Ultrafast Analog Fourier Transform Using 2-D LC Lattice

We describe how a 2-D rectangular lattice of inductors and capacitors can serve as an analog Fourier transform device, generating an approximate discrete Fourier transform (DFT) of an arbitrary input vector of fixed length. The lattice displays diffractive and refractive effects and mimics the combined optical effects of a thin-slit aperture and lens. Diffraction theories in optics are usually derived for 3-D media, whereas our derivations proceed in 2-D. Analytical and numerical results show agreement between lattice output and the true DFT. Potentially, this lattice can be used for an extremely low latency and high throughput analog signal processing device. The lattice can be fabricated on-chip with frequency of operation of more than 10 GHz

Quantum Phonon Optics: Coherent and Squeezed Atomic Displacements

In this paper we investigate coherent and squeezed quantum states of phonons. The latter allow the possibility of modulating the quantum fluctuations of atomic displacements below the zero-point quantum noise level of coherent states. The expectation values and quantum fluctuations of both the atomic displacement and the lattice amplitude operators are calculated in these states---in some cases analytically. We also study the possibility of squeezing quantum noise in the atomic displacement using a polariton-based approach.Comment: 6 pages, RevTe

Diffraction on the Two-Dimensional Square Lattice

We solve the thin-slit diffraction problem for two-dimensional lattice waves. More precisely, for the discrete Helmholtz equation on the semi-infinite square lattice with data prescribed on the left boundary (the aperture), we use lattice Green's functions and a discrete Sommerfeld outgoing radiation condition to derive the exact solution everywhere in the lattice. The solution is a discrete convolution that can be evaluated in closed form for the wave number $k=2$. For other wave numbers, we give a recursive algorithm for computing the convolution kernel

Photonic crystal cavity based optical induced transparency

Nowadays, information technology has been deeply integrated in our daily life. However, within its rapid development, it faces a serious bottleneck due to the prohibitive power consumption and limited transmission bandwidth of electrical interconnects. Silicon photonics introduces a potential solution for information technology based on optical communication. In this field, delay-bandwidth devices offer a high bandwidth optical interconnection and low power consumption for the next generation information communication technology. Through introducing the slow light effect, I can realise time domain control and store the light to achieve a new functional component, which is the optical buffer for optical information processing. The optical buffer allows us to control and store the light, using as the optical information process and transit. However, the current optical buffer devices are limited by high optical loss and the ability to produced tunable group delay of the light. In this thesis, I examine different configurations of the coupled photonic crystal resonator system and then introduce a novel tuneable delay line, based on photonic crystal cavity structures. Through the optical analog to electromagnetically induced transparency (EIT), an EIT-like transmission spectrum has been achieved in coupled photonic crystal cavities. By tuning the phase difference between two coupled resonators and resonance wavelength, I can achieve the desired analog conditions and reach to a maximum group delay of 360 ps. By adding thermal tuning pattern, I have demonstrated a tuning of the group delay of over 120 ps range at a low input power and a maximum delay of 300 ps group delay in coupled photonic crystal cavities system. All devices are with a footprint at only 200 μm², and with integrated compatibles as well. By employing a new vertical coupling technique, a record low loss 15 dB/ns is presented making this system very promising for practical optical information applications

Quantum Computing

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future.Comment: 26 pages, 7 figures, 291 references. Early draft of Nature 464, 45-53 (4 March 2010). Published version is more up-to-date and has several corrections, but is half the length with far fewer reference

Flexible-Resolution, Arbitrary-Input and Tunable Rotman Lens Spectrum Decomposer (RL-SD)

We present an enhanced design -- in terms of resolution flexibility, input port position arbitrariness and frequency-range tunability -- of the planar Rotman lens spectrum decomposer (RL-SD). This enhancement is achieved by manipulating the output port locations through proper sampling of the frequency-position law of the RL-SD, inserting a calibration array compensating for frequency deviation induced by input modification and introducing port switching, respectively. A complete design procedure is provided and two enhanced RL-SD prototypes, with uniform port distribution and uniform frequency resolution, respectively, are numerically and experimentally demonstrated

Femtosecond Covariance Spectroscopy

In order to reveal a signal arising from a nonlinear interaction, several spectroscopic techniques are nowadays adopted. In spite of their practical and fundamental differences, they have in common to rely on pulse to pulse consistency to deliver information on a nonlinear process. With the work presented in this thesis we show, instead, that we can successfully leverage upon experimental noise. To achieve this goal, we exploited the fact that a weak nonlinear signal introduces a strong spectral correlation, which can be revealed even when the output spectra fully spectrally and spatially overlap with the excitation pulse. Based on these principles, we proposed a novel approach to a nonlinear spectroscopy experiment, called Femtosecond Covariance Spectroscopy. To provide a solid basis for the validation of the technique, we focused on a third order nonlinear process, inelastic light scattering, which is prompted by the mixing of intense electric fields in a transparent material. The interaction implies that the measured intensity at some point in the transmitted spectrum is statistically related to the intensity at other points of the spectrum, whenever their energy distance coincides with an energy level of the sample involved in the scattering. We performed inelastic light scattering experiments from vibrational modes of a benchmark sample, quartz. We employed a near infrared laser with central wavelength in a transparency region of the sample, and bandwidth larger than its lowest energy vibrational modes. We found in the correlation coefficient sidebands that reproduce the vibrational spectrum of the sample. Their lineshape changes according to the presence or absence of a non modulated portion of the spectrum, heterodyning the scattered radiation. In fact we find that a partial spectral randomization is most efficient in preparing a pulse with no pre-existent correlation, that, at the same time, provides a local oscillator for the sample-induced fluctuations to be amplified. In this scheme, the ultrashort pulse provides, at the same time, intense electric fields to stimulate a response, and noninteracting components to reveal it. The self-heterodyned nature of the acquisition is accounted for in a fully quantum model. The technique can be adapted to a pump - probe scheme by exciting the sample with a separate, intense and spectrally coherent, pump pulse. Our measurements of the average transmitted probe intensity performed using a pump to excite coherent vibrational states, reveal that oscillations in the response are initiated in-phase by the pump and evolve at the vibrational frequencies. Such a response is an ideal candidate to test a covariance based probe, as the spectrum undergoes a red-shift or a blue-shift alternatively in time, and the correlation coefficient is found to oscillate in time at the phonon frequency. The investigation we started with this Thesis aims, primarily, at establishing the signatures in the correlation that resolve a thermal from a coherent vibrational state. In fact, if a quantum optics model describes accurately the results of a standard pump probe experiment on quartz, the theoretical framework must be completed in order to describe a pump probe approach employing randomized pulses and a covariance based retrieval. The experiments have shown that consistent information is present in the correlation maps, but more incisive analytical and conceptual tools are needed to assess the different contributions. The proposed method has proven to be a powerful probing scheme in a optical spectroscopy experiment, and can be successfully translated into the language of stochastic X-ray pulses, complex materials, electronic scattering processes. To fully characterize the FCS technique there are still steps to take. Nonetheless we believe that the present work sets the basis for the development of a technique that successfully conveys information beyond traditional schemes