Compressive sensing spectroscopy with a single pixel camera.

Spectrometry requires high spectral resolution and high photometric precision while also balancing cost and complexity. We address these requirements by employing a compressive-sensing camera capable of improving signal acquisition speed and sensitivity in limited signal scenarios. In particular, we implement a fast single pixel spectrophotometer with no moving parts and measure absorption and emission spectra comparable with commercial products. Our method utilizes Hadamard matrices to sample the spectra and then minimizes the total variation of the signal. The experimental setup includes standard optics and a grating, a low-cost digital micromirror device, and an intensity detector. The resulting spectrometer produces a 512 pixel spectrum with low mean-squared error and up to a 90% reduction in data acquisition time when compared with a standard spectrophotometer.

Null values and quantum state discrìmination.

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models.

We investigate disordered one- and two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin- and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.

Compressive sensing for spatial and spectral flame diagnostics.

Combustion research requires the use of state of the art diagnostic tools, including high energy lasers and gated, cooled CCDs. However, these tools may present a cost barrier for laboratories with limited resources. While the cost of high energy lasers and low-noise cameras continues to decline, new imaging technologies are being developed to address both cost and complexity. In this paper, we analyze the use of compressive sensing for flame diagnostics by reconstructing Raman images and calculating mole fractions as a function of radial depth for a highly strained, N2-H2 diffusion flame. We find good agreement with previous results, and discuss the benefits and drawbacks of this technique.

Ultrasensitive beam deflection measurement via interferometric weak value amplification.

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 400+/-200 frad and the linear travel of a piezo actuator down to 14+/-7 fm.

All optical waveguiding in a coherent atomic rubidium vapor.

We demonstrate an all optical waveguide imprinted by a low power Laguerre Gaussian control laser beam using a coherent Raman process in warm atomic rubidium vapor. We show that the signal beam propagates with a small spot size over several diffraction lengths. We also show that the coupling efficiency of the signal beam into the waveguide varies linearly with the signal power.