We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the $D_2$ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments, laser-induced fluorescence components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components, we were able to see structures not visible in the difference graphs, which give deeper insight into the processes responsible for these signals. We studied how these signals are dependent on intensity and how they are affected when the exciting laser is tuned to different hyperfine transitions. The comparison between experiment and theory was carried out fulfilling the nonlinear absorption conditions. The theoretical curves described the experimental measurements satisfactorily, reproducing even small features in the shapes of the curves.

We theoretically and numerically study Bogoliubov-wave turbulence in three-dimensional atomic Bose-Einstein condensates with the Gross-Pitaevskii equation, investigating three spectra for the macroscopic wave function, the density distribution, and the Bogoliubov-wave distribution. In this turbulence, Bogoliubov waves play an important role in the behavior of these spectra, so that we call it Bogoliubov-wave turbulence. In a previous study [Proment et al., Phys. Rev. A 80, 051603(R) (2009)], a $-3/2$ power law in the spectrum for the macroscopic wave function was suggested by using weak wave turbulence theory, but we find that another $-7/2$ power law appears in both theoretical and numerical calculations. Furthermore, we focus on the spectrum for the density distribution, which can be observed in experiments, discussing the possibility of experimental observation. Through these analytical and numerical calculations, we also demonstrate that the previously neglected condensate dynamics induced by the Bogoliubov waves is remarkably important.

Despite its unique capability of distinguishing molecular handedness, chiroptical spectroscopy suffers from the weak-signal problem, which has restricted more extensive applications. The quasi-null-polarization-detection (QNPD) method has been shown to be useful for enhancing the chiroptical signal. Here, the underlying enhancement mechanism in the QNPD method combined with a heterodyne detection scheme is elucidated. It is experimentally demonstrated that the optical rotatory dispersion signal can be amplified by a factor of ∼400, which is the maximum enhancement effect achievable with our femtosecond laser setup. The upper limit of the QNPD enhancement effect of chiroptical measurements could, in practice, be limited by imperfection of the polarizer and finite detection sensitivity. However, we show that there exists an intrinsic limit in the enhancement with the QNPD method due to the weak but finite contribution from the homodyne chiroptical signal. This is experimentally verified by measuring the optical rotation of linearly polarized light with the QNPD scheme. We further provide discussions on the connection between this intrinsic limitation in the QNPD scheme for enhanced detection of weak chiroptical signals and those in optical enantioselectivity and Raman optical activity with a structured chiral field. We anticipate that the present work could be useful in further developing time-resolved nonlinear chiroptical spectroscopy.

Nondiffractive Bessel beams are well known to have infinite energy and infinite orbital angular momentum (OAM). However, when normalized to unity of energy, their OAM is finite. In this work, we derive an analytical relationship for calculating the normalized OAM of the superposition of off-axis Bessel beams characterized by the same topological charge. We show that if the constituent beams of the superposition have real-valued weight coefficients, the total OAM of the superposition of the Bessel beams equals that of an individual nonshifted Bessel beam. This property enables generating nondiffractive beams with different intensity distributions but identical OAM. The superposition of a set of identical Bessel beams centered on an arbitrary-radius circle is shown to be equivalent to an individual constituent Bessel beam put in the circle center. As a result of a complex shift of the Bessel beam, the transverse intensity distribution and OAM of the beam are also shown to change. We show that, in the superposition of two or more complex-shifted Bessel beams, the OAM may remain unchanged, while the intensity distribution is changed. Numerical simulation is in good agreement with theory.

The spectrum of the second harmonic signal generated in quadratic nonlinear photonic crystals, having different types of edge dislocations, was studied theoretically and experimentally. In the case of a dislocation with a fractional topological charge, we observed an asymmetric spectral conversion efficiency response, where the degree of asymmetry depends on the value of the fractional charge. Moreover, we have found that the conversion efficiency spectrum exhibits a periodic dependence on the topological charge value. In addition, nonlinear photonic crystals with multiple edge dislocations were studied. We show that for any number of dislocations characterized by even topological charge, the nonlinear spectral response will be identical to the response of the ideal, dislocation-free structure. This is a generalization of a previous observation that was made for crystals with a single even charge dislocation. Furthermore, for any number of dislocations with odd topological charge, two new peaks of maximal efficiency are observed in the second harmonic spectrum, in addition to a series of local efficiency peaks that are governed by the total number of dislocations. This is also a generalization of a previous observation that was made for a single dislocation case having an odd topological charge.

We introduce a nanowire-based photonic-crystal waveguide system capable of controllably mediating the photon coupling between two quantum dots which are macroscopically separated. Using a rigorous Green-function-based master equation approach, our two-dot system is shown to provide a wide range of interesting quantum transport regimes. In particular, we demonstrate the formation of long-lived entangled states and study the resonance fluorescence spectrum which contains clear signatures of the coupled quantum dot pair. Depending upon the operating frequency, one can obtain a modified Mollow triplet spectrum or a Mollow nonuplet, namely, a spectrum with nine spectral peaks. These multiple peaks are explained in the context of photon-exchange-mediated dressed states. Results are robust with respect to scattering loss, and spatial filtering via propagation allows for each quantum dot's emission to be observed individually.

We show that any finite quantum system $S$ can be coupled to a dephasing environment in such a way that the internal mechanism responsible for relaxation of observables acting on $S$ can be effectively canceled. By adjusting this coupling, the difference between the initial and the long–time expectation values of any observable on $S$ can be tuned to an arbitrarily small, but nonzero, value. This statement is exemplified and visualized by numerical studies of relaxation in a generic one-dimensional system of interacting fermions.

We discuss the prospect of $\mathcal{PT}$-symmetric Hamiltonians finding applications in quantum information science, and conclude that such evolution is unlikely to provide any benefit over existing techniques. Although it has been known for some time that $\mathcal{PT}$-symmetric quantum theory, when viewed as a unitary theory, is exactly equivalent to standard quantum mechanics, proposals continue to be put forward for schemes in which $\mathcal{PT}$-symmetric quantum theory can outperform standard quantum theory. The most recent of these is the suggestion to use $\mathcal{PT}$-symmetric Hamiltonians to perform an exponentially fast database search, a task known to be impossible with a quantum computer. Further, such a scheme has been shown to apparently produce effects in conflict with fundamental information-theoretic principles, such as the impossibility of superluminal information transfer, and the invariance of entanglement under local operations. In this paper we propose three inequivalent experimental implementations of $\mathcal{PT}$-symmetric Hamiltonians, with careful attention to the resources required to realize each such evolution. Such an operational approach allows us to resolve these apparent conflicts, and evaluate fully schemes proposed in the literature for faster time evolution and state discrimination.

We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-$P$ representation. We predict values of the Clauser-Horne-Shimony-Holt (CHSH) parameter up to $S\simeq 2.5$ for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by $S\le 2$.

A crucial property of quantum networks is the entanglement between different network nodes. We demonstrate that entanglement in quantum networks can be created and controlled by introducing quantum-coherent time-delayed self-feedback at single nodes.

In this work we obtain analytical expressions for the nonadditivity effects in the dispersive interaction between two atoms and a perfectly conducting surface of arbitrary shape in the nonretarded regime. We show that this three-body quantum-mechanical problem can be solved by mapping it onto a two-body electrostatic one. We apply the general formulas developed in this paper in several examples. First we rederive the London interaction as a particular case of our formalism. Then we investigate other interesting examples, such as the setup where two atoms lie inside a plane capacitor. Here we show that the nonadditivity is strikingly manifest since the planes lead to an exponential suppression of the interaction of the atoms. As a last example we deal with two atoms in the presence of a sphere, both grounded and isolated. We show that for realistic experimental parameters the nonadditivity may be relevant for the force in each atom.

We determine the ground-state energy and Tan's contact of attractively interacting few-fermion systems in a one-dimensional harmonic trap, for a range of couplings and particle numbers. Complementing those results, we show the corresponding density profiles. The calculations were performed with a lattice Monte Carlo approach based on a nonuniform discretization of space, defined via Gauss-Hermite quadrature points and weights. This particular coordinate basis is natural for systems in harmonic traps, and can be generalized to traps of other shapes. In all cases, it yields a position-dependent coupling and a corresponding nonuniform Hubbard-Stratonovich transformation. The resulting path integral is performed with hybrid Monte Carlo as a proof of principle for calculations at finite temperature and in higher dimensions. We present results for $N=4,...,20$ particles (although the method can be extended beyond that) to cover the range from few- to many-particle systems. This method is exact up to statistical and systematic uncertainties, which we account for—and thus also represents an ab initio calculation of this system, providing a benchmark for other methods and a prediction for ultracold-atom experiments.

We investigate the properties of a homogeneous dipolar Bose gas in a weak three-dimensional isotropic speckle disorder at finite temperatures. By using the Bogoliubov theory (beyond the mean field), we calculate the condensate and the superfluid fractions as a function of density and strengths of disorder and interaction. The disorder impact on the anomalous density, the chemical potential, and the ground-state energy is also analyzed. We show that the peculiar interplay of the dipole-dipole interaction and weak disorder makes the superfluid fraction and sound velocity anisotropic.

We investigate the response of a polariton laser driven slightly off-resonantly using light fields differing from the routinely studied coherent pump sources. The response to driving light fields with thermal and displaced thermal statistics with varying correlation times shows significant differences in the transmitted intensity, its noise, and the position of the nonlinear threshold. We predict that adding more photons on average may actually reduce the transmission through the polariton system.

We present an approach for the description of fluorescence from optically active materials embedded in layered periodic structures. Based on an exact electromagnetic Green's tensor analysis, we determine the radiative properties of emitters such as the local photonic density of states, Lamb shifts, linewidths, etc. for a finite or infinite sequence of thin alternating plasmonic and dielectric layers. In the effective-medium limit, these systems may exhibit hyperbolic dispersion relations so that the large wave-vector characteristics of all constituents and processes become relevant. These include the finite thickness of the layers, the nonlocal properties of the constituent metals, and local-field corrections associated with an emitter's dielectric environment. In particular, we show that the corresponding effects are nonadditive and lead to considerable modifications of an emitter's luminescence properties.

We report generation of a broadband supercontinuum (SC) in a birefringent crystal upon irradiation by intense, near-infrared, femtosecond laser pulses and investigate its dependence on incident laser power and the initial laser polarization. We choose as our sample $\alpha -{\mathrm{BaB}}_2{\mathrm{O}}_4$ ($\alpha$-BBO), a material in which the third order is the lowest order of nonvanishing nonlinear optical susceptibility. Three different SC generation mechanisms are identified under our experimental conditions; these are found to depend upon the pump power $P_{pu}$. Close to the critical power for self-focusing ($P_{pu}\sim 5$ MW), the spectrum is dominated by Kerr nonlinearity or self-phase modulation, whereas at intermediate pumping $P_{pu}\sim 125$ MW, Raman amplification on the Stokes side is a dominating mechanism. At higher pump power $\sim 300$ MW, significant asymmetric broadening extending up to $\sim 570$ nm is observed due to the coherent anti-Stokes Raman scattering. Our study provides an intuitive explanation for the observed power- and polarization-dependent SC generation in $\alpha$-BBO crystals.

In a previous publication, we showed how group actions can be used to generate Bell inequalities. The group action yields a set of measurement probabilities whose sum is the basic element in the inequality. The sum has an upper bound if the probabilities are a result of a local, realistic theory, but this bound can be violated if the probabilities come from quantum mechanics. In our previous paper, we considered the case of only two parties making the measurements and single-generator groups. Here we show that the method can be extended to three parties, and it can also be extended to non-Abelian groups. We discuss the resulting inequalities in terms of nonlocal games.

We introduce two families of sum-of-squares (SOS) decompositions for the Bell operators associated with the tilted Clauser-Horne-Shimony-Holt (CHSH) expressions introduced in Acín et al. [Phys. Rev. Lett. 108, 100402 (2012)]. These SOS decompositions provide tight upper bounds on the maximal quantum value of these Bell expressions. Moreover, they establish algebraic relations that are necessarily satisfied by any quantum state and observables yielding the optimal quantum value. These algebraic relations are then used to show that the tilted CHSH expressions provide robust self-tests for any partially entangled two-qubit state. This application to self-testing follows closely the approach of Yang and Navascués [Phys. Rev. A 87, 050102(R) (2013)], where we identify and correct two nontrivial flaws.

We present a cavity dissipation scheme to prepare a hybrid system of an atomic ensemble and a moving mirror in squeezed and entangled states. This scheme is based on four-wave mixing in the atoms and radiation pressure on the mirror, both of which combine to lead to Bogoliubov interactions of the atoms and the mirror with the cavity fields. Under adiabatic conditions, the cavity fields cause the hybrid Bogoliubov modes to evolve into the vacuum states, which correspond to the two-mode squeezed and entangled states. The dependence of the hybrid entanglement on the system parameters is also presented in and beyond the Bogoliubov interactions.