The analytical expansion of linearly, azimuthally, and radially polarized rigorous beam-type solutions of Maxwell's equations into vector spherical harmonics (VSHs) is presented. We report on the dominance of higher order multipoles in highly focused radially and azimuthally polarized beams compared to linearly polarized beams under similar conditions. Furthermore, we theoretically investigate a scenario in which highly focused azimuthally and radially polarized beams interact with a linear polarizer placed in the focal plane and expand the resulting fields into VSHs. The generalized Mie theory is used afterwards to investigate the scattering of the studied beams off a spherical gold nanoparticle.

We present a practical scheme for measuring completely unknown phases with a precision beyond the shot-noise limit even in the presence of loss. Our scheme consists of sending a sequence of unentangled particles and NOON states through an interferometer and analyzing the measurement outcomes using a Bayesian analysis. We compare our results with two recent schemes [L. Pezzé and A. Smerzi, Europhys. Lett. 78, 30004 (2007); B. L. Higgins et al., Nature 450, 393 (2007)] that are closely related but operate in the lossless regime. We show that our technique outperforms the previous schemes when even a modest amount of loss is present and so may prove to be a valuable technique for making precision measurements beyond the classical limit in a range of practical scenarios.

We investigate energy exchange in fast optical soliton collisions in Kerr nonlinear waveguides with weak linear loss, cubic gain, and quintic loss, i.e., with a Ginzburg-Landau (GL) gain-loss profile. We find that the amplitude shift in a single two-soliton collision in the presence of quintic loss is quartic in the initial soliton amplitudes, and that three-soliton interaction gives a significant contribution to the amplitude shift in a three-soliton collision. Moreover, we show that collision-induced dynamics of soliton amplitudes in a two-channel waveguide system with a GL gain-loss profile is described by a Lotka-Volterra (LV) model with quadratic and quartic interaction terms. Using the LV model, we show that linearly stable transmission with equal prescribed amplitudes can be achieved by a proper choice of the time-slot width and the ratio between the cubic gain and quintic loss coefficients. The linear stability of the transmission is confirmed by the numerical solution of a perturbed system of coupled nonlinear Schrödinger equations. Further numerical simulations show that transmission in waveguides with a GL gain-loss profile is less susceptible to radiation emission effects compared with waveguides with linear gain and cubic loss.

The intracavity power, and hence sensitivity, of optomechanical sensors is commonly limited by parametric instability. Here we characterize the degradation of sensitivity induced by parametric instability in a micron-scale cavity optomechanical system. Feedback via optomechanical transduction and electrical gradient force actuation is applied to suppress the parametric instability. As a result a $5.4$-fold increase in mechanical motion transduction sensitivity is achieved to a final value of $1.9\times {10}^{-18}{\mathrm{mHz}}^{-1/2}$.

Advancing quantum information processing is predicated on the preparation of ever-larger multiqubit states. Photonic realizations of such states may be achieved by increasing the number of photons populating the state or the number of qubits encoded per photon. Typical approaches to the latter strategy utilize distinct degrees of freedom of the photon field. We present here an approach that encodes two qubits per photon in the spatial parity of its transverse spatial profile. Simple linear optical devices transform each parity qubit separately or the two qubits jointly. Furthermore, we demonstrate that entangled photon pairs produced by spontaneous parametric down-conversion may be used to prepare arbitrary four-qubit states through sculpting the spatial profile of the classical optical pump. Two examples are highlighted—the preparation of two-photon four-qubit Greenberger-Horne-Zeilinger and $W$ states, whose encoding in a photon pair has thus far eluded other approaches.

We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.

We study theoretically the transfer of quantum information along bends in two-dimensional discrete lattices. Our analysis shows that the fidelity of the transfer decreases considerably as a result of interactions in the neighborhood of the bend. It is also demonstrated that such losses can be controlled efficiently by the inclusion of a defect. The present results are of relevance to various physical implementations of quantum networks, where geometric imperfections with finite spatial extent may arise as a result of bending, residual stress, etc.

The femtosecond laser reaction dynamics of the 3,5-difluoro-3′,5′-dibromo-biphenyl (DFDBrBPh) molecule is investigated using time-dependent density-functional theory combined with molecular-dynamics (TDDFT-MD) simulation. This work is based on a recent experiment that monitored torsional motion of the DFDBrBPh molecule by femtosecond time-resolved Coulomb explosion imaging [Madsen et al., Phys. Rev. Lett. 102, 073007 (2009)]. The results confirm that the probe pulse triggers a Coulomb explosion and the kick pulse induces the torsional motion of two phenyl rings, using the experimental settings of the lasers. The Coulomb explosion dynamics simulation verifies that the F and Br atoms dissociate to the ion detector while maintaining their initial alignment with respect to the phenyl rings, which is the fundamental basis of Coulomb explosion imaging of molecular torsion. Furthermore, the period and amplitude of the torsional motion obtained by the simulation are consistent with the experimental values. This validates the ability of the TDDFT-MD method to reveal the underlying mechanism of experimentally observed molecular torsional dynamics.

Fermi gases with repulsive interactions are characterized by measuring their compressibility as a function of interaction strength. The compressibility is obtained from in-trap density distributions monitored by phase-contrast imaging. For interaction parameters $k_{F}a>0.25$, fast decay of the gas prevents the observation of equilibrium profiles. For smaller interaction parameters, the results are adequately described by first-order perturbation theory. We have developed a phase-contrast imaging method that compensates for dispersive distortions of the images.

We present experimental results on nondegenerate four-wave mixing in a thermal vapor cell of rubidium atoms via highly excited Rydberg states. We observe sub-Doppler spectral features and a large sensitivity of the mixed light mode to small electric fields due to the large polarizabilities of the involved Rydberg state. We observe a saturation of the optical response due to the nonlinear four-level physics. The strong interaction between Rydberg atoms and the associated Rydberg blockade could potentially increase the nonlinearity dramatically.

We study the nonequilibrium dynamics of quantum jumps in a one-dimensional chain of atoms. Each atom is driven on a strong transition to a short-lived state and on a weak transition to a metastable state. We choose the metastable state to be a Rydberg state so that when an atom jumps to the Rydberg state, it inhibits or enhances jumps in the neighboring atoms. This leads to rich spatiotemporal dynamics that are visible in the fluorescence of the strong transition.

We investigate an array of metal nanoparticles as a channel for nanophotonic quantum communication and the generation of quantum plasmonic interference. We consider the transfer of quantum states, including single qubits as plasmonic wave packets, and highlight the necessity of a quantum-mechanical description by comparing the predictions of quantum theory with those of classical electromagnetic theory. The effects of loss in the metal are included, thus putting our investigation into a practical setting and enabling the quantification of the performance of realistic nanoparticle arrays as plasmonic quantum channels. We explore the interference of single plasmons, finding nonlinear absorption effects associated with the quantum properties of the plasmon excitations. This work highlights the benefits and drawbacks of using nanophotonic periodic systems for quantum plasmonic applications, such as quantum communication and the generation of quantum interference.

We analytically show that inserting a driven, two-level system inside a microcavity can improve its optical properties. In this approach, the strong dispersion induced by a pump via population oscillations increases the cavity lifetime experienced by a slightly detuned probe. We further predict that if the cavity is pumped through a resonant channel, optical absorptive or dispersive bistability can be combined with the population-oscillation-induced steep material dispersion to obtain a strong quality-factor enhancement. Moreover, differential amplification coming from the nonlinear feature of the pump transfer function can be used to drastically increase the probe transmission beyond intrinsic characteristics of the resonator. The $Q$-factor enhancement and the differential amplification can be advantageously combined with a frequency pulling effect to stabilize or readjust the microcavity resonance frequency.

Measurements of the fine structure pattern in high-$L$, $n$ = 37 Rydberg levels of Th${}^{3+}$ have been extended and improved to allow more precise determinations of the dipole and quadrupole polarizabilities of the Rn-like Th${}^{4+}$ core of the Th${}^{3+}$ Rydberg system. The improved precision is partly due to the recent availability of theoretical calculations that limit the size of higher-order contributions to the fine structure pattern. The measured polarizabilities are ${\alpha }_D$ = 7.702(6) a.u. and ${\alpha }_Q$ = 29.1(1.9) a.u.

The line shape of radio-frequency spectra of tightly bound Feshbach molecules in strong transverse confinement can be described by a simple analytic formula that includes final-state interactions. By direct comparison to experimental data, we clarify the role of effective-range corrections to two-body bound-state energies in lower dimensions.

We investigate magnetic properties in the superfluid and Mott-insulating states of two-component bosons with spin-orbit (SO) coupling in two-dimensional square optical lattices. The spin-independent hopping integral $t$ and SO coupled one $\lambda$ are fitted from band-structure calculations in the continuum, which exhibit oscillations with increasing SO coupling strength. The magnetic superexchange model is derived in the Mott-insulating state with one particle per site, characterized by the Dzyaloshinsky-Moriya interaction. In the limit of $\left|\lambda \right|\ll \left|t\right|$, we find a spin spiral Mott state whose pitch value is the same as that in the incommensurate superfluid state, while in the opposite limit $\left|t\right|\ll \left|\lambda \right|$, the ground state exhibits a $2\times 2$ in-plane spin pattern.

Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of situations. There is a single clear conceptual principle, based on purely logical consistency conditions, which underlies our notion of logical Bell inequalities. We show that in a precise sense, all Bell inequalities can be taken to be of this form. Our approach is very general. It applies directly to any family of sets of commuting observables. Thus it covers not only the $n$-partite scenarios to which Bell inequalities are standardly applied, but also Kochen-Specker configurations, and many other examples. There is much current work on experimental tests for contextuality. Our approach directly yields, in a systematic fashion, testable inequalities for a very general notion of contextuality. There has been much work on obtaining proofs of Bell's theorem “without inequalities” or “without probabilities.” These proofs are seen as being in a sense more definitive and logically robust than the inequality-based proofs. On the hand, they lack the fault-tolerant aspect of inequalities. Our approach reconciles these aspects, and in fact shows how the logical robustness can be converted into systematic, general derivations of inequalities with provable violations. Moreover, the kind of strong non-locality or contextuality exhibited by the GHZ argument or by Kochen-Specker configurations can be shown to lead to maximal violations of the corresponding logical Bell inequalities. Thus the qualitative and the quantitative aspects are combined harmoniously.

We consider the dynamics of composite quantum systems in the particular case that the state operator relaxes towards the Born approximation. For this we augment the von Neumann equation by a relaxation operator imposing a finite relaxation time ${\tau }_r$. Under the premise that the relaxation is the dominant process we obtain a hierarchy of non-Markovian master equations. The latter arises from an expansion of the total state operator in powers of the relaxation time ${\tau }_r$. In the Born-Markov limit ${\tau }_r\to 0$ the Lindblad master equation is recovered. Higher-order contributions enable a systematic treatment of correlations and non-Markovian dynamics in a recursive manner.

Modifications of quantum mechanics are considered, in which the state vector of any system, large or small, undergoes a stochastic evolution. The general class of theories is described, in which the probability distribution of the state vector collapses to a sum of $\delta$ functions, one for each possible final state, with coefficients given by the Born rule.