Pump-shaping of non-collinear and non-degenerate entangled photons.

Free-space quantum key distribution is gaining increasing interest as a leading platform for long range quantum communication. However, the sensitivity of quantum correlations to scattering induced by turbulent atmospheric links limits the performance of such systems. Recently, a method for compensating for the scattering of entangled photons was demonstrated, allowing for real-time optimization of their quantum correlations. In this Letter, we demonstrate the use of wavefront shaping for compensating for the scattering of non-collinear and non-degenerate entangled photons. These results demonstrate the applicability of wavefront shaping schemes for protocols utilizing the large bandwidth and emission angle of the entangled photons.

Real-time shaping of entangled photons by classical control and feedback.

Quantum technologies hold great promise for revolutionizing photonic applications such as cryptography. Yet, their implementation in real-world scenarios is challenging, mostly because of sensitivity of quantum correlations to scattering. Recent developments in optimizing the shape of single photons introduce new ways to control entangled photons. Nevertheless, shaping single photons in real time remains a challenge due to the weak associated signals, which are too noisy for optimization processes. Here, we overcome this challenge and control scattering of entangled photons by shaping the classical laser beam that stimulates their creation. We discover that because the classical beam and the entangled photons follow the same path, the strong classical signal can be used for optimizing the weak quantum signal. We show that this approach can increase the length of free-space turbulent quantum links by up to two orders of magnitude, opening the door for using wavefront shaping for quantum communications.

Erratum: Author Correction: Complete polarization control in multimode fibers with polarization and mode coupling.

[This corrects the article DOI: 10.1038/s41377-018-0047-4.].

Spatially entangled Airy photons.

Over the past decade, Airy beams have been the subject of extensive research, leading to new physical insights and various applications. In this Letter, we extend the concept of Airy beams to the quantum domain. We generate entangled photons in a superposition of two-photon Airy states via spontaneous parametric down conversion, pumped by a classical Airy beam. We show that the entangled Airy photons preserve the intriguing properties of classical Airy beams, such as free acceleration and reduced diffraction, while exhibiting non-classical anti-correlations. Finally, we discuss the advantages offered by entangled Airy photons for high-dimensional free-space quantum communications.

Introducing non-local correlations into laser speckles.

Laser speckles have become a fundamental component of the modern optics-research toolbox. Not only are speckle patterns the basis of numerous imaging techniques, but also, they are employed to generate optical potentials for cold atoms and colloidal particles. The ability to manipulate a speckle pattern's spatial intensity correlations, particularly long-range (non-local) ones, is essential in numerous applications. A typical fully-developed speckle pattern, however, only possesses short-ranged (local) intensity correlations which are determined by the spatial field correlations. Here we experimentally demonstrate and theoretically develop a general method for creating fully-developed speckles with strong non-local intensity correlations. The functional form of the spatial intensity correlations can be arbitrarily tailored without altering the field correlations. Our approach provides a versatile and utilitarian framework for enhancing and controlling non-local correlations in speckle patterns.

Complete polarization control in multimode fibers with polarization and mode coupling.

Multimode optical fibers have seen increasing applications in communication, imaging, high-power lasers, and amplifiers. However, inherent imperfections and environmental perturbations cause random polarization and mode mixing, causing the output polarization states to be different from the input polarization states. This difference poses a serious issue for employing polarization-sensitive techniques to control light-matter interactions or nonlinear optical processes at the distal end of a fiber probe. Here, we demonstrate complete control of polarization states for all output channels by only manipulating the spatial wavefront of a laser beam into the fiber. Arbitrary polarization states for individual output channels are generated by wavefront shaping without constraining the input polarization. The strong coupling between the spatial and polarization degrees of freedom in a multimode fiber enables full polarization control with the spatial degrees of freedom alone; thus, wavefront shaping can transform a multimode fiber into a highly efficient reconfigurable matrix of waveplates for imaging and communication applications.

Principal modes in multimode fibers: exploring the crossover from weak to strong mode coupling.

We present experimental and numerical studies on principal modes in a multimode fiber with mode coupling. By applying external stress to the fiber and gradually adjusting the stress, we have realized a transition from weak to strong mode coupling, which corresponds to the transition from single scattering to multiple scattering in mode space. Our experiments show that principal modes have distinct spatial and spectral characteristic in the weak and strong mode coupling regimes. We also investigate the bandwidth of the principal modes, in particular, the dependence of the bandwidth on the delay time, and the effects of the mode-dependent loss. By analyzing the path-length distributions, we discover two distinct mechanisms that are responsible for the bandwidth of principal modes in weak and strong mode coupling regimes. Their interplay leads to a non-monotonic transition of the average principal mode bandwidth from weak to strong mode coupling. Taking into account the mode-dependent loss in the fiber, our numerical results are in qualitative agreement with our experimental observations. Our study paves the way for exploring potential applications of principal modes in communication, imaging and spectroscopy.

Control of Energy Density inside a Disordered Medium by Coupling to Open or Closed Channels.

We demonstrate experimentally the efficient control of light intensity distribution inside a random scattering system. The adaptive wave front shaping technique is applied to a silicon waveguide containing scattering nanostructures, and the on-chip coupling scheme enables access to all input spatial modes. By selectively coupling the incident light to the open or closed channels of the disordered system, we not only vary the total energy stored inside the system by a factor of 7.4, but also change the energy density distribution from an exponential decay to a linear decay and to a profile peaked near the center. This work provides an on-chip platform for controlling light-matter interactions in turbid media.

Spatiotemporal Control of Light Transmission through a Multimode Fiber with Strong Mode Coupling.

We experimentally generate and characterize eigenstates of the Wigner-Smith time-delay matrix, called principal modes, in a multimode fiber with strong mode coupling. The unique spectral and temporal properties of principal modes enable global control of temporal dynamics of optical pulses transmitted through the fiber, despite random mode mixing. Our analysis reveals that well-defined delay times of the eigenstates are formed by multipath interference, which can be effectively manipulated by spatial degrees of freedom of input wave fronts. This study is essential to controlling dynamics of wave scattering, paving the way for coherent control of pulse propagation through complex media.

Generation of multiphoton entangled quantum states by means of integrated frequency combs.

Complex optical photon states with entanglement shared among several modes are critical to improving our fundamental understanding of quantum mechanics and have applications for quantum information processing, imaging, and microscopy. We demonstrate that optical integrated Kerr frequency combs can be used to generate several bi- and multiphoton entangled qubits, with direct applications for quantum communication and computation. Our method is compatible with contemporary fiber and quantum memory infrastructures and with chip-scale semiconductor technology, enabling compact, low-cost, and scalable implementations. The exploitation of integrated Kerr frequency combs, with their ability to generate multiple, customizable, and complex quantum states, can provide a scalable, practical, and compact platform for quantum technologies.

Broadband Coherent Enhancement of Transmission and Absorption in Disordered Media.

Spatial modulation of the incident wave front has become a powerful method for controlling the diffusive transport of light in disordered media; however, such interference-based control is intrinsically sensitive to frequency detuning. Here, we show analytically and numerically that certain wave fronts can exhibit strongly enhanced total transmission or absorption across bandwidths that are orders of magnitude broader than the spectral correlation width of the speckles. Such broadband enhancement is possible due to long-range correlations in coherent diffusion, which cause the spectral degrees of freedom to scale as the square root of the bandwidth rather than the bandwidth itself.

Full-field interferometric confocal microscopy using a VCSEL array.

We present an interferometric confocal microscope using an array of 1200 vertical cavity surface emitting lasers (VCSELs) coupled to a multimode fiber. Spatial coherence gating provides ~18,000 continuous virtual pinholes, allowing an entire en face plane to be imaged in a snapshot. This approach maintains the same optical sectioning as a scanning confocal microscope without moving parts, while the high power of the VCSEL array (∼5 mW per laser) enables high-speed image acquisition with integration times as short as 100 µs. Interferometric detection also recovers the phase of the image, enabling quantitative phase measurements and improving the contrast when imaging phase objects.

Noise analysis of spectrometers based on speckle pattern reconstruction.

Speckle patterns produced by a disordered medium or a multimode fiber can be used as a fingerprint to uniquely identify the input light frequency. Reconstruction of a probe spectrum from the speckle pattern has enabled the realization of compact, low-cost, and high-resolution spectrometers. Here we investigate the effects of experimental noise on the accuracy of the reconstructed spectra. We compare the accuracy of a speckle-based spectrometer to a traditional grating-based spectrometer as a function of the probe signal intensity and bandwidth. We find that the speckle-based spectrometers provide comparable performance to a grating-based spectrometer when measuring intense or narrowband probe signals, whereas the accuracy degrades in the measurement of weak or broadband signals. These results are important to identify the applications that would most benefit from this new class of spectrometer.

Dual-modality fluorescence and full-field optical coherence microscopy for biomedical imaging applications.

Full-field optical coherence microscopy (FFOCM) is a high-resolution interferometric technique that is particularly attractive for biomedical imaging. Here we show that combining it with structured illumination fluorescence microscopy on one platform can increase its versatility since it enables co-localized registration of optically sectioned reflectance and fluorescence images. To demonstrate the potential of this dual modality, a fixed and labeled mouse retina was imaged. Results showed that both techniques can provide complementary information and therefore the system could potentially be useful for biomedical imaging applications.

Quantum walks of correlated photons.

Quantum walks of correlated particles offer the possibility of studying large-scale quantum interference; simulating biological, chemical, and physical systems; and providing a route to universal quantum computation. We have demonstrated quantum walks of two identical photons in an array of 21 continuously evanescently coupled waveguides in a SiO(x)N(y) chip. We observed quantum correlations, violating a classical limit by 76 standard deviations, and found that the correlations depended critically on the input state of the quantum walk. These results present a powerful approach to achieving quantum walks with correlated particles to encode information in an exponentially larger state space.

Bloch oscillations of path-entangled photons.

We show that when photons in N-particle path-entangled |N,0)+|0,N) or N00N states undergo Bloch oscillations, they exhibit a periodic transition between spatially bunched and antibunched states. The period of the bunching-antibunching oscillation is N times faster than the period of the oscillation of the photon density, manifesting the unique coherence properties of N00N states. The transition occurs even when the photons are well separated in space.

Quantum correlations in two-particle Anderson localization.

We predict quantum correlations between noninteracting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether or not the other particle is localized. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of nonclassical light and ultracold atoms.

Universal correlations in a nonlinear periodic 1D system.

When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when the system is nonlinear, correlations are spontaneously formed. We find that for strong nonlinearities, the intensity histograms approach a narrow Gaussian distributed around their mean and phase correlations are formed between neighboring sites. Sites tend to be out of phase for a positive nonlinearity and in phase for a negative one. Most impressively, the field correlation takes a universal shape independent of parameters. These results are relevant to bosonic gas in 1D optical lattices as well as to nonlinear optical waveguide arrays, which are used to demonstrate experimentally some of the features of this equilibrium state.

Quantum and classical correlations in waveguide lattices.

We study quantum and classical Hanbury Brown-Twiss correlations in waveguide lattices. We develop a theory for the propagation of photon pairs in the lattice, predicting the emergence of nontrivial quantum interferences unique to lattice systems. Experimentally, we observe the classical counterpart of these interferences using intensity-correlation measurements. We discuss the correspondence between the classical and quantum correlations, and consider path-entangled input states which do not have a classical analogue. Our results demonstrate that waveguide lattices can be used as a robust and highly controllable tool for manipulating quantum states, and offer new ways of studying the quantum properties of light.

Broadband sum-frequency generation as an efficient two-photon detector for optical tomography.

We describe a novel non-linear detection method for optical tomography that does not rely on detection of interference fringes and is free of optical background. The method exploits temporally coherent broadband illumination such as ultrashort pulses, and a non-linear two-photon detection process such as sum-frequency generation (SFG). At the detection stage, the reference beam and the sample beam are mixed in a thick non-linear crystal, and only the mixing term, which is free of optical background, is detected. Consequently, the noise limitations posed by the background in standard OCT (excess and shot noise), do not exist here. Due to the non-linearity, the signal to noise ratio scales more favorably with the optical power compared to standard OCT, yielding an inherent improvement for high speed tomographic scans. Careful design of phase matching in the crystal enables non-linear mixing which is both highly efficient and broadband, yielding both high sensitivity and high depth resolution.