-like wave packets propagating with constant envelope velocity and invariant waist through coupled resonator optical waveguides (CROW) via an external resonator coupled to multiple sites of the CROW. We calculate the analytical reflectance and transmittance using standard scattering methods from waveguide quantum electrodynamics and show it is possible to approximate them for an external resonator detuned to the CROW. Our analytical and approximate results are in good agreement with numerical simulations.

Non-classical light state transfer in su(2) resonator networks.

We use a normal mode approach to show full and partial state transfer in a class of coupled resonator networks with underlying su(2) symmetry that includes the so-called [Formula: see text] photonic lattice. Our approach defines an auxiliary Hermitian coupling matrix describing the network that yields the normal modes of the system and its time evolution in terms of orthogonal polynomials. Our results provide insight on the full quantum state reconstruction time in a general su(2) network of any size and the full quantum transfer time in the [Formula: see text] network of size [Formula: see text] with [Formula: see text] For any other network sizes, the Fock state probability distribution of the initial state is conserved but the amplitudes suffer a phase shift proportional to [Formula: see text] that results in partial quantum state transfer.