Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays

We investigate the design of free-space optical interconnects (FSOIs) based on arrays of vertical-cavity surface-emitting lasers (VCSELs), microlenses, and photodetectors. We explain the effect of the modal structure of a multimodeVCSEL beam on the performance of a FSOI with microchannel architecture. A Gaussian-beam diffraction model is used in combination with the experimentally obtained spectrally resolved VCSEL beam profiles to determine the optical channel crosstalk and the signal-to-noise ratio (SNR) in the system. The dependence of the SNR on the feature parameters of a FSOI is investigated. We found that the presence of higher-order modes reduces the SNR and the maximum feasible interconnect distance. We also found that the positioning of a VCSEL array relative to the transmitter microlens has a significant impact on the SNR and the maximum feasible interconnect distance. Our analysis shows that the departure from the traditional confocal system yields several advantages including the extended interconnect distance and/or improved SNR. The results show that FSOIs based on multimode VCSELs can be efficiently utilized in both chip-level and board-level interconnects. (C) 2002 Optical Society of America.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Transmission of optical coherent-state qubits

We discuss the long-distance transmission of qubits encoded in optical coherent states. Through absorption, these qubits suffer from two main types of errors, namely the reduction of the amplitude of the coherent states and accidental application of the Pauli Z operator. We show how these errors can be fixed using techniques of teleportation and error-correcting codes.

Demonstration of the spatial separation of the entangled quantum sidebands of an optical field

Quantum optics experiments on bright beams are based on the spectral analysis of field fluctuations and typically probe correlations between radio-frequency sideband modes. However, the extra degree of freedom represented by this dual-mode picture is generally ignored. We demonstrate the experimental operation of a device which can be used to separate the quantum sidebands of an optical field. We use this device to explicitly demonstrate the quantum entanglement between the sidebands of a squeezed beam.

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Universality of quantum critical dynamics in a planar optical parametric oscillator

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the quantum image critical point. This zero-temperature nonequilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition.

Quantum gate based on Stark tunable nanocrystal interactions with ultrahigh-Q/V field modes in fused silica microcavities

We investigate the use of nanocrystal quantum dots as a quantum bus element for preparing various quantum resources for use in photonic quantum technologies. Using the Stark-tuning property of nanocrystal quantum dots as well as the biexciton transition, we demonstrate a photonic controlled-NOT (CNOT) interaction between two logical photonic qubits comprising two cavity field modes each. We find the CNOT interaction to be a robust generator of photonic Bell states, even with relatively large biexciton losses. These results are discussed in light of the current state of the art of both microcavity fabrication and recent advances in nanocrystal quantum dot technology. Overall, we find that such a scheme should be feasible in the near future with appropriate refinements to both nanocrystal fabrication technology and microcavity design. Such a gate could serve as an active element in photonic-based quantum technologies.

Investigation of the Effect of Array Geometry on the Performance of Free-Space Optical Interconnects

The effect of transmitter and receiver array configurations on the stray-light and diffraction-caused crosstalk in free-space optical interconnects was investigated. The optical system simulation software (Code V) is used to simulate both the stray-light and diffraction-caused crosstalk. Experimentally measured, spectrally-resolved, near-field images of VCSEL higher order modes were used as extended sources in our simulation model. In addition, we have included the electrical and optical noise in our analysis to give more accurate overall performance of the FSOI system. Our results show that by changing the square lattice geometry to a hexagonal configuration, we obtain an overall signal-to-noise ratio improvement of 3 dB. Furthermore, system density is increased by up to 4 channels/mm2.

Novel array geometries for free-space optical interconnects with improved signal-to-noise ratio

We investigate the effect of transmitter and receiver array configurations on the stray-light and diffraction-caused crosstalk in free-space optical interconnects. The optical system simulation software (Code V) is used to simulate both the stray-light and diffraction-caused crosstalk. Experimentally measured, spectrally-resolved, near-field images of VCSEL higher order modes were used as extended sources in our simulation model. Our results show that by changing the square lattice geometry to a hexagonal configuration, we obtain the reduction in the stray-light crosstalk of up to 9 dB and an overall signal-to-noise ratio improvement of 3 dB.

Norwegian long-distance reflexives: Lectal variation and speaker attitudes

10 lectal variables were examined with respect to Norwegian speakers' acceptance of long-distance reflexives (LDR), using a questionnaire to elicit grammaticality judgements on 50 potential LDR sentences. A sample of 180 speakers completed the questionnaire. The data was analysed using a general linear model univariate model, and Spearman's correlation. In this sample the results showed that dialect and level of education had significant effects on speakers' acceptance of long-distance reflexives, while sex, age, being a native speaker, having both native-speaker parents, living in the city or the country, and the speaker's attitudes to the two Norwegian writing languages had no influence on speakers' acceptance of long-distance reflexives. It is suggested that the influence of Danish on Norwegian writing and on the southern dialects may be the cause of the observed variation with respect to LDR in Norwegian.

A method to lower the detection limit for optical beat signals from a frequency-dithered stabilized laser

A narrow absorption feature in an atomic or molecular gas (such as iodine or methane) is used as the frequency reference in many stabilized lasers. As part of the stabilization scheme an optical frequency dither is applied to the laser. In optical heterodyne experiments, this dither is transferred to the RF beat signal, reducing the spectral power density and hence the signal to noise ratio over that in the absence of dither. We removed the dither by mixing the raw beat signal with a dithered local oscillator signal. When the dither waveform is matched to that of the reference laser the output signal from the mixer is rendered dither free. Application of this method to a Winters iodine-stabilized helium-neon laser reduced the bandwidth of the beat signal from 6 MHz to 390 kHz, thereby lowering the detection threshold from 5 pW of laser power to 3 pW. In addition, a simple signal detection model is developed which predicts similar threshold reductions.

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Refractive index tomography of turbid media by bifocal optical coherence refractometry

We demonstrate tomographic imaging of the refractive index of turbid media using bifocal optical coherence refractometry (BOCR). The technique, which is a variant of optical coherence tomography, is based on the measurement of the optical pathlength difference between two foci simultaneously present in a medium of interest. We describe a new method to axially shift the bifocal optical pathlength that avoids the need to physically relocate the objective lens or the sample during an axial scan, and present an experimental realization based on an adaptive liquid-crystal lens. We present experimental results, including video clips, which demonstrate refractive index tomography of a range of turbid liquid phantoms, as well as of human skin in vivo.