A theory of coherent transients is developed in which a sequence of optical pulses is incident on a sample of trapped atoms and gives rise to phase-matched emission from the sample. The trapping potential for the atoms can be state dependent, necessitating a quantum treatment of the center-of-mass motion. A source-field approach is followed, modified to account for the quantized motion of the atoms. The theory is illustrated with two examples, one involving the creation of ground-Rydberg level coherence in an optical lattice and the second Raman coherence between two ground-state sublevels of atoms in a dipole trap. For state-independent potentials, a comparison is made with a theory in which the center-of-mass motion is treated classically.

We propose a mechanism to realize nontrivial spin dynamics in a one-dimensional spin-orbit-coupled Bose-Einstein condensate by abruptly shaking the harmonic trap. Continuously varying the shaking strength, it is found that the Bose-Einstein condensate may exhibit exotic nonequilibrium spin dynamics. Specifically, at some special values of the shaking strength, the time-averaged spin polarization shows sharp resonant peaks, whereas it tends to be zero at any other positions. Furthermore, the spacings between any two nearest peaks depend only on the system parameters and are thus identical to each other. By simplifying this time-dependent system to an exactly solvable “quantum quench” model, we show that the essential physics behind the exotic spin dynamics comes from periodic suppressing and enhancing of the out-of-phase interference. It is further shown that the presented physical picture persists under weak atomic interactions. This work may shed light on the ongoing research of spin-based quantum control and quantum information.

We investigate the effects of an extended Bose-Hubbard model with a long-range hopping term on the Mott insulator-superfluid quantum phase transition. We consider the effects of a power-law decaying hopping term, and we show that the Mott phase is shrunk in the parameters' space. We provide an exact solution for one-dimensional lattices and also two reliable approximations for higher dimensions. Finally, we extend these results to a more realistic situation in which long-range hopping is made by a combination of power-law and screening terms, studying the main effects on the Mott lobes.

The light scattered by cold atoms induces mutual optical forces between them, which can lead to bound states. In addition to the trapping potential, this light-induced interaction generates a velocity-dependent force which damps or amplifies the stretching vibrational mode of the two-atom “molecule.” This velocity-dependent force acts on time scales much longer than the mode period or the dipole dynamics, determining the true stability of the bound state. We show that, for two atoms, the stochastic heating due to spontaneous emission always exceeds the bounding effect, so pairs of cold atoms cannot be truly stable without an extra cooling mechanism.

The different mechanisms that bring about the creation of optical nonlinear waves in a waveguide containing a graphene monolayer (or graphene-like two-dimensional material) are studied in the general case when resonant and nonresonant nonlinearities are simultaneously included. The conditions for the formation of optical hybrid, nonresonant, and resonant phase-modulated breathers in graphene, for waveguide transverse electric modes, are presented. It is shown that the characteristic parameters of these optical nonlinear waves depends on the graphene Kerr-type third-order susceptibility, the graphene conductivity, the reciprocal of Beer's absorption length, and the initial values of the ensemble of the atomic system and/or the semiconductor quantum dots that are embedded in the transition layer. In the case of the amplifier (active atomic system) transition layer, the conditions for the existence of a dark (topological) breather and the conditions when a nonlinear wave cannot be formed are determined. An explicit analytical expression for the profile of an optical nonlinear wave is also presented.

Topological phases of matter have attracted much attention over the years. Motivated by analogy with photonic lattices, here we examine the edge states of a one-dimensional trimer lattice in the phases with and without inversion symmetry protection. In contrast to the Su-Schrieffer-Heeger model, we show that the edge states in the inversion-symmetry broken phase of the trimer model turn out to be chiral, i.e., instead of appearing in pairs localized at opposite edges they can appear at a single edge. Interestingly, these chiral edge states remain robust to large amounts of disorder. In addition, we use the Zak phase to characterize the emergence of degenerate edge states in the inversion-symmetric phase of the trimer model. Furthermore, we capture the essentials of the whole family of trimers through a mapping onto the commensurate off-diagonal Aubry-André-Harper model, which allows us to establish a direct connection between chiral edge modes in the two models, including the calculation of Chern numbers. We thus suggest that the chiral edge modes of the trimer lattice have a topological origin inherited from this effective mapping. Also, we find a nontrivial connection between the topological phase transition point in the trimer lattice and the one in its associated two-dimensional parent system, in agreement with results in the context of Thouless pumping in photonic lattices.

We introduce the concept of multichannel dynamically modulated perfect absorbers (DMPAs), which are periodically modulated lossy interferometric traps that completely absorb incident monochromatic waves. The proposed DMPA protocols utilize a Floquet engineering approach which produces a variety of emerging phenomena and features: reconfigurability of perfect absorption (PA) for a broad range of frequencies of the incident wave; PA for infinitesimal local losses, and PA via critical coupling with high-$Q$ modes by inducing back-reflection dynamical mirrors.

We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show that the connectivity discriminates between the diffusive and the Anderson localized regimes. For practical measurements, the connectivity is encoded in the second-order coherence function characterizing the intensity emitted by two incoherent classical or quantum dipole sources. The analysis applies to all processes in which spatially localized modes build up, and to all kinds of waves.

We propose an approach to achieve achromatic pure geometric phase shaping of light from anisotropic media by exploiting the fundamental laws of electromagnetic waves. Its practical implementation requires a cover layer made of a dispersive isotropic medium. The approach applies to any anisotropic material and any geometric phase spatial distribution and preserves the geometric phase reversal upon the reversal of the incident polarization handedness. An experimental demonstration is made over the whole visible range but can be extended to any wavelength range without conceptual issues.

In this paper, we designed Maxwell's fish-eye lens in a square shape from a conformal mapping and constructed it into a waveguide and a photonic crystal. We studied the unidirectional self-imaging effect from both geometric optics and wave optics. Ray tracing and full-wave simulations were performed to validate this effect. Specifically, the designed waveguide is of a finite width while having the same imaging properties as the ideal infinite waveguide—the Mikaelian lens, the refractive index profile of which is 1/cosh ($x$) [Mikaelian and Prokhorov, Prog. Opt. 17, 279 (1980)].

We construct a general theoretical model for analyzing the intensity correlation of the field formed by mixing two independent multi-temporal-mode thermal fields. In the model, we use the intensity correlation function $g^{\left(2\right)}$ to characterize the mode property of the mixed thermal field. We find that $g^{\left(2\right)}$ of the mixed field is always less than that of the individual thermal field with less average mode number unless the two thermal fields are identical in mode property. The amount of drop in $g^{\left(2\right)}$ of the interference field depends on the relative overlap between the mode structures of two thermal fields and their relative strength. We successfully derive the analytical expressions of the upper bound and lower limit for $g^{\left(2\right)}$ of the interference field. Moreover, we verify the theoretical analysis by performing a series of experiments when the mode structures of two independent thermal fields are identical, orthogonal, and partially overlapped, respectively. The experimental results agree with theoretical predictions. Our investigation is useful for analyzing the signals carried by the intensity correlation of thermal fields.

Irradiation of a medium by short intense pulses from x-ray (XUV) free-electron lasers can result in saturated photoionization of inner electronic shells. As a result an inversion of populations between core levels appears. The resulting fluorescent radiation can be amplified during its propagation through the inverted medium and results in intense, quasi-transform-limited radiation bursts. While the optical counterpart of this phenomena, known as superfluorescence, was intensively investigated, a generalized treatment is needed in the x-ray (XUV) domain, where the dynamics of pumping and evolution due to fast decay processes play a crucial role. To provide a general theoretical approach, we start from the fundamental, quantized minimal coupling Hamiltonian of light-matter interaction and after a series of approximations arrive at a closed system of equations for the two-point correlation function of atomic coherences and the two-time correlation function of the emitted field. The obtained formalism enables us to investigate collective spontaneous emission in various regimes. It is extended consistently to include incoherent processes that are relevant in the x-ray (XUV) domain. These processes are introduced into the formalism by corresponding Lindblad superoperators. The connection to other approaches is discussed and numerical examples related to recent experiments are presented.

Artificial atoms coupled to surface acoustic waves (SAWs) have played a crucial role in the recent development of circuit quantum acoustodynamics. In this paper, we have investigated the interaction of an artificial atom and SAWs beyond the weak-coupling regime, focusing on the role of the interdigital transducer (IDT) that enables the coupling. We find a parameter regime in which the IDT acts as a cavity for the atom, rather than an antenna. In other words, the atom forms its own cavity. Similar to an atom coupled to an explicit cavity, this regime is characterized by vacuum-Rabi splitting, as the atom hybridizes with the phononic vacuum inside the IDT. This hybridization is possible because of the interdigitated coupling, which has a large spatial extension, and the slow propagation speed of SAWs. We work out a criterion for entering this regime from a model based on standard circuit-quantization techniques, taking only material parameters as inputs. Most notably, we find this regime hard to avoid for an atom on top of a strong piezoelectric material, such as lithium niobate (${\mathrm{LiNbO}}_3$). The SAW-coupled atom on top of ${\mathrm{LiNbO}}_3$ can thus be regarded as an atom-cavity-bath system. On weaker piezoelectric materials, the number of IDT electrodes needs to be large in order to reach this regime.

We have theoretically constructed light fields that can generate optical potentials representing rectangular arrays of dark optical traps on the surface of a torus. The arrays are not diffraction limited, and their period can in principle be deeply subwavelength. We discuss the challenges anticipated in realizing such potentials, which will be of great interest for quantum simulations.

To characterize the statistics and indistinguishability of a source, it is common to measure the correlation functions of the emitted field using various interferometers. Here, we present a theoretical framework for the computation of the correlation functions of a two-level system that is resonantly driven by a realistic noisy cw excitation laser. Analytic expressions of the first- and second-order autocorrelation functions are obtained where the various contributions of the noisy excitation source are correctly taken into account. We predict that, even in the low power regime, the noise source has a strong influence on the two-level system dynamics, which is not anticipated by simpler models. The characterization of photon indistinguishability in the pulsed excitation regime is usually done by measuring the value of the zero-delay intensity correlation obtained with a Hong-Ou-Mandel interferometer. We show that this figure is irrelevant in the cw excitation regime and we introduce the coalescence time window, a figure of merit based on a probabilistic interpretation of the notion of photon indistinguishability. We finally use the coalescence time window to quantify how noisy cw excitation influences photon indistinguishability.

We propose a scheme to significantly increase quadratic optomechanical couplings of optomechanical systems with the help of a nonlinear medium and two driving lasers. The nonlinear medium is driven by one laser, and the optical cavity mode is driven by a strong laser. We derive an effective Hamiltonian using squeezing transformation and rotating wave approximation. The effective quadratic optomechanical coupling strength can be larger than the decay rate of the cavity mode by adjusting the two optical driving fields. The thermal noise of squeezed cavity mode can be suppressed totally with the help of a squeezed vacuum field. Then a driving field is applied to the mechanical mode. We investigate the equal-time second-order correlations and find there are photon, phonon, and photon-phonon blockades even when the original single-photon quadratic coupling is much smaller than the decay rate of the optical mode. In addition, the sub-Poissonian window of the two-time second-order correlations can be controlled by the mechanical driving field. Finally, we show the squeezing and entanglement of the model could be tuned by the driving fields of the nonlinear medium and mechanical mode.

In a recent paper, M. F. Sacchi [Phys. Rev. A 96, 042325 (2017)] addressed the general problem of approximating an unavailable quantum state by the convex mixing of different available states. For the case of qubit mixed states, we show that the analytical solutions in some cases are invalid. In this Comment, we present complete analytical solutions for the optimal convex approximation. Our solutions can be viewed as correcting and supplementing the results in the aforementioned paper.

The possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, has been known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states, were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace being larger than the trace left by a single particle passing through the channel. This made the claim of counterfactuality of these protocols at best controversial. However, a simple modification of these recent protocols eliminates the trace in the transmission channel, making all these protocols counterfactual.

We show that an array of identical two-level systems coupled losslessly to a one-dimensional waveguide is able to realize a high-fidelity conditional phase shift useful for quantum logic. We propose two arrangements of emitters (one that relies on direct interactions between the emitters, and one that does not), and describe possible physical realizations and limitations.

The scattering-quantum-random-walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs, consisting of $N^2$ nodes. We simulate these quantum systems using classical computational methods and find that the probability distributions that arise are very favorable for a hybrid quantum-classical algorithm. We then examine how this hybrid algorithm handles varying types of randomness in both location of the special vertex and later random obstacles placed throughout the geometry, showing that the algorithm is resilient to both cases.