The Glauber-Sudarshan and Kirkwood-Rihaczec functions

It is shown how to write the Kirkwood-Rihaczec quasiprobability distribution as an expectation value of the vacuum state. We do this, by writing the position eigenstates as a "displacment" of the vacumm. We also give a relation between the Glauber-Sudarshan and Kirkwood-Rihaczec quasiprobability distributions

Optical Production of the Husimi Function of Two Gaussian Functions

The intensity distribution of the Husimi function (HF) and the squared modulus of the Wigner function (WF) are detected in the phase space of an astigmatic optical processor. These results, obtained in the laboratory, are compared against numerical results generated by using analytical calculation for the HF and WF. The signal function is the superposition of two Gaussian functions with a separation between them, having the same amplitude but a different variance

Quantum derivation of Manley Rowe type relations

The Ermakov Lewis quantum invariant for the time dependent harmonic oscillator is expressed in terms of number and phase operators. The identification of these variables is made in accordance with the correspondence principle and the amplitude and phase representation of the classical orthogonal functions invariant. The relationship between the number and phase operators is established through this invariant as the system evolves from one frequency to another. In the specific case where the excitations represent the photon number, these relations are equivalent to the power density transport equations derived in nonlinear optical processes.Comment: 10 pages, no figure

Optical simulation of Majorana physics

We show a procedure to classically simulate the Majorana equation in 1+1 dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose a novel approach that uses a bi-chromatic refractive index distribution and nearest neighbor couplings of the type found in Glauber-Fock lattices. This allows us to escape the restriction of staying near the Brillouin zone imposed by the classical simulation of Dirac dynamics with bi-chromatic lattices. Furthermore, it is possible to simulate the evolution of Gaussian wavepackets under the Majorana/Dirac equation with light impinging only into the first waveguide of our bi-chromatic-Glauber-Fock lattice.Comment: 10 pages, 2 figure

Optical Bistability in a cavity with one moving mirror

We analyze the behaviour of a coherent field driving a single mode optical cavity with one perfectly reflecting moving mirror and a partially reflecting fixed mirror, and show that this system's output exhibits optical bistability due to radiation pressure acting over the moving mirror.Comment: 6 pages, 1 figur

An optical analog of quantum optomechanics

We present a two-dimensional array of nearest-neighbor coupled waveguides that is the optical analog of a quantum optomechanical system. We show that the quantum model predicts the appearance of effective column isolation, diagonal-coupling and other non-trivial couplings in the two-dimensional photonic lattice under a standard approximation from ion-trap cavity electrodynamics. We provide an approximate impulse function for the case of effective column isolation and compare it with exact numerical propagation in the photonic lattice.Comment: 10 pages, 4 figure

On the quantum phase problem

We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value $\pi^2/3$ which are the fluctuations for a classical random phase distribution. The formalism is shown to have consistency subjected to different approaches.Comment: 5 pages, no figure

NOON states in cavities

We show how NOON states may be generated entangling two cavities by passing atoms through them. The atoms interact with each cavity via two-photon resonant transitions. We take advantage of the fact that depending on the state the atom enter (excite or ground), it leaves or takes two photons per interaction and leaves the cavities in a pure state

Normal and anti-normal ordered expressions for annihilation and creation operators

We give the normal and anti-normal order expressions of the number operator to the power $k$ by using the commutation relation between the annihilation and creation operators. We use those expressions to give general formulae for functions of the number operator in normal and anti-normal order

Photon transport in binary photonic lattices

We present a review on the mathematical methods used to theoretically study classical propagation and quantum transport in arrays of coupled photonic waveguides. We focus on analysing two types of binary photonic lattices where self-energies or couplings are alternated. For didactic reasons, we split the analysis in classical propagation and quantum transport but all methods can be implemented, mutatis mutandis, in any given case. On the classical side, we use coupled mode theory and present an operator approach to Floquet-Bloch theory in order to study the propagation of a classical electromagnetic field in two particular infinite binary lattices. On the quantum side, we study the transport of photons in equivalent finite and infinite binary lattices by couple mode theory and linear algebra methods involving orthogonal polynomials. Curiously the dynamics of finite size binary lattices can be expressed as roots and functions of Fibonacci polynomials.Comment: 13 pages, 4 figure