We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase—an interaction-driven topological insulator—using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest- and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches, which are affected in different ways. The upper branch experiences a modulational instability, which is stabilized by a long-wave–short-wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg–de Vries equation or by the Gardner equation, depending on the value of the parameters of the system.

We introduce a semiclassical-wave-function (SCWF) model for strong-field physics and attosecond science. When applied to high-harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation, and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B 43, 122001 (2010)]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories.

We show that an image, embedded into a speckle pattern, is robust against distortions during its transmission through obstacles. The robustness depends on the coherence length of the speckles and obstruction size. This behavior is based on the self-reconfiguration effect, where, even though some speckles have been blocked by an opaque obstacle, the speckle-pattern intensity is reestablished during propagation at the point where the signature of the obstacle disappears. We evaluated the self-reconfiguration ability of the image using the concepts of visibility and similarity.

This paper introduces a quasiequilibrium one-dimensional Bose-Einstein condensation of photons trapped in a microtube. Light modes with a cutoff frequency (a photon's “mass”) interact through different processes of absorption, emission, and scattering on molecules and atoms. In this paper we study the conditions for the one-dimensional condensation of light and the role of photon-photon interactions in the system. The technique in use is the Matsubara Green's functions formalism modified for the quasiequilibrium system under study.

We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantum systems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantum systems for potential applications in quantum architectures.

We demonstrate a solid-state spin-wave optical memory based on stopped light in a spectral hole. A long-lived narrow spectral hole is created by optical pumping in the inhomogeneous absorption profile of a ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. Optical pulses sent through the spectral hole experience a strong reduction of their group velocity and are spatially compressed in the crystal. A short Raman pulse transfers the optical excitation to the spin state before the light pulse exits the crystal, effectively stopping the light. After a controllable delay, a second Raman pulse is sent, which leads to the emission of the stored photons. We reach storage and retrieval efficiencies for bright pulses of up to $39\%$ in a 5-mm-long crystal. We also show that our device works at the single-photon level by storing and retrieving $3-\mu \mathrm{s}$-long weak coherent pulses with efficiencies up to $31\%$, demonstrating the most efficient spin-wave solid-state optical memory at the single-photon level so far. We reach an unconditional noise level of $(9\pm 1)\times {10}^{-3}$ photons per pulse in a detection window of $4\mu \mathrm{s}$, leading to a signal-to-noise ratio of $33\pm 4$ for an average input photon number of 1, making our device promising for long-lived storage of nonclassical light.

This paper studies a particle subjected to an infinite potential well in the circumstance of a fractional dimensional Lévy path. To obtain analytic expression for the wave functions and energy levels, we introduce the fractional corresponding operator and a generalized de Moivre's theorem. Phase transitions of the energy and wave functions are found when the Lévy path dimension changes from integer to noninteger in nature. More importantly, we demonstrate the existence of stable bound states in the continuum in a simple potential. The results predict a phenomenon in which all bound states energy levels of the particle are continuous and the particle remains in bound states. This phenomenon can be demonstrated that this is a characteristic phenomenon of a fractional system. This phenomenon provides both an a priori criterion for theoretically describing an unknown quantum system with fractional derivatives and a sufficient condition for verifying the preparation of a fractional quantum system in experiment. Finally, we compare our results for fractional quantum systems with the existing results and explain the cause of the reported phenomenon.

We investigate $k$-nonseparability of $n$-partite quantum states which is an important kind of correlations characterizing multipartite entanglement. We derive some $k$-nonseparability criteria in the form of variance and quantum Fisher information, and illustrate their complementary features in the detection of $k$-nonseparability through several examples.

By driving a Bose-Einstein condensate trapped in a single-mode high-$Q$ optical resonator and coupled to a classical transverse running-wave field above a Dicke-like superradiant phase transition, the resulting cavity field-induced spin-orbit coupling leads to a band structure with doubly degenerate ground states. We show theoretically that the effective bosonic mode defined by interstate hopping can be entangled with the cavity field via the combined effect of spin-orbit coupling and dissipation.

Assessing the role of interference in natural and artificial quantum dynamical processes is a crucial task in quantum information theory. To this aim, an appropriate formalism is provided by the decoherent histories framework. While this approach has been deeply explored from different theoretical perspectives, it still lacks of a comprehensive set of tools able to concisely quantify the amount of coherence developed by a given dynamics. In this paper, we introduce and test different measures of the (average) coherence present in dissipative (Markovian) quantum evolutions, at various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we apply them to a paradigmatic quantum process where the role of coherence is being hotly debated: exciton transport in photosynthetic complexes. To spot out the essential features that may determine the performance of the transport, we focus on a relevant trimeric subunit of the Fenna-Matthews-Olson complex and we use a simplified (Haken-Strobl) model for the system-bath interaction. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to a quantum recoil avoiding effect on the exciton dynamics, that preserves and sustains the benefits of the initial fast quantum delocalization of the exciton over the network. Indeed, for intermediate levels of decoherence, the bath is seen to selectively kill the negative interference between different exciton pathways, while retaining the initial positive one. The concepts and tools here developed show how the decoherent histories approach can be used to quantify the relation between coherence and efficiency in quantum dynamical processes.

We present a $B$-spline $K$-matrix method for three-active-electron atoms in the presence of a polarizable core, with which it is possible to compute multichannel single-ionization scattering states with good accuracy. We illustrate the capabilities of the method by computing the parameters of several autoionizing states of the boron atom, with ${}^{2}S^e$, ${}^{2}P^{e,o}$, and ${}^{2}D^e$ symmetry, up to at least the $2p^2\left({}^{1}S\right)$ excitation threshold of the B ii parent ion, as well as selected portions of the photoionization cross section from the ground state. Our results exhibit remarkable gauge consistency, they significantly extend the existing sparse record of data for the boron atom, and they are in good agreement with the few experimental and theoretical data available in the literature. These results open the way to extend to three-active-electron systems the spectral analysis of correlated wave packets in terms of accurate scattering states that has already been demonstrated for two-electron atoms in Argenti and Lindroth [Phys. Rev. Lett. 105, 053002 (2010)].

The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s$ ${}^2{S}_{1/2}$, $7p$ ${}^2{P}_{1/2,3/2}$, and $8s$ ${}^2{S}_{1/2}$ levels of the $7s$ ${}^2{S}_{1/2}-7p$ ${}^2{P}_{1/2,3/2}$ and $7s$ ${}^2{S}_{1/2}-8s$ ${}^2{S}_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600–700 nm and 700–1000 nm regions, which are blue and red detuned with the $7s-7p$ and $7s-8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground $7s$ ${}^2{S}_{1/2}$ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.

We provide a numerical method to calculate comprehensively the microwave and the laser spectra of ultracold bosonic atoms in optical lattices at finite temperatures. Our formulation is built up with the sum rules, up to the second order, derived from the general principle of spectroscopy. The sum rule approach allows us to discuss the physical origins of a spectral peak shift and also a peak broadening. We find that a spectral broadening of superfluid atoms can be determined from number fluctuations of atoms, while that of normal-state atoms is mainly attributed to quantum fluctuations resulting from hopping of atoms. To calculate spectra at finite temperatures, based on the sum rule approach, we provide a two-mode approximation assuming that spectra of the superfluid and normal state atoms can be calculated separately. Our method can properly deal with multipeak structures of spectra resulting from thermal fluctuations and also coexisting of the superfluid and the normal states. By combining the two-mode approximation with a finite temperature Gutzwiller approximation, we calculate spectra at finite temperatures by considering realistic systems, and the calculated spectra show nice agreements with those in experiments.

We investigate ultracold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.

We study the nonlinear quantum Rabi model—both in the two-photon and the intensity-dependent coupling scheme—by utilizing the perturbation method in the off- and near-resonance regimes characterized by the field and the atomic transition frequencies. We consider the weak-coupling condition, the perturbation parameter being the ratio between the coupling constant and the atomic frequency. For both models we determine the first- and second-order corrections to energy eigenvalues and eigenstates, disclosing the doublet structure characterizing the energy spectrum. Then we apply our findings to both the coupling schemes in order to calculate the time evolution of a general initial state and the atomic population inversion for an initial state composed by a mixture of excited and unexcited atoms.