Full Phase-Control Of Chip-Scale Infrared Frequency Combs
Paolo De Natale1*, Francesco Cappelli 1, Luigi Consolino1, Saverio Bartalini1,2
1CNR-INO – Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Firenze FI, Italy & LENS – European Laboratory for Non-Linear Spectroscopy, Via Nello Carrara 1, 50019 Sesto Fiorentino FI, Italy
2ppqSense Srl, Via Gattinella 20, 50013 Campi Bisenzio, FI, Italy
In the last twenty years, the workhorse for frequency metrology, the Frequency Comb synthesizer (FC), has undergone many transformations, aiming to cover new spectral ranges, as well as to miniaturize this broadband though highly-coherent source (for a detailed description see, e.g., ref. 1). Quantum Cascade Lasers appeared as ideal candidates to cover the huge infrared spectral window, from around 2 to few hundred ？m (i.e. THz frequency range) wavelength. In addition, these devices promise to deliver an all-in-one (i.e. a single, miniature, active device) frequency comb with a mm-scale overall size and with the unique possibility to tailor their spectral emission by band structure engineering. Following the first proposal to use QCLs as FC amplifiers (3), a practical realization of a multi-frequency directly emitting QCL was achieved only in 2012 (4). However, a full characterization of the emission properties of QCLs had to wait several more years, with several intermediate steps (see, e.g., ref. 5,6). Indeed, a genuine FC emission not only requires equally spaced frequencies but also a high degree of phase-coherence throughout the entire comb emission band. Very recently, we have proposed a novel technique, that we named FACE (Fourier-transform Analysis of Comb Emission), for simultaneous phase characterization, that makes use of a Fourier transform analysis of the QCL comb emission (7). With this technique, full phase stabilization and independent control of the two degrees of freedom (offset and mode spacing) of a quantum cascade laser frequency comb (QCL-FC), by combining driving current modulation and radio-frequency (RF) injection, was finally achieved (8). This result enables the most challenging applications in a number of areas, in a spectral region as wide as the Infrared range itself.
1) Maddaloni, P., Bellini, M., De Natale, P.: “Laser-Based Measurements for Time and Frequency Domain Applications: A Handbook”,1st Edition ISBN 9781439841518 CRC Press (2013).
2) P. De Natale “Frequency Metrology with Quantum Cascade Lasers”, IQCLSW Workshop and School, Monte Verita-Ascona (Switzerland) (2008).
3) Hugi, A. et al., Nature 492, 229 (2012).
4) Burghoff, D. et al., Opt. Express 23, 1190–1202 (2015).
5) Cappelli, F. et al., Laser Photonics Rev. 10, 623–630 (2016).
6) Cappelli, F. et al. Nature Photonics https://doi.org/10.1038/s41566-019-0451-1(2019).
7) Consolino, L. et al., Nature Communications 10, 2938 (2019).
Organic Quantum Integrated Devices
1CNR-INO and LENS, Istituto Nazionale di Ottica, Via Carrara 1, 50019 Sesto F.no, Italy
Organic molecules of polyaromatic hydrocarbons were the first system in the solid state to show single photon emission [1,2]. However they are still consideredunconventional sources of non-classical light. I will try to unveil part of the mysterybehind such quantum emitters and show how they could effectively contribute tointegrated quantum photonic platforms.
I will report on fluorescence coupling from a single molecule to a planar optical antenna  and a single-mode dielectric waveguide  (Fig. 1, left), discuss the integration of single quantum emitters into hybrid dielectric-plasmonic devices  and the coupling with 2D materials . I will present our recent results about the fabrication of single-molecule doped nancrystals, preserving the optical properties of the bulk system, i.e. negligible blinking and spectral diffusion  (Fig.1, right). Eventually, I will report on ultrafast time-resolved transient spectroscopy on a single molecule .
Figure 1: Left, concept for the device showing single molecule emission into an
integrated photonic waveguide. Right, optical characterization of DBT-doped
 W. E. Moerner and L. Kador, Phys. Rev. Lett. 62, 2535 (1989).
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 K. Schaedler et al., submitted
 S. Pazzagli et al., ACS Nano 12, 4295？4303 (2018)
 M. Liebel et al., Nat. Phot. 12, 45-49 (2017)
Ultra-Sensitive Laser Absorption Spectroscopy - Noise immune cavity enhanced optical heterodyne molecular spectrometry
Weiguang Ma1,2*, Gang Zhao, Yueting Zhou, Jianxing Liu, Songjie Guo, Fei Xu, Wangbao Yin, Liantuan Xiao, Suotang Jia
1State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan
2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan
Laser absorption spectroscopy (LAS) is a powerful technique for trace gas detection that is often characterized by high sensitivity and selectivity and therefore has been successfully applied to a number of fields, including environmental monitoring, industrial process control, defense and homeland security, and medical diagnostics. While direct absorption spectroscopy (DAS), the most basic realization of LAS, is quite limited in terms of sensitivity due to low-frequency (especially 1/f) noise, therefore more sensitive LAS methods have been developed. One way to improve the sensitivity of LAS is to move the analytical information to higher detection frequencies by the use of a modulation technique. The most commonly used ones are wavelength modulation spectroscopy (WMS) and frequency modulation spectroscopy (FMS). An alternative means is to extend the interaction length between the light and analyte by use of a multipass cell  or a resonant cavity. The latter has proven to be the most powerful by providing effective absorption lengths of ~km in laboratory environments, therefore it has been developed to different schemes, such as cavity enhanced absorption spectroscopy (CEAS), cavity ring down spectroscopy (CRDS), off-axis integrated cavity output spectroscopy (OA-ICOS) and noise immune cavity enhanced optical heterodyne molecular spectroscopy (NICE-OHMS).
Up to now, NICE-OHMS is one of the most sensitive techniques for detection of molecular species. It combines CEAS, to increase the interaction length between the light and the analyte, with FMS, to reduce 1/f noise, especially relative intensity noise. Since the matching of the modulation frequency of the FMS to the free spectral range (FSR) of the cavity provides an immunity to frequency-to-amplitude noise, which is the main limitation in CEAS, it has been prophesized that the technique can be a powerful technique for ultra-sensitive trace gas detection and that it can provide shot-noise-limited detection under some realistically feasible conditions. In fact, by use of cavity dither paired with wavelength modulation for additional noise-reduction, a detection sensitivity of 1′10-14 cm-1 over a 1 s integration time, only 1.5 times above the shot noise limit, was obtained in one of its first realizations by J. Ye et.al . In this case, a well-stabilized fixed-frequency Nd:YAG laser was locked to a cavity with a finesse of 105 while addressing a sub-Doppler feature of C2HD at 1064 nm. Despite the fact that the technique, since then, has been constructed around a variety of tunable lasers in various configurations by the groups from Japan, New Zealand, USA, Netherland, England and Sweden. The most persistent development of the technique has been performed based on Erbium-doped fiber lasers (EDFL), which simplified the NICE-OHMS system. Recently a NICE-OHMS performance with a factor of 1.44 times above the shot noise limit and a detection sensitivity of 2.2′10-14cm-1 was obtained by the collaboration between Ove Axner’s group and our group when a Doppler broadened absorption spectrum (in the order of several hundreds MHz) was addressed .
For trace gas detection, a gas sample with atmospheric pressure is preferred for the field applications. Although NICE-OHMS keeps the record of sensitivity for gas detection, there are no experiments performed on the atmospheric sample. Therefore one of our on-working projects is to develop a NICE-OHMS spectrometer to measure the atmospheric sample by adopting a EDFL or WGM semiconductor laser with wavelength tuning range of larger than 10 GHz and a high-performance servo for laser to cavity frequency locking. Another project is to develop a state of art NICE-OHMS spectrometer to seek an even higher sensitivity for trace gas detection by use of the ultra-narrow linewidth laser and fiber coupled single sideband modulator .
 P. Kluczynski, J. Gustafsson, A.M. Lindberg, O. Axner, Wavelength modulation absorption spectrometry - an extensive scrutiny of the generation of signals, Spectrochimica Acta Part B-Atomic Spectroscopy, 56(2001) 1277-354.
 V.L. Kasyutich, C.E. Canosa-Mas, C. Pfrang, S. Vaughan, R.P. Wayne, Off-axis continuous-wave cavity-enhanced absorption spectroscopy of narrow-band and broadband absorbers using red diode lasers, Applied Physics B-Lasers and Optics, 75(2002) 755-61.
 National Nature Science Foundation of China (2016)
 National Nature Science Foundation of China (2018)
Quantum coherent single molecule microscopy
Chengbing Qin, Yao Li, and Liantuan Xiao
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan
Preparation and manipulation of the coherent states of a single molecule make it a potential candidate for single qubits in quantum computers. Researches on quantum sensors and optoelectronic devices based on single molecules also have made important breakthroughs. Especially in recent years, the rise of quantum biology has led to increasing attentions to the study of the single-molecule quantum coherence and its ultrafast dynamics. Here, we develop a quantum coherent single molecule microscopy, based on the manipulation of the excited state population probability of a single molecule. By analyzing the quantum coherent modulation intensity of single molecules, we obtain their quantum coherent information. We can quantitatively describe the single-molecule quantum coherent information through defining quantum coherent visibility, as well as realize the visualization and real-time observation of single-molecule quantum coherent information. By using this technique to study quantum coherent imaging of organisms, the physiological processes of cells are revealed, which are not available with conventional fluorescence intensity imaging. We will show that two orders of magnitude improvement in single-molecule imaging contrast can be readily achieved by modulating the probability of single-molecule excited states through this new technique. At last, we will also present our recent experimental results on the investigation of ultrafast dynamics of single gold nanoparticles by using pump-probe techniques.
. Zhou, H.; Qin, C.; Chen, R.; Liu, Y.; Zhou, W.; Zhang, G.; Gao, Y.; Xiao, L.; Jia, S., Quantum Coherent Modulation-Enhanced Single-Molecule Imaging Microscopy. The Journal of Physical Chemistry Letters 2019, 10, 223-228.
. Zhou, H.; Qin, C.; Chen, R.; Zhou, W.; Zhang, G.; Gao, Y.; Xiao, L.; Jia, S., Accurate Investigation on the Fluorescence Resonance Energy Transfer between Single Organic Molecules and Monolayer WSe2 by Quantum Coherent Modulation-Enhanced Single-Molecule Imaging Microscopy. The Journal of Physical Chemistry Letters 2019, 2849-2856.
Quantum Zeno effect in ultracold atoms
Francesco Saverio Cataliotti
European Laboratory for Non-Linear Spectroscopy (LENS),
University of Florence, via N. Carrara 1, 50019 Sesto F.no (FI), Italy
QSTAR, Largo Enrico Fermi 2, 50125 Firenze, Italy.
A European reference point for research with light waves, based on a fundamental multi-disciplinary approach. This is LENS, the European Laboratory for Non-linear Spectroscopy, since its birth in 1991 as center of excellence of the University of Florence. A place where physicists, chemists and biologists work together every day, sharing instrumentation, experiences, research themes, scientific perspectives and ideas with the common aim of using laser light to investigate matter from different points of view and under different conditions. Research interests include atomic physics, photonics, biophysics, and chemistry, without forgetting advanced training of young researchers, thanks to e.g. a EU Marie Curie training program, through high quality PhD courses and a rich Post Doctoral fellowship program.
Quantum light state and mode engineering
Istituto Nazionale di Ottica CNR-INO, Florence, ITALY
Light is a perfect candidate for exploring and exploiting the quantum properties of nature. It can be used to test fundamental quantum rules and beat conventional classical limits in measurement, communication, and computation. To do so, one needs to produce, manipulate, and characterize nonclassical light states with single-photon-level accuracies in well-defined spectral and temporal modes.
I will illustrate some of the experiments recently carried out at CNR-INO, based on the controlled addition and subtraction of single photons on arbitrary modes. I will present advanced applications of these basic quantum tools and of their different combinations to a variety of nonclassical light states, with illustrations of some of the most fundamental concepts of quantum mechanics at play in the lab.
Quantum Communications: from non-classical light sources to in-field demonstrations in fiber links
1Consiglio Nazionale delle Ricerche - Istituto Nazionale di Ottica (CNR-INO), Via N. Carrara 1, 50019 Sesto F.no, Firenze (Italy).
2LENS and Università di Firenze, Sesto F.no, Firenze (Italy).
Nonclassical states of light are crucial for both establishing new quantum communications protocols and developing future quantum networks . In this direction, we mainly succeed in the generation and manipulations quantum states of light such as multiphoton entangled states , squeezed light at telecom wavelengths , and narrowband-entangled states from four wave mixing in atomic ensembles . Recently, we realized in field trial tests of quantum key distribution protocols over a metropolitan network . Here we present a simple, practical and efficient QKD scheme, performed over a 21 dB-losses fiber link installed in the metropolitan area of Florence (Italy). Coexistence of quantum and weak classical communication is also demonstrated by transmitting an optical synchronization signal through the same fiber link.
 D. Bouwmeester, A.K. Ekert, A. Zeilinger (Eds.), The Physics of Quantum Information: Quantum Cryptography Quantum Teleportation, Quantum Computation, Springer, Berlin, 2000.
 N. Gisin, G. Ribordy, W. Tiffel and H. Zbinden, “Quantum cryptography”, Rev. Mod. Phys. 74, 145 (2002).
 N. Biagi, L. S. Costanzo, M. Bellini, and A. Zavatta, arXiv:1811.10466 (2018).
 F. Kaiser, B. Fedrici, A. Zavatta, V. D’Auria, and S. Tanzilli, “A fully guided-wave squeezing experiment for fiber quantum networks”, Optica 3, 362 (2016).
 A. Zavatta, M. Artoni and G. C. La Rocca, “Engineering of heralded narrowband color-entangled states”, Phys. Rev. A 99, 031802 (2019).
 D. Bacco, I. Vagniluca, B. Da Lio, N. Biagi, A. Della Frera, D. Calonico, C. Toninelli, F. S. Cataliotti, M. Bellini, L. K. Oxenl？we, A. Zavatta, “ Field trial of a finite-key quantum key distribution system in the Florence metropolitan area”, arXiv:1903.12501 (2019).
Geometry of bounded critical phenomena
[in collaboration with Giacomo Gori]
1 CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy
2 SISSA, Via Bonomea 265, I-34136 Trieste, Italy
We devise a geometric description of bounded systems at criticality in any dimension d. This is achieved by altering the flat metric with a space dependent scale factor γ(x), x belonging to a general bounded domain Ω. γ(x) is chosen in order to have a scalar curvature to be constant and negative, the proper notion of curvature being -- as called in the mathematics literature -- the fractional Q-curvature. The equation for γ(x) is found to be the Fractional Yamabe Equation (to be solved in Ω) that, in absence of anomalous dimension, reduces to the usual Yamabe Equation in the same domain. From the scale factor γ(x) we obtain novel predictions for the scaling form of one-point correlation functions. A (necessary) virtue of the proposed approach is that it encodes and allows to naturally retrieve the purely geometric content of two-dimensional boundary conformal field theory. From the critical magnetization profile in presence of boundaries one can extract the scaling dimension of the order parameter, Δ？. For the 3D Ising model we find Δ？=0.518142(8) which favorably compares (at the fifth decimal place) with the state-of-the-art estimate. A nontrivial prediction is the structure of two-point correlators at criticality. They should depend on the fractional Q-hyperbolic distance calculated from the metric, in turn depending only on the shape of the bounded domain and on Δ？. Numerical simulations of the 3D Ising model on a slab geometry are found to be in agreement with such predictions.
Giacomo Gori and Andrea Trombettoni, Geometry of bounded critical phenomena, arXiv:1904.08919
Multipartite entanglement in topologiocal quantum systems
QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy.
We introduce a novel measure of entanglement with a measurable lower bound given by the Fisher information  and associated to entanglement-enhanced metrology. We study this lower bound in the ground state of many-body systems , focusing in particular to the Kitaev wire , an important model showing topological quantum phases. A super-extensive scaling of the Fisher information characterizes non-trivial topological phases and phase transition of this model, showing that multipartite entanglement detected by the Fisher information is an intrinsic property of non-trivial topological phases. Finally, we show that this metrological multipartite entanglement is not affected by local imperfections  and low temperature fluctuations , paving the way to robust "topological quantum metrology".
 A. Smerzi and L. Pezzè, in preparation.
 M. Gabrielli, L. Lepori, and L. Pezzè, NJP 21, 033039 (2019)
 L. Pezze', M. Gabbrielli, L. Lepori and A. Smerzi, PRL 119, 250401 (2017)
 L. Pezzè and L. Lepori, in preparation.
 M. Gabbirelli, A. Smerzi and L. Pezzè, SCI. REP 8, 15663 (2018)
Quantum Mixture Experiment at LENS
Alessia Burchianti1,2, C. D’Errico1,2, C. Fort1,2, F. Minardi1,2,3
1Istituto Nazionale di Ottica, CNR-INO, Sesto Fiorentino, Italy
2LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, Sesto Fiorentino, Italy
3Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy
In this talk, we discuss recent results and future perspectives of our quantum mixture experiment at LENS (European Laboratory for Non-linear Spectroscopy).
We have recently build up a new experimental set-up for producing two-component quantum gases of rubidium and potassium, with tunable interactions. We actually produce dual-species Bose-Einstein Condensates (BECs) of 41K and 87Rb in a hybrid trap, consisting of a magnetic quadrupole and an optical dipole trap. In the hybrid potential 87Rb is first magnetically and then optically evaporated, while 41K is sympathetically cooled by 87Rb. We finally produce, in a pure optical trap, dual-species BECs with about 105 atoms either in the (F=2,mF=2)  or in the (F=1,mF=1) state. In the latter case, we exploit Feshbach resonances for tuning the interspecies interaction. After compensating the differential gravitational sag of the two species with a magnetic field gradient, we let the binary mixture expand both in free space and in an optical waveguide. In the attractive regime, by increasing the strength of intraspecies interaction we observe in both geometries the transition from expanding clouds to self-bound states, which we identify with liquid-like quantum droplets .
In the next future, we will implement a high-resolution imaging system for both atomic detection and imprinting of engineered optical potentials. We plan to produce and to study self-bound states, vortex states and emerging quantum phenomena in multicomponent superfluids.
 A. Burchianti, C. D'Errico, S. Rosi, A. Simoni, M. Modugno, C. Fort, and F. Minardi, “Dual-species Bose-Einstein condensate of 41K and 87Rb in a hybrid trap”, Phys. Rev. A 98, 063616 (2018)
 C. D’Errico, A. Burchianti, M. Prevedelli, L. Salasnich, F. Ancilotto, M. Modugno, F. Minardi and C. Fort, “Observation of Quantum Droplets in a Heteronuclear Bosonic Mixture”, submitted (2019)
Fano-Feshbach resonances in ultracold atoms
School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032. INDIA
Both Fano and Feshbach resonances arise from continuum-bound coherence, whereby continuum and bound states can form a coherent superposition. Historically, Fano  formulated his theoretical method to explain asymmetric line shape of auto-ionization spectrum, while Feshbach  developed his theory to explain a class of scattering resonances in nuclear physics. With the recent advancement in science with cold atoms and molecules, Fano and Feshbach resonances have become essential tools for manipulating quantum states at an interface of continuum and bound states of atoms. In this talk, we will highlight the significance of Fano-Feshbach resonances in ultracold atomic collisions in the presence of external magnetic and optical fields [3,4,5,6]. An external magnetic field can induce a multichannel scattering resonance, known as magnetic Feshbach resonance (MFR), between two ground-state atoms, while simultaneous application of an external optical field can induce a photoassociation (PA) transition to an excited molecular bound state. About a decade ago, the experiment by Junker et al  reported dispersive spectral shift in PA close to an MFR. A recent experiment by Li et al.  has revealed several intriguing features of Fano-Feshbach resonances including spectral shifts, which can be explained with a theoretical model of dual Fano-Feshbach resonances. We will discuss in some detail several prospective applications of Fano-Feshbach resonances, such as (a) controlling atom-atom interactions , (b) electromagnetically induced transparency in atom-molecule coupled systems, (c) dispersion management for light propagating through an atom-molecule coupled system, etc.
 U. Fano, Phys. Rev. 124, 1866 (1961).
 H. Feshbach, Ann. Phys. 5, 357 (1958).
 B. Deb and G. S. Agarwal, J. Phys. B: At. Mol. Opt. Phys. 42, 215203 (2009).
 B. Deb and A. Rakshit, J. Phys. B: At. Mol. Opt. Phys. 42, 195202 (2009).
 M. Junker, D. Dries, C. Welford, J. Hitchcock, Y. P. Chen and R. G. Hulet, Phys. Rev. Lett. 101, 060406 (2008).
 Y. Li, G. Feng, J. Wu, J. Ma, B. Deb, A. Pal, L. Xiao and S. Jia, Phys. Rev. A 99, 022702 (2019).
 B. Deb, J. Phys. B: At. Mol. Opt. Phys. 43, 085208 (2010).
Dynamics and localization of one-dimensional lattice gases withpower-law interactions
Leibniz Universit¨at Hannover
Power-law interactions play an important role in a large variety of physical systems, ranging from magnetic atoms and polar molecules to Rydberg atoms, NV centers, and trapped ions. Lattice gases of particles with power-law interactions present peculiar transport properties both in what concerns Hubbard and spin dynamics.
We first comment on 1D spin models. In these systems, spin excitations move amongst otherwise pinned particles via exchange mediated by power-law interactions. We show that in the presence of disorder and quasi-disorder single spin excitations present intriguing localization properties [1,2]. We then discuss many-body localization in the case of a gas of spin excitations, which present an intriguing algebraic growth of the entanglement entropy .
In a second part I discuss the Hubbard dynamics of polar lattice gases , of particular interest for on-going experiments with magnetic atoms. I will show that such dynamics is severely constrained by the interplay between dipolar interactions, energy conservation, and finite bandwidth. In particular, in the absence of disorder, quasi-localization via dimer clusterization may occur even for surprisingly low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets.
 X. Deng et al., Phys. Rev. Lett. 120, 110602 (2018).
 X. Deng et al., Phys. Rev. Lett. 123, 025301 (2019).
 X. Deng et al., in preparation
 W. Li et al., arXiv:1901.09762
Topology Far From Equilibrium with Ultracold Atoms
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, Shanxi 030006, China
I will present some work on topology far from equilibrium. The first is relevant to ongoing experiments aimed at realizing synthetic quantum Hall materials with ultracold atoms with dynamical means. At zero temperature, the direct correspondence between the Chern number of the ground state and Hall conductance is well established. Yet, non-equilibrium scenarios generically occur in atomic setups, where starting from a topologically trivial initial state, the Hamiltonian is driven into a topological regime. However, the system can never enter a topological insulator state under coherent dynamics, raising the challenge as to which manifestations of topology can be actually observed. Remarkably, we show that a quantized non-equilibrium Hall response can build up without a topological state . Then I will discuss how periodic driving can be harnessed to transcend fundamental constraints in equilibrium systems. Specifically, I show that perfect spin momentum locking, which is fundamentally forbidden in 1D static periodic systems, can emerge in the stroboscopic dynamics of 1D lattice systems . Finally, I will discuss dynamics of Majorana edge correlations in presence of noise. While in general noise will induce heating and dephasing, we identify examples of long-lived quantum correlations due to motional narrowing, where a fast noise drives the system between the topological and non-topological phases.
. YH, Peter Zoller, Jan Carl Budich, Dynamical Buildup of a Quantized Hall Response from Non-Topological States, Phys. Rev. Lett. 117, 126803 (2016); Long Zhang, Lin Zhang, YH, Sen Niu, Xiongjun Liu, arXiv: 1903.09144 (2019)
. Jan Carl Budich, YH, Peter Zoller, Helical Floquet Channels in 1D Lattices, Phys. Rev. Lett. 118, 105302 (2017)
. YH, Zi Cai, Mikhail A. Baranov, Peter Zoller, Majorana Fermions in Noisy Kitaev Wires, Phys. Rev. B. 92, 165118 (2015)
Quantum neural networks to denoise quantum data
Institut f¨ur Theoretische Physik, Leibniz Universit¨at Hannover, Appelstr. 2, DE-30167 Hannover, Germany
Neural networks are a prominent example of machine learning algorithms and enjoy widespread success both in research and industry. With the imminent advent of quantum technologies, analogous quantum algorithms for the efficient processing of quantum data become increasingly interesting. In this talk, I will first introduce the class of universal quantum neurons proposed in . As an exemplary application I will then discuss the denoising of highly entangled states. I will show how we construct quantum autoencoders from the above neurons, and demonstrate the successful denoising of small Greenberger-Horne-Zeilinger states subject to spin-flip errors and random unitary noise.
 Efficient Learning for Deep Quantum Neural Networks, K. Beer et al., arXiv:1902.10445
Certifying quantum light under non-ideal conditions
QSTAR and INO-CNR, Largo Enrico Fermi 2, 50125 Firenze, Italy
The certification of nonclassical quantum states and the verification of quantum correlations are fundamental tasks in quantum science. The faithful detection of such genuine quantum features is not only of importance for the basic understanding of quantum physics but also provides the foundation for quantum-technological applications. Unfortunately, in many realistic scenarios, the verification of quantum properties is hindered due to various kinds of imperfections such as low detection efficiencies, finite detector resolution, or background noise. Therefore, it is crucial to develop efficient and robust theoretical and experimental tools for the certification of quantum features under realistic, non-idealized conditions.
In this contribution, we present efficient methods of the verification of quantum light under various kinds of imperfections. First, we consider the possibility of extending quantum optical experiments to the mid-infrared region. In particular, we are interested in certifying quantum correlations of light emitted from quantum cascade lasers. In the mid-infrared region, only detectors with rather low detection efficiency exist which makes it very hard to certify quantum features, such as squeezing, by traditional measurement schemes (balanced homodyne detection). We propose to implement different kinds of correlation measurement, such as homodyne correlation measurements, which overcome the problem of low detection efficiencies and may pave the way for quantum optical experiments in the mid-infrared spectral region. Second, we study the case of detecting light in the few photon regime with click-counting multiplexing devices. Such detection systems split the incoming light into several detection modes and each mode is detected with an on-off detector. These provide only a limited information about the recorded light and, in particular, does not provide photon-number resolution and may be further affected by detection losses and dark-count noise. We motivate, derive, and apply different kinds of nonclassicality conditions which allow for the faithful certification of quantum light directly from the measured data under such non-ideal detection. This includes correlation conditions, phase-sensitive detection, the sampling of generalized phase-space functions, and detection-device independent nonclassicality criteria.