Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection.

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

Experimental Implementation of the Optical Fractional Fourier Transform in the Time-Frequency Domain.

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of optical signals in their time-frequency degree of freedom bypasses the digitization step and presents an opportunity to enhance many protocols in quantum and classical communication, sensing, and computing. In this Letter, we present the experimental realization of the fractional Fourier transform in the time-frequency domain using an atomic quantum-optical memory system with processing capabilities. Our scheme performs the operation by imposing programmable interleaved spectral and temporal phases. We have verified the FrFT by analyses of chroncyclic Wigner functions measured via a shot-noise limited homodyne detector. Our results hold prospects for achieving temporal-mode sorting, processing, and superresolved parameter estimation.

Variable electro-optic shearing interferometry for ultrafast single-photon-level pulse characterization.

Despite the multitude of available methods, the characterization of ultrafast pulses remains a challenging endeavor, especially at the single-photon level. We introduce a pulse characterization scheme that maps the magnitude of its short-time Fourier transform. Contrary to many well-known solutions it does not require nonlinear effects and is therefore suitable for single-photon-level measurements. Our method is based on introducing a series of controlled time and frequency shifts, where the latter is performed via an electro-optic modulator allowing a fully-electronic experimental control. We characterized the full spectral and temporal width of a classical and single-photon-level pulse and successfully tested the applicability of the reconstruction algorithm of the spectral phase and amplitude. The method can be extended by implementing a phase-sensitive measurement and is naturally well-suited to partially-incoherent light.

Quantum Optics of Spin Waves through ac Stark Modulation.

We bring the set of linear quantum operations, important for many fundamental studies in photonic systems, to the material domain of collective excitations known as spin waves. Using the ac Stark effect we realize quantum operations on single excitations and demonstrate a spin-wave analog of the Hong-Ou-Mandel effect, realized via a beam splitter implemented in the spin-wave domain. Our scheme equips atomic-ensemble-based quantum repeaters with quantum information processing capability and can be readily brought to other physical systems, such as doped crystals or room-temperature atomic ensembles.

Visibility-Based Hypothesis Testing Using Higher-Order Optical Interference.

Many quantum information protocols rely on optical interference to compare data sets with efficiency or security unattainable by classical means. Standard implementations exploit first-order coherence between signals whose preparation requires a shared phase reference. Here, we analyze and experimentally demonstrate the binary discrimination of visibility hypotheses based on higher-order interference for optical signals with a random relative phase. This provides a robust protocol implementation primitive when a phase lock is unavailable or impractical. With the primitive cost quantified by the total detected optical energy, optimal operation is typically reached in the few-photon regime.

Spatially resolved control of fictitious magnetic fields in a cold atomic ensemble.

Effective and unrestricted engineering of atom-photon interactions requires precise spatially resolved control of light beams. The significant potential of such manipulations lies in a set of disciplines ranging from solid-state to atomic physics. Here we use a Zeeman-like ac-Stark shift caused by a shaped laser beam to perform rotations of spins with spatial resolution in a large ensemble of cold rubidium atoms. We show that inhomogeneities of light intensity are the main source of dephasing and, thus, decoherence; yet, with proper beam shaping, this deleterious effect is strongly mitigated allowing rotations of 15 rad within one spin-precession lifetime. Finally, as a particular example of a complex manipulation enabled by our scheme, we demonstrate a range of collapse-and-revival behaviors of a free-induction decay signal by imprinting comb-like patterns on the atomic ensemble.

Beating the Rayleigh Limit Using Two-Photon Interference.

Multiparameter estimation theory offers a general framework to explore imaging techniques beyond the Rayleigh limit. While optimal measurements of single parameters characterizing a composite light source are now well understood, simultaneous determination of multiple parameters poses a much greater challenge that in general requires implementation of collective measurements. Here we show, theoretically and experimentally, that Hong-Ou-Mandel interference followed by spatially resolved detection of photons provides precise information on both the separation and the centroid for a pair of point emitters, avoiding trade-offs inherent to single-photon measurements.

Wavevector multiplexed atomic quantum memory via spatially-resolved single-photon detection.

Parallelized quantum information processing requires tailored quantum memories to simultaneously handle multiple photons. The spatial degree of freedom is a promising candidate to facilitate such photonic multiplexing. Using a single-photon resolving camera, we demonstrate a wavevector multiplexed quantum memory based on a cold atomic ensemble. Observation of nonclassical correlations between Raman scattered photons is confirmed by an average value of the second-order correlation function [Formula: see text] in 665 separated modes simultaneously. The proposed protocol utilizing the multimode memory along with the camera will facilitate generation of multi-photon states, which are a necessity in quantum-enhanced sensing technologies and as an input to photonic quantum circuits.

High-Capacity Angularly Multiplexed Holographic Memory Operating at the Single-Photon Level.

We experimentally demonstrate an angularly multiplexed holographic memory capable of intrinsic generation, storage, and retrieval of multiple photons, based on an off-resonant Raman interaction in warm rubidium-87 vapors. The memory capacity of up to 60 independent atomic spin-wave modes is evidenced by analyzing angular distributions of coincidences between Stokes and time-delayed anti-Stokes light, observed down to the level of single spin-wave excitation during the several-microsecond memory lifetime. We also propose how to practically enhance rates of single- and multiple-photon generation by combining our multimode emissive memory with existing fast optical switches.

Phase matching alters spatial multiphoton processes in dense atomic ensembles.

Multiphoton processes in dense atomic vapors such as four-wave mixing or coherent blue light generation are typically viewed from single-atom perspective. Here we study the surprisingly important effect of phase matching near two-photon resonances that arises due to spatial extent of the atomic medium within which the multiphoton process occurs. The non-unit refractive index of the atomic vapor may inhibit generation of light in nonlinear processes, significantly shift the efficiency maxima in frequencies and redirect emitted beam. We present these effects on an example of four-wave mixing in dense rubidium vapors in a double-ladder configuration. By deriving a simple theory that takes into account essential spatial properties of the process, we give precise predictions and confirm their validity in the experiment. The model allows us to improve on the geometry of the experiment and engineer more efficient four-wave mixing.

Quantum memory receiver for superadditive communication using binary coherent states.

We propose a simple architecture based on multimode quantum memories for collective readout of classical information keyed using a pair coherent states, exemplified by the well-known binary phase shift keying format. Such a configuration enables demonstration of the superadditivity effect in classical communication over quantum channels, where the transmission rate becomes enhanced through joint detection applied to multiple channel uses. The proposed scheme relies on the recently introduced idea to prepare Hadamard sequences of input symbols that are mapped by a linear optical transformation onto the pulse position modulation format [Guha, S. Phys. Rev. Lett.2011, 106, 240502]. We analyze two versions of readout based on direct detection and an optional Dolinar receiver which implements the minimum-error measurement for individual detection of a binary coherent state alphabet.

Correlation steering in the angularly multimode Raman atomic memory.

We present the possibility of steering the direction of correlations between the off-resonant Raman scattered photons from the angularly multimode atomic memory based on warm rubidium vapors. Using acousto-optic deflectors (AOD) driven by different modulation frequencies, we experimentally change the angle of incidence of the laser beams on the atomic ensemble. By performing correlation measurements for various deflection angles, we verify that we can choose the anti-Stokes light propagation direction independently of the correlated Stokes scattered light in a continuous way. As a result we can select the spatial mode of photons retrieved from the memory, which may be important for future development of quantum information processing.

Calibration of wavefront distortion in light modulator setup by Fourier analysis of multibeam interference.

We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far-field images of several Gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images reveals phase differences among typically five movable points on the modulator. Repeating this measurement yields a wavefront surface. Next, the amplitude efficiency is calibrated for registering the near-field image. For verification, we produced a superposition of seventh and eighth Bessel beams with different phase velocities and observed their interference.

Mode engineering for realistic quantum-enhanced interferometry.

Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques. Practical quantum-enhanced interferometry is, however, vulnerable to imperfections such as partial distinguishability of interfering photons. Here we introduce a method where appropriate design of the modal structure of input photons can alleviate deleterious effects caused by another, experimentally inaccessible degree of freedom. This result is accompanied by a laboratory demonstration that a suitable choice of spatial modes combined with position-resolved coincidence detection restores entanglement-enhanced precision in the full operating range of a realistic two-photon Mach-Zehnder interferometer, specifically around a point which otherwise does not even attain the shot-noise limit due to the presence of residual distinguishing information in the spectral degree of freedom. Our method highlights the potential of engineering multimode physical systems in metrologic applications.

Hamiltonian design in readout from room-temperature Raman atomic memory.

We present an experimental demonstration of the Hamiltonian manipulation in light-atom interface in Raman-type warm rubidium-87 vapor atomic memory. By adjusting the detuning of the driving beam we varied the relative contributions of the Stokes and anti-Stokes scattering to the process of four-wave mixing which reads out a spatially multimode state of atomic memory. We measured the temporal evolution of the readout fields and the spatial intensity correlations between write-in and readout as a function of detuning with the use of an intensified camera. The correlation maps enabled us to resolve between the anti-Stokes and the Stokes scattering and to quantify their contributions. Our experimental results agree quantitatively with a simple, plane-wave theoretical model we provide. They allow for a simple interpretation of the coaction of the anti-Stokes and the Stokes scattering at the readout stage. The Stokes contribution yields additional, adjustable gain at the readout stage, albeit with inevitable extra noise. Here we provide a simple and useful framework to trace it and the results can be utilized in the existing atomic memories setups. Furthermore, the shown Hamiltonian manipulation offers a broad range of atom-light interfaces readily applicable in current and future quantum protocols with atomic ensembles.

High-fidelity spatially resolved multiphoton counting for quantum imaging applications.

We present a method for spatially resolved multiphoton counting based on an intensified camera with the retrieval of multimode photon statistics fully accounting for nonlinearities in the detection process. The scheme relies on one-time quantum tomographic calibration of the detector. Faithful, high-fidelity reconstruction of single- and two-mode statistics of multiphoton states is demonstrated for coherent states and their statistical mixtures. The results consistently exhibit classical values of the Mandel parameter and the noise reduction factor in contrast to raw statistics of camera photo-events. Detector operation is reliable for illumination levels up to the average of one detected photon per an event area-substantially higher than in previous approaches to characterize quantum statistical properties of light with spatial resolution.

Secondary scoliosis after thoracotomy in patients with aortic coarctation and patent ductus arteriosus.

The aim of this study was to determine the influence of lateral thoracotomy on the development of scoliosis in subjects undergoing repair of coarctation of the aorta (CoAo) and patent ductus arteriosus (PDA). A group of 133 patients with CoAo and PDA was evaluated. Forty-five patients with CoAo and 38 with PDA were operated on using lateral thoracotomy (operative group) while 12 patients with CoAo and 31 with PDA were treated using balloon dilatation and stent or coil implantation (non-operative group). Clinical examination and the evaluation of spinal roentgenograms were performed. Among the operated patients 46.6% of those with CoAo and 39.5% of those with PDA had clinical scoliosis. In the non-operated patients scoliosis was present in only 16.6% of those with CoAo and 12.9% of those with PDA. Scoliosis ranged between 10° and 42° and it was mild in the majority of cases. In 90.4% of the operated scoliotic patients with CoAo and 73.3% of those with PDA the curve was thoracic and in 47.6% of the CoAo group and 53,3% of the PDA group the curve was left sided. All curves were right sided in non-operated subjects. Scoliosis in the operated group was higher in males than in females (63.3% versus 60% in CoAo and 68.2% versus 37.5% in PDA). The prevalence of scoliosis after thoracotomy was significantly higher than after non-surgical methods of treatment of both CoAo and PDA as well as in the general population. The rate of single thoracic and the rate of left thoracic curves in patients after thoracotomy is higher than in patients treated non-surgically or in idiopathic scoliosis. The rate of scoliosis after thoracotomy is higher in males than females especially following thoracotomy for PDA.

Operative treatment of isthmic spondylolisthesis with posterior stabilization and ALIF. Cages versus autogenous bone grafts.

In the following study the use of cages and autogenous bone grafts were compared in the operative treatment of isthmic spondylolisthesis with the posterior stabilization and Anterior Lumbosacral Interbody Fusion (ALIF). 55 patients were divided into two groups. Autogenous bone grafts were used in the first group (34 patients) and titanium interbody implants (cages) in the second group (21 patients). The mean follow up period in the first group was 8.6 years and 3.4 years in the second group. The radiological outcome was based upon the evaluation of the degree of spondylolisthesis, the angle of the lumbar lordosis, the height of the interbody space and intervertebral foramen and the evaluation of the spinal fusion. The objective clinical outcome assessment was based on Oswestry Disability Index. Subjective clinical evaluation was performed with the use of Visual Analog Pain Score (VAS) and the two questions concerning the evaluation of success of the operative treatment and a possible agreement to the following operation if necessary. The use of autogenous bone grafts alone in ALIF was related to the significant loss of achieved segmental spine anatomy restoration. The implantation of the cages prevented the loss of slippage correction, permanently reconstructed the anatomical conditions in the area of the operated spinal segment.

Intraoperative Neurophysiologic Monitoring (INM) in scoliosis surgery.

Even among skilled spinal deformity surgeons, neurologic deficits are inherent potential complications of spine surgery. The aim was to assess the meaning of changes and to evaluate the critical rates of Somatosensory Evoked Potentials (SEP) and Motor Evoked Potentials (MEP) for Neurologic Deficit (ND) occurrence associated with scoliosis surgery. A Group of 30 patients with idiopathic scoliosis treated surgically by posterior correction and stabilisation were included. Patients were matched by age, sex, aetiology, Cobb angle, and surgical criteria. Data on three planar scoliosis correction and concomitant (INM) alarms were compared. Radiographic assessment was performed from radiographs taken before surgery and just after it. The (INM) was performed with the use of ISSIS (Inomed) in every patients the same fashion. The average thoracic curve correction was 69.7% and lumbar 69.8%. The average preoperative Apical Vertebral Rotation was 23.5° for thoracic and 27.9° for lumbar curves and postoperatively 10.9° and 14.3° respectively. There was a significant variability of SEP during surgery with only 7 (23%) patients with stable SEP. 15(50%) patients had a decrease of SEP below 50% and 8(27%) had severe decrease of SEP below 50% what caused us to stop surgery or to decrease correction of curves. There was a MEP decrease in 11(37%) patients and in 6 (20%) directly after correction up to 50% of normal value. In 5 of 30 (17%) patients there was a significant decrease of MEP below 50% and we immediately released the implant. The SEP decrease up to 50% without any MEP change did not influenced the outcome. There was no correlation between flexibility and correction of the curve and SEP and MEP decrease. The safe level for MEP was not determined but its meaning for the outcome was more important than SEP value. The need of (INM) during scoliosis surgery to avoid (ND) was confirmed.

Generation and delayed retrieval of spatially multimode Raman scattering in warm rubidium vapors.

We apply collective Raman scattering to create, store and retrieve spatially multimode light in warm rubidium-87 vapors. The light is created in a spontaneous Stokes scattering process. This is accompanied by the creation of counterpart collective excitations in the atomic ensemble - the spin waves. After a certain storage time we coherently convert the spin waves into the light in deterministic anti-Stokes scattering. The whole process can be regarded as a delayed four-wave mixing which produces pairs of correlated, delayed random images. Storage of higher order spatial modes up to microseconds is possible owing to usage of a buffer gas. We study the performance of the Raman scattering, storage and retrieval of collective excitations focusing on spatial effects and the influence of decoherence caused by diffusion of rubidium atoms in different buffer gases. We quantify the number of modes created and retrieved by analyzing statistical correlations of intensity fluctuations between portions of the light scattered in the far field.