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Quasicrystals are a class of materials that are long-range ordered yet not periodic. These unique features make them a fascinating middle ground between order and disorder, thus providing an ideal platform for studying a wealth of physical phenomena. This thesis contains three experimental works that my colleagues and I achieved during my PhD period, in which we explored the properties of quasicrystals in many aspects. The first experiment (Chapter 5) focus on the long-range order in quasicrystals. We report on the first experimental realisation of a two-dimensional (2D) quasicrystalline optical lattice for ultracold atoms and conduct matter-wave diffraction experiment using shot, intense lattice pulses. We reveal the different diffraction dynamics between periodic and quasiperiodic lattices and demonstrate the capability to simulate quantum walks on four-dimensional tight-binding lattices using the diffraction dynamics of 2D quasicrystalline lattices on short timescales. The second (Chapter 6) and the third (Chapter 7) experiments concentrate on studying the disorder nature of quasicrystals. In particular, we investigate disorder-induced localisation transition in the ground state of non-interacting and weakly interacting Bose gases in a 2D quasicrystalline lattice. The second experiment is mainly performed in the non-interacting limit, in which we probe the localisation transition by employing triangular lattice pulses and studying the time scale required for adiabatic loading. We observe a localisation transition at around a critical lattice depth of Vloc ≈ 1.78 Erec for noninteracting systems. In addition, we demonstrate that weak repulsive interactions can shift transition to deeper lattices. In the third experiment, we further study the interplay between the interactions and disorder, and constitute the first experimental realisation of the 2D Bose glass, an insulating but compressible groundstate phase without long-range phase coherence. By probing the coherent properties of the system, we observe a Bose glass to superfluid transition and map out the phase diagram in the weakly interacting regime. Moreover, we reveal the non-ergodic nature of the Bose glass by probing the capability of restoring coherence. Our observations are in good agreement with recent quantum Monte Carlo predictions and pave the way for experimentally testing of the connection between the Bose glass and many-body localisation.

This thesis details the construction and operation of a new quantum simulation experiment for studying bosonic (and in the future fermionic) atoms in interesting triangular superlattice structures. We show that this machine can reliably and stably produce samples of ultracold potassium and rubidium in the lowest band of the kagome lattice. We discuss the characterisation and validation of the apparatus as well as preliminary results towards probing the flat energy band of the kagome lattice, a key experimental goal of the group. A major obstacle to faithfully implementing the kagome lattice, as well as other superlattices, is the stringent control of the optical phase of the lattice laser beams. We discuss the mechanisms which have been developed to achieve the required control and stability; and demonstrate that our machine has sufficient control to allow us to deterministically prepare and probe a range of interesting lattice types. In addition to superlattice structures, our apparatus also allows us to prepare monochromatic triangular and honeycomb optical lattices and preliminary experiments in these lattice geometries are discussed. The use of potassium in our experiment affords us the ability to tune atom interactions by means of a Feshbach resonance. We demonstrate control of tunnelling and interactions in the many-body system to observe the Mott-insulator transition in the triangular and kagome lattices. We also detail current progress towards achieving a state in thermodynamic equilibrium in the kagome flat band and demonstrate the creation of a negative absolute temperature state for potassium atoms in the triangular lattice. In the future we hope to realise a quantum gas microscope capable of single-site imaging of the individual atoms in the superlattice. We discuss progress towards this goal including the characterisation of an in-vacuum objective, as well as proposed super-resolution techniques which harness excited state light shifts to partition the lattice.

Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν = 1. We reveal the nature of the low energy spin-singlet states around ν ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- T c superconductivity.

Parity-Time ( P T $\mathcal{P}\mathcal{T}$ ) symmetry has become an important concept in the design of synthetic optical materials, with exotic functionalities such as unidirectional transport and nonreciprocal reflection. At exceptional points, this symmetry is spontaneously broken, and solutions transition from those with conserved intensity to exponential growth or decay. Here, we analyze a quantum-photonic surface formed by a single layer of atoms in an array with light mediating strong cooperative many-body interactions. We show how delocalized collective excitation eigenmodes can exhibit an effective P T $\mathcal{P}\mathcal{T}$ symmetry and nonexponential decay. This effective symmetry is achieved in a passive system without gain by balancing the scattering of a bright mode with the loss from a subradiant dark mode. These modes coalesce at exceptional points, evidenced by the emergence of coherent perfect absorption where coherent incoming light is perfectly absorbed and scattered only incoherently. We also show how P T $\mathcal{P}\mathcal{T}$ symmetry can be generated in total reflection and by balancing scattering and loss between different polarizations of collective modes.

Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a two-particle dynamics on a multi-dimensional lattice has hitherto been limited to continuous-time evolutions. To fully exploit the computational capabilities of quantum interference it is crucial to develop platforms handling multiple photons that propagate across multi-dimensional lattices. Here, we report a discrete-time quantum walk of two correlated photons in a two-dimensional lattice, synthetically engineered by manipulating a set of optical modes carrying quantized amounts of transverse momentum. Mode-couplings are introduced via the polarization-controlled diffractive action of thin geometric-phase optical elements. The entire platform is compact, efficient, scalable, and represents a versatile tool to simulate quantum evolutions on complex lattices. We expect that it will have a strong impact on diverse fields such as quantum state engineering, topological quantum photonics, and Boson Sampling., 18 pages, 11 figures

Accurately manipulating quantum states is a fundamental strategy for improving the performance of quantum metrology, computing, and simulation. However, the quantum state is susceptible to dephasing due to the temperature and density of the atomic ensembles. In this paper, we experimentally study the effect of Floquet engineering (FE) on the dephasing process in an 87Sr optical clock. By measuring the Rabi flopping process under different temperatures of the cold ensemble and numbers of atoms trapped in the lattice, our results show that the FE can suppress the dephasing due to high temperatures or a large number of atoms. Indeed, when the temperature and the number of atoms are 3.8 μK and 6300, respectively, the FE can obviously suppress the dephasing effect and improve the maximum excitation fraction of the Rabi spectrum by 15.4%.

Ultracold atoms in optical lattices are a versatile tool for precisely-controlled quantum simulation of a range of condensed matter phenomena. This thesis describes work to apply this tool in two areas: the simulation of quasicrystalline materials with a novel lattice geometry, and the use of Floquet driving to engineer behaviours qualitatively different from static systems. In particular I will present our work using periodic driving to make a continuous quantum phase transition become discontinuous, which to our knowledge has never been done before. Quasicrystals are a fascinating but still relatively under-explored class of materials existing as an intermediate between periodic and disordered systems. This makes them an ideal context for studying non-ergodic behaviour, especially with the tunable interactions allowed by ultracold atom physics. At the same time quasicrystals have an intriguing link to higher dimensions, so that a two-dimensional quasicrystal can be used to simulate systems with more than three spatial dimensions. I will describe two experiments performed by our group that use a quasicrystalline optical lattice to explore higher dimensions and non-ergodic states respectively, which we hope are a stepping stone towards future work with many-body localisation and higher-dimensional topological effects. The other part of the story is Floquet physics: the study of time-periodic Hamiltonians. Time dependence allows us to break many of the usual rules of quantum systems, adding a whole new set of control parameters and allowing qualitatively different behaviours. In this thesis I will discuss the application of Floquet driving to a periodic optical lattice and present our experimental observation of a discontinuous form of the well-known Mott insulator to superfluid quantum phase transition. While interesting in itself, we view this work too as a stepping stone towards Floquet engineering with the full optical quasicrystal.

25 pags., 14 figs., 3 apps., Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work [J. Argüello-Luengo, Nature (London) 574, 215 (2019)NATUAS0028-083610.1038/s41586-019-1614-4], ultracold fermionic atoms have been proposed for this purpose by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these results in several ways. First, we numerically benchmark the working conditions of the analog simulator and find less demanding experimental setups where chemistry-like behavior in three dimensions can still be observed. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite-size effects and provide a way to mitigate them. Finally, we benchmark the simulator characterizing the behavior of two-electron atoms (He) and molecules (HeH+) beyond the example considered in the original work., J.A.-L. acknowledges support from “la Caixa” Foundation (Grant No. 100010434) through the fellowship LCF/BQ/ES18/11670016, the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” program (Grant No. CEX2019-000910-S), Fundació Privada Cellex, Fundació Mir-Puig, and Generalitat de Catalunya through the CERCA program and QuantumCat (Grant No. 001-P-001644). T.S. acknowledges the support from NSFC Grant No. 11974363. A.G.-T. acknowledges support from the Spanish Project No. PGC2018-094792-B-100 (MCIU/AEI/FEDER, EU) and from the CSIC Research Platform on Quantum Technologies No. PTI-001.

We demonstrate that the interplay between a nonlinearity and PT symmetry in a periodic potential results in peculiar features of nonlinear periodic solutions. These include thresholdless symmetry breaking and asymmetric (multi-)loop structures of the nonlinear Bloch spectrum, persistence of unbroken PT symmetry even after the gap is closed, nonmonotonic dependence of the PT phase transition on the defocusing nonlinearity, and enhanced stability of the nonlinear states corresponding to the loop structures. The asymmetry and the loop structure of the spectrum are explained within the framework of a two-mode approximation and an effective potential theory and are validated numerically.

We report on a compact, ultrahigh-vacuum compatible optical assembly to create large-scale, two-dimensional optical lattices for use in experiments with ultracold atoms. The assembly consists of an octagon-shaped spacer made from ultra-low-expansion glass, to which we optically contact four fused-silica cavity mirrors, making it highly mechanically and thermally stable. The mirror surfaces are nearly plane-parallel which allows us to create two perpendicular cavity modes with diameters $\sim$1 mm. Such large mode diameters are desirable to increase the optical lattice homogeneity, but lead to strong angular sensitivities of the coplanarity between the two cavity modes. We demonstrate a procedure to precisely position each mirror substrate that achieves a deviation from coplanarity of $d = 1(5)$ $\mu$m. Creating large optical lattices at arbitrary visible and near infrared wavelengths requires significant power enhancements to overcome limitations in the available laser power. The cavity mirrors have a customized low-loss mirror coating that enhances the power at a set of relevant wavelengths from the visible to the near infrared by up to three orders of magnitude., Comment: 4 pages, 4 figures, 1 page supplemental material

Funder: Royal Society under the Newton International Fellowship, The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in the form of Peierls phases) that can be experimentally engineered in optical lattices, rather than the magnetic field, we find that the time required for adiabatic state preparation dramatically depends on which pattern of Peierls phases is used. This can be understood intuitively by noting that different patterns of time-dependent Peierls phases that all give rise to the same magnetic field ramp, generally lead to different artificial electric fields during the ramp. As an intriguing result, we find that an optimal choice allows for preparing the ground state almost instantaneously in the non-interacting system, which can be related to the concept of counterdiabatic driving. Remarkably, we find extremely short preparation times also in the strongly-interacting regime. Our findings open new possibilities for robust state preparation in atomic quantum simulators.

We utilize the dark state in a ∧-type three-level system to cool an ensemble of ⁸⁵Rb atoms in an optical lattice [Morigi et al., Phys. Rev. Lett. 85, 4458 (2000)]. The common suppression of the carrier transition of atoms with different vibrational frequencies allows them to reach a subrecoil temperature of 100 nK after being released from the optical lattice. A nearly zero vibrational quantum number is determined from the time-of-flight measurements and adiabatic expansion process. The features of sideband cooling are examined in various parameter spaces. Our results show that dark-state sideband cooling is a simple and compelling method for preparing a large ensemble of atoms into their vibrational ground state of a harmonic potential and can be generalized to different species of atoms and molecules for studying ultracold physics that demands recoil temperature and below. Ministry of Education (MOE) National Research Foundation (NRF) Published version This work is supported by the Singapore National Research Foundation under Grant No. NRFF2013-12 and QEP-P4, and the Singapore Ministry of Education under Grant No. MOE2017-T2-2-066.

6 pags., 4 figs., Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete two-dimensional quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, such as the discrete versions of H and H+2, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular hydrogen in two dimensions. We extend this approach to larger systems by introducing as many mediating atoms as fermions, and derive the effective repulsion law. In all cases, we analyze how the continuous limit is approached for increasing optical lattice sizes., We acknowledge support from the ERC Advanced Grant QUENOCOBA under the EU Horizon 2020 program (Grant Agreement No. 742102). J.A.-L. acknowledges support from “la Caixa” Foundation (ID 100010434) through the fellowship No. LCF/BQ/ES18/11670016, the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” program (SEV-2015-0522), Fundació Privada Cellex, Fundació Mir-Puig, and Generalitat de Catalunya through the CERCA program. A.G.-T. acknowledges support from the Spanish project No. PGC2018-094792-B-100 (MCIU/aEI/FEDER, EU) and from the CSIC Research Platform on Quantum Technologies PTI-001. T.S. acknowledges the Thousand-Youth-Talent Program of China and is supported by the NSFC No. 11974363. P.Z. acknowledges the EU Quantum Flagship PASQuanS.

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than four orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks., Comment: 6 pages, 4 figures + 6 pages supplemental material

Many-body systems are very hard to simulate due to the explosion of parameters with the system size. Quantum computers can help in this task, although one may need scalable systems, something that is out of reach in the short run. An attractive alternative is provided by analog quantum simulators which, even though they are not universal, they can still be tuned to study interesting problems. Atoms in optical lattices seem to be ideally suited for that task. Most of the proposals of such simulators have focused so far on condensed matter or high energy physics problems. In this talk I will show how one can extend the range of problems to other scenarios, especially to quantum chemistry., {"references":["Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yua, \"Quantum computational chemistry\", Reviews of Modern Physics 92, 015003 (2020), DOI:10.1103/RevModPhys.92.015003","Christian Gross and Immanuel Bloch, \"Quantum simulations with ultracold atoms in optical lattices\", Science 357, 995 (2017), DOI:10.1126/science.aal3837","Javier Argüello-Luengo, Alejandro González-Tudela, Tao Shi, Peter Zoller, and Juan Ignacio Cirac, \"Analogue quantum chemistry simulation\", Nature 574, 215 (2015), DOI:10.1038/s41586-019-1614-4"]}

Colloidal CsPbX3 (X = Br, Cl, and I) perovskite nanocrystals (NCs) have emerged as promising phosphors and solar cell materials due to their remarkable optoelectronic properties. These properties can be tailored by not only controlling the size and shape of the NCs but also postsynthetic composition tuning through topotactic anion exchange. In contrast, property control by cation exchange is still underdeveloped for colloidal CsPbX3 NCs. Here, we present a method that allows partial cation exchange in colloidal CsPbBr3 NCs, whereby Pb2+ is exchanged for several isovalent cations, resulting in doped CsPb1xMxBr3 NCs (M= Sn2+, Cd2+, and Zn2+; 0 < x ≤ 0.1), with preservation of the original NC shape. The size of the parent NCs is also preserved in the product NCs, apart from a small (few %) contraction of the unit cells upon incorporation of the guest cations. The partial Pb2+ for M2+ exchange leads to a blue-shift of the optical spectra, while maintaining the high photoluminescence quantum yields (>50%), sharp absorption features, and narrow emission of the parent CsPbBr3 NCs. The blue-shift in the optical spectra is attributed to the lattice contraction that accompanies the Pb2+ for M2+ cation exchange and is observed to scale linearly with the lattice contraction. This work opens up new possibilities to engineer the properties of halide perovskite NCs, which to date are demonstrated to be the only known system where cation and anion exchange reactions can be sequentially combined while preserving the original NC shape, resulting in compositionally diverse perovskite NCs.

The self-comparison method is a powerful tool in the uncertainty evaluation of optical lattice clocks, but any drifts will cause a frequency offset between the two compared clock loops and thus lead to incorrect measurement result. We propose a drift-insensitive self-comparison method to remove this frequency offset by adjusting the clock detection sequence. We also experimentally demonstrate the validity of this method in a one-dimensional 87Sr optical lattice clock. As the clock laser frequency drift exists, the measured frequency difference between two identical clock loops is (240 ± 34) mHz using the traditional self-comparison method, while it is (−15 ± 16) mHz using the drift-insensitive self-comparison method, indicating that this frequency offset is cancelled within current measurement precision. We further use the drift-insensitive self-comparison technique to measure the collisional shift and the second-order Zeeman shift of our clock and the results show that the fractional collisional shift and the second-order Zeeman shift are 4.54(28) × 10−16 and 5.06(3) × 10−17, respectively.

Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature. In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system. The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution. Ph. D. Ultracold atoms in optical lattices, a periodic potential generated by laser beams, offer an important tool for quantum simulations in a pristine environment. Motivated by recent optical lattice experiments with the implementation of disorder and synthetic spin-orbit coupling, we utilize Gutzwiller mean-field theory (GMFT) to study the dynamics of disordered state in an optical lattice under the sudden shift of the harmonic trap, the domain wall expansion of strongly interacting bosons in 2D lattices with disorder, and spin-orbit-driven transitions in the Bose-Hubbard model. We argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our findings show that evidence for many-body localization claimed in experiments [J.-y. Choi et al., Science 352, 1547 (2016)] must lie in the differences between GMFT and experiments. We also find that strong spin-orbit coupling alone can generate superfluids with finite momentum and staggered phase patterns.

12 pags., 5 figs., 4 apps., Quantum computers hold the promise to provide outstanding computational speed ups in chemical problems, like the determination of the electronic ground state energy of molecules. Here, we demonstrate that the same goal can be achieved with an analog quantum simulator which combines two well-established technologies, namely, ultra-cold atoms in optical lattices and cavity QED. In the proposed simulator, fermionic atoms hopping in an optical potential play the role of electrons, additional optical potentials provide the nuclear attraction, while a single spin excitation over a Mott insulator mediates the electronic Coulomb repulsion. We analyze the impact of discretization and finite size effects of the lattice, and provide the working conditions required for the precise determination of the electronic energy of simple molecules., The authors acknowledge the ERC Advanced Grant QENOCOBA under the EU Horizon 2020 program (grant agreement 742102). TS acknowledges the Thousand-Youth-Talent Program of China. PZ was supported by the ERC Synergy Grant UQUAM, and SFB FoQus by the Austrian Science Fundation.

It is shown that in the Bose-Fermi-Hubbard model which is used for a description of the ultracold atomic boson-fermion mixture in the optical lattice, the $n_\text{B}\leqslant 2$ restriction enables one to analyze a more general case of separated lobes Mott insulator in comparison with the case of $n_\text{B} \leqslant 1$ (hard-core bosons). It also showed that the restriction to no more than 2 bosons on site is enough to comprehend the structure of $(\mu, |t_0|)$ diagrams at arbitrary $n^\text{b}$ values with an account of a possibility of the 1st order phase transition., Comment: 8 pages, 5 figures

We present a technique to diagnose the condensate fraction in a one-dimensional optical lattice of weakly interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the Multi-Configuration Time Dependent Hartree method for Bosons (MCTDHB) that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt which depends directly on the amount of phase coherence between the lattice sites is linearly proportional to the condensate fraction. The atom-atom interactions only change the slope of the linear relationship. We discuss the applications of this scheme in magnetic field gradiometery., 7 pages, 5 figures

Spectroscopic characterization of lanthanum beryllate La2Be2O5 (BLO) single crystals doped with trivalent ions of Eu, Nd or Pr, was carried out in the ultraviolet-visible spectral range using synchrotron radiation spectroscopy in combination with conventional optical absorption and luminescence spectroscopy techniques. On the basis of the obtained data, the energy level diagram for these trivalent impurity ions in BLO host lattice was developed; the optical and electronic properties of the crystals were determined; the possibility of the 4f-4f, 4f-5d and charge transfer transitions was analyzed; spectroscopic properties of the lattice defects formed during the introduction of trivalent impurity ions in the BLO host lattice, were investigated. We found that the lattice defects are responsible for a wide-band photoluminescence (PL) in the energy region of 400–600 nm. The most efficient excitation of the defect photoluminescence in the energy gap of BLO occurs in broad PL excitation-bands at 270 and 240 nm. The PL intensity of defects depends on the type of impurity ion and increases in the sequence: Pr-Nd-Er. © 2016, Pleiades Publishing, Ltd.

The purpose of this paper is to review a interessan method for the generation of nonlinear optical pulses solutions and present an analytical proof of this method, not yet existing in the literature. We explore a new class of solutions of Nonlinear Schrodinger-like Equation (NLS) that represent profiles of optical beams propagating in waveguides. This solutions have several application properties such as prapagation without dispersion and almost no loss energy. This class of solutions that we explore are characterized by parity-time ( PT ) symmetric potentials. This approach is based on non-Hermitian Hamiltonians that can exhibit entirely real spectra provided they respect paritytime ( PT ) symmetrie. These solutions establish a deep relationship between the nonlinear electrodynamics and quantum mechanics. We analyzed the potential applications of such solutions in design to the optical fiber sensors, optical networks and crystals which can act as natural selectors optical band. This paper is divided as follows: in Section 1 we present the basis of our research and highlight the technological applications of the method revised in this paper on the recognition, selection and processing of optical signals that the method model. Section 2 provides a brief description of nonlinear Schrodinger equation (NLS) governing the dynamics of nonlinear optical pulses. Section 3 presents the concept of non-Hermitian optical systems and the concept of PT symmetry at which such systems are based and discuss some of these optical systems applications. In Section 4 we present a review of new class of non-Hermitian solutions to a non-linear optical beam and a review of method for generating new non-Hermitian systems from existing ones and also discuss some original applications of the method reviewed here. Section 5 presents the conclusions and comments, section 6 references and the appendix section presents a rigorous proof of the method, that has not been done in the literature.

We discuss the most prominent and intensively studied S = 1 pseudospin formalism for the extended bosonic Hubbard model (EBHM) with the on-site Hilbert space truncated to the three lowest occupation states n = 0, 1, 2. The EBHM Hamiltonian is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. The generalized non-Heisenberg effective pseudospin Hamiltonian does provide a deep link with a boson system and a physically clear description of “the myriad of phases,” from uniform Mott insulating phases and density waves to two types of superfluids and supersolids. We argue that the 2D pseudospin system is prone to a topological phase separation and focus on several types of unconventional skyrmion-like topological structures in 2D boson systems, which have not been analyzed until now. The structures are characterized by a complicated interplay of insulating and two superfluid phases with a single- boson and two-boson condensation, respectively. © 2015, Pleiades Publishing, Inc.

International audience; Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly-correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi-Hubbard model with ultracold atoms. After introducing the Fermi-Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-Tc superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.; Les gaz atomiques ultrafroids offrent un excellente flateforme pour réaliser des simulateurs quantiques etétudieretétudier une grande diversité de modèles introduits initialement en physique de lamatì ere condensée ou d'autres domaines. L'une des applications les plus prometteuses de la simulation quantique est l'´ etude des gaz de Fermi fortement corrélés, pour lesquels des résultats théoriques exacts ne sont pas toujours disponibles. Nous présentons ici une revue des progrès réalisés récemment sur la simulation quantique de l'emblématique modèle de Fermi-Hubbard avec des atomes ultrafroids. Après avoir présenté le modèle de Fermi-Hubbard dans le contexte de lamatì ere condensée, sa réalisation avec des atomes ultrafroids et son diagramme de phase, nous présentons les réalisations expérimentales les plus marquantes, de l'observation initiale de l'apparition de la dégénérescence quantique et de la superfluidité fermioniquesàfermioniques`fermioniquesà la mise enévidenceenévidence du régime de l'isolant de Mott et de l'´ emergence d'un ordre anti-ferromagnétiquè a longue portée. Nous concluons par une discussion des défis futurs, dont la possibilité d'observer la supraconductivité supraconductivité`supraconductivitéà haute température, les propriétés de transport et la compétition de fortes corrélations et du désordre ou de la topologie. Pour citer cet article : L. Tarruell and L. Sanchez-Palencia, C. R. Physique X (2018).

We introduce an efficient iterative method to prepare a target state in Hilbert spaces with high dimensionality using a combination of unitary evolution, measurements, and quantum Zeno dynamics. The latter confines the evolution within Zeno subspaces of decreasing size. This gives an exponential speedup relative to the case of states evolving in the full Hilbert space between projective measurements. We demonstrate our approach on the control problem of rapidly transferring a superfluid into the Mott insulator in the Bose-Hubbard model. We discuss the general applicability of the method by preparing arbitrary superpositions with random Hamiltonians.

Highly crystalline copper nitride (Cu3N) thin films have been deposited on glass substrates at room temperature by a novel and commercially viable growth technique, known as modified activated reactive evaporation (MARE). The effects of change in radio frequency (RF) power and deposition pressure on the structural and optical properties of the films have been investigated. RF power plays a significant role for the preferential growth of these films along a particular plane whereas the deposition pressure has comparatively lesser impact on the same. However, the lattice parameter, film thickness and optical band gap are found to be strongly dependent on the deposition pressure. The MARE grown Cu3N films undergo complete decomposition into metallic Cu upon vacuum annealing at 400 �C which makes them promising candidates to be used in write once optical recording media. � 2014 Elsevier B.V. All rights reserved.

Cataloged from PDF version of article. The preparation conditions for Co doping process into the ZnO structure were studied by the ultrasonic spray pyrolysis technique. Structural and optical properties of the Co:ZnO thin films as a function of Co concentrations were examined. It was observed that hexagonal wurtzite structure of ZnO is dominant up to the critical value, and after the value, the cubic structural phase of the cobalt oxide appears in the X-ray diffraction patterns. Every band-edge of Co:ZnO films shifts to the lower energies and all are confirmed with the PL measurements. Co substitution in ZnO lattice has been proved by the optical transmittance measurement which is observed as the loss of transmission appearing in specific region due to Co2+ characteristic transitions. © 2014 Elsevier B.V. All rights reserved.

Due to the fact that it is possible to manipulate light with photonic crystals (PCs), PCs hold a great potential for designing new optical devices. There has been an increase in research on tuning the optical properties of PCs to design devices. We presented a numerical study of optical properties of metamaterial-based devices by liquid crystal infiltration. The plane wave expansion method and finite-difference time-domain method for both TE and TM modes revealed optical properties in photonic crystal structures in an air background for a square lattice. E7 type has been used as a nematic liquid crystal and SrTiO3as a ferroelectric material. We showed the possibility of the metamaterials for a two-dimensional photonic crystal cavity on a ferroelectric base infiltrated with a nematic liquid crystal. © 2014, Springer-Verlag Berlin Heidelberg.

We classify symmetry-protected and symmetry-breaking dynamical solutions for nonlinear saturable bosonic systems that display a non-hermitian charge-conjugation symmetry, as realized in a series of recent groundbreaking experiments with lasers and exciton polaritons. In particular, we show that these systems support stable symmetry-protected modes that mirror the concept of zero-modes in topological quantum systems, as well as symmetry-protected power-oscillations with no counterpart in the linear case. In analogy to topological phases in linear systems, the number and nature of symmetry-protected solutions can change. The spectral degeneracies signalling phase transitions in linear counterparts extend to bifurcations in the nonlinear context. As bifurcations relate to qualitative changes in the linear stability against changes of the initial conditions, the symmetry-protected solutions and phase transitions can also be characterized by topological excitations, which set them apart from symmetry-breaking solutions. The stipulated symmetry appears naturally when one introduces nonlinear gain or loss into spectrally symmetric bosonic systems, as we illustrate for one-dimensional topological laser arrays with saturable gain and two-dimensional flat-band polariton condensates with density-dependent loss.

We show how angular momentum conservation can stabilize a symmetry-protected quasitopological phase of matter supporting Majorana quasiparticles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong interorbital interactions - have been experimentally realized over the last two years.

The competition between the length scales associated with the periodicity of a lattice potential and the cyclotron radius of a uniform magnetic field is known to have dramatic effects on the single-particle properties of a quantum particle, e.g., the fractal spectrum is known as the Hofstadter butterfly. Having this intricate competition in mind, we consider a two-component Fermi gas on a square optical lattice with opposite synthetic magnetic fields for the components, and study its effects on the many-body BCS-pairing phenomenon. By a careful addressing of the distinct superfluid transitions from the semi-metal, quantum spin-Hall insulator or normal phases, we explore the low-temperature phase diagrams of the model, displaying lobe structures that are reminiscent of the well-known Mott-insulator transitions of the Bose-Hubbard model., Comment: 5 pages with 4 figures in the Main text, and 3 additional figures Online. To appear in Phys. Rev. Lett

We study the dynamics of an interacting classical gas trapped in a double-well potential at finite temperature. Two model potentials are considered: a cubic box with a square barrier in the middle, and a harmonic trap with a gaussian barrier along one direction. The study is performed using the Boltzmann equation, solved numerically via the test-particle method. We introduce and discuss a simple analytical model that allows to provide estimates of the relaxation time, which are compared with numerical results. Finally, we use our findings to make numerical and analytical predictions for the case of a fermionic mixture in the normal-fluid phase in a realistic double-well potential relevant for experiments with cold atoms., 15 pages, 9 figures

International audience; Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson-boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks-Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [33]). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real-and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.

We investigate the magnetic shell structure of repulsively interacting two-component Fermi gases trapped in a two-dimensional harmonic potential and loaded on the optical Lieb lattices. We employ the real-space dynamical mean-field theory (R-DMFT) to explicitly consider the trap potential in a self-consistent way. Computing the profiles of particle density and local magnetization across the lattice sites in the trap, we find that the incompressible core with ferrimagnetic ordering appears with the density plateau at the trap center, which is surrounded by the shell of the normal metallic phase. We examine the incompressibility of the core by adding more particles and creating the higher spin-population imbalance. While the core area expands from the outer shell with added particles and increased polarization, the excess particles are prohibited from going inside the core, and thus the density plateau is unchanged at the half-filling with the same magnetic ordering. In addition, we find that the feature of the phase separation differs with the sublattices, where the interstitial sites causing the flat band dispersion shows the signature of the abrupt transition in the density and magnetization at the boundary between the core and surrounding shells.

We investigate several dynamical regimes characterizing a bosonic binary mixture loaded in a ring trimer, with particular reference to the persistence of demixing. The degree of phase separation is evaluated by means of the "Entropy of mixing", an indicator borrowed from Statistical Thermodynamics. Three classes of demixed stationary configurations are identified and their energetic and linear stability carefully analyzed. An extended set of trajectories originating in the vicinity of fixed points are explicitly simulated and chaos is shown to arise according to three different mechanisms. In many dynamical regimes, we show that chaos is not able to disrupt the order imposed by phase separation, i.e. boson populations, despite evolving in a chaotic fashion, do not mix. This circumstance can be explained either with energetic considerations or in terms of dynamical restrictions., 21 pages, 9 figures

We report the experimental study of a harmonic oscillator in the relativistic regime. The oscillator is composed of Bose-condensed lithium atoms in the third band of an optical lattice, which have an energy-momentum relation nearly identical to that of a massive relativistic particle, with an effective mass reduced below the bare value and a greatly reduced effective speed of light. Imaging the shape of oscillator trajectories at velocities up to 98% of the effective speed of light reveals a crossover from sinusoidal to nearly photon-like propagation. The existence of a maximum velocity causes the measured period of oscillations to increase with energy; our measurements reveal beyond-leading-order contributions to this relativistic anharmonicity. We observe an intrinsic relativistic dephasing of oscillator ensembles, and a monopole oscillation with exactly the opposite phase of that predicted for non-relativistic harmonic motion. All observed dynamics are in quantitative agreement with longstanding but hitherto-untested relativistic predictions., 10 pages; 4 figures

Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to an harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For sufficiently large disorder correlation length the enhancement in the inverse compressibility diminishes., 11 pages, 6 figures, submitted

We report on the fabrication of optical lattice-like waveguide structures in an Nd:YAP laser crystal by using direct femtosecond laser writing. With periodically arrayed laser-induced tracks, the waveguiding cores can be located in either the regions between the neighbored tracks or the central zone surrounded by a number of tracks as outer cladding. The polarization of the femtosecond laser pulses for the inscription has been found to play a critical role in the anisotropic guiding behaviors of the structures. The confocal photoluminescence investigations reveal different stress-induced modifications of the structures inscribed by different polarization of the femtosecond laser beam, which are considered to be responsible for the refractive index changes of the structures. Under optical pump at 808 nm, efficient waveguide lasing at ∼1 μm wavelength has been realized from the optical lattice-like structure, which exhibits potential applications as novel miniature light sources., National Natural Science Foundation of China (NSFC) (11274203); Ministerio de Economia y Competitividad (MINECO) (FIS2013-44174-P, MAT2010-21270-C04-01).

We investigate the behavior of identical dipolar fermions with aligned dipole moments in two-dimensional multilayers at zero temperature. We consider density instabilities that are driven by the attractive part of the dipolar interaction and, for the case of bilayers, we elucidate the properties of the stripe phase recently predicted to exist in this interaction regime. When the number of layers is increased, we find that this "attractive" stripe phase exists for an increasingly larger range of dipole angles, and if the interlayer distance is sufficiently small, the stripe phase eventually spans the full range of angles, including the situation where the dipole moments are aligned perpendicular to the planes. In the limit of an infinite number of layers, we derive an analytic expression for the interlayer effects in the density-density response function and, using this result, we find that the stripe phase is replaced by a collapse of the dipolar system., Comment: 9 pages, 8 figures

Over the past several decades, rapid progress has been made toward the accurate characterization and control of atoms, made possible largely by the development of narrow-linewidth lasers and techniques for trapping and cooling at ultracold temperatures. Extending this progress to molecules will have exciting implications for chemistry, condensed matter physics, and precision tests of physics beyond the Standard Model. These possibilities are all consequences of the richness of molecular structure, which is governed by physics substantially different from that characterizing atomic structure. This same richness of structure, however, increases the complexity of any molecular experiment manyfold over its atomic counterpart, magnifying the difficulty of everything from trapping and cooling to the comparison of theory with experiment. This thesis describes work performed over the past six years to establish the state of the art in manipulation and quantum control of ultracold molecules. Our molecules are produced via photoassociation of ultracold strontium atoms followed by spontaneous decay to a stable ground state. We describe a thorough set of measurements characterizing the rovibrational structure of very weakly bound (and therefore very large) ⁸⁸Sr₂ molecules from several different perspectives, including determinations of binding energies; linear, quadratic, and higher order Zeeman shifts; transition strengths between bound states; and lifetimes of narrow subradiant states. The physical intuition gained in these experiments applies generally to weakly bound diatomic molecules, and suggests extensive applications in precision measurement and metrology. In addition, we present a detailed analysis of the thermally broadened spectroscopic lineshape of molecules in a non-magic optical lattice trap, showing how such lineshapes can be used to directly determine the temperature of atoms or molecules in situ, addressing a long-standing problem in ultracold physics. Finally, we discuss the measurement of photofragment angular distributions produced by photodissociation, leading to an exploration of quantum-state-resolved ultracold chemistry.

Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.

Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of [T. Keilmann et al., Nature Commun. 2, 361 (2011)], allowing as well for an exact realization of the two-body hard-core constraint, and for controllable effective interactions without the need of Feshbach resonances. We show that the combination of anyonic statistics and two-body hard-core constraint leads to a rich ground state physics, including Mott insulators with attractive interactions, pair superfluids, dimer phases, and multicritical points. Moreover, the anyonic statistics results in a novel two-component superfluid of holon and doublon dimers, characterized by a large but finite compressibility and a multipeaked momentum distribution, which may be easily revealed experimentally., Comment: 5 pages, 4 figures

Recent advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically nontrivial energy spectra. Self-similar fractal energy structures generally known as Hofstadter butterflies depend sensitively on the geometry of the underlying lattice, as well as the applied magnetic field. The recent demonstration of an adjustable lattice geometry [L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature (London) 483, 302 (2012)NATUAS0028-083610.1038/nature10871] presents a unique opportunity to study this dependence. In this paper, we calculate the Hofstadter butterflies that can be obtained in such an adjustable lattice and find three qualitatively different regimes. We show that the existence of Dirac points at zero magnetic field does not imply the topological equivalence of spectra at finite field. As the real-space structure evolves from the checkerboard lattice to the honeycomb lattice, two square-lattice Hofstadter butterflies merge to form a honeycomb lattice butterfly. This merging is topologically nontrivial, as it is accomplished by sequential closings of gaps. Ensuing Chern number transfer between the bands can be probed with the adjustable lattice experiments. We also calculate the Chern numbers of the gaps for qualitatively different spectra and discuss the evolution of topological properties with underlying lattice geometry.

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices. Fil: Jezek, Dora Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Cataldo, Horacio Maximo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We uncover that the breaking point of the PT-symmetry in optical waveguide arrays has a dramatic impact on light localization induced by the off-diagonal disorder. Specifically, when the gain/loss control parameter approaches a critical value at which PT-symmetry breaking occurs, a fast growth of the coupling between neighboring waveguides causes diffraction to dominate to an extent that light localization is strongly suppressed and statistically averaged width of the output pattern substantially increases. Beyond the symmetry-breaking point localization is gradually restored, although in this regime the power of localized modes grows upon propagation. The strength of localization monotonically increases with disorder at both, broken and unbroken PT-symmetry., Comment: 14 pages, 6 figures, to appear in Laser and Photonics Reviews

We study multiple period states of a two-component unpolarized superfluid Fermi gas in an optical lattice along the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. The existence of states whose period is a multiple of the lattice spacing is a direct consequence of the non-linear behavior of the gas, which is due to the presence of the order parameter associated with superfluidity. By solving Bogoliubov-de Gennes equations for a superfluid flow with finite quasimomentum, we find that, in the BCS side of the crossover, the multiple period states can be energetically favorable compared to the normal Bloch states and their survival time against dynamical instability drastically increases, suggesting that these states can be accessible in current experiments, in sharp contrast to the situation in BECs., Comment: 16 pages, 9 figures; to appear in New J. Phys

We have observed the phenomenon of stochastic resonance on the Brillouin propagation modes of a dissipative optical lattice. Such a mode has been excited by applying a moving potential modulation with phase velocity equal to the velocity of the mode. Its amplitude has been characterized by the center-of-mass (CM) velocity of the atomic cloud. At Brillouin resonance, we studied the CM-velocity as a function of the optical pumping rate at a given depth of the potential wells. We have observed a resonant dependence of the CM velocity on the optical pumping rate, corresponding to the noise strength. This corresponds to the experimental observation of stochastic resonance in a periodic potential in the low-damping regime.

Light propagation in optical lattices of driven cold atoms exhibits non-Hermitian degeneracies when the first-order modulation amplitudes of real and imaginary parts of the probe susceptibility are manipulated to be balanced. At these degeneracies, one may observe complete unidirectional reflectionless light propagation. This strictly occurs with no gain and can be easily tuned and fully reversed as supported by the transfer-matrix calculations and explained via a coupled-mode analysis.

We studied the superfluid-to-Mott-insulator transition for bosonic hard spheres loaded in asymmetric three-dimensional optical lattices by means of diffusion Monte Carlo calculations. The onset of the transition was monitored through the change in the chemical potential around the density corresponding to one particle per potential well. With this method, we were able to reproduce the results given in the literature for three-dimensional symmetric lattices and for systems whose asymmetry makes them equivalent to a set of quasi-one-dimensional tubes. The location of the same transition for asymmetric systems akin to a stack of quasi-two-dimensional lattices will be also given. Our results were checked against those given by a Bose-Hubbard model for similar arrangements., Universidad Pablo de Olavide. Departamento de Sistemas Físicos, Químicos y Naturales, Versión del editor