Partial spatial coherence effects in digital holographic microscopy with a laser source

We investigate a digital holographic microscope that permits us to modify the spatial coherence state of the sample illumination by changing the spot size of a laser beam on a rotating ground glass. Out-of-focus planes are refocused by digital holographic reconstruction with numerical implementation of the Kirchhoff-Fresnel integral. The partial coherence nature of the illumination reduces the coherent artifact noise with respect to fully coherent illumination. The investigated configuration allows the spatial coherence state to be changed without modifying the illumination level of the sample. The effect of the coherence state on the digital holographic reconstruction is theoretically and experimentally evaluated. We also show how multiple reflection interferences are limited by the use of reduced spatial coherent illumination.     

Coupled-mode theory for infrared and submillimeter wave detectors

We present a comprehensive, spatiotemporal, modal theory of submillimeter-wave and far-infrared power detectors. The theory is based on the contraction of the coherence tensor of the light with another coherence tensor that incorporates all of the physics of the detector. The theory is extremely general and applies to detectors of any bandwidth, with light in any state of polarization and spatiotemporal coherence. The theory applies equally to quasi-monochromatic and pulsed systems. We show that the tensor associated with the detector is a measureable quantity and outline a procedure for its experimental determination. We derive expressions for the statistical properties of a detector's output, including the correlations between the outputs of different detectors, say, in an array or interferometer. The theory provides a clear conceptual understanding of how any general detector couples to the modes of an optical system and thereby provides a powerful and flexible way of modeling the behavior of detectors and instruments.     

Control of population and atomic coherence by adiabatic rapid passage and optimization of coherent anti-Stokes Raman scattering signal by maximal coherence

Abstract

Robust control of atomic coherence and population transfer among Zeeman sublevels in the ground states of rubidium atom is investigated using adiabatic rapid passage in a nanosecond time scale, which is smaller than the lifetime of first excited Rb. It is shown that a slight change in the pump pulse time delay relative to the Stokes pulse leads to a significant modification of atomic coherence and population transfer, consequently having remarkable impacts on the generation of coherent anti-Stokes Raman scattering (CARS) signal and probe pulse absorption. This coherent control of quantum state and population is presented by numerical simulations based on self-consistent set of density matrix equations and Maxwell equations as well as experimental demonstration in rubidium atom with different atomic densities. Experimental observations are in good agreement with numerical calculations.     

Parametric Stimulated Raman Scattering With Solid Hydrogen

We investigate solid hydrogen as a nonlinear optical medium. We carry out stimulated Raman scattering (SRS) experiments using a large Raman coherence prepared with two single frequency pulsed lasers. We show that multiorder SRS generation proceeds collinearly to the pump beam axis without stringent restriction of phase matching. We show also that the SRS generation dominantly occurs for negative two-photon detunings for which the Raman coherence can follow the antiphased state coherence.     

Polariton parametric amplification in semiconductor microcavities

Modifying the photonic environment of a semiconductor quantum well by embedding it in a high-reflectivity microcavity gives rise to new fundamental optical excitations, half-quantum well excitons, half-photons. These particles, called polaritons, have a light mass, as cavity photons, meaning that they have a large De Broglie wavelength. On the other hand, polaritons, like excitons, are subject to Coulomb interaction, a feature generating strong optical nonlinearities. Such properties favour quantum degeneracy and collective phenomena related to the bosonic statistics of polaritons. We review experiments on stimulated scattering of polaritons. In particular we concentrate on the resonant excitation of polaritons somewhere on the dispersion curve and the stimulation of their scattering into the fundamental state by means of an optical probe beam. The process is called polariton parametric amplification and results in very large and ultrafast optical amplification of the probe beam. The model, based on a Hamiltonian of interacting bosons, suggests that the amplification is related to the coherence between polaritons. We demonstrate that in clearly designed samples, this coherence can be preserved almost up to room temperature, so that intersting applications of this phenomenon can be conceived. At the same time we have been able to improve dramatically the efficiency of the parametric process, making the microcavity an unprecedented optical amplifier.     

Permanently disentangled states of atom–field system via spontaneously generated coherence

Abstract

The effect of spontaneously generated coherence on evolution of the entanglement between a driven four-level Y-type atom and its spontaneous emission field is studied. We have shown that the atom will be entangled to its spontaneous emission field due to spontaneously generated coherence and coherent population trapping at the steady state. It is found that the degree of entanglement strongly depends on the initial atomic state. So, it can be controlled by the pumping laser pulses used for preparing an initial atomic system. More interestingly, the atom–field system can be found in a permanently disentangled state for a properly prepared atom.     

Spatial coherence properties of a multiple aperture system an analysis based on the Walsh functions

Abstract

Analysis of the spatial coherence of the light transmitted by an optical device composed of a periodical array of identical apertures is developed by employing an approach based on the properties of the binary Walsh functions. The successive interactions between each aperture, and the mutual intensity characterizing the coherence state of the transmitted light, can be adequately explained through the behaviour of the Walsh-Hadamard spectrum associated with the intensity distribution resulting from the far-field propagated light at the output of the aperture array.     

Pulse-mode study of the quantum correlation of photons in an N-photon Dicke model

Abstract

We find the N-photon state emitted by an N-step Dicke model and provide a method to construct the field coherence functions based on it. Our effort is concentrated on the second order coherence, or the one-photon density matrix. When expressed in its canonical representation, this matrix gives the photon number occupying each ‘pulse eigenmode’. This number serves as an indicator of the correlation between photons. By studying the evolution of the one-photon density matrix we can trace the creation of such correlation during the emission. From the asymptotic solution we are able to find approximate scaling law relations between the photon degeneracy in the eigenmodes and the total number of photons involved.     

Spatial coherence wavelets and phase-space representation of diffraction

The phase-space representation of the Fresnel-Fraunhofer diffraction of optical fields in any state of spatial coherence is based on the marginal power spectrum carried by the spatial coherence wavelets. Its structure is analyzed in terms of the classes of source pairs and the spot of the field, which is treated as the hologram of the map of classes. Negative values of the marginal power spectrum are interpreted as negative energies. The influence of the aperture edge on diffraction is stated in terms of the distortion of the supports of the complex degree of spatial coherence near it. Experimental results are presented.     

Task-based optimization and performance assessment in optical coherence imaging

Optimization of an optical coherence imaging (OCI) system on the basis of task performance is a challenging undertaking. We present a mathematical framework based on task performance that uses statistical decision theory for the optimization and assessment of such a system. Specifically, we apply the framework to a relatively simple OCI system combined with a specimen model for a detection task and a resolution task. We consider three theoretical Gaussian sources of coherence lengths of 2, 20, and 40 microm. For each of these coherence lengths we establish a benchmark performance that specifies the smallest change in index of refraction that can be detected by the system. We also quantify the dependence of the resolution performance on the specimen model being imaged.     

Effect of a Squeezed Vacuum on Coherent Population Trapping in a Three-level Lambda System

Abstract

Master equation methods are used to investigate the effects of a broad-band squeezed vacuum on a three-level atom of the lambda configuration. The two-mode squeezed vacuum is treated as a Markovian reservoir in a non-stationary phase-dependent state. In addition to the squeezed vacuum the atom is driven by two coherent laser fields each of which, depending on the polarization, can couple to one or both of the atomic transitions. We show that in general the optical Bloch equations for the atomic density matrix elements have oscillatory coefficients, thereby necessitating the use of Floquet methods. For the case of equal laser frequencies, which are also equal to the carrier frequency of the squeezed vacuum, the coefficients of the Bloch equations become time independent and stationary solutions for the populations and coherences are obtained by standard matrix methods. For the ordinary vacuum the usual coherent population trapping effect at two-photon resonance is obtained, with the upper state population being zero. An unsqueezed thermal field partially destroys the trapping effect as the upper state population is no longer zero at two-photon resonance. The squeezed vacuum has the effect of improving the trapping in that the coherence hole becomes more pronounced for some values of the relative phase between the squeezed vacuum and the driving fields. The additional effects of a coherence transfer rate between the two optical coherences, which occurs for special choices of angular momentum quantum numbers are also studied. For the case of equal laser frequencies, the inclusion of this coherence transfer process destroys population trapping and reduces the lambda system to a two-level system. However, for the case of unequal laser frequencies, the coherence transfer process in combination with the squeezed vacuum can restore to some extent the population trapping. We show that other features that do not occur for two-level atoms, such as stationary population inversions between pairs of the atomic levels, also depend on the relative phase and can be enhanced in the squeezed vacuum. In the case of unequal frequencies of the driving fields the population in the upper state depends on the relative phase only when the carrier frequency of the squeezed vacuum is equal to one of the two frequencies of the driving fields. When the carrier frequency of the squeezed vacuum is slightly detuned from both frequencies of the driving fields, the population in the upper state is insensitive to the relative phase but is dependent on the degree of squeezing. For large detunings, the population does not show any dependence on the degree of squeezing and its distribution in function of the two-photon detuning is similar to that in the thermal vacuum field.     

Coherence theory of electromagnetic wave propagation through stratified N-layer media

The theory of second-order coherence in connection with wave propagation through a stratified N-layer (SNL) medium is developed. Especially, the influence of the SNL medium on the propagation of the coherence generated by a given state of coherence at the entrance plane of the medium is considered. The generalization of the van Cittert-Zernike theorem is obtained, and the propagation of the second-order coherence from a quasi-homogeneous surface distribution or a rough surface is calculated. Furthermore, the influence of SNL media on the coherence properties of a pulse is calculated.     

Coherence effects in digital in-line holographic microscopy

We analyze the effects of partial coherence in the image formation of a digital in-line holographic microscope (DIHM). The impulse response is described as a function of cross-spectral density of the light used in the space-frequency domain. Numerical simulation based on the applied model shows that a reduction in coherence of light leads to broadening of the impulse response. This is also validated by results from experiments wherein a DIHM is used to image latex beads using light with different spatial and temporal coherence.     

Ultrahigh-resolution full-field optical coherence tomography

We have developed a white-light interference microscope for ultrahigh-resolution full-field optical coherence tomography of biological media. The experimental setup is based on a Linnik-type interferometer illuminated by a tungsten halogen lamp. En face tomographic images are calculated by a combination of interferometric images recorded by a high-speed CCD camera. Spatial resolution of 1.8 microm x 0.9 microm (transverse x axial) is achieved owing to the extremely short coherence length of the source, the compensation of dispersion mismatch in the interferometer arms, and the use of relatively high-numerical-aperture microscope objectives. A shot-noise-limited detection sensitivity of 90 dB is obtained in an acquisition time per image of 4 s. Subcellular-level images of plant, animal, and human tissues are presented.     

Andreev Spectroscopy for Superconducting Phase Qubits

We propose a new method to measure the coherence time ofsuperconducting phase qubits based on the analysis of themagnetic-field dependent dc nonlinear Andreev current across ahigh-resistance tunnel contact between the qubit and a dirtymetal wire and derive a quantitative relation between thesubgap I–V characteristic and the internal correlationfunction of the qubit.     

Scattering coherent and partially coherent space-time pulses through few-mode optical systems

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.     

Prediction of wave-front sensor slope measurements with artificial neural networks

For adaptive optical systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave-front sensor (WFS) and corrected with a deformable mirror. One limitation in this process is the time delay between the measurement of the aberrated wave front and implementation of the proper correction. Statistical techniques exist for predicting the atmospheric aberrations at the time of correction based on the present and past measured wave fronts. However, for the statistical techniques to be effective, key parameters of the atmosphere and the adaptive optical system must be known. These parameters include the Fried coherence length r(0), the atmospheric wind-speed profile, and the WFS slope measurement error. Neural networks provide nonlinear solutions to adaptive optical problems while offering the possibility to function under changing seeing conditions without actual knowledge of the current state of the key parameters. We address the use of neural networks for WFS slope measurement prediction with only the noisy WFS measurements as inputs. Where appropriate, we compare with classical statistical-based methods to determine if neural networks offer true benefits in performance.     

Dissociation Dynamics of Ultracold Atom-Molecule Mixtures in an Optical Lattice

We consider a gas of two-component fermionic atoms coupled to bosonic molecules via photoassociation in an optical lattice. The system consists initially of bosonic molecules only, assumed to be in a ground state corresponding to either a Mott-Insulator phase or a Superfluid phase. We show that in the strong fermion-fermion interaction limit the dissociation dynamics is governed by a spin-boson lattice Hamiltonian. In the framework of a mean-field analysis based on the Gutzwiller ansatz, we then examine the crossover of the dissociation from a regime of independent single-site dynamics to a regime of cooperative dynamics as the molecular tunneling increases. We also show that the observation of Rabi-like oscillations between atomic and molecular populations detects the number statistics and coherence properties between different lattice sites, and then provides useful information on the many-body ground states and interactions in the system.