Label-free detection of single biological molecules using microtoroid optical resonators

Being able to detect a single molecule without the use of labels has been a long standing goal of bioengineers and physicists. This would simplify applications ranging from single molecular binding studies to those involving public health and security, improved drug screening, medical diagnostics, and genome sequencing. One promising technique that has the potential to detect single molecules is the microtoroid optical resonator. The main obstacle to detecting single molecules, however, is decreasing the noise level of the measurements such that a single molecule can be distinguished from background. We have used laser frequency locking in combination with balanced detection and data processing techniques to reduce the noise level of these devices and report the detection of a wide range of nanoscale objects ranging from nanoparticles with radii from 100 to 2.5 nm, to exosomes, ribosomes, and single protein molecules (mouse immunoglobulin G and human interleukin-2). We further extend the exosome results towards creating a non-invasive tumor biopsy assay. Our results, covering several orders of magnitude of particle radius (100 nm to 2 nm), agree with the `reactive' model prediction for the frequency shift of the resonator upon particle binding. In addition, we demonstrate that molecular weight may be estimated from the frequency shift through a simple formula, thus providing a basis for an ``optical mass spectrometer'' in solution. We anticipate that our results will enable many applications, including more sensitive medical diagnostics and fundamental studies of single receptor-ligand and protein-protein interactions in real time. The thesis summarizes what we have achieved thus far and shows that the goal of detecting a single molecule without the use of labels can now be realized.

A study of a new electromechanical energy conversion process using superconducting frequency modulated resonators

Experimental demonstrations and theoretical analyses of a new electromechanical energy conversion process which is made feasible only by the unique properties of superconductors are presented in this dissertation. This energy conversion process is characterized by a highly efficient direct energy transformation from microwave energy into mechanical energy or vice versa and can be achieved at high power level. It is an application of a well established physical principle known as the adiabatic theorem (Boltzmann-Ehrenfest theorem) and in this case time dependent superconducting boundaries provide the necessary interface between the microwave energy on one hand and the mechanical work on the other. The mechanism which brings about the conversion is another known phenomenon - the Doppler effect. The resonant frequency of a superconducting resonator undergoes continuous infinitesimal shifts when the resonator boundaries are adiabatically changed in time by an external mechanical mechanism. These small frequency shifts can accumulate coherently over an extended period of time to produce a macroscopic shift when the resonator remains resonantly excited throughout this process. In addition, the electromagnetic energy in s ide the resonator which is proportional to the oscillation frequency is al so accordingly changed so that a direct conversion between electromagnetic and mechanical energies takes place. The intrinsically high efficiency of this process is due to the electromechanical interactions involved in the conversion rather than a process of thermodynamic nature and therefore is not limited by the thermodynamic value.

A highly reentrant superconducting resonator resonating in the range of 90 to 160 MHz was used for demonstrating this new conversion technique. The resonant frequency was mechanically modulated at a rate of two kilohertz. Experimental results showed that the time evolution of the electromagnetic energy inside this frequency modulated (FM) superconducting resonator indeed behaved as predicted and thus demonstrated the unique features of this process. A proposed usage of FM superconducting resonators as electromechanical energy conversion devices is given along with some practical design considerations. This device seems to be very promising in producing high power (~10W/cm^3) microwave energy at 10 - 30 GHz.

Weakly coupled FM resonator system is also analytically studied for its potential applications. This system shows an interesting switching characteristic with which the spatial distribution of microwave energies can be manipulated by external means. It was found that if the modulation was properly applied, a high degree (>95%) of unidirectional energy transfer from one resonator to the other could be accomplished. Applications of this characteristic to fabricate high efficiency energy switching devices and high power microwave pulse generators are also found feasible with present superconducting technology.

Radio frequency studies of surface resistance and critical magnetic field of type I and type II superconductors

The surface resistance and the critical magnetic field of lead electroplated on copper were studied at 205 MHz in a half-wave coaxial resonator. The observed surface resistance at a low field level below 4.2°K could be well described by the BCS surface resistance with the addition of a temperature independent residual resistance. The available experimental data suggest that the major fraction of the residual resistance in the present experiment was due to the presence of an oxide layer on the surface. At higher magnetic field levels the surface resistance was found to be enhanced due to surface imperfections.

The attainable rf critical magnetic field between 2.2°K and T_c of lead was found to be limited not by the thermodynamic critical field but rather by the superheating field predicted by the one-dimensional Ginzburg-Landau theory. The observed rf critical field was very close to the expected superheating field, particularly in the higher reduced temperature range, but showed somewhat stronger temperature dependence than the expected superheating field in the lower reduced temperature range.

The rf critical magnetic field was also studied at 90 MHz for pure tin and indium, and for a series of SnIn and InBi alloys spanning both type I and type II superconductivity. The samples were spherical with typical diameters of 1-2 mm and a helical resonator was used to generate the rf magnetic field in the measurement. The results of pure samples of tin and indium showed that a vortex-like nucleation of the normal phase was responsible for the superconducting-to-normal phase transition in the rf field at temperatures up to about 0.98-0.99 T_c' where the ideal superheating limit was being reached. The results of the alloy samples showed that the attainable rf critical fields near T_c were well described by the superheating field predicted by the one-dimensional GL theory in both the type I and type II regimes. The measurement was also made at 300 MHz resulting in no significant change in the rf critical field. Thus it was inferred that the nucleation time of the normal phase, once the critical field was reached, was small compared with the rf period in this frequency range.

Double injection: high frequency noise and temperature dependence

Noise measurements from 140°K to 350°K ambient temperature and between 10kHz and 22MHz performed on a double injection silicon diode as a function of operating point indicate that the high frequency noise depends linearly on the ambient temperature T and on the differential conductance g measured at the same frequency. The noise is represented quantitatively by〈i^2〉 = α•4kTgΔf. A new interpretation demands Nyquist noise with α ≡ 1 in these devices at high frequencies. This is in accord with an equivalent circuit derived for the double injection process. The effects of diode geometry on the static I-V characteristic as well as on the ac properties are illustrated. Investigation of the temperature dependence of double injection yields measurements of the temperature variation of the common high-level lifetime τ(τ ∝ T^2), the hole conductivity mobility µ_p (µ_p ∝ T^(-2.18)) and the electron conductivity mobility µ_n(µ_n ∝ T^(-1.75)).

Application of sample-and-hold circuits in the laser frequency-shifting

A new method of frequency-shifting for a diode laser is realized. Using a sample-and-hold circuit, the error signal can be held by the circuit during frequency shifting. It can avoid the restraint of locking or even lock-losing caused by the servo circuit when we input a step-up voltage into piezoelectric transition (PZT) to achieve laser frequency-shifting.

Trapping of neutral atoms with a radio-frequency field

Based on the dressed-atom approach, we discuss a two-dimensional (2D) radio-frequency trap for neutral atoms, in which the trap potential derives from the magnetic-dipole transition among the hyperfine Zeeman sublevels. By adjusting the detuning of the radiation from resonance, the trapping states will be changed predominantly from the bare states Of m(FgF) > 0 to other states of m(FgF) < 0, where m(F) and g(F) are the quantum numbers of Zeeman sublevels and the Lande factor, respectively. This character contrasts finely with that, of a static magnetic, trap that can only trap or guide the states of m(FgF) > 0. In comparison to the optical field, the radio-frequency trap eliminates the spontaneous emission heating of the atoms. Unlike other oscillating traps reported in the e literature, the configuration of the radio-frequency trap is suitable for realization of a miniature magnetic guide.

Phase variations and phase shift in a TE011 mode microwave cavity used for in a miniature Rb fountain frequency standard

It is the first time in China that the phase variations and phase shift of microwave cavity in a miniature Rb fountain frequency standard are studied, considering the effect of imperfect metallic walls. Wall losses in the microwave cavity lead to small traveling wave components that deliver power from the cavity feed to the walls of cavity. The small traveling wave components produce a microradian distribution of phase throughout the cavity ity, and therefore distributed cavity phase shifts need to be considered. The microwave cavity is a TE011 circular cylinder copper cavity, with round cut-hole of end plates (14mm in diameter) for access for the atomic flux and two small apertures in the center of the side wall for coupling in microwave power. After attenuation alpha is calculated, field variations in cavity are solved. The field variations of the cavity are given. At the same time, the influences of loaded quality factor QL and diameter/height (2a/d) of the microwave cavity on the phase variations and phase shift are considered. According to the phase variation and phase shift of microwave cavity we select the parameters of cavity, diameter 2a = 69.2mm, height d = 34.6mm, QL = 5000, which will result in an uncertainty delta(Delta f / f0 ) < 4.7 x 10(-17) and meets the requirement for the miniature Rb fountain frequency standard with accuracy 10(-15).

Valley evolution by meandering rivers

Fluvial systems form landscapes and sedimentary deposits with a rich hierarchy of structures that extend from grain- to valley scale. Large-scale pattern formation in fluvial systems is commonly attributed to forcing by external factors, including climate change, tectonic uplift, and sea-level change. Yet over geologic timescales, rivers may also develop large-scale erosional and depositional patterns that do not bear on environmental history. This dissertation uses a combination of numerical modeling and topographic analysis to identify and quantify patterns in river valleys that form as a consequence of river meandering alone, under constant external forcing. Chapter 2 identifies a numerical artifact in existing, grid-based models that represent the co-evolution of river channel migration and bank strength over geologic timescales. A new, vector-based technique for bank-material tracking is shown to improve predictions for the evolution of meander belts, floodplains, sedimentary deposits formed by aggrading channels, and bedrock river valleys, particularly when spatial contrasts in bank strength are strong. Chapters 3 and 4 apply this numerical technique to establishing valley topography formed by a vertically incising, meandering river subject to constant external forcing—which should serve as the null hypothesis for valley evolution. In Chapter 3, this scenario is shown to explain a variety of common bedrock river valley types and smaller-scale features within them—including entrenched channels, long-wavelength, arcuate scars in valley walls, and bedrock-cored river terraces. Chapter 4 describes the age and geometric statistics of river terraces formed by meandering with constant external forcing, and compares them to terraces in natural river valleys. The frequency of intrinsic terrace formation by meandering is shown to reflect a characteristic relief-generation timescale, and terrace length is identified as a key criterion for distinguishing these terraces from terraces formed by externally forced pulses of vertical incision. In a separate study, Chapter 5 utilizes image and topographic data from the Mars Reconnaissance Orbiter to quantitatively identify spatial structures in the polar layered deposits of Mars, and identifies sequences of beds, consistently 1-2 meters thick, that have accumulated hundreds of kilometers apart in the north polar layered deposits.

Surface planar ion chip for linear radio-frequency Paul traps

We propose a surface planar ion chip which forms a linear radio frequency Paul ion trap. The electrodes reside in the two planes of a chip, and the trap axis is located above the chip surface. Its electric field and potential distribution are similar to the standard linear radio frequency Paul ion trap. This ion trap geometry may be greatly meaningful for quantum information processing.