Quantum metasurface for multiphoton interference and state reconstruction.

With recent advances in nanophotonics, metasurfaces based on nano-resonators have facilitated novel types of optical devices. In particular, the interplay between different degrees of freedom, involving polarization and spatial modes, boosted classical polarization measurements and imaging applications. However, the use of metasurfaces for measuring the quantum states of light remains largely unexplored. Conventionally, the task of quantum state tomography is realized with several bulk optical elements, which need to be reconfigured multiple times. Such setups can suffer from decoherence, and there is a fundamental and practical interest in developing integrated solutions for measurement of multi-photon quantum states. We present a new concept and the first experimental realization of all-dielectric metasurfaces with no tuneable elements for imaging-based reconstruction of the full quantum state of entangled photons. Most prominently, we implement multi-photon interferometric measurements on a sub-wavelength thin optical element, which delivers ultimate miniaturization and extremely high robustness. Specifically, we realize a highly transparent all-dielectric metasurface, which spatially splits different components of quantum-polarization states. Then, a simple one-shot measurement of correlations with polarization-insensitive on-off click detectors enables complete reconstruction of multi-photon density matrices with high precision. In our experiment, we prepare sets of polarization states and reconstruct their density matrices with a high fidelity of over 99% for single photon states and above 95% for two-photon states. Our work provides a fundamental advance in the imaging of quantum states, where multi-photon quantum interference takes place at sub-wavelength scale.

Optical nanoantennas have shown a great capacity for efficient extraction of photons from the near to the far field, enabling directional emission from nanoscale single-photon sources. However, their potential for the generation and extraction of multi-photon quantum states remains unexplored. Here we experimentally demonstrate the nanoscale generation of two-photon quantum states at telecommunication wavelengths based on spontaneous parametric down-conversion in an optical nanoantenna. The antenna is a crystalline AlGaAs nanocylinder, possessing Mie-type resonances at both the pump and the bi-photon wavelengths, and when excited by a pump beam it generates photon pairs with a rate of 35 Hz. Normalized to the pump energy stored by the nanoantenna, this rate corresponds to 1.4 GHz/Wm, being 1 order of magnitude higher than conventional on-chip or bulk photon-pair sources. Our experiments open the way for multiplexing several antennas for coherent generation of multi-photon quantum states with complex spatial-mode entanglement and applications in free-space quantum communications and sensing.

Optical nanoantennas have shown a great capacity for efficient extraction of photons from the near to the far-field, enabling directional emission from nanoscale single-photon sources. However, their potential for the generation and extraction of multi-photon quantum states remains unexplored. Here we demonstrate experimentally the nanoscale generation of two-photon quantum states at telecommunication wavelengths based on spontaneous parametric down-conversion in an optical nanoantenna. The antenna is a crystalline AlGaAs nanocylinder, possessing Mie-type resonances at both the pump and the bi-photon wavelengths and when excited by a pump beam generates photonpairs with a rate of 35 Hz. Normalized to the pump energy stored by the nanoantenna, this rate corresponds to 1.4 GHz/Wm, being one order of magnitude higher than conventional on-chip or bulk photon-pair sources. Our experiments open the way for multiplexing several antennas for coherent generation of multi-photon quantum states with complex spatial-mode entanglement and applications in free-space quantum communications and sensing.

We present theoretical and experimental advances on photon-pair generation through spontaneous parametric down-conversion (SPDC) in nonlinear nanostructures and metasurfaces, underpinning quantum entanglement engineering at sub-wavelength scale for photon shaping with tailored polarization and spatial correlations. We derive explicit theoretical expressions for the measurable photon counts and quantum correlations, incorporating material dispersion and absorption characteristics [Phys. Rev. Lett. 117, 123901 (2016)], and demonstrate experimentally the generation of quantum heralded photon pairs from a single AlGaAs nanodisk [Optica 6, 1416 (2019)]. We further reveal the opportunities to enhance the generation rate through high-Q resonances including bound states in the continuum [doi:10.1117/12.2539888 (2019)]. We also outline the applications of metasurfaces for the manipulation and measurement of multi-photon quantum states for free-space quantum imaging and communications.

Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.

The two-photon state generated by spontaneous parametric down-conversion (SPDC) exhibit spatial entanglement embedded in the corresponding mode function. The control of the spatial characteristics of the generated two-photon state is an issue of paramount importance. For example, the spatial entanglement of the two down converted photons forms the basis of quantum imaging, and entanglement in orbital angular momentum has opened a new scenario for implementing multidimensional Hilbert spaces. We put forward several techniques to engineer the spatial structure of entangled two-photon states generated in SPDC. The first strategy we consider for spatial control of the quantum state makes use of the direct manipulation of the pump beam. This technique makes feasible to prepare arbitrary engineered entangled states in any d-dimensional Hilbert space. The second strategy is based on the proper preparation of the down-converting crystal itself, namely quantum state manipulation by quasi-phase-matching (QPM) engineering. We use properly designed transversely varying QPM gratings in nonlinear crystals.

Integrated single-photon detectors open new possibilities for monitoring inside quantum photonic circuits. We present a concept for the in-line measurement of spatially-encoded multi-photon quantum states, while keeping the transmitted ones undisturbed. We theoretically establish that by recording photon correlations from optimally positioned detectors on top of coupled waveguides with detuned propagation constants, one can perform robust reconstruction of the density matrix describing the amplitude, phase, coherence and quantum entanglement. We report proof-of-principle experiments using classical light, which emulates single-photon regime. Our method opens a pathway towards practical and fast in-line quantum measurements for diverse applications in quantum photonics.

We report the implementation of a high-rate source of single- and two-photon states. By combining the advantages of short pulses and cavities, heralding rates as high as 200 kHz have been obtained for the single photons, as well as 250 Hz for the two-photon states. In this setup, homodyne measurements are conditioned by the heralding of the quantum states thanks to the introduction of a low-loss optical delay line in the heralded states path. This enables the detection of most of the heralded events, and fidelities reaching 68.5% (91% with correction for detection efficiency) and 50.4% (85% with correction) were obtained for the single- and two-photon states, respectively. Such high rates and fidelities in the generation of elementary Fock states may open the path for the production of complex quantum states.

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

Quantum state reconstruction, or state reconstruction for short, aims at identifying an unknown quantum state ( states in quantum mechanics) on the basis of experimentally accessible data. The Quantum Optics community usually refers to this inverse problem as quantum (state) tomography while the expression quantum state estimation is often used in the field of Quantum computation. Reconstruction procedures depend on the physical context defined by the system carrying the unknown state, the experimentally accessible observables, the size of the ensemble of systems prepared in the unknown state, and the precision of the measured data. A two-level system (such as a spin-1/2, a qubit, or the two polarizations of a photon) prepared in a state with density matrix ρ is sufficient to illustrate the idea of state reconstruction. With two non-negative eigenvalues summing to one, the density matrix is a positive operator, and it depends on three real parameters. In the Bloch representation, the parameters combine to a real vector n with length |n| 1,

We propose to use multiphoton interferences of photons emitted from statistically independent thermal light sources in combination with linear optical detection techniques to reconstruct, i.e., image, arbitrary source geometries in one dimension with subclassical resolution. The scheme is an extension of earlier work [S. Oppel etal., Phys. Rev. Lett. 109, 233603 (2012)], where N regularly spaced sources in one dimension were imaged by use of the Nth-order intensity correlation function. Here, we generalize the scheme to reconstruct any number of independent thermal light sources at arbitrary separations in one dimension, exploiting intensity correlation functions of order m≥3. We present experimental results confirming the imaging protocol and provide a rigorous mathematical proof for the obtained subclassical resolution.

In this manuscript we analyze the emergence of protected multiphoton states in scattering problems with cylindrical symmetry. In order to do that, we first provide a formal definition of the concept of postselected symmetry-protection. We show that the notion of symmetry-protection is not limited to one- or two-photon states, on the contrary, it can be formally extended to the multiphoton case. In addition, we prove for the case of cylindrical symmetry that all possible multiphoton protected states are constructed from a small set of one- and two-photon states. Finally, we point out possible applications that symmetry-protected states may have in quantum communications, concretely, in the construction of decoherence-free subspaces.

Quantum science and technology have seen rapid progress in recent decades, finding applications in computation, information processing, communication, and sensing. Accurate characterization and manipulation of quantum states is essential to the successful implementation of these applications. Moreover, optimal quantum state estimation is closely related to fundamental questions, such as limits on how fast information can be extracted about quantum systems. In this thesis, we present several contributions to efficiently estimating and transforming quantum states. We discuss optimal quantum state estimation, both in the regime of few available quantum systems as well as the asymptotic regime. We numerically investigate how assuming a pure-state can affect the performance of tomographic methods, and where adaptive quantum state tomography is in fact advantageous. While collective measurements have been formally considered as optimal solutions to various problems in quantum information, their implementation has been largely neglected due to experimental challenges. We present a proof-of-concept experiment realizing Massar and Popescu's optimal collective measurement for quantum state estimation, utilizing two-photon interference and polarization-dependent loss to achieve non-maximally entangled state projections. We demonstrate that collective strategies can outperform the best separable measurements. Furthermore, we introduce and experimentally implement a fast and automated optical polarization compensation scheme using liquid crystal variable retarders and rotating quarter-wave plate tomography. Desired accuracy thresholds can be achieved within a few compensation steps. Finally, we use a matrix-model approach to investigate the realization of spatial unitary transformations via sequences of thin phase gratings and free-space propagation. We numerically demonstrate that the grating parameters and propagation distances can be optimized to achieve various two-beam and three-beam unitary transformations, such as Pauli gates and the discrete Fourier transform. Through experimental and numerical approaches, this thesis offers new perspectives on methods for quantum state estimation and unitary transformation.

The identification of nonclassical features of multiphoton quantum states represents a crucial task in the development of many quantum photonic technologies. Under realistic experimental conditions, a photonic quantum state gets affected by its interaction with several nonideal optoelectronic devices, including those used to guide, detect, or characterize it. The result of such noisy interaction is that the nonclassical features of the original quantum state get considerably reduced or are completely absent in the detected, final state. In this work, the self-learning features of artificial neural networks are exploited to experimentally show that the nonclassicality of multiphoton quantum states can be assessed and fully characterized, even in the cases in which the nonclassical features are concealed by the measuring devices. Our work paves the way toward artificial-intelligence-assisted experimental-setup characterization, as well as quantum state nonclassicality identification. Published by the American Physical Society 2024

All-dielectric metasurfaces provide unique solutions for advanced wavefront manipulation of light with complete control of amplitude and phase at sub-wavelength scales. One limitation, however, for most of these devices is the lack of any post-fabrication tunability of their response. To break this limit, a promising approach is employing phase-change materials (PCMs), which provide fast, low energy, and non-volatile means to endow metasurfaces with a switching mechanism. In this regard, great advancements have been done in the mid-infrared and near-infrared spectrum using different chalcogenides. In the visible spectral range, however, very few devices have demonstrated full phase manipulation, high efficiencies, and reversible optical modulation. In this work, a programmable all-dielectric Huygens' metasurface made of antimony sulfide (Sb2 S3 ) PCM is experimentally demonstrated, a low loss and high-index material in the visible spectral range with a large contrast (≈0.5) between its amorphous and crystalline states. ≈2π phase modulation is shown with high associated transmittance and it is used to create programmable beam-steering devices. These novel chalcogenide PCM metasurfaces have the potential to emerge as a platform for next-generation spatial light modulators and to impact application areas such as programmable and adaptive flat optics, light detection and ranging (LiDAR), and many more.