We investigate how entanglement spreads along small Bose-Hubbard chains, with only the first well initially occupied by a mesoscopic number of atoms, as the number of sites increases. For two- and three-well chains in the noninteracting case, we are able to obtain analytical solutions and show that the presence of entanglement depends on having a sub-Poissonian state of the atoms in the first well. In these cases, the correlations we calculate are completely periodic. Restoring the collisional interactions or moving to a four-well chain necessitates a numerical treatment, for which we use the fully quantum positive-P representation. We examine two different correlations and find that adding collisional interactions destroys the periodicity of the correlations and causes them to degrade with time. This happens well before there is a noticeable effect on the periodicity of the solutions for the number of atoms in each well.

We study quantum transport of an interacting confined one-dimensional Bose gas across a barrier. A sudden shift of the confining potential induces dipolar oscillations in the cloud. We find that the dipole mode frequency strongly depends on the interaction strength between the particles, yielding information on the classical screening of the barrier and on its renormalization due to quantum fluctuations. We predict a parity effect that becomes most prominent in the strongly correlated regime.

We present one-dimensional simulation results for the cold-atom tunneling experiments by the Heidelberg group [Zürn et al., Phys. Rev. Lett. 108, 075303 (2012); Zürn et al., Phys. Rev. Lett. 111, 175302 (2013)] on one or two ${}^6\mathrm{Li}$ atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic-field gradient. At the noninteracting particle level, we find that the Wentzel-Kramers-Brillouin approximation may not be used as a reliable tool to extract the trapping potential parameters from the experimentally measured tunneling data. We use our numerical calculations along with the experimental tunneling rates for the noninteracting system to reparametrize the trapping potential. The reparametrized trapping potentials serve as input for our simulations of two interacting particles. For two interacting (distinguishable) atoms on the upper branch, we reproduce the experimentally measured tunneling rates, which vary over several orders of magnitude, fairly well. For infinitely strong interaction strength, we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics. For two attractively interacting atoms on the molecular branch, we find that single-particle tunneling dominates for weakly attractive interactions, while pair tunneling dominates for strongly attractive interactions. Our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates. We obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement.

In this paper intermodal modulational instability (IM-MI) is analyzed in a multimode fiber where several spatial and polarization modes propagate. The coupled nonlinear Schrödinger equations describing the modal evolution in the fiber are linearized and reduced to an eigenvalue problem. As a result, the amplification of each mode can be described by means of the eigenvalues and eigenvectors of a matrix that stores the information about the dispersion properties of the modes and the modal power distribution of the pump. Some useful analytical formulas are also provided that estimate the modal amplification as function of the system parameters. Finally, the impact of third-order dispersion and of absorbtion losses is evaluated, which reveals some surprising phenomena into the IM-MI dynamics. These outcomes generalize previous studies on bimodal MI, related to the interaction between two spatial or polarization modes, to the most general case of $N>2$ interacting modes. Moreover, they pave the way towards the realization of wideband multimode parametric amplifiers.

In this paper, a meaningful classification of optical caustic beams in two dimensions is presented. It is demonstrated that the phase symmetry of the beam's angular spectrum governs the optical catastrophe, which describes the wave properties of ray singularities, for cusp (symmetric phase) and fold (antisymmetric phase) caustics. In contrast to the established idea, the caustic classification arises from the phase symmetry rather than from the phase power, thus breaking the commonly accepted concept that fold and cusp caustics are related to the Airy and Pearcey functions, respectively. Nevertheless, the role played by the spectral phase power is to control the degree of caustic curvature. These findings provide straightforward engineering of caustic beams by addressing the spectral phase into a spatial light modulator or glass plate.

The influence of Raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. The Raman effect introduces a threshold value in the resonator quality factor above which the frequency-locked solitons cannot exist, and instead, a rich dynamics characterized by generation of self-frequency-shifting solitons and dispersive waves is observed. A mechanism for broadening the Cherenkov radiation through Hopf instability of the frequency-locked solitons is also reported.

The complex internal atomic structure involved in radiative transitions has an effect on the spectrum of fluctuations (noise) of the transmitted light. A degenerate transition has different properties in this respect than a pure two-level transition. We investigate these variations by studying a certain transition between two degenerate atomic levels for different choices of the polarization state of the driving laser. For circular polarization, corresponding to the textbook two-level-atom case, the optical spectrum shows the characteristic Mollow triplet for strong laser drive, while the corresponding noise spectrum exhibits squeezing in some frequency ranges. For a linearly polarized drive, corresponding to the case of a multilevel system, additional features appear in both optical and noise spectra. These differences are more pronounced in the regime of a weakly driven transition: whereas the two-level case essentially exhibits elastic scattering, the multilevel case has extra noise terms related to spontaneous Raman transitions. We also discuss the possibility to experimentally observe these predicted differences for the commonly encountered case where the laser drive has excess noise in its phase quadrature.

We analyze theoretically measurement schemes of the mean output work and its fluctuations in a recently proposed optomechanical quantum heat engine [Zhang et al., Phys. Rev. Lett. 112, 150602 (2014)]. After showing that this work can be operationally determined by continuous measurements of the intracavity photon number, we discuss both dispersive and absorptive measurement schemes and analyze their back-action effects on the efficiency of the engine. Both measurements are found to reduce the efficiency of the engine, but their back-action is both qualitatively and quantitatively different. For dispersive measurements the efficiency decreases as a result of the mixing of photonic and phononic excitations, while for absorptive measurements, its reduction arises from photon losses due to the interaction with the quantum probe.

It has been predicted that particles with imaginary mass, called tachyons, would be able to travel faster than the speed of light. There has not been any experimental evidence for tachyons occurring naturally. Here, we propose how to experimentally simulate Dirac tachyons with trapped ions. Quantum measurement on a Dirac particle simulated by a trapped ion causes it to have an imaginary mass so that it may travel faster than the effective speed of light. We show that a Dirac tachyon must have spinor-motion correlation in order to be superluminal. We also show that it exhibits significantly more Klein tunneling than a normal Dirac particle. We provide numerical simulations of realistic ion systems and show that our scheme is feasible with current technology.

We consider estimating the parameter associated with the qubit depolarizing channel when the available initial states that might be employed are mixed. We use quantum Fisher information as a measure of the accuracy of estimation to compare protocols which use collections of qubits in product states to one in which the qubits are in a correlated state. We show that, for certain parameter values and initial states, the correlated-state protocol can yield a greater accuracy per channel invocation than the product-state protocols. We show that, for some parameters and initial states, using more than two qubits and channel invocations is advantageous. These results stand in contrast to the known optimal case that uses pure initial states and a single channel invocation on a pair of entangled qubits.

We show that three distant parties, $A$, $B$, and $C$, having no prior entanglement can establish a shared GHZ state by mediating two particles which remain separable from each other and from all the other parties throughout the process. The success probability is $1/7$. We prove this in a general framework for systematic distribution of entangled states between two and more parties with separable states in $d$ dimensions. The proposed method may facilitate the construction of multinode quantum networks and many other processes which use multipartite entangled states.

Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian-distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.

We propose a scheme to realize a pseudospin-$1/2$ model of the ${}^1\mathrm{\Sigma }(v=0)$ bialkali polar molecules with the spin states corresponding to two sublevels of the first excited rotational level. We show that the effective dipole-dipole interaction between two spin-$1/2$ molecules couples the rotational and orbital angular momenta and is highly tunable via a microwave field. We also investigate the ground-state properties of a spin-$1/2$ molecular condensate. A variety of nontrivial quantum phases, including the doubly quantized vortex states, are discovered. Our scheme can also be used to create spin-1 model of polar molecules. Thus we show that the ultracold gases of bialkali polar molecules provide a unique platform for studying the spinor condensates of rotating molecules.

We theoretically study high-order harmonic generation from an inhomogeneous field originated by the interaction between an ultrashort laser pulse and a gold nanostructure and demonstrate that ultrashort isolated attosecond pulses can be generated by reducing the harmonic chirp with the spatially inhomogeneous electric field. It can be found that the instants of ionized electrons coming back to the core are highly concentrated in the case of the spatially inhomogeneous electric field and a broadband supercontinuum harmonic spectrum with less chirp can be produced. Then an isolated 127-as pulse close to the Fourier transform limit can be directly generated without phase compensation.

The Kochen–Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes the impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedures). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two-party information theoretic game. Thus, using resources of a given operational theory, the maximum success probability achievable in such a game suffices as a bona fide measure of preparation contextuality for the underlying theory. In this work we show that preparation contextuality in quantum theory is more restricted compared to a general operational theory known as box world. Moreover, we find that this limitation of quantum theory implies the quantitative bound on quantum nonlocality as depicted by the Cirel'son bound.

We have shown that it is possible to formulate the consistent and probability-preserving description of the $\mathit{CP}$-symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavor oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated $\mathit{CP}$ symmetry and found the evolution of any observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the $\mathit{CP}$-preserved values.

Since several years, the preparation and manipulation of a small number of quantum systems in a controlled and coherent way is feasible in many experiments. In fact, these experiments are nowadays commonly used for quantum simulation and quantum computation. As recently shown, such a system can, however, also be utilized to simulate specific behaviors of exponentially larger systems. That is, certain quantum computations can be performed by an exponentially smaller quantum computer. This compressed quantum computation can be employed to observe, for instance, the quantum phase transition of the one-dimensional (1D) $XY$ model using very few qubits. We extend here this notion to simulate the behavior of thermal as well as excited states of the 1D $XY$ model. In particular, we consider the 1D $XY$ model of a spin chain of $n$ qubits and derive a quantum circuit processing only $log\left(n\right)$ qubits which simulates the original system. We demonstrate how the behavior of thermal as well as any eigenstate of the system can be efficiently simulated in this compressed fashion and present a quantum circuit on $log\left(n\right)$ qubits to measure the magnetization, the number of kinks, and correlations occurring in the thermal as well as any excited state of the original systems. Moreover, we derive compressed circuits to study time evolutions.