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. This highlights the photon transverse spatial degree of freedom as a versatile platform for testing the fundamental aspects of quantum multiparticle systems.

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. We show that the quantum model, under this parameter range and external optical driving, may be approximated into parametric interaction models for all involved modes. As an example, we study the effect of detuning in the optical resonant frequencies modes and optical driving resolved to mechanical sidebands and show an optical beam splitter with interaction strength dressed by the mechanical excitation number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer where the optical state mediates the interaction strength between the mechanical modes.

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. For the sake of validation, we provide an analytic solution to the historical Caldirola-Kanai quantum harmonic oscillator and show that there exists a unitary transformation within our framework that takes a generalized version of it onto the Paul trap Hamiltonian. In addition, we show how our approach provides the dynamics of generalized models whose Schrödinger equation becomes numerically unstable in the laboratory frame.

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. We engineer various configurations using an external resonator coupled to two sites of a CROW to show light trapping with effective exponential decay between the coupling sites, wave packet splitting into two pairs of identical Gaussian-like wave packets, and a non-local Mach-Zehnder interferometer.

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.

Underlying SUSY in a generalized Jaynes-Cummings model.

We present a general qubit-boson interaction Hamiltonian that describes the Jaynes-Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes-Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations.

[Formula: see text] -symmetry from Lindblad dynamics in a linearized optomechanical system.

We analyze a lossy linearized optomechanical system in the red-detuned regime under the rotating wave approximation. This so-called optomechanical state transfer protocol provides effective lossy frequency converter (quantum beam-splitter-like) dynamics where the strength of the coupling between the electromagnetic and mechanical modes is controlled by the optical steady-state amplitude. By restricting to a subspace with no losses, we argue that the transition from mode-hybridization in the strong coupling regime to the damped-dynamics in the weak coupling regime, is a signature of the passive parity-time ([Formula: see text]) symmetry breaking transition in the underlying non-Hermitian quantum dimer. We compare the dynamics generated by the quantum open system (Langevin or Lindblad) approach to that of the [Formula: see text]-symmetric Hamiltonian, to characterize the cases where the two are identical. Additionally, we numerically explore the evolution of separable and correlated number states at zero temperature as well as thermal initial state evolution at room temperature. Our results provide a pathway for realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum level.

Optimal crosstalk suppression in multicore fibers.

We study propagation in a cyclic symmetric multicore fiber where the core radii randomly fluctuate along the propagation direction. We propose a hybrid analytic-numerical method to optimize the amplitude and frequency of the fluctuations that suppress power transfer between outer and inner cores. This framework allows us to analytically find noise amplitude parameters that optimally suppress crosstalk. Our predictions are confirmed by numerical experiments using finite difference beam propagation methods for realistic C-band fibers. The analytic part of our method is general, provides the optimum fluctuation amplitude independent of the array geometry, as long as normal modes can be calculated. It works for both correlated and uncorrelated fluctuations allowing its use for any given optical system described by coupled mode theory.

Robust optomechanical state transfer under composite phase driving.

We propose a technique for robust optomechanical state transfer using phase-tailored composite pulse driving with constant amplitude. Our proposal is inspired by coherent control techniques in lossless driven qubits. We demonstrate that there exist optimal phases for maximally robust excitation exchange in lossy strongly-driven optomechanical state transfer. In addition, our proposed composite phase driving also protects against random variations in the parameters of the system. However, this driving can take the system out of its steady state. For this reason, we use the ideal optimal phases to produce smooth sequences that both maintain the system close to its steady state and optimize the robustness of optomechanical state transfer.

Engineering SU(1, 1) ⊗ SU(1, 1) vibrational states.

We propose an ideal scheme for preparing vibrational SU(1, 1) ⊗ SU(1, 1) states in a two-dimensional ion trap using red and blue second sideband resolved driving of two orthogonal vibrational modes. Symmetric and asymmetric driving provide two regimes to realize quantum state engineering of the vibrational modes. In one regime, we show that time evolution synthesizes so-called SU(1, 1) Perelomov coherent states, that is separable squeezed states and their superposition too. The other regime allows engineering of lossless 50/50 SU(2) beam splitter states that are entangled states. These ideal dynamics are reversible, thus, the non-classical and entangled states produced by our schemes might be used as resources for interferometry.

Simulating para-Fermi oscillators.

Quantum mechanics allows for a consistent formulation of particles that are neither bosons nor fermions. These para-particles are rather indiscernible in nature. Recently, we showed that strong coupling between a qubit and two field modes is required to simulate even order para-Bose oscillators. Here, we show that finite-dimensional representations of even order para-Fermi oscillators are feasible of quantum simulation under weak coupling. This opens the door to their potential implementation in different contemporaneous quantum electrodynamics platforms. We emphasize the intrinsic value of para-particles for the quantum state engineering of bichromatic field modes. In particular, we demonstrate that binomial two field mode states result from the evolution of para-Fermi vacuum states in the quantum simulation of these oscillators.

Symmetry in optics and photonics: a group theory approach.

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.

Polarization dynamics in twisted fiber amplifiers: a non-Hermitian nonlinear dimer model.

We study continuous-wave light propagation through a twisted birefringent single-mode fiber amplifier with saturable nonlinearity. The corresponding coupled-mode system is isomorphic to a non-Hermitian nonlinear dimer and gives rise to analytic polarization-mode dynamics. It provides an optical simulation of the semi-classical non-Hermitian Bose-Hubbard model and suggests its use for the design of polarization circulators and filters, as well as sources of polarized light.

All-optical PT-symmetric conversion of amplitude (phase) modulation to phase (amplitude) modulation.

We study electromagnetic field propagation through a planar three-waveguide coupler with linear gain or loss in a configuration that is the optical analog of a quantum PT-symmetric system. This model is experimentally feasible on at least four proven architectures: lossy waveguide couplers, pumped waveguides couplers, non-Hermitian electronics and coupled pumped whispering gallery mode resonators. We show that our device provides all-optical amplitude (phase) to phase (amplitude) conversion in the PT-symmetric regime at given propagation lenghts. The device has a π amplitude to phase conversion range if an extra binary phase is allowed in the reference signal, and a phase to amplitude conversion range that depends linearly on the gain-to-coupling ratio of the system. Our scheme may prove valuable in implementing phase shift keying formats, which have longer unrepeated transmission distance than intensity modulation schemes.

Optical finite representation of the Lorentz group.

We implement a finite-dimensional representation of the 2+1D Lorentz group with a PT-symmetric waveguide array. Our device can be engineered to behave like a multi-port oscillator or directional coupler with amplification. We show that the two-waveguide coupler with linear losses, the Vernier effect in coupled asymmetric micro-cavity lasers, and the so-called linear PT-symmetric dimer belong to this symmetry class of optical systems.

Gilmore-Perelomov symmetry based approach to photonic lattices.

We revisit electromagnetic field propagation through tight-binding arrays of coupled photonic waveguides, with properties independent of the propagation distance, and recast it as a symmetry problem. We focus our analysis on photonic lattices with underlying symmetries given by three well-known groups, SU(2), SU(1, 1) and Heisenberg-Weyl, to show that disperssion relations, normal states and impulse functions can be constructed following a Gilmore-Perelomov coherent state approach. Furthermore, this symmetry based approach can be followed for each an every lattice with an underlying symmetry given by a dynamical group.

Ermakov-Lewis symmetry in photonic lattices.

We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator, where the mass and frequency depend on the propagation distance. In these photonic lattices, refractive indices and second-neighbor couplings define the mass and frequency of the analog quantum oscillator, while first-neighbor couplings are a free parameter to adjust the model. The quantum model conserves the Ermakov-Lewis invariant, thus the photonic crystal also possesses this symmetry.

Jacobi photonic lattices and their SUSY partners.

We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these one-dimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the corresponding quantum optical model. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1, 1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.

A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices: reply to comment.

We regret that such a misleading comment [Opt. Express (2013)] has been made to our paper. First Lo states in his abstract that "However, the nonlinear Rabi model has already been rigorously proven to be undefined" to later recoil and use the contradictory statement "(. . . ) regarding the BS model with the counter-rotating terms (. . . ) Lo and his co-authors have proven that the model is well defined only if the coupling stregth g is smaller than a critical value gc = ω/4". While Lo focuses on the validity of the quantum optics Hamiltonians and gives a misleading assesment of our manuscript, the focus of our paper is the method to map such a set of Hamiltonians from quantum optics to photonic lattices. Our method is valid for the given class of Hamiltonians and, indeed, precaution must be exerted on the paramater ranges where those Hamiltonians are valid and where their classical simulation is feasible. These parameter ranges have to be specified in for each particular case studied. Furthermore, we gave as example the Buck-Sukumar model including counter-rotating terms which is a valid Hamiltonian for some coupling parameters.

A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices.

The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.