We experimentally control the spectral structure of photon pairs created via spontaneous four-wave mixing in microstructured fibers. By fabricating fibers with designed dispersion, one can manipulate the photons' wavelengths, joint spectrum, and, thus, entanglement. As an example, we produce photon pairs with no spectral correlations, allowing direct heralding of single photons in pure-state wave packets without filtering. We achieve an experimental purity of (85.9+/-1.6)%, while theoretical analysis and preliminary tests suggest that 94.5% purity is possible with a much longer fiber.

Quantum states and measurements exhibit wave-like -continuous, or particle-like -discrete, character. Hybrid discrete-continuous photonic systems are key to investigating fundamental quantum phenomena [1][2][3], generating superpositions of macroscopic states [4], and form essential resources for quantum-enhanced applications [5], e.g. entanglement distillation [6,7] and quantum computation [8], as well as highly efficient optical telecommunications [9,10]. Realizing the full potential of these hybrid systems requires quantum-optical measurements sensitive to complementary observables such as field quadrature amplitude and photon number [11][12][13]. However, a thorough understanding of the practical performance of an optical detector interpolating between these two regions is absent. Here, we report the implementation of full quantum detector tomography, enabling the characterization of the simultaneous wave and photonnumber sensitivities of quantum-optical detectors. This yields the largest parametrization to-date in quantum tomography experiments, requiring the development of novel theoretical tools. Our results reveal the role of coherence in quantum measurements and demonstrate the tunability of hybrid quantum-optical detectors.Accurate knowledge of a quantum-optical detector is essential for its fruitful utilization, be it in foundational investigations or technological applications. Photodetectors are normally characterized by several parameters, including detectivity, spectral sensitivity and noiseequivalent power [14]. For quantum detectors, additional information is required for a complete specification of the detector. This information is the set of operators that link the input quantum state of the light field to the classical detector output, known as postiveoperator-valued measure (POVM). It may be estimated by means of quantum detector tomogrpahy (QDT) [15][16][17][18], and is needed if the detector is to be used reliably. To date, QDT has been successfully applied to avalanche photodiodes (APDs) [19], time-multiplexed detectors [18,20,21], transition-edge sensors [22], and super-conducting nanowire detectors [23]. The matrix representations of the POVMs for these detectors are diagonal in the photon-number basis. Consequently the reconstruction problem is linear and positive, and therefore amenable to solution by means familiar to classical signal processing [24]. This is not true for a general quantum detector: the POVM elements can have non-zero offdiagonals due to coherent superpositions. Even in conventional optical communications, coherent modulation and detection can increase the data transmission rate by an order of magnitude. Moreover, exploration and utilization of the full Hilbert space of a quantum system requires a detector capable of implementing a tomographically complete set of measurements [25]. Such a capability is also vital to fully harness the potential of hybrid quantum systems operating at the confluence of discrete and continuous variable regimes. To this end, phasesensitiv...

The linear birefringence of uniaxial crystal plates is known since the 17 th century, and it is widely used in numerous optical setups and devices. Here we demonstrate, both theoretically and experimentally, a fine lateral circular birefringence of such crystal plates. This effect is a novel example of the spin-Hall effect of light, i.e., a transverse spin-dependent shift of the paraxial light beam transmitted through the plate. The well-known linear birefringence and the new circular birefringence form an interesting analogy with the Goos-Hänchen and Imbert-Fedorov beam shifts that appear in the light reflection at a dielectric interface. We report the experimental observation of the effect in a remarkably simple system of a tilted half-wave plate and polarizers using polarimetric and quantum-weak-measurement techniques for the beam-shift measurements. In view of great recent interest in spin-orbit interaction phenomena, our results could find applications in modern polarization optics and nano-photonics.

Photonic spin Hall effect in transmission is a transverse beam shift of the out-coming beam depending on polarization of the in-coming beam.The effect can be significantly enhanced by materials with high anisotropy. We report the first experimental demonstration of the photonic spin Hall effect in a multilayer hyperbolic metamaterial at visible wavelengths (wavelengths of 520 nm and 633 nm). The metamaterial is composed of alternating layers of gold and alumina with deeplysubwavelength thicknesses, exhibiting extremely large anisotropy. The angle resolved polarimetric measurements showed the shift of 165 µm for the metamaterial of 176 nm in thickness. Additionally the transverse beam shift is extremely sensitive to the variations of the incident angle changing theoretically by 270 µm with one milli-radian (0.057 • ). These features can lead to minituarized spin Hall switches and filters with high angular resolution.

We have observed Bragg scattering of photons from quantum degenerate 87 Rb atoms in a threedimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wavefunction whose position and momentum width is Heisenberg-limited. The spatial coherence of the wavefunction leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.

We study the generation of planar quantum squeezed (PQS) states by quantum non-demolition (QND) measurement of a cold ensemble of 87 Rb atoms. Precise calibration of the QND measurement allows us to infer the conditional covariance matrix describing the Fy and Fz components of the PQS, revealing the dual squeezing characteristic of PQS. PQS states have been proposed for singleshot phase estimation without prior knowledge of the likely values of the phase. We show that for an arbitrary phase, the generated PQS gives a metrological advantage of at least 3.1 dB relative to classical states. The PQS also beats traditional squeezed states generated with the same QND resources, except for a narrow range of phase values. Using spin squeezing inequalities, we show that spin-spin entanglement is responsible for the metrological advantage. Estimation of interferometric phases is at the heart of precision sensing, and is ultimately limited by quantum statistical effects [1]. Entangled states can improve sensitivity beyond the "classical limits" that restrict sensing with independent particles, and a diversity of entangled states have been demonstrated for this task, including photonic squeezed states [2,3] and spin-squeezed states [4]. These give improved sensitivity for a narrow range of phases, but worsened sensitivity for most phases. Optical "NOON" states [5] give improved sensitivity over the whole phase range, but introduce additional phase ambiguity that increases with the size, and thus sensitivity advantage, of the NOON state. Recent proposals [6-8] suggest using planar quantum squeezed (PQS) states to obtain an entanglement-derived advantage for all phase angles, with no additional phase ambiguity. A natural application is in high-bandwidth atomic sensing [9][10][11], in which the precession angle may not be predictable in advance. PQS states may also be valuable for ab initio phase estimation using feedback [12][13][14].Discussion of such states under the name "intelligent spin states" [15] predates modern squeezing terminology, and analogous states have been studied with optical polarization [16][17][18]. Generation of PQS states in material systems has been proposed using two-well BoseEinstein condensates with tunable and attractive interactions [7,8], and using quantum non-demolition (QND) measurements [19]. Here we take the latter approach, using Faraday rotation QND measurements [20,21] applied to an ensemble of cold atomic spins with f = 1. As the ensemble spin precesses about the x axis in an external magnetic field [22][23][24], we measure the y and z spin components to generate measurement-induced squeezing in these two components, creating a PQS state. The resulting state has enhanced sensitivity to precession angle, i.e., to Zeeman-shift induced phase. The demonstrated PQS state beats the best possible classical state at any precession angle, and beats traditional spin-squeezed states when averaged over the possible angles. Spin-squeezing inequalities [7,8,25] detect spin entanglement in the PQS state...

Planar squeezed states, i.e. quantum states which are squeezed in two orthogonal spin components, have recently attracted attention due to their applications in atomic interferometry and quantum information (He et al 2012 New J. Phys. 14 093012). While canonical variables such as quadratures of the radiation field can be squeezed in at most one component, simultaneous squeezing in two orthogonal spin components can be achieved due to the angular momentum commutation relations. We present a novel scheme for planar squeezing via quantum non-demolition (QND) measurements in spin-1 systems. The QND measurement is achieved via near-resonant paramagnetic Faraday rotation probing, and the planar squeezing is obtained by sequential QND measurement of two orthogonal spin components. We compute the achievable squeezing for a variety of optical depths, initial conditions and probing strategies. The planar squeezed states generated in this way contain entanglement detectable 3

Given an experimental set-up and a fixed number of measurements, how should one take data in order to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [1]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of 'minimal tomography'. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. We find that these two designs are generally similar. Monte-Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.