arXiv subjects

Lee E. Harrell

Publications and source records attributed to Lee E. Harrell.

7 recordsLinked to original sources

arXiv2021

Improved optical standing-wave beam splitters for dilute Bose-Einstein condensates

Bose-Einstein condensate (BEC)-based atom interferometry exploits low temperatures and long coherence lengths to facilitate high-precision measurements. Progress in atom interferometry promises improvements in navigational devices like gyroscopes and accelerometers, as well as applications in fundamental physics such as accurate determination of physical constants. Previous work demonstrates that beam splitters and mirrors for coherent manipulation of dilute BEC momentum in atom interferometers can be implemented with sequences of non-resonant standing-wave light pulses. While previous work focuses on the optimization of the optical pulses' amplitude and duration to produce high-order momentum states with high fidelity, we explore how varying the shape of the optical pulses affects optimal beam-splitter performance, as well as the effect of pulse shape on the sensitivity of optimized parameters in achieving high fidelity in high-momentum states. In simulations of two-pulse beam splitters utilizing optimized square, triangle, and sinc-squared pulse shapes applied to dilute BECs, we, in some cases, reduce parameter sensitivity by an order of magnitude while maintaining fidelity.

cond-mat.quant-gas↗

arXiv2019

Lagrangian and impedance spectroscopy treatments of electric force microscopy

Scanning probe microscopy is often extended beyond topographic imaging to study electrical forces and sample properties, with the most widely used experiment being frequency-modulated Kelvin probe force microscopy. The equations commonly used to interpret this experiment, however, rely on two hidden assumptions: (1) the tip charge oscillates in phase with the cantilever motion to keep the tip voltage constant, and (2) any changes in the tip-sample interaction happen slowly. Starting from an electro-mechanical model of the cantilever-sample interaction, we use Lagrangian mechanics to derive coupled equations of motion for the cantilever position and charge. This general approach rigorously describes scanned probe experiments even in the case when the usual assumptions of fast tip charging and slowly changing samples properties are violated. We develop a Magnus-expansion approximation to illustrate how abrupt changes in the tip-sample interaction cause abrupt changes in the cantilever amplitude and phase. We show that feedback-free time-resolved electric force microscopy cannot uniquely determine sub-cycle photocapacitance dynamics. We then use first-order perturbation theory to relate cantilever frequency shift and dissipation to the sample impedance even when the tip charge oscillates out of phase with the cantilever motion. Analogous to the treatment of impedance spectroscopy in electrochemistry, we apply this approximation to determine the cantilever frequency shift and dissipation for an arbitrary sample impedance in (broadband) local dielectric spectroscopy experiments. The general approaches we develop provide a path forward for rigorously modeling the coupled motion of the cantilever position and charge in the wide range of electrical scanned probe microscopy experiments where the hidden assumptions of the conventional equations are violated or inapplicable.

cond-mat.mes-hall↗

arXiv2016

Wavefunction collapse through backaction of counting weakly interacting photons

We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle's wavefunction toward a narrow Gaussian wavepacket at the location $x_\mathrm{est}$ determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle's position, as calculated from the post-measurement wavefunction agrees precisely with shot-noise limited uncertainty of the measured $x_\mathrm{est}$. Both the identification of the absolute square of the particle's initial wavefunction as the probability density for $x_\mathrm{est}$ and the de Broglie hypothesis emerge as consequences of interpreting the intensity of the optical field as proportional to the probability of detecting a photon. Linear momentum information that is encoded in the particle's initial wavefunction survives the measurement, and the pre-measurement expectation values are preserved in the ensemble average.

quant-ph↗

arXiv2008

Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems

This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given.

quant-ph↗

arXiv2002

170 Nanometer Nuclear Magnetic Resonance Imaging using Magnetic Resonance Force Microscopy

We demonstrate one-dimensional nuclear magnetic resonance imaging of the semiconductor GaAs with 170 nanometer slice separation and resolve two regions of reduced nuclear spin polarization density separated by only 500 nanometers. This is achieved by force detection of the magnetic resonance, Magnetic Resonance Force Microscopy (MRFM), in combination with optical pumping to increase the nuclear spin polarization. Optical pumping of the GaAs creates spin polarization up to 12 times larger than the thermal nuclear spin polarization at 5 K and 4 T. The experiment is sensitive to sample volumes containing $\sim 4 \times 10^{11}$ $^{71}$Ga$/\sqrt{Hz}$. These results demonstrate the ability of force-detected magnetic resonance to apply magnetic resonance imaging to semiconductor devices and other nanostructures.

physics.ins-det↗

arXiv2002

Temperature measurement at the end of a cantilever using oxygen paramagnetism in solid air

We demonstrate temperature measurement of a sample attached to the end of a cantilever using cantilever magnetometry of solid air ``contamination'' of the sample surface. In experiments like our Magnetic Resonance Force Microscopy (MRFM), the sample is mounted at the end of a thin cantilever with small thermal conductance. Thus, the sample can be at a significantly different temperature than the bulk of the instrument. Using cantilever magnetometry of the oxygen paramagnetism in solid air provides the temperature of the sample, without any modifications to our MRFM (Magnetic Resonance Force Microscopy) apparatus.

physics.ins-det↗

arXiv2002

Spin polarization contrast observed in GaAs by force-detected nuclear magnetic resonance

We applied the recently developed technique of force-detected nuclear magnetic resonance (NMR) to observe 71Ga, 69Ga, and 75As in GaAs. The nuclear spin-lattice relaxation time is 21$\pm$5 min for 69Ga at $\sim 5$ K and 4.6 Tesla. We have exploited this long relaxation time to first create and then observe spatially varying nuclear spin polarization within the sample, demonstrating a new form of contrast for magnetic resonance force microscopy (MRFM). Such nuclear spin contrast could be used to indirectly image electron spin polarization in GaAs-based spintronic devices.

cond-mat.mtrl-sci↗