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We consider the fundamental roles of frequency versus phase in parameter estimation, specifically in the Sagnac effect. We describe a novel, ultrasensitive gyroscope based on the extremely steep frequency-dependent gain of a liquid crystal light valve. We provide compelling experimental evidence that the Doppler shift is fundamental in the Sagnac effect giving clarity to a long-debated question. We experimentally show orders of magnitude improvement in sensitivity relative to the standard quantum limit of a gyroscope based on phase estimation.

We derive a general, tilt-dependent, nighttime, radiative deficit model with an eye towards improved dew collection. The model incorporates atmospheric/environmental incoming radiation, a linear precipitable water vapor transmittance function dependent on local meteo data and the influence of near-horizon obstacles. A brief discussion of cloud cover is given. The model is then used more specifically to predict radiative deficits for an ideal blackbody emitter in an environment with an isotropic temperature. Knowing the tilt angle, near-horizon obstacles and local meteo-data, it is then possible to estimate the radiative deficit of a given emitter. We consider errors resulting from the assumption that the ground and obstacles are at the same temperature as the air. We also analyze the errors arising from the linear precipitable water vapor transmittance function by comparing the results against high-resolution, full-spectrum Modtran® data Modtran, 2021 . We show that for typical tilt angles, the isotropic temperature model is a reasonable approximation as long as the above-horizon environmental heating is small. We believe these results will be broadly valuable for the field of radiative cooling where a general radiative treatment has yet to be made and in particular the field of dew water harvesting.

We discuss interferometric parameter estimation of the amplitude, instead of the phase, via weak value amplification. The considered weak interaction introduces modulation on the amplitude of the wave function; therefore, the two-party state experiences a nonunitary evolution. With the same pre- and postselection states as those of original weak value amplification, a much larger anomalous amplification factor can be attained. The shift in the intensity profile at the dark port and the signal-to-noise ratio for the parameter of interest get further amplified by the weak value, compared to phase-based weak value amplification. Although the nonunitary evolution introduces loss, more information about the parameter of interest can be extracted. Thus the weak value amplification is extended to measurement of amplitude and nonunitary processes. We also discuss possible applications of this idea for precisely measuring tiny rotations or enhancing the image contrast of transparent objects.

Claude Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure., 10 Figures

We present an inexpensive architecture for converting a frequency-modulated continuous-wave LiDAR system into a compressive-sensing based depth-mapping camera. Instead of raster scanning to obtain depth-maps, compressive sensing is used to significantly reduce the number of measurements. Ideally, our approach requires two difference detectors. % but can operate with only one at the cost of doubling the number of measurments. Due to the large flux entering the detectors, the signal amplification from heterodyne detection, and the effects of background subtraction from compressive sensing, the system can obtain higher signal-to-noise ratios over detector-array based schemes while scanning a scene faster than is possible through raster-scanning. %Moreover, we show how a single total-variation minimization and two fast least-squares minimizations, instead of a single complex nonlinear minimization, can efficiently recover high-resolution depth-maps with minimal computational overhead. Moreover, by efficiently storing only $2m$ data points from $m

Using weak values amplification angular resolution limits, we theoretically investigate the gravitational sensing of objects. By inserting a force-sensing pendulum into a weak values interferometer, the optical response can sense accelerations to a few 10's of $\mathrm{zepto}\text{-}\mathrm{g}/\sqrt{\mathrm{Hz}}$, with optical powers of $1~\mathrm{mW}$. We convert this precision into range and mass sensitivity, focusing in detail on simple and torsion pendula. Various noise sources present are discussed, as well as the necessary cooling that should be applied to reach the desired levels of precision., 9 pages, 4 figures, Quantum Stud.: Math. Found. (2018)

We create an optical frequency, polarization independent, narrow band-pass filter of 1.3 GHz (3 dB bandwidth), using the steep dispersion near the Rubidium D1 atomic transitions within a prism-shaped vapor cell. This enables us to clean the amplified spontaneous emission from a laser by more than 3 orders of magnitude. Such a filter could find uses in fields such as quantum information processing and Raman spectroscopy., 5 pages, 5 figures

The measurement of extremely small displacements is of utmost importance, both for fundamental studies [1-4], and practical applications [5-7]. One way to estimate a small displacement is to measure the Doppler shift generated in light reflected off an object moving with a known periodic frequency. This remote sensing technique converts a displacement measurement into a frequency measurement, and has been considerably successful [8-14]. The displacement sensitivity of this technique is limited by the Doppler frequency noise floor and by the velocity of the moving object. Other primary limitations are hours of integration time [12,13] and optimal operation only in a narrow Doppler frequency range. Here we show a sensitive device capable of measuring $\mu$Hz/$\sqrt{\text{Hz}}$ Doppler frequency shifts corresponding to tens of fm displacements for a mirror oscillating at 2 Hz. While the Doppler shift measured is comparable to other techniques [12.13], the position sensitivity is orders of magnitude better, and operates over several orders of magnitude of Doppler frequency range. In addition, unlike other techniques which often rely on interferometric methods, our device is phase insensitive, making it unusually robust to noise., Comment: 6 pages, 5 figures

Optical phase-spaces represent fields of any spatial coherence, and are typically measured through phase-retrieval methods involving a computational inversion, interference, or a resolution-limiting lenslet array. Recently, a weak-values technique demonstrated that a beam's Dirac phase-space is proportional to the measurable complex weak-value, regardless of coherence. These direct measurements require scanning through all possible position-polarization couplings, limiting their dimensionality to less than 100,000. We circumvent these limitations using compressive sensing, a numerical protocol that allows us to undersample, yet efficiently measure high-dimensional phase-spaces. We also propose an improved technique that allows us to directly measure phase-spaces with high spatial resolution and scalable frequency resolution. With this method, we are able to easily measure a 1.07-billion-dimensional phase-space. The distributions are numerically propagated to an object placed in the beam path, with excellent agreement. This protocol has broad implications in signal processing and imaging, including recovery of Fourier amplitudes in any dimension with linear algorithmic solutions and ultra-high dimensional phase-space imaging., 7 pages, 5 figures. Added new larger dataset and fixed typos

Precision measurements of ultra-small linear velocities of one of the mirrors in a Michelson interferometer are performed using two different weak-values techniques. We show that the technique of Almost-Balanced Weak Values (ABWV) offers practical advantages over the technique of Weak-Value Amplification (WVA), resulting in larger signal-to-noise ratios and the possibility of longer integration times due to robustness to slow drifts. As an example of the performance of the ABWV protocol we report a velocity sensitivity of 60 fm/s after 40 hours of integration time. The sensitivity of the Doppler shift due to the moving mirror is of 150 nHz.

Slow-light media are of interest in the context of quantum computing and enhanced measurement of quantum effects, with particular emphasis on using slow-light with single photons. We use light-in-flight imaging with a single photon avalanche diode camera-array to image in situ pulse propagation through a slow light medium consisting of heated rubidium vapour. Light-in-flight imaging of slow light propagation enables direct visualisation of a series of physical effects including simultaneous observation of spatial pulse compression and temporal pulse dispersion. Additionally, the single-photon nature of the camera allows for observation of the group velocity of single photons with measured single-photon fractional delays greater than 1 over 1 cm of propagation., Comment: 6 pages, 5 figures, 2 supplemental movies

We demonstrate single photon imaging at a megapixel-resolution in the short-wave infrared region using compressive imaging. The timing resolution of our system is 150 ps, enabling high-resolution single-photon time-of-flight imaging.

We examine the effect of different sources of technical noise on inverse weak value-based precision phase measurements. We find that this type of measurement is similarly robust to technical noise as related experiments in the weak value regime. In particular, the measurements considered here are robust to additive Gaussian white noise and angular jitter noise commonly encountered in optical experiments. Additionally, we show the same techniques used for precision phase measurement can be used with the same technical advantages for optical frequency measurements., Comment: 6 pages, 4 figures

We propose `digital cloaking' as a method for practical cloaking, where space, angle, spectrum, and phase are discretized. At the sacrifice of spatial resolution, a good approximation to an `ideal' cloak can be achieved- a cloak that is omnidirectional, broadband, operational for the visible spectrum, three- dimensional (3D), and phase-matching for the light field, among other attributes. Experimentally, we demonstrate a two-dimensional (2D), planar, ray optics version of our proposed digital cloak by using lenticular lenses, similar to `integral imaging' for 3D displays. With the continuing improvement in commercial digital technology, the resolution limitations of a digital cloak will be minimized, and a wearable cloak can be developed in the future.

We measure a transverse momentum kick in a Sagnac interferometer using weak-value amplification with two postselections. The first postselection is controlled by a polarization dependent phase mismatch between both paths of a Sagnac interferometer and the second postselection is controlled by a polarizer at the exit port. By monitoring the darkport of the interferometer, we study the complementary amplification of the concatenated postselections, where the polarization extinction ratio is greater than the contrast of the spatial interference. In this case, we find an improvement in the amplification of the signal of interest by introducing a second postselection to the system.

We use weak-value amplification to enhance the polarization-sensitive fast-light effect from induced Raman absorption in hot rubidium vapor. We experimentally demonstrate that projecting the output signal into an appropriate polarization state enables a pulse advancement of $4.2\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which is more than 15 times larger than that naturally caused by dispersion. More significantly, we show that combining weak-value amplification with the dispersive response of an atomic system provides a clear advantage in terms of the maximum pulse advance achievable for a given value of loss. This technique has potential applications for designing novel quantum-information-processing gates and optical buffers for telecommunication systems.

We present a short-wave infrared (SWIR) single photon camera based on a single superconducting nanowire single photon detector (SNSPD) and compressive imaging. We show SWIR single photon imaging at a megapixel resolution with a low signal-to-background ratio around 0.6, show SWIR video acquisition at 20 frames per second and 64x64 pixel video resolution, and demonstrate sub-nanosecond resolution time-of-flight imaging. All scenes were sampled by detecting only a small number of photons for each compressive sampling matrix. In principle, our technique can be used for imaging faint objects in the mid-IR regime.

Digital signal processing, holography, and quantum and classical information processing rely heavily upon recording the amplitude and phase of coherent optical signals. One method for achieving coherent information storage makes use of electromagnetically induced transparency. Storage is achieved by compressing the optical pulse using the steep dispersion of the electromagnetically induced transparency medium and then mapping the electric field to local atomic quantum-state superpositions. Here we show that nonlinear optical processes may enhance pulse compression and storage, and that information about the nonlinear process itself may be stored coherently. We report on a pulse storage scheme in hot atomic rubidium vapour, in which a four-wave-mixing normal mode is stored using a double- configuration. The entire (broadened) waveform of the input signal is recovered after several hundred microseconds (1/e time of about 120 s), as well as a new optical mode (idler) generated from the four-wave-mixing process.

We present an experimental demonstration of quantum data locking as a quantum enigma machine that encrypts 6 bits per photon with less than 6 bits per photon of encryption key while remaining information-theoretically secure.

The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the entropic formulation of the uncertainty principle. Traditionally, uncertainty relations correspond to resolution limits; increasing a detector's position sensitivity decreases its momentum sensitivity and vice-versa. However, this is not required in general; for example, position information can instead be extracted at the cost of noise in momentum. Using random, partial projections in position followed by strong measurements in momentum, we efficiently determine the transverse-position and transverse-momentum distributions of an unknown optical field with a single set of measurements. The momentum distribution is directly imaged, while the position distribution is recovered using compressive sensing. At no point do we violate uncertainty relations; rather, we economize the use of information we obtain., Comment: 7 pages, 5 figures

We experimentally implement the proposal of Plansinis et al.[PRL 115, 183910 (2015)] using slow light in Rubidium vapor. Time-dependent frequency shifts on probe pulses behave like angles in the analogous spatial reflection and refraction from classical optics.

I will discuss the use of weak values for performing precision deflection, spectral, velocity and gravimetric measurements. I will show that the concepts behind weak values can lead to technical noise suppression. Article not available.

The technique of almost-balanced weak values amplification (ABWV) was recently proposed [Phys. Rev. Lett. 116: 100803 (2016)]. We demonstrate this technique using a modified Sagnac interferometer, where the counter-propagating beams are spatially separated. The separation between the two beams provides additional amplification, with respect to using colinear beams in a Sagnac interferometer. As a demonstration of the technique, we perform measurements of the angular velocity in one of the mirrors of the interferometer. Within the same setup, the weak-value amplification technique is also performed for comparison. Much higher amplification factors can be obtained using the almost-balanced weak values technique, with the best one achieved in our experiments being as high as $1.2\times10^7$. In addition, the amplification factor monotonically increases with decreasing post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification at small post-selection phases., Comment: 4 pages, 3 figures. comments are welcome

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 million-dimensional image in less than 10 minutes. Within a subspace of that image exists a 3.2 million-dimensional bi-photon probability distribution. In addition, we demonstrate how the marginal distributions can aid in the accuracy of joint space distribution reconstructions.

Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Though Bell nearly showed a violation using the CHSH inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he doesn't give a quantitative estimation of the maximum achievable violation for the wavefunction he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of $2\sqrt{2}$. Although Bell's wavefunction does not produce a large violation of the CHSH inequality, other states may yet do so., 6 pages, 3 figures

Measurements on quantum systems are always constrained by uncertainty relations. For traditional, projective measurements, uncertainty relations correspond to resolution limitations; a detector's position resolution is increased at the cost of its momentum resolution and vice-versa. However, many experiments in quantum measurement are now exploring non- or partially-projective measurements. For these techniques, measurement disturbance need not manifest as a blurring in the complementary domain. Here, we describe a technique for complementary imaging | obtaining sharp position and momentum distributions of a transverse optical field with a single set of measurements. Our technique consists of random, partially-projective filtering in position followed by projective measurements in momentum. The partial-projections extract information about position at the cost of injecting a small amount of noise into the momentum distribution, which can still be directly imaged. The position distribution is recovered via compressive sensing.

Here, we discuss the development of a new inequality in information theory; a Fano inequality suitable for continuous variables. With this inequality, we show how one can demonstrate Einstein-Podolsky-Rosen (EPR) steering in the position-momentum statistics of entangled photon pairs from spontaneous parametric down-conversion (SPDC). More importantly, we show how with sufficiently strong position and momentum correlations, we can demonstrate continuous-variable EPR steering without having to assume the photo-detectors have access to the entire joint intensity distribution. Moreover, we demonstrate this experimentally with the position and momentum statistics of entangled photon pairs in SPDC.

As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a Double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such Double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC., 17 pages, 6 figures, 1 table (essential typos corrected in birth zone formulae)

We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in \emph{all} the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs., 5 pages, 1 figure

We present our results on utilizing an SNSPD array and compressive imaging techniques to perform single photon imaging and present our progress toward a high-resolution single-photon camera for the mid-IR.