Quantum optomechanics with silicon nanostructures

Mechanical resonators are the most basic and ubiquitous physical systems known. In on-chip form, they are used to process high frequency signals in every cell phone, television, and laptop. They have also been in the last few decades in different shapes and forms, a critical part of progress in quantum information sciences with kilogram-scale mirrors for gravitational wave detection measuring motion at its quantum limits, and the motion of single ions being used to link qubits for quantum computation.

Optomechanics is a field primarily concerned with coupling light to the motion of mechanical structures. This thesis contains descriptions of recent work with mechanical systems in the megahertz to gigahertz frequency range, formed by nanofabricating novel photonic/phononic structures on a silicon chip. These structures are designed to have both optical and mechanical resonances, and laser light is used to address and manipulate their motional degrees of freedom through radiation pressure forces. We laser cool these mechanical resonators to their ground states, and observe for the first time the quantum zero-point motion of a nanomechanical resonator. Conversely, we show that engineered mechanical resonances drastically modify the optical response of our structures, creating large effective optical nonlinearities not present in bulk silicon. We experimentally demonstrate aspects of these nonlinearities by proposing and observing ``electromagnetically induced transparency'' and light slowed down to 6 m/s, as well as wavelength conversion, and generation of nonclassical optical radiation. Finally, the application of optomechanics to longstanding problems in quantum and classical communications are proposed and investigated.

Controllable group velocity of the probe light in a Lambda-type system with two fold levels

The group velocities of the probe laser field are studied in a A-type system where one lower state has two fold levels coupled by a control field. It is found that the interaction of double dark states leads to controllable group velocity of the probe field in this system. It can be easily realized, due to the interacting double dark resonances, that one of the group velocities at transparency positions is much slower than the other by tuning the control field to be off resonance. In particular, when the control field is on resonance. we can obtain two equal slow group velocities with a broader EIT width, which provides potential applications in quantum storage and retrieval of light. (c) 2005 Elsevier B.V. All rights reserved.

Coupled plasmonic systems and devices : applications in visible metamaterials, nanophotonic circuits, and CMOS imaging

With the size of transistors approaching the sub-nanometer scale and Si-based photonics pinned at the micrometer scale due to the diffraction limit of light, we are unable to easily integrate the high transfer speeds of this comparably bulky technology with the increasingly smaller architecture of state-of-the-art processors. However, we find that we can bridge the gap between these two technologies by directly coupling electrons to photons through the use of dispersive metals in optics. Doing so allows us to access the surface electromagnetic wave excitations that arise at a metal/dielectric interface, a feature which both confines and enhances light in subwavelength dimensions - two promising characteristics for the development of integrated chip technology. This platform is known as plasmonics, and it allows us to design a broad range of complex metal/dielectric systems, all having different nanophotonic responses, but all originating from our ability to engineer the system surface plasmon resonances and interactions. In this thesis, we demonstrate how plasmonics can be used to develop coupled metal-dielectric systems to function as tunable plasmonic hole array color filters for CMOS image sensing, visible metamaterials composed of coupled negative-index plasmonic coaxial waveguides, and programmable plasmonic waveguide network systems to serve as color routers and logic devices at telecommunication wavelengths.

The ^(26)Al(p,γ)^(27)Si reaction : stellar origins of galactic ^(26)Al

To explain the ^(26)Mg isotopic anomaly seen in meteorites (^(26)Al daughter) as well as the observation of 1809-keV γ rays in the interstellar medium (live decay of 26Al) one must know, among other things, the destruction rate of ^(26)Al. Properties of states in ^(27)Si just above the ^(26)Al + p mass were investigated to determine the destruction rate of ^(26)Al via the ^(26)Al(p,γ)^(27)Si reaction at astrophysical temperatures.

Twenty micrograms of ^(26)Al were used to produce two types of Al_2O_3 targets by evaporation of the oxide. One was onto a thick platinum backing suitable for (p,γ) work, and the other onto a thin carbon foil for the (^3He,d) reaction.

The ^(26)Al(p,γ)^(27)Si excitation function, obtained using a germanium detector and voltage-ramped target, confirmed known resonances and revealed new ones at 770, 847, 876, 917, and 928 keV. Possible resonances below the lowest observed one at E_p = 286 keV were investigated using the ^(26)Al(^3He,d)^(27)Si proton-transfer reaction. States in 27Si corresponding to 196- and 286-keV proton resonances were observed. A possible resonance at 130 keV (postulated in prior work) was shown to have a strength of wγ less than 0.02 µeV.

By arranging four large Nal detector as a 47π calorimeter, the 196-keV proton resonance, and one at 247 keV, were observed directly, having wγ = 55± 9 and 10 ± 5 µeV, respectively.

Large uncertainties in the reaction rate have been reduced. At novae temperatures, the rate is about 100 times faster than that used in recent model calculations, casting some doubt on novae production of galactic ^(26)Al.

Phase control of gain and dispersion in an open lambda-type inversionless lasing system

The control role of the relative phase between the probe and driving fields on the gain and dispersion in an open Lambda-type inversionless lasing system with spontaneously generated coherence (SGC) is investigated. It is shown that the inversionless gain and dispersion are quite sensitive to variation in the relative phase; by adjusting the value of the relative phase, electromagnetically induced transparency (EIT), a high refractive index with zero absorption and a larger inversionless gain can be realized. It is also shown that, in the contributions to the inversionless gain ( absorption) and dispersion, the contribution from SGC is always much larger than that from the dynamically induced coherence for any value of the relative phase. Our analysis shows that variation in the SGC effect will cause the spectrum regions and values of the inversionless gain and dispersion to vary evidently. We also found that, under the same conditions, the values of the inversionless gain and dispersion in the open system are evidently larger than those in the corresponding closed system; EIT occurs in the open system but cannot occur in the closed system.

Structurally engineered cytochromes c with novel ligand-binding properties

Semisynthesis of horse heart cytochrome c and site-directed mutagenesis of Saccharomyces cerevisiae (S. c.) iso-1-cytochrome c have been utilized to substitute Ala for the cytochrome c heme axial ligand Met80 to yield ligand-binding proteins (horse heart Ala80cyt c and S.c. Ala80cyt c) with spectroscopic properties remarkably similar to those of myoglobin. Both species of Fe(II)Ala80cyt c form exceptionally stable dioxygen complexes with autoxidation rates 10-30x smaller and O₂ binding constants ~ 3x greater than those of myoglobin. The resistance of O₂-Fe(II)Ala80cyt c to autoxidation is attributed in part to protection of the heme site from solvent as exhibited by the exceptionally slow rate of CO binding to the heme as well as the low quantum yield of CO photodissociation.

UV/vis, EPR, and paramagnetic NMR spectroscopy indicate that at pH 7 the Fe(III)Ala80cyt c heme is low-spin with axial His-OH^- coordination and that below pH ~6.5, Fe(III)Ala80cyt cis high-spin with His-H₂O heme ligation. Significant differences in the pH dependence of the ¹H NMR spectra of S.c. Fe(III)Ala80cyt c compared to wild-type demonstrate that the axial ligands influence the conformational energetics of cytochrome c.

¹H NMR spectroscopy has been utilized to determine the solution structure of the cyanide derivative of S.c. Fe(III)Ala80cyt c. 82% of the resonances in the ¹H NMR spectrum of S.c. CN-Fe(III)Ala80cyt c have been assigned through 1D and 2D experiments. The RMSD values after restrained energy minimization of the family of 17 structures obtained from distance geometry calculations are 0.68 ± 0.11 Å for the backbone and 1.32 ± 0.14 Å for all heavy atoms. The solution structure indicates that a tyrosine in the "distal" pocket of CN-Fe(III)Ala80cyt c forms a hydrogen bond with the Fe(III)-CN unit, suggesting that it may play a role analogous to that of the distal histidine in myoglobin in stabilizing the dioxygen adduct.

Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in polar molecules

Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in a two-level polar molecule are investigated theoretically by solving the density-matrix equations without invoking any of the standard approximations. It is shown due to the effects of permanent dipole moments, that the population accumulation of multiphoton transitions can be obtained in the polar molecule. Moreover, the population accumulations depend crucially on the relative phase between two sequential pulses, and the period in which the maximum population accumulation occurs is 2 pi/N in N-photon transitions.

Enhancement of Kerr nonlinearity with vanishing absorption in a tripod scheme

The giant enhancement of Kerr nonlinearity in a four-level tripod type system is investigated theoretically. By tuning the value of the Rabi frequency of the coherent control field, owing to the double dark resonances, the giant-enhanced Kerr nonlinearity can be achieved within the right transparency window. The in fluence of Doppler broadening is also discussed.

Quantum interference effects of two coherent population trapping states on the atomic spectral lines of a F-e=0 -> F-g=1 transition

We investigate the fluorescence spectrum in a nearly degenerate atomic system of a F-e = 0 -> F-g = 1 transition by analytically solving Schrodinger equations. An ultranarrow fluorescence spectral line in between the two coherent population trapping windows has been found. Our analytic solutions clearly show the origin of the ultranarrow spectral line. Due to quantum interference effects between two coherent population trapping states, the width and intensity of the central spectral line can be controlled by an external magnetic field. Such an effect may be used to detect a magnetic field.

Quantum superchemistry in an output coupler of coherent matter waves

We investigate the quantum superchemistry or Bose-enhanced atom-molecule conversions in a coherent output coupler of matter waves, as a simple generalization of the two-color photoassociation. The stimulated effects of molecular output step and atomic revivals are exhibited by steering the rf output couplings. The quantum noise-induced molecular damping occurs near a total conversion in a levitation trap. This suggests a feasible two-trap scheme to make a stable coherent molecular beam.

Temperature dependence of dark lines in coherent population trapping

We measure the signal amplitude and linewidth of a dark line in coherent population trapping in the Rb vapour cell filled with mixed buffer gas N-2 and Ar as a function of cell temperature. We find that the dark line signal amplitude increases with temperature up to a maximum at 49 degrees C and then drops at higher temperatures due to quenching effects of N-2. The linewidth of the dark line remains basically constant, at 1080 Hz. We also measure the linewidth of the dark line as a function of laser intensity. The linewidth increases linearly with laser intensity. An intrinsic linewidth (FWHM=896 Hz at 3.4 GHz) of the Rb cell is obtained.

Nonlinear spectroscopy of cold atoms in diffuse laser light

The nonlinear spectroscopy of cold atoms in the diffuse laser cooling system is studied in this paper. We present the theoretical models of the recoil-induced resonances (RIR) and the electromagnetically-induced absorption (EIA) of cold atoms in diffuse laser light, and show their signals in an experiment of cooling Rb-87 atomic vapor in an integrating sphere. The theoretical results are in good agreement with the experimental ones when the light intensity distribution in the integrating sphere is considered. The differences between nonlinear spectra of cold atoms in the diffuse laser light and in the optical molasses are also discussed. (c) 2009 Optical Society of America

Fiber-optic integration and efficient detection schemes for optomechanical resonators

With the advent of the laser in the year 1960, the field of optics experienced a renaissance from what was considered to be a dull, solved subject to an active area of development, with applications and discoveries which are yet to be exhausted 55 years later. Light is now nearly ubiquitous not only in cutting-edge research in physics, chemistry, and biology, but also in modern technology and infrastructure. One quality of light, that of the imparted radiation pressure force upon reflection from an object, has attracted intense interest from researchers seeking to precisely monitor and control the motional degrees of freedom of an object using light. These optomechanical interactions have inspired myriad proposals, ranging from quantum memories and transducers in quantum information networks to precision metrology of classical forces. Alongside advances in micro- and nano-fabrication, the burgeoning field of optomechanics has yielded a class of highly engineered systems designed to produce strong interactions between light and motion.

Optomechanical crystals are one such system in which the patterning of periodic holes in thin dielectric films traps both light and sound waves to a micro-scale volume. These devices feature strong radiation pressure coupling between high-quality optical cavity modes and internal nanomechanical resonances. Whether for applications in the quantum or classical domain, the utility of optomechanical crystals hinges on the degree to which light radiating from the device, having interacted with mechanical motion, can be collected and detected in an experimental apparatus consisting of conventional optical components such as lenses and optical fibers. While several efficient methods of optical coupling exist to meet this task, most are unsuitable for the cryogenic or vacuum integration required for many applications. The first portion of this dissertation will detail the development of robust and efficient methods of optically coupling optomechanical resonators to optical fibers, with an emphasis on fabrication processes and optical characterization.

I will then proceed to describe a few experiments enabled by the fiber couplers. The first studies the performance of an optomechanical resonator as a precise sensor for continuous position measurement. The sensitivity of the measurement, limited by the detection efficiency of intracavity photons, is compared to the standard quantum limit imposed by the quantum properties of the laser probe light. The added noise of the measurement is seen to fall within a factor of 3 of the standard quantum limit, representing an order of magnitude improvement over previous experiments utilizing optomechanical crystals, and matching the performance of similar measurements in the microwave domain.

The next experiment uses single photon counting to detect individual phonon emission and absorption events within the nanomechanical oscillator. The scattering of laser light from mechanical motion produces correlated photon-phonon pairs, and detection of the emitted photon corresponds to an effective phonon counting scheme. In the process of scattering, the coherence properties of the mechanical oscillation are mapped onto the reflected light. Intensity interferometry of the reflected light then allows measurement of the temporal coherence of the acoustic field. These correlations are measured for a range of experimental conditions, including the optomechanical amplification of the mechanics to a self-oscillation regime, and comparisons are drawn to a laser system for phonons. Finally, prospects for using phonon counting and intensity interferometry to produce non-classical mechanical states are detailed following recent proposals in literature.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

Excitation energies and decay properties of T = 3/2 states in ^(17)O, ^(17)F and ^(21)Na

The two lowest T = 3/2 levels in ²¹Na have been studied in the ¹⁹F(³He, n), ²⁰Ne (p,p) and ²⁰Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in ¹⁷O and ¹⁷F to the ground state and first two excited states of ¹⁶O, by studying the ¹⁵N(³He,n) ¹⁷F*(p) ¹⁶O and ¹⁸O(³He, α)¹⁷O*(n) ¹⁶O reactions.

The ¹⁹F(³He,n) ²¹Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J ^π = ½⁺, Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.

These two levels were also obsesrved as isospin-forbidden resonances in the ²⁰Ne(p,p) and ²⁰Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:

E_x = 8.973 ± 0.007 MeV, J ^π = 5/2 ⁺ or 3/2⁺, Γ ≤ 1.2 keV,

^Γp_o = 0.1 ± 0.05 keV; E_x = 9.217 ± 0.007 MeV, J^π = ½ ⁺,

Γ = 2.3 ± 0.5 keV, ^Γp_o = 1.1 ± 0.3 keV.

Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.

Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in ¹⁷F were measured by the ¹⁵N(³He,n) ¹⁷ F*(p) ¹⁶O reaction to be 0.088 ± 0.016 to the ground state of ¹⁶O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of ¹⁶O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in ¹⁷O, were measured by the ¹⁶O(³He, α)¹⁷O*(n)¹⁶O reaction to be 0.91 ± 0.15 to the ground state of ¹⁶O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T_z.