Quantum optomechanics offers the potential to investigate quantum effects in macroscopic quantum systems in extremely well-controlled experiments. In this paper we discuss one such situation, the dynamic stabilization of a mechanical system such as an inverted pendulum. The specific example that we study is a “membrane-in-the-middle” mechanical oscillator coupled to a cavity field via a quadratic optomechanical interaction, with cavity damping the dominant source of dissipation. We show that the mechanical oscillator can be dynamically stabilized by a temporal modulation of the radiation pressure force. We investigate the system both in the classical and quantum regimes highlighting similarities and differences.

One-way quantum computing uses single-qubit projective measurements performed on a cluster state (a highly entangled state of multiple qubits) in order to enact quantum gates. The model is promising due to its potential scalability; the cluster state may be produced at the beginning of the computation and operated on over time. Continuous variables (CV) offer another potential benefit in the form of deterministic entanglement generation. This determinism can lead to robust cluster states and scalable quantum computation. Recent demonstrations of CV cluster states have made great strides on the path to scalability, utilizing either time or frequency multiplexing in optical parametric oscillators (OPO), both above and below threshold. The techniques relied on a combination of entangling operators and beam-splitter transformations. Here we show that an analogous transformation exists for amplifiers with Gaussian inputs states operating on multiple spatial modes. By judicious selection of local oscillators, the spatial mode distribution is analogous to the optical frequency comb consisting of axial modes in an OPO cavity. We outline an experimental system that generates cluster states across the spatial frequency comb, which can also scale the amount of quantum noise reduction to potentially larger than in other systems.

Quantum spin chains may be used to transfer quantum states between elements of a quantum information processing device. A scheme discovered recently [Phys. Rev. A 85, 022312 (2012)] was shown to have favorable transfer properties for single-qubit states even in the presence of built-in static disorder caused by manufacturing errors. We extend that scheme in a way suggested already in Bruderer et al. [Phys. Rev. A 85, 022312 (2012)] and study the transfer of the four Bell states which form a maximally entangled basis in the two-qubit Hilbert space. We show that perfect transfer of all four Bell states separately and of arbitrary linear combinations may be achieved for chains with hundreds of spins. For simplicity we restrict ourselves to systems without disorder.

Spontaneous parametric down-conversion (SPDC) in a nonlinear crystal generates two single photons (signal and idler) with random phases. Thus, no first-order interference between them occurs. However, coherence can be induced in a cascaded setup of two crystals if, e.g., the idler modes of both crystals are aligned to be indistinguishable. Due to the effect of phase memory it is found that the first-order interference of the signal beams can be controlled by the phase delay between the pump beams. Even for pump photon delays much larger than the coherence length of the SPDC photons, the visibility is above $90\%$. The high visibilities reported here prove an almost perfect phase memory effect across the two interferometers for the pump and the signal photon modes.

We contribute to a long-standing debate on the supposed failure of the fluctuation dissipation theorem (FDT) for the Davies master equation (DME), an important class of Lindblad quantum master equations, describing time-driven quantum systems weakly coupled to a heat bath. First we propose two simple and natural criteria on the driving which guarantee compatibility with the FDT. We show through our setting that, contrary to what is often stated in the literature, the DME is fully compatible with the FDT. We thus argue that the cause of the dispute lies in the adopted perturbation scheme, rather than in the Lindblad character of the master equation itself. We confirm our statement by proving that the Grabert master equation, first proposed by Grabert [Projection Operator Techniques in Nonequilibrium Statistical Mechanics (Springer, Berlin, 1982)] as an alternative linear dynamics fulfilling the FDT, is nothing else than the incriminated DME. Our criteria for the FDT can also be used in the analysis of the nonlinear thermodynamical master equation, first obtained in the Brownian motion limit [H. Grabert, Z. Phys. B 49, 161 (1982)] and later independently rediscovered and generalized on purely thermodynamic grounds [H. C. Öttinger, Europhys. Lett. 94, 10006 (2011)].

We study the (2 + 1)-dimensional Dirac oscillator in a homogeneous magnetic field in the noncommutative plane. It is shown that the effect of noncommutativity is twofold: (i) momentum noncommuting coordinates simply shift the critical value $\left(B_{\text{cr}}\right)$ of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); (ii) noncommutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\text{cr}}^{*}$, where there is a second quantum phase transition (right-left): this critical point disappears in the commutative limit. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetization of the system. Possible applications to the physics of silicene and graphene are briefly discussed.

We study the x-ray emission following the collision of a ${\mathrm{Bi}}^{83+}$ ion with a neutral Xe atom at the projectile energy 70 MeV/u. The collisional and post-collisional processes are treated separately. The probabilities of various many-electron processes at the collision are calculated within a relativistic independent electron model using the coupled-channel approach with atomiclike Dirac-Fock-Sturm orbitals. The analysis of the post-collisional processes resulting in the x-ray emission is based on the fluorescence yields, the radiation, and Auger decay rates, and allows one to derive intensities of the x-ray emission and compare them with experimental data. A reasonable agreement between the theoretical results and the recent experimental data is observed. The role of the relativistic effects is investigated.

We present measurements of resistive and sympathetic cooling of ion clouds confined in a Penning trap. For resistive cooling of a cloud consisting of one ion species, we observe a significant deviation from exponential cooling behavior which is explained by an energy-transfer model. The observed sympathetic cooling of simultaneously confined ion species shows a quadratic dependence on the ion charge state and is hence in agreement with expectations from the physics of dilute non-neutral plasmas.

We study the evolution of correlations in a quasi-two-dimensional dipolar gas driven out of equilibrium by a sudden ramp of the interactions. On short time scales, rotonlike excitations coherently oscillate in and out of the condensate, giving rise to pronounced features in the time evolution of the momentum distribution, excited fraction, and the density-density correlation function. The evolution of these correlation functions following a quench can thus be used to probe the spectrum of the dipolar gas. We also find that density fluctuations induced by the presence of rotons following the quench, dramatically slows down the rate of spreading of correlations in the system: Near the roton instability, correlations take infinitely long to build up and show deviations from light-cone-like behavior.

On the basis of the Maxwell-Lorentz local-field equations and nonlocal linear response theory, a self-consistent microscopic Green function theory of diffraction of light from a single hole in a thin and plane metallic screen is established. By subtracting the scattering of identical incident fields from screens with and without a hole, a causal effective optical aperture response tensor is introduced. An approximate expression is derived for the aperture response tensor in the limit where the screen behaves like an electric-dipole absorber and radiator. In this limit the internal electron dynamics is that of a quantum well. For a screen so thin that its bound electron motion can be described by a single quantum level, a approach for a quantum mechanical calculation of the aperture response tensor is presented. When the linear dimensions of the hole become sufficiently small the so-called aperture field, defined as the difference between the prevailing electric field with and that without a hole, becomes identical to the field from an incident-field-induced electric dipole with anisotropic linear polarizability. Our theory is formulated in such a manner that preknowledge only of (i) the incident electromagnetic field and (ii) the light-unperturbed optical electron properties (the microscopic conductivity tensor) of the screen with the geometrically given hole is needed. Since the microscopic theory allows for the presence of an (oscillating) component of the sheet current density perpendicular to the plane of the screen, a generalization of (i) the standard jump conditions of the field across the sheet and (ii) the reflection symmetries of the various fields in the plane of the screen is worked out. As our theory deviates radically from the approach of all classical diffraction theories, which are based on the macroscopic Maxwell equations and some kind of pheno-menological expression for the screen conductivity $\sigma$ (often just $\sigma \to \infty )$, we give a brief review of classical diffraction theory, formulated in such a manner that a comparison to the microscopic theory is made easier. In particular, the Bethe-Bouwkamp theory of classical diffraction from a small hole in an infinitely thin and perfectly conducting $\left(\sigma \to \infty \right)$ screen is our focus. We suggest that experimental frequency and angular resolved studies of the interference of the diffracted fields from quantum wells with and without holes are undertaken to obtain detailed insight into the microscopic aperture response functions, not least in the optical near-field domain.

We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon time-dependent spectrum reveals the time required for the fully resolved spectrum to build up as a result of the single photon creating one phonon after the other. The time-dependent spectrum also manifests the order (in time) in which the blue and red resonances (sidebands) appear in the spectrum identifying the two different mechanisms responsible for the production of these sidebands. Our study includes the coupling of the movable mirror to a mechanical heat bath. We use quantum trajectory theory combined with the input-output formalism for all calculations, but we also show how a dressed-state picture can be used to explain positions and relative strengths of all resonances.

We employ a quasimode representation of the adjoint master equation to study nonlinear pair-generation dynamics via spontaneous four-wave mixing in coupled-cavity systems in the presence of scattering loss. Perturbative analytic solutions for signal and idler photon-number operators are derived, which enable us to examine the effect of scattering loss on pair-generation dynamics. In particular, for a simple three-mode system, we show that any loss mismatch for the signal and idler photons increases the probability of finding unpaired photons. While decreasing the loss rates for signal and idler photons increases the pair signal brightness, it also results in higher generation rates for multiple pairs in the system, which can result in lower operational signal-to-noise ratios.

We study mode properties in multimode optical waveguides with parity-time $\left(\mathcal{PT}\right)$ symmetry. We find that two guiding modes with successive orders $2m-1$ and $2m$ form a mode pair in the sense that the two components of the pair evolve into the same mode when the loss and gain coefficient increases to some critical values, and they experience $\mathcal{PT}$ symmetry breaking simultaneously. For waveguides that in their conservative limit support an odd number of guiding modes, a new mode with a proper order emerges upon the increase of the gain and loss level, so that it pairs with the already existing highest-order mode and then breaks their $\mathcal{PT}$ symmetry simultaneously. Depending on the specific realizations of $\mathcal{PT}$-symmetric potentials, higher-order mode pairs may experience symmetry breaking earlier or later than the lower-order mode pairs do.

In this paper we investigate the propagation of an intense linearly polarized laser through an ionizing gaseous medium in the presence of an axial strong magnetic field, addressing the modulation of laser polarization. Our simulation indicates that the laser polarization can be dramatically modulated and shows complicated temporal patterns (Lissajous curves). This striking phenomenon can be attributed to the collective movement of ionized electrons, in contrast to the traditional Faraday rotation in which the rotation angle of the laser polarization derived from the linear response of the medium is time independent. We take the weighted average of the rotation angle over the whole pulse duration and find that it explicitly relies on strong magnetic strength as well as the incident laser intensity. Our finding has implications in strong magnetic diagnosis, laser intensity calibration, and the generation of polarization-modulated light sources.

We demonstrate the stabilization of an unstable steady state in an optomechanical system for low and high pump rates. The optomechanical system consists of a pumped cavity with one movable mirror. The stabilization is achieved by applying Pyragas control, i.e., feeding back the cavity field by an external mirror. This way, a maximal cavity field in the low pumping regime can be achieved, which corresponds to a large displacement of the movable mirror.

We derive a general approximate solution to the problem of minimizing the conditional entropy of a qudit-qubit system resulting from a local measurement on the qubit, which is valid for general entropic forms and becomes exact in the limit of weak correlations. This entropy measures the average conditional mixedness of the postmeasurement state of the qudit, and its minimum among all local measurements represents a generalized entanglement of formation. In the case of the von Neumann entropy, it is directly related to the quantum discord. It is shown that at the lowest nontrivial order, the problem reduces to the minimization of a quadratic form determined by the correlation tensor of the system, the Bloch vector of the qubit and the local concavity of the entropy, requiring just the diagonalization of a $3\times 3$ matrix. A simple geometrical picture in terms of an associated correlation ellipsoid is also derived, which illustrates the link between entropy optimization and correlation access and which is exact for a quadratic entropy. The approach enables a simple estimation of the quantum discord. Illustrative results for two-qubit states are discussed.

Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous-variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.

For any $N\otimes N$-type bipartite system with even $N>2$, two-parameter continuous families of unital block-dephasing quantum channels and of weakly optimal entanglement witnesses are constructed from special forms of a parametrized positive map. The parameter domains of the families are complementary subsets of a convex set and this fact reveals unusual combination rules of quantum channels and entanglement witnesses. These rules make it possible to develop many physically implementable direct entanglement-detection methods that provide a unified framework to accomplish both information-processing and entanglement-detection tasks by means of smooth quantum channels, without any reference to entanglement witnesses.

Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and excited states. However, it is difficult to ascertain the exact value of the energy gap. In this paper, we put forward a theorem on the existence of nonzero energy gap for the Hamiltonians used in adiabatic quantum computation. It can help to effectively identify a large class of the Hamiltonians without energy-level crossing between the ground and excited states.