The master equation of quantum optical density operator is transformed to the equation of characteristic function. The parametric amplification and amplitude damping as well as the phase damping are considered. The solution for the most general initial quantum state is obtained for parametric amplification and amplitude damping. The purity of one mode Gaussian system and the entanglement of two mode Gaussian system are studied.
We present a novel technique for measuring the characteristics of a magneto-optical trap for cold atoms by monitoring the spontaneous emission from trapped atoms coupled into the guided mode of a tapered optical nanofiber. We show that the nanofiber is highly sensitive to very small numbers of atoms close to its surface. The size and shape of the MOT, determined by translating the cold atom cloud across the tapered fiber, is in excellent agreement with measurements obtained using the conventional method of fluorescence imaging using a CCD camera. The coupling of atomic fluorescence into the ta…
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic tomogram of the quantum state is clarified. The stationary states corresponding to quantum energy levels are associated with the probability representation of the von Neumann and Moyal equations written for the optical tomograms. Classical Liouville equation for optical tomogram is obtained. Example of parametric oscillator is considered in detail.
We find time evolution law of negative binomial optical field in diffusion channel. We reveal that by adjusting the diffusion parameter, photon number can controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.
Collective electronic excitations "excitons" in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. Excitons for long wave numbers and polarizations orthogonal to the lattice plane exhibit superradiance with a very short life time and a tightly confined emission direction. For shorter wavelength and in plane polarization they can posses a long life time, which beyond a critical wave number tends to infinity. Those excitons thus become metastable and decoupled from the free radiation field. The…
We study the transmission characteristics of sub-wavelength diameter silica optical nanofibers (ONF's) surrounded with a xenon plasma produced by a low-pressure inductive RF discharge. In contrast to related experiments using rubidium vapor, we find essentially no degradation of optical transmission through the ONF's as a function of time. We also observe a pronounced ONF transmission modulation effect that depends on the conditions of the xenon plasma.
We present a new optical scheme enabling the implementation of highly stable and configurable non-Markovian dynamics. Here one photon qubit can circulate in a multipass bulk geometry consisting of two concatenated Sagnac interferometers to simulate the so called collisional model, where the system interacts at discrete times with a vacuum environment. We show the optical features of our apparatus and three different implementations of it, replicating a pure Markovian scenario and two non-Markovian ones, where we quantify the information backflow by tracking the evolution of the initial entangl…
The stationary eigenstates and eigenvalues for the ponderomotive potential of an optical crystal confined in a one-dimensional infinite square well are numerically obtained. The initial states of the incoming particles taken as Gaussian, are expanded in the basis of the stationary eigenstates of the ponderomotive potential, to obtain the subsequent time evolution of the wave function of the particle during the interaction with the optical crystal. From the results of the time evolution of the probability density, it is observed that the particles get localized at equidistant positions in the t…
First, we use the theory of characteristics of first order partial differential equations to derive the guiding equation directly from the Quantum Evolution Equation (QEE). After obtaining the general result, we apply it to a set of evolution equations (Schroedinger, Pauli, Klein-Gordon, Dirac) to show how the guiding equation is, actually, the characteristic velocity of the corresponding matter field equations.
We study the evolution of twin-beam propagating inside active media that may be used to establish a continuous variable entangled channel between two distant users. In particular, we analyze how entanglement is degraded during propagation, and determine a threshold value for the interaction time, above which the state become separable, and thus useless for entanglement based manipulations. We explicitly calculate the fidelity for coherent state teleportation and show that it is larger than one half for the whole range of parameters preserving entanglemenent.
We provide a general approach for the analysis of optical state evolution under conditional measurement schemes, and identify the necessary and sufficient conditions for such schemes to simulate unitary evolution on the freely propagating modes. If such unitary evolution holds, an effective photon nonlinearity can be identified. Our analysis extends to conditional measurement schemes more general than those based solely on linear optics.
Recently, much research concerning the combination of nano-scale waveguides with nano-crystals and other nano-particles has been reported, because of possible applications in the field of quantum information and communication. The most useful and convenient method to verify the nature of such systems is optical detection. However, due to the diffraction limit, optical identification of characteristics such as particle type, particle position, etc is difficult or impossible. However, if such particles are placed on a waveguide, the coupling of scattered light to the waveguide guided modes can r…
We measure the quantum speed of the state evolution of the field in a weakly-driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment assisted speed-up is realized: the quantum speed of the state re-population in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the n…
We study characteristics of quantum evolution which can be called curvature and torsion. The curvature shows a deviation of the state vector in quantum evolution from the geodesic line. The torsion shows a deviation of state vector from the plane of evolution (a two-dimensional subspace) at a given time.
Optical characterization of AlGaAs microdisk resonant cavities with a quantum dot active region is presented. Direct passive measurement of the optical loss within AlGaAs microdisk resonant structures embedded with InAs/InGaAs dots-in-a-well (DWELL) is performed using an optical-fiber-based probing technique at a wavelength (lambda~1400 nm) that is red-detuned from the dot emission wavelength (lambda~1200 nm). Measurements in the 1400 nm wavelength band on microdisks of diameter D = 4.5 microns show that these structures support modes with cold-cavity quality factors as high as 360,000. DWELL-…
We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally entangled state. We argue that the truncated Wigner approximation being a natural generalization of the Gross-Pitaevskii classical equations of motion is adequate to correctly describe the time evolution including both collapse and revival of the condensate.
When a phase singularity is suddenly imprinted on the axis of an ordinary Gaussian beam, an optical vortex appears and starts to grow radially, by effect of diffraction. This radial growth and the subsequent evolution of the optical vortex under focusing or imaging can be well described in general within the recently introduced theory of circular beams, which generalize the hypergeometric-Gaussian beams and which obey novel kinds of ABCD rules. Here, we investigate experimentally these vortex propagation phenomena and test the validity of circular-beam theory. Moreover, we analyze the differen…
The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. For finding solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2xN2. When N is very large, evaluating the element…
The Poincare Equivalence Theorem states that any optical element which contains no absorbing components can be replaced by an equivalent optical model which consists of one linear retarder and one rotator only, both of which are uniquely determined. This has many useful applications in the field of Optics of Polarized Light. In particular, it arises naturally in attempts to reconstruct spatially varying refractive tensors or dielectric tensors from measurements of the change of state of polarization of light beams passing through the medium, a field which is known as Tensor Tomography. A speci…
We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight binding approximation and apply this to a two-cavity system as well as to a coupled resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time dependant cross correlation between the photons in different cavities to …
