Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic iterations) required to find an optimal control field appears to be essentially invariant to the complexity of the system. The present work explores this matter in a series of systematic optimizations of the state-to-state transition probability on model quantum systems with the number of states $N$ ranging from 5 through 100. The optimizations occur over a landscape defined by the transition probability as a function of the control field. Previous theoretical studies on the topology of quantum control landscapes established that they should be free of suboptimal traps under reasonable physical conditions. The simulations in this work include nearly 5000 individual optimization test cases, all of which confirm this prediction by fully achieving optimal population transfer of at least 99.9$\%$ on careful attention to numerical procedures to ensure that the controls are free of constraints. Collectively, the simulation results additionally show invariance of required search effort to system dimension $N$. This behavior is rationalized in terms of the structural features of the underlying control landscape. The very attractive observed scaling with system complexity may be understood by considering the distance traveled on the control landscape during a search and the magnitude of the control landscape slope. Exceptions to this favorable scaling behavior can arise when the initial control field fluence is too large or when the target final state recedes from the initial state as $N$ increases.

A single-photon incident on a beam splitter produces an entangled field state, and in principle could be used to violate a Bell inequality, but such an experiment (without postselection) is beyond the reach of current experiments. Here we consider the somewhat simpler task of demonstrating Einstein-Podolsky-Rosen (EPR) steering with a single photon (also without postselection). We demonstrate that Alice’s choice of measurement on her portion of the entangled state can affect Bob’s portion of the entangled state in his laboratory, in a sense rigorously defined by us and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]. Previous work by Lvovsky and coworkers [Phys. Rev. Lett. 92, 047903 (2004)] has addressed this phenomenon (which they called remote preparation) experimentally using homodyne measurements on a single photon. Here we show that, unfortunately, their experimental parameters do not meet the bounds necessary for a rigorous demonstration of EPR steering with a single photon. However, we also show that modest improvements in the experimental parameters, and the addition of photon counting to the arsenal of Alice’s measurements, would be sufficient to allow such a demonstration.

The number of defects which are generated upon crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is $T\sim \pi /\Delta$, where $\Delta$ is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is nonadiabatic; this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action $s=T\Delta$.

Permanent planar alignment of gas-phase linear molecules is achieved by a pair of delayed perpendicularly polarized short laser pulses. The experiment is performed in a supersonic jet, ensuring a relatively high number density of molecules with moderately low rotational temperature. The effect is optically probed on a femtosecond time scale by the use of a third short pulse, enabling a time-resolved birefringence detection performed successively in two perpendicular planes of the laboratory frame. The technique allows for an unambiguous estimation of the molecular planar delocalization produced within the polarization plane of the pulse pair after the turn-off of the field. The measurements are supported by numerical simulations which lead to the quantification of the observed effect and provide more physical insights into the phenomenon.

By the use of an effective boundary condition we derive a two-dimensional integral equation for the scattering amplitude in the Rayleigh representation of the electric field of a surface-plasmon polariton scattered from a two-dimensional dielectric surface defect. This integral equation is transformed into a set of coupled one-dimensional integral equations by representing the dependence of the amplitude on the azimuthal angle by means of a rotational expansion. Exemplifying the usefulness of this approach, numerical results are obtained for defects of the shape of an anisotropic Gaussian function and a hemiellipsoid with a finite footprint when the surface-plasmon polariton incident on the defect from an arbitrary direction is either a plane wave or a Gaussian beam. Inspecting the near-field distribution of the radiation caused by the scattering, we find a localized increase of surface-plasmon polariton intensity in the vicinity of the dielectric defect, which indicates a focusing for both forms of the incident surface-plasmon polariton.

We study Anderson localization and propagation of partially spatially incoherent wavepackets in linear disordered potentials, motivated by the insight that interference phenomena resulting from multiple scattering are affected by the coherence of the waves. We find that localization is delayed by incoherence: the more incoherent the waves are, the longer they diffusively spread while propagating in the medium. However, if all the eigenmodes of the system are exponentially localized (as in one- and two-dimensional disordered systems), any partially incoherent wavepacket eventually exhibits localization with exponentially decaying tails, after sufficiently long propagation distances. Interestingly, we find that the asymptotic behavior of the incoherent beam is similar to that of a single instantaneous coherent realization of the beam.

We consider the interaction between a single rubidium atom and a photonic crystal nanocavity. Because of the ultrasmall mode volume of the nanocavity, an extremely strong coupling regime can be achieved in which the atom can shift the cavity resonance by many cavity linewidths. We show that this shift can be exploited to trap a single atom above the cavity. The atom is trapped by light that is only inside the cavity as a result of the shift of the cavity resonance caused by the proximity of the atom itself. This atom trap requires only a fraction of a photon inside the cavity. Surprisingly, the damping of the cavity plays a pivotal role in this trapping mechanism.

We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only $O(s\ln (d))$ experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a $d$-dimensional system, provided that the Hamiltonian is nearly $s$ sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.

The probability current for a quantum spinless relativistic particle is introduced based on the Hamiltonian dynamics approach utilizing the Salpeter equation as an alternative for the Klein-Gordon equation. The correctness of the presented formalism is illustrated by examples of exact solutions to the Salpeter equation including the new ones introduced in this work.

We develop a simple and efficient theoretical model to understand the quantum properties of broadband continuous variable quantum teleportation. We show that, if stated properly, the problem of multimode teleportation can be simplified to teleportation of a single effective mode that describes the input state temporal characteristic. Using that model, we show how the finite bandwidth of squeezing and external noise in the classical channel affect the output teleported quantum field. We choose an approach that is especially relevant for the case of non-Gaussian nonclassical quantum states and we finally back-test our model with recent experimental results.

We characterize the quantum gate fidelity in a state-independent manner by giving an explicit expression for its variance. The method we provide can be extended to calculate all higher order moments of the gate fidelity. Using these results, we obtain a simple expression for the variance of a single-qubit system and deduce the asymptotic behavior for large-dimensional quantum systems. Applications of these results to quantum chaos and randomized benchmarking are discussed.

We address the problem of energy-error tradeoff in the discrimination between two linear passive quantum optical devices with a single use. We provide an analytical derivation of the optimal strategy for beamsplitters and an iterative algorithm converging to the optimum in the general case. We then compare the optimal strategy with a simpler strategy using coherent input states and homodyne detection. It turns out that the former requires much less energy in order to achieve the same performances.

We derive quantum theory from purely informational principles. Five elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—define a broad class of theories of information processing that can be regarded as standard. One postulate—purification—singles out quantum theory within this class.

Cartesian components of the collision-induced (CI) hyperpolarizability $\Delta \mathit{\beta }$ tensor are computed for the linear, T-shaped, and 45${}^{°}$ configurations of the ${\mathrm{H}}_2$-Ne pair in the intermolecular range 3 to 14 bohr. Symmetry-adapted components $\Delta {\beta }_{\lambda \hspace{0.5em}L}^{(K)}(R)$ of the vector ($K=1$) part, as well as the septor ($K=3$) part, of the ${\mathrm{H}}_2$-Ne CI hyperpolarizability are calculated starting from the ab initio Cartesian hyperpolarizability tensor values transformed into their spherical counterparts. By applying these quantities, the vector together with the septor collision-induced hyper-Rayleigh (CIHR) spectra for the ${\mathrm{H}}_2$-Ne binary gas mixture are determined in the frequency range from $-1250$ to 2500 cm${}^{-1}$. The profiles are partially employed as a benchmarking device to estimate the importance of the short intermolecular distance part of the $\Delta \mathit{\beta }(R)$ dependence. The depolarization ratio of the CIHR spectra in the whole frequency range is also calculated. The nature of the CIHR signal and the feasibility of the related experiments are discussed and analyzed.

We have carried out calculations of the polarizabilities of the two-electron positive ions Li${}^{+}$, Be${}^{2+}$, ${\mathrm{B}}^{3+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, and ${\mathrm{O}}^{6+}$ interacting with screened Coulomb potentials. Highly accurate correlated exponential wave functions are used to represent correlation effects on the charged particles. The dipole, quadrupole, and octupole polarizabilities for the screening parameters in the range 0–$1a_0^{-1}$ are reported. Reported results for the unscreened case are comparable with the available results and for the screened case show some interesting behavior with increasing nuclear charge.

The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order $(Z\alpha ){}^4\hspace{0.5em}\mu {}^3/m_N^2$ is evaluated for muonic hydrogen and deuterium and muonic helium ions ($\mu$ is the reduced mass and $m_N$ is the nuclear mass). Relativistic corrections to vacuum polarization of order $\alpha (Z\alpha ){}^4\mu$ are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order $\alpha (Z\alpha ){}^5\hspace{0.5em}\ln {}^2(Z\alpha )\mu {}^2/m_N$ is obtained in leading logarithmic approximation. The results emphasize the need for a unified treatment of relativistic corrections to vacuum polarization in muonic hydrogen, muonic deuterium, and muonic helium ions, where the mass ratio of the orbiting particle to the nuclear mass is larger than the fine-structure constant.

By solving the two-active-electron time-dependent Schrödinger equation in an intense, ultrashort laser field, we investigate evidence of electron correlations in the high-order harmonic generation spectrum of helium. As the frequency of the driving laser pulse varies from 4.6 to 6.6 eV, the 13th, 11th, and 9th harmonics sequentially become resonant with the transition between the ground state and the isolated $2s2p({}^{1}P)$ autoionizing state of helium, which dramatically enhances these harmonics and changes their profiles. When each of the 9th and 13th harmonics are in resonance with this autoionizing state, there is also a low-order multiphoton resonance with a Rydberg state, resulting in a particularly large enhancement of these harmonics relative to neighboring harmonics. When the 11th harmonic is in resonance with the $2s2p({}^{1}P)$ autoionizing state, the 13th harmonic is simultaneously in resonance with numerous higher-energy autoionizing states, resulting in a competition between these two harmonics for intensity. These results demonstrate that even electron correlations occurring over a narrow energy interval can have a significant effect on strong-field processes such as harmonic generation.

In rare-gas atoms, an inner-valence shell $\mathit{ns}$ hole cannot be filled by Auger decay because of an energy deficiency. We show theoretically and experimentally that by adding a moderately intense infrared laser, Auger decay is possible with decay rates increasing dramatically for laser intensities $⩾{10}^{13}$ W/cm${}^2$. For Xe atoms, the simulated laser-enabled Auger decay yields are comparable with the experimental one, while for Ar atoms, the simulated ones are much smaller. We attribute the discrepancies to screening effects of the photoelectron. Laser-enabled Auger decay is of fundamental importance for understanding attosecond science, and is also important for experimental applications in ultrafast atomic, molecular, and materials dynamics using x rays. More importantly it may provide a way to control the Auger decay time and selectively break chemical bonds of molecules using a control infrared laser field.