High-efficiency interface between multi-mode and single-mode fibers.

Multi-mode fibers (MMFs) and single-mode fibers (SMFs) are widely used in optical communication networks. MMFs are the practical choice in terms of cost in applications that require short distances. Beyond that, SMFs are necessary because of the modal dispersion in MMFs. Here, we present a method capable of interfacing an MMF with an SMF using a re-programmable multi-plane light conversion scheme (MPLC). We demonstrate that only three phase modulations are necessary to achieve MMF-SMF coupling efficiencies from 30% to 70%, i.e., an insertion loss from 5 dB to 1.5 dB, for MMFs with core diameters up to 200 µm. We show how the obtained coupling efficiency can be recovered if the output field of the MMF changes entirely, e.g., through strong deformation of the fiber, by simple monitoring of the field. Furthermore, we test the influence of the resolution of both essential devices (field reconstruction and MPLC) on coupling efficiencies. We find that commercially available devices with increased speed and efficiency, such as wavefront sensors and deformable mirrors, are sufficient for establishing an MMF-SMF interface that auto-corrects any decoupling in the kilohertz regime.

Two-photon interference: the Hong-Ou-Mandel effect.

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

High-Dimensional Two-Photon Interference Effects in Spatial Modes.

Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides implementing the analog of the Hong-Ou-Mandel interference using a two-dimensional spatial-mode splitter, we extend the scheme to observe coalescence and anticoalescence in different three- and four-dimensional spatial-mode multiports. The operation within spatial modes, along a single beam path, lifts the requirement for interferometric stability and opens up new pathways of implementing linear optical networks for complex quantum information tasks.

Photonic Angular Superresolution Using Twisted N00N States.

The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100 ℏ, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular supersensitivity and accessible generation of N00N states between any transverse light fields.

High-accuracy longitudinal position measurement using self-accelerating light.

Radially self-accelerating light exhibits an intensity pattern that describes a spiraling trajectory around the optical axis as the beam propagates. In this article, we show in simulation and experiment how such beams can be used to perform a high-accuracy distance measurement with respect to a reference using simple off-axis intensity detection. We demonstrate that generating beams whose intensity pattern simultaneously spirals with fast and slow rotation components enables a distance measurement with high accuracy over a broad range, using the high and low rotation frequency, respectively. In our experiment, we achieve an accuracy of around 2 µm over a longitudinal range of more than 2 mm using a single beam and only two quadrant detectors. Because our method relies on single-beam interference and only requires a static generation and simple intensity measurements, it is intrinsically stable and could find applications in high-speed measurements of longitudinal position.

Entanglement: quantum or classical?

From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.

Near-perfect measuring of full-field transverse-spatial modes of light.

Along with the growing interest in using the transverse-spatial modes of light in quantum and classical optics applications, developing an accurate and efficient measurement method has gained importance. Here, we present a technique relying on a unitary mode conversion for measuring any full-field transverse-spatial mode. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We experimentally test the technique using a single spatial light modulator and achieve an average error of 4.2 % for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. Moreover, as the method can also be used to measure any complex superposition state, we demonstrate its potential for quantum cryptography applications and in high-dimensional quantum state tomography.

Influence of pump coherence on the generation of position-momentum entanglement in optical parametric down-conversion.

We examine experimentally how the degree of position-momentum entanglement of photon pairs depends on the transverse coherence of the pump beam that excites them in a process of spontaneous parametric down-conversion. Using spatially incoherent light from a light-emitting diode, we obtain strong position correlation of the photons, but we find that transverse momentum correlation, and thus entanglement, is entirely absent. When we continuously vary the degree of spatial coherence on the pump beam, we observe the emergence of stronger momentum correlations and entanglement. We present theoretical arguments that explain our experimental results. Our results shed light on entanglement generation and can be applied to control entanglement for quantum information applications.

Measurement of the Photon-Plasmon Coupling Phase Shift.

Scattering processes have played a crucial role in the development of quantum theory. In the field of optics, scattering phase shifts have been utilized to unveil interesting forms of light-matter interactions. Here we investigate the phase shift experienced by a single photon as it scatters into a surface plasmon polariton and vice versa. This coupling phase shift is of particular relevance for quantum plasmonic experiments. Therefore, we demonstrate that the photon-plasmon interaction at a plasmonic slit can be modeled through a quantum-mechanical tritter, a six-port scattering element. We show that the visibilities of a double-slit and a triple-slit interference patterns are convenient observables to characterize the interaction at a slit and determine the coupling phase. Our accurate and simple model of the interaction, validated by simulations and experiments, has important implications not only for quantum plasmonic interference effects, but is also advantageous to classical applications.

Quantum entanglement of angular momentum states with quantum numbers up to 10,010.

Photons with a twisted phase front carry a quantized amount of orbital angular momentum (OAM) and have become important in various fields of optics, such as quantum and classical information science or optical tweezers. Because no upper limit on the OAM content per photon is known, they are also interesting systems to experimentally challenge quantum mechanical prediction for high quantum numbers. Here, we take advantage of a recently developed technique to imprint unprecedented high values of OAM, namely spiral phase mirrors, to generate photons with more than 10,000 quanta of OAM. Moreover, we demonstrate quantum entanglement between these large OAM quanta of one photon and the polarization of its partner photon. To our knowledge, this corresponds to entanglement with the largest quantum number that has been demonstrated in an experiment. The results may also open novel ways to couple single photons to massive objects, enhance angular resolution, and highlight OAM as a promising way to increase the information capacity of a single photon.

Twisted light transmission over 143 km.

Spatial modes of light can potentially carry a vast amount of information, making them promising candidates for both classical and quantum communication. However, the distribution of such modes over large distances remains difficult. Intermodal coupling complicates their use with common fibers, whereas free-space transmission is thought to be strongly influenced by atmospheric turbulence. Here, we show the transmission of orbital angular momentum modes of light over a distance of 143 km between two Canary Islands, which is 50× greater than the maximum distance achieved previously. As a demonstration of the transmission quality, we use superpositions of these modes to encode a short message. At the receiver, an artificial neural network is used for distinguishing between the different twisted light superpositions. The algorithm is able to identify different mode superpositions with an accuracy of more than 80% up to the third mode order and decode the transmitted message with an error rate of 8.33%. Using our data, we estimate that the distribution of orbital angular momentum entanglement over more than 100 km of free space is feasible. Moreover, the quality of our free-space link can be further improved by the use of state-of-the-art adaptive optics systems.

Measuring azimuthal and radial modes of photons.

With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency, and arrival time of a photon have been developed. However, the transverse spatial degree of freedom still lacks a measurement scheme that allows the reconstruction of its full transverse structure with a simple implementation and a high level of accuracy. Here we show a method to measure the azimuthal and radial modes of Laguerre-Gaussian beams with a greater than 99 % accuracy, using a single phase screen. We compare our technique with previous commonly used methods and demonstrate the significant improvements it presents for quantum key distribution and state tomography of high-dimensional quantum states of light. Moreover, our technique can be readily extended to any arbitrary family of spatial modes, such as mutually unbiased bases, Hermite-Gauss, and Ince-Gauss. Our scheme will significantly enhance existing quantum and classical communication protocols that use the spatial structure of light, as well as enable fundamental experiments on spatial-mode entanglement to reach their full potential.

Quantum cryptography with twisted photons through an outdoor underwater channel.

Quantum communication has been successfully implemented in optical fibres and through free-space. Fibre systems, though capable of fast key and low error rates, are impractical in communicating with destinations without an established fibre link. Free-space quantum channels can overcome such limitations and reach long distances with the advent of satellite-to-ground links. However, turbulence, resulting from local fluctuations in refractive index, becomes a major challenge by adding errors and losses. Recently, an interest in investigating the possibility of underwater quantum channels has arisen. Here, we investigate the effect of turbulence on an underwater quantum channel using twisted photons in outdoor conditions. We study the effect of turbulence on transmitted error rates, and compare different quantum cryptographic protocols in an underwater quantum channel, showing the feasibility of high-dimensional encoding schemes. Our work may open the way for secure high-dimensional quantum communication between submersibles, and provides important input for potential submersibles-to-satellite quantum communication.

Quantum cryptography with structured photons through a vortex fiber.

Optical fiber links and networks are integral components within and between cities' communication infrastructures. Implementing quantum cryptographic protocols on either existing or new fiber links will provide information-theoretical security to fiber data transmissions. However, there is a need for ways to increase the channel bandwidth. Using the transverse spatial degree of freedom is one way to transmit more information and increase tolerable error thresholds by extending the common qubit protocols to high-dimensional quantum key distribution (QKD) schemes. Here we use one type of vortex fiber where the transverse spatial modes serves as an additional channel to encode quantum information by structuring the spin and orbital angular momentum of light. In this proof-of-principle experiment, we show that two-dimensional structured photons can be used in such vortex fibers in addition to the common two-dimensional polarization encryption, thereby paving the path to QKD multiplexing schemes.

Twisted photon entanglement through turbulent air across Vienna.

Photons with a twisted phase front can carry a discrete, in principle, unbounded amount of orbital angular momentum (OAM). The large state space allows for complex types of entanglement, interesting both for quantum communication and for fundamental tests of quantum theory. However, the distribution of such entangled states over large distances was thought to be infeasible due to influence of atmospheric turbulence, indicating a serious limitation on their usefulness. Here we show that it is possible to distribute quantum entanglement encoded in OAM over a turbulent intracity link of 3 km. We confirm quantum entanglement of the first two higher-order levels (with OAM=± 1h and ± 2h). They correspond to four additional quantum channels orthogonal to all that have been used in long-distance quantum experiments so far. Therefore, a promising application would be quantum communication with a large alphabet. We also demonstrate that our link allows access to up to 11 quantum channels of OAM. The restrictive factors toward higher numbers are technical limitations that can be circumvented with readily available technologies.

Generation of Caustics and Rogue Waves from Nonlinear Instability.

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Generation and confirmation of a (100 x 100)-dimensional entangled quantum system.

Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.

Automated Search for new Quantum Experiments.

Quantum mechanics predicts a number of, at first sight, counterintuitive phenomena. It therefore remains a question whether our intuition is the best way to find new experiments. Here, we report the development of the computer algorithm Melvin which is able to find new experimental implementations for the creation and manipulation of complex quantum states. Indeed, the discovered experiments extensively use unfamiliar and asymmetric techniques which are challenging to understand intuitively. The results range from the first implementation of a high-dimensional Greenberger-Horne-Zeilinger state, to a vast variety of experiments for asymmetrically entangled quantum states-a feature that can only exist when both the number of involved parties and dimensions is larger than 2. Additionally, new types of high-dimensional transformations are found that perform cyclic operations. Melvin autonomously learns from solutions for simpler systems, which significantly speeds up the discovery rate of more complex experiments. The ability to automate the design of a quantum experiment can be applied to many quantum systems and allows the physical realization of quantum states previously thought of only on paper.

Direct characterization of linear-optical networks.

We introduce an efficient method for fully characterizing multimode linear-optical networks. Our approach requires only a standard laser source and intensity measurements to directly and uniquely determine all moduli and non-trivial phases of the matrix describing a network. We experimentally demonstrate the characterization of a 6×6 fiber-optic network and independently verify the results via nonclassical two-photon interference.

Twisted photons: new quantum perspectives in high dimensions.

Twisted photons can be used as alphabets to encode information beyond one bit per single photon. This ability offers great potential for quantum information tasks, as well as for the investigation of fundamental questions. In this review article, we give a brief overview of the theoretical differences between qubits and higher dimensional systems, qudits, in different quantum information scenarios. We then describe recent experimental developments in this field over the past three years. Finally, we summarize some important experimental and theoretical questions that might be beneficial to understand better in the near future.