High-throughput Imaging of Self-luminous Objects through a Single Optical Fiber

Imaging through a single optical fiber offers attractive possibilities in many applications such as microendoscopy or remote sensing. However, the direct transmission of an image through an optical fiber is difficult because spatial information is scrambled upon propagation. We demonstrate an image transmission strategy where spatial information is first converted to spectral information. Our strategy is based on a principle of spread-spectrum encoding, borrowed from wireless communications, wherein object pixels are converted into distinct spectral codes that span the full bandwidth of the object spectrum. Image recovery is performed by numerical inversion of the detected spectrum at the fiber output. We provide a simple demonstration of spread-spectrum encoding using Fabry-Perot etalons. Our technique enables the 2D imaging of self-luminous (i.e. incoherent) objects with high throughput in principle independent of pixel number. Moreover, it is insensitive to fiber bending, contains no moving parts, and opens the possibility of extreme miniaturization

Quench dynamics as a probe of quantum criticality

Quantum critical points of many-body systems can be characterized by studying response of the ground-state wave function to the change of the external parameter, encoded in the ground-state fidelity susceptibility. This quantity characterizes the quench dynamics induced by sudden change of the parameter. In this framework, I analyze scaling relations concerning the probability of excitation and the excitation energy, with the quench amplitude of this parameter. These results are illustrated in the case of one-dimensional sine-Gordon model.Comment: 4 page

Single-exposure profilometry using partitioned aperture wavefront imaging

We demonstrate a technique for instantaneous measurements of surface topography based on the combination of a partitioned aperture wavefront imager with a standard lamp-based reflection microscope. The technique can operate at video rate over large fields of view, and provides nanometer axial resolution and sub-micron lateral resolution. We discuss performance characteristics of this technique, which we experimentally compare with scanning white light interferometry.Comment: 4 page

Excitation of the dissipationless Higgs mode in a fermionic condensate

The amplitude mode of a fermionic superfluid, analogous to the Higgs Boson, becomes undamped in the strong coupling regime when its frequency is pushed inside the BCS energy gap. We argue that this is the case in cold gases due to the energy dispersion and nonlocality of the pairing interaction, and propose to use the Feshbach resonance regime for parametric excitation of this mode. The results presented for the BCS pairing dynamics indicate that even weak dispersion suppresses dephasing and gives rise to persistent oscillations. The frequency of oscillations extracted from our simulation of the BCS dynamics agrees with the prediction of the many-body theory.Comment: 4 pages, 4 figure

Dynamical Selection in Emergent Fermionic Pairing

We consider evolution of a Fermi gas in the presence of a time-dependent BCS interaction. The pairing amplitude in the emergent BCS state is found to be an oscillatory function of time with predictable characteristics. The interplay of linear instability of the unpaired state and nonlinear interactions selects periodic soliton trains of a specific form, described by the Jacobi elliptic function dn. While the parameters of the soliton train, such as the period, amplitude, and time lag, fluctuate among different realizations, the elliptic function form remains robust. The parameter variation is accounted for by the fluctuations of particle distribution in the initial unpaired state.Comment: 15 pgs, 9 fg

High-resolution 3D phase imaging using a partitioned detection aperture: a wave-optic analysis

Quantitative phase imaging has become a topic of considerable interest in the microscopy community. We have recently described one such technique based on the use of a partitioned detection aperture, which can be operated in a single shot with an extended source [Opt. Lett. 37, 4062 (2012)]. We follow up on this work by providing a rigorous theory of our technique using paraxial wave optics, where we derive fully three-dimensional spread functions for both phase and intensity. Using these functions we discuss methods of phase reconstruction for in- and out-of-focus samples, insensitive to weak attenuations of light. Our approach provides a strategy for detection-limited lateral resolution with an extended depth of field, and is applicable to imaging smooth and rough samples.Comment: 12 page

The Higgs resonance in fermionic pairing

The Higgs boson in fermionic condensates with the BCS pairing interaction describes the dynamics of the pairing amplitude. I show that the existence and properties of this mode are sensitive to the energy dispersion of the interaction. Specifically, when the pairing is suppressed at the Fermi level, the Higgs mode may become unphysical (virtual) state or a resonance with finite lifetime, depending on the details of interaction. Conversely, the Higgs mode is discrete for the pairing interaction enhanced at the Fermi level. This work illustrates conceptual difficulties associated with introducing collective variables in the many-body pairing dynamics.Comment: 4 pages, 2 figure

Solitons and Rabi Oscillations in a Time-Dependent BCS Pairing Problem

Motivated by recent efforts to achieve cold fermions pairing near a Feshbach resonance, we consider the dynamics of formation of the Bardeen-Cooper-Schrieffer (BCS) state. At times shorter than the quasiparticle energy relaxation time, after the interaction is turned on, the dynamics of the system is nondissipative. We show that this collective nonlinear evolution of the BCS-Bogoliubov amplitudes (u,v) along with the pairing function, is an integrable dynamical problem, and obtain a family of exact solutions in the form of single solitons and soliton trains. We interpret the collective oscillations as Bloch precession of Anderson pseudospins, where each soliton causes a pseudospin full Rabi rotation. Numerical simulations demonstrate robustness of the solitons with respect to noise and damping.Comment: 5 pages, 2 figure

Cross-correlation Imaging for Waveguide Characterization

Confined geometries, such as optical waveguides, support a discrete set of eigen-modes. In multimoded structures, depending on the boundary conditions, superposition states can propagate. Characterization of these states is a fundamental problem important in waveguide design and testing, especially for optical applications. In this work, I have developed a novel interferometric method that provides complete characterization of optical waveguide modes and their superposition states. The basic idea of the method is to study the interference of the beam radiated from an optical waveguide with an external reference beam, and detect different waveguide modes in the time-domain by changing the relative optical paths of the two beams. In particular, this method, called cross-correlation or C$^2$-imaging, provides the relative amplitudes of the modes and their group delays. For every mode, one can determine the dispersion, intensity and phase distributions, and also local polarization properties. As a part of this work, I have developed the mathematical formalism of C$^2$-imaging and built an experimental setup implementing the idea. I have carried out an extensive program of experiments, confirming the ability of the method to completely characterize waveguide properties.Comment: M. S. Thesis; 66 page

Conjugate adaptive optics in widefield microscopy with an extended-source wavefront sensor

Adaptive optics is a strategy to compensate for sample-induced aberrations in microscopy applications. Generally, it requires the presence of "guide stars" in the sample to serve as localized reference targets. We describe an implementation of conjugate adaptive optics that is amenable to widefield (i.e. non-scanning) microscopy, and can provide aberration corrections over potentially large fields of view without the use of guide stars. A unique feature of our implementation is that it is based on wavefront sensing with a single-shot partitioned-aperture sensor that provides large dynamic range compatible with extended samples. Combined information provided by this sensor and the imaging camera enable robust image de-blurring based on a rapid estimation of sample and aberrations obtained by closed-loop feedback. We present the theoretical principle of our technique and proof of concept experimental demonstrations