Optical Bloch equations and enhanced decay of Rabi oscillations in strong driving fields

Optical Bloch equations are widely used for describing dynamics in a system consisting molecules, electromagnetic waves, and a thermal bath. We analyze applicability of these equations to a single molecule imbedded in a solid matrix. Classical Bloch equations and the limits of their applicability are derived from more general master equations. Simple and intuitively appealing picture based on stochastic Bloch equations shows that at low temperatures, contrary to common believes, a strong driving field can not only suppress but can also increase decay rates of Rabi oscillations. A physical system where predicted effects can be observed experimentally is suggested. (c) 2005 Elsevier B.V. All rights reserved.

NONLINEAR EFFECTS IN MAGNETIC GARNET FILMS AND NONRECIPROCAL OPTICAL BLOCH OSCILLATIONS IN WAVEGUIDE ARRAYS

This dissertation presents detailed experimental and theoretical investigations of nonlinear and nonreciprocal effects in magnetic garnet films. The dissertation thus comprises two major sections. The first section concentrates on the study of a new class of nonlinear magneto-optic thin film materials possessing strong higher order magnetic susceptibility for nonlinear optical applications. The focus was on enlarging the nonlinear performance of ferrite garnet films by strain generation and compositional gradients in the sputter-deposition growth of these films. Under this project several bismuth-substituted yttrium iron garnet (Bi,Y) 3 (Fe,Ga)5 O12(acronym as Bi:YIG) films have been sputter-deposited over gadolinium gallium garnet (Gd 3 Ga5 O12 ) substrates and characterized for their nonlinear optical response. One of the important findings of this work is that lattice mismatch strain drives the second harmonic (SH) signal in the Bi:YIG films, in agreement with theoretical predictions; whereas micro-strain was found not to correlate significantly with SH signal at the micro-strain levels present in these films. This study also elaborates on the role of the film's constitutive elements and their concentration gradients in nonlinear response of the films. Ultrahigh sensitivity delivered by second harmonic generation provides a new exciting tool for studying magnetized surfaces and buried interfaces, making this work important from both a fundamental and application point of view. The second part of the dissertation addresses an important technological need; namely the development of an on-chip optical isolator for use in photonic integrated circuits. It is based on two related novel effects, nonreciprocal and unidirectional optical Bloch oscillations (BOs), recently proposed and developed by Professor Miguel Levy and myself. This dissertation work has established a comprehensive theoretical background for the implementation of these effects in magneto-optic waveguide arrays. The model systems we developed consist of photonic lattices in the form of one-dimensional waveguide arrays where an optical force is introduced into the array through geometrical design turning the beam sideways. Laterally displaced photons are periodically returned to a central guide by photonic crystal action. The effect leads to a novel oscillatory optical phenomenon that can be magnetically controlled and rendered unidirectional. An on-chip optical isolator was designed based on the unidirectionality of the magneto-opticBloch oscillatory motion. The proposed device delivers an isolation ratio as high as 36 dB that remains above 30 dB in a 0.7 nm wavelength bandwidth, at the telecommunication wavelength 1.55 μm. Slight modifications in isolator design allow one to achieve an even more impressive isolation ratio ~ 55 dB, but at the expense of smaller bandwidth. Moreover, the device allows multifunctionality, such as optical switching with a simultaneous isolation function, well suited for photonic integrated circuits.

Coherent properties and Rabi oscillations in two-level donor systems

Coherent properties and Rabi oscillations in two-level donor systems, under terahertz excitation, are theoretically investigated. Here we are concerned with donor states in bulk GaAs and GaAs-(Ga,Al)As quantum dots. We study confinement effects, in the presence of an applied magnetic field, on the electronic and on-center donor states in GaAs- (Ga,Al)As dots, as compared to the situation in bulk GaAs, and estimate some of the associated decay rate parameters. Using the optical Bloch equations with damping, we study the time evolution of the Is and 2p(+) states in the presence of an applied magnetic field and of a terahertz laser. We also discuss the role played by the distinct dephasing rates on the photocurrent and calculate the electric dipole transition moment. Results indicate that the Rabi oscillations are more robust as the total dephasing rate diminishes, corresponding to a favorable coherence time.

Fluctuations and single molecules

The fluorescence of single molecules coupled to a thermal bath is studied both experimentally and theoretically. The effect of different fluctuations on the coherence properties of resonance fluorescence is considered first. Coherence is measured in an interference experiment where a single molecule is used as a light source. A standard approach based on the optical Bloch equations apparently provides quite an accurate description of the interference experiment. Systems with long correlation times (where spectra are time dependent on any timescale) are considered next. It is shown that intensity-time-frequency correlation spectroscopy, which provides both high signal-to-noise ratio and high time resolution, is very suitable for such a case. The Bloch equations are further tested in an experiment where the shape of an excitation spectral line of a single molecule is accurately measured over six orders of magnitude of the exciting laser power. Significant deviations from the predictions of the Bloch equations are found. The role of critical parameters-the correlation time of the bath, the Rabi oscillation period, and the coupling constant between the bath and the molecule-is discussed. The paper also includes a short general introduction to the methodology of single-molecule studies.

Resonant gradient force on atom interacting with laser field

The gradient force, as a function of position and velocity, is derived for a two-level atom interacting with a standing-wave laser field. Basing on optical Bloch equations, the numerical solutions for the gradient force f_(|_;n) (n = 0, 1, 2, 3, 4, ...) pointing in the direction of the transverse of the laser beam are given. It is shown the higher order gradient force plays important role at strong intensity (G = 64), the contribution of them can not be neglected.

Degenerate Gases of Strontium for Studies of Quantum Magnetism

We describe the construction and characterization of a new apparatus that can produce degenerate quantum gases of strontium. The realization of degenerate gases is an important first step toward future studies of quantum magnetism. Three of the four stable isotopes of strontium have been cooled into the degenerate regime. The experiment can make nearly pure Bose-Einstein condensates containing approximately 1x10^4 atoms, for strontium-86, and approximately 4x10^5 atoms, for strontium-84. We have also created degenerate Fermi gases of strontium-87 with a reduced temperature, T/T_F of approximately 0.2. The apparatus will be able to produce Bose-Einstein condensates of strontium-88 with straightforward modifications. We also report the first experimental and theoretical results from the strontium project. We have developed a technique to accelerate the continuous loading of strontium atoms into a magnetic trap. By applying a laser addressing the 3P1 to 3S1 transition in our magneto-optical trap, the rate at which atoms populate the magnetically-trapped 3P2 state can be increased by up to 65%. Quantum degenerate gases of atoms in the metastable 3P0 and 3P2 states are a promising platform for quantum simulation of systems with long-range interactions. We have performed an initial numerical study of a method to transfer the ground state degenerate gases that we can currently produce into one of the metastable states via a three-photon transition. Numerical simulations of the Optical Bloch equations governing the three-photon transition indicate that >90% of a ground state degenerate gas can be transferred into a metastable state.

Simulação de sinais de RMN através das equações de Bloch

The aim of this paper was to present a simple and fast way of simulating Nuclear Magnetic Resonance signals using the Bloch equations. These phenomenological equations describe the classical behavior of macroscopic magnetization and are easily simulated using rotation matrices. Many NMR pulse sequences can be simulated with this formalism, allowing a quantitative description of the influence of many experimental parameters. Finally, the paper presents simulations of conventional sequences such as Single Pulse, Inversion Recovery, Spin Echo and CPMG.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

MP2RAGE, a self bias-field corrected sequence for improved segmentation and T-1-mapping at high field

The large spatial inhomogeneity in transmit B, field (B-1(+)) observable in human MR images at hi h static magnetic fields (B-0) severely impairs image quality. To overcome this effect in brain T-1-weighted images the, MPRAGE sequence was modified to generate two different images at different inversion times MP2RAGE By combining the two images in a novel fashion, it was possible to create T-1-weigthed images where the result image was free of proton density contrast, T-2* contrast, reception bias field, and, to first order transmit field inhomogeneity. MP2RAGE sequence parameters were optimized using Bloch equations to maximize contrast-to-noise ratio per unit of time between brain tissues and minimize the effect of B-1(+) variations through space. Images of high anatomical quality and excellent brain tissue differentiation suitable for applications such as segmentation and voxel-based morphometry were obtained at 3 and 7 T. From such T-1-weighted images, acquired within 12 min, high-resolution 3D T-1 maps were routinely calculated at 7 T with sub-millimeter voxel resolution (0.65-0.85 mm isotropic). T-1 maps were validated in phantom experiments. In humans, the T, values obtained at 7 T were 1.15 +/- 0.06 s for white matter (WM) and 1.92 +/- 0.16 s for grey matter (GM), in good agreement with literature values obtained at lower spatial resolution. At 3 T, where whole-brain acquisitions with 1 mm isotropic voxels were acquired in 8 min the T-1 values obtained (0.81 +/- 0.03 S for WM and 1.35 +/- 0.05 for GM) were once again found to be in very good agreement with values in the literature. (C) 2009 Elsevier Inc. All rights reserved.

MP2RAGE, a self bias-field corrected sequence for improved segmentation and T1-mapping at high field.

The large spatial inhomogeneity in transmit B(1) field (B(1)(+)) observable in human MR images at high static magnetic fields (B(0)) severely impairs image quality. To overcome this effect in brain T(1)-weighted images, the MPRAGE sequence was modified to generate two different images at different inversion times, MP2RAGE. By combining the two images in a novel fashion, it was possible to create T(1)-weighted images where the result image was free of proton density contrast, T(2) contrast, reception bias field, and, to first order, transmit field inhomogeneity. MP2RAGE sequence parameters were optimized using Bloch equations to maximize contrast-to-noise ratio per unit of time between brain tissues and minimize the effect of B(1)(+) variations through space. Images of high anatomical quality and excellent brain tissue differentiation suitable for applications such as segmentation and voxel-based morphometry were obtained at 3 and 7 T. From such T(1)-weighted images, acquired within 12 min, high-resolution 3D T(1) maps were routinely calculated at 7 T with sub-millimeter voxel resolution (0.65-0.85 mm isotropic). T(1) maps were validated in phantom experiments. In humans, the T(1) values obtained at 7 T were 1.15+/-0.06 s for white matter (WM) and 1.92+/-0.16 s for grey matter (GM), in good agreement with literature values obtained at lower spatial resolution. At 3 T, where whole-brain acquisitions with 1 mm isotropic voxels were acquired in 8 min, the T(1) values obtained (0.81+/-0.03 s for WM and 1.35+/-0.05 for GM) were once again found to be in very good agreement with values in the literature.

The impact of spatial resolution and respiratory motion on MR imaging of atherosclerotic plaque.

PURPOSE: To examine the impact of spatial resolution and respiratory motion on the ability to accurately measure atherosclerotic plaque burden and to visually identify atherosclerotic plaque composition. MATERIALS AND METHODS: Numerical simulations of the Bloch equations and vessel wall phantom studies were performed for different spatial resolutions by incrementally increasing the field of view. In addition, respiratory motion was simulated based on a measured physiologic breathing pattern. RESULTS: While a spatial resolution of > or = 6 pixels across the wall does not result in significant errors, a resolution of < or = 4 pixels across the wall leads to an overestimation of > 20%. Using a double-inversion T2-weighted turbo spin echo sequence, a resolution of 1 pixel across equally thick tissue layers (fibrous cap, lipid, smooth muscle) and a respiratory motion correction precision (gating window) of three times the thickness of the tissue layer allow for characterization of the different coronary wall components. CONCLUSIONS: We found that measurements in low-resolution black blood images tend to overestimate vessel wall area and underestimate lumen area.

Motion artifact reduction and vessel enhancement for free-breathing navigator-gated coronary MRA using 3D k-space reordering.

Breathing-induced bulk motion of the myocardium during data acquisition may cause severe image artifacts in coronary magnetic resonance angiography (MRA). Current motion compensation strategies include breath-holding or free-breathing MR navigator gating and tracking techniques. Navigator-based techniques have been further refined by the applications of sophisticated 2D k-space reordering techniques. A further improvement in image quality and a reduction of relative scanning duration may be expected from a 3D k-space reordering scheme. Therefore, a 3D k-space reordered acquisition scheme including a 3D navigator gated and corrected segmented k-space gradient echo imaging sequence for coronary MRA was implemented. This new zonal motion-adapted acquisition and reordering technique (ZMART) was developed on the basis of a numerical simulation of the Bloch equations. The technique was implemented on a commercial 1.5T MR system, and first phantom and in vivo experiments were performed. Consistent with the results of the theoretical findings, the results obtained in the phantom studies demonstrate a significant reduction of motion artifacts when compared to conventional (non-k-space reordered) gating techniques. Preliminary in vivo findings also compare favorably with the phantom experiments and theoretical considerations. Magn Reson Med 45:645-652, 2001.

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

A dual resonance, image -guided, volume localization technique for magnetic resonance spectroscopy

An interleaved, dual resonance, volume localization technique for $\sp1$H/$\sp{31}$P magnetic resonance spectroscopy has been designed, implemented on a 2 T imager/spectrometer, and verified with phantom studies.^ Localization techniques, including several single voxel techniques and spectroscopic imaging, were implemented, and studies were performed to compare the efficiency of each sequence of $\sp1$H/$\sp{31}$P spectral acquisitions. The sequence chosen was a hybrid of the stimulated echo single voxel technique and the spectroscopic imaging technique.^ Water suppression during the $\sp1$H spectral acquisitions was accomplished by the use of three narrow bandwidth RF saturation pulses in combination with three spoiler gradients. The spoiler gradient amplitudes were selected on the basis of a numerical solution of the Bloch equations. A post-acquisition water suppression algorithm was used to minimize any residual water signal.^ For interleaved $\sp1$H/$\sp{31}$P acquisitions, a dual resonance RF coil was constructed and interfaced to the existing RF detection system via a custom-designed dual resonance transcoupler and switching system. Programmable attenuators were incorporated to allow for changes in receiver and transmitter attenuation "on the fly".^ To provide the rapidly switched gradient fields required for the $\sp1$H/$\sp{31}$P acquisitions, an actively screened gradient coil system was designed and implemented. With this system, gradient field rise times on the order of 100 $\mu$s were obtained. These rapid switching times were necessary for minimizing intrasequence delays and for improving localization quality and water suppression efficiency.^ The interleaved $\sp1$H/$\sp{31}$P volume localization technique was tested using a two-compartment phantom. Analysis of the data showed that the spectral contamination was less than three percent. One-to-one spatial correspondence of the $\sp1$H and $\sp{31}$P spectra was verified and allowed for direct correlation of the spectral data with a standard magnetic resonance image. ^