Universal energy scaling law for optimally excited nonlinear oscillators.

We compute the optimal temporal profile for an external driving force F(t) that can maximize the energy absorption of any driven nonlinear oscillator. The technique is based on constraining the maximum amplitude of the force field such that optimal control theory can provide quasianalytical solutions. We illustrate this computational technique for the undamped Duffing oscillator as well as for a driven quantum mechanical two-level system. We find that under optimal force conditions the asymptotic time-dependence of the maximum amplitude growth is given by a power law X(t)∼t^{2/α}, where the (possibly noninteger) exponent is determined by the highest degree of the oscillator's nonlinearity α. As a universal result, this predicts that the maximal energy absorption of any nonlinear oscillator grows (under an optimized force field) quadratically in time. We also find for the two-level system that-even under optimized excitation conditions-the maximally achievable inversion does not monotonically increase with the force amplitude. It is characterized by an interesting sequence of n-cycle thresholds as well as a self-termination of the growth.

Symbiotic versus nonsymbiotic optimization for spatial and temporal degrees of freedom in pair creation.

The field-induced decay of the quantum vacuum state associated with the creation of electron-positron pairs can be caused independently by either multiphoton transitions or by tunneling processes. The first mechanism is usually induced by appropriate temporal variations of the external field while the second (Schwinger-like) process occurs if a static but spatially dependent electric field is of supercritical strength. The ultimate goal is to construct an optimal space-time profile of an electromagnetic field that can maximize the creation of particle pairs. The simultaneous optimization of parameters that characterize the spatial and temporal features of both fields suggests that the optimal two-field configuration can be remarkably similar to that predicted from two independent optimizations for the spatial and temporal fields separately.

Dirac Vacuum as a Transport Medium for Information.

Usually, the transport of information requires either an electromagnetic field or matter as a carrier. It turns out that the Dirac vacuum modes could be exploited as a potentially loss-free carrier of information between two distant locations in space. At the first location, a spatially localized electric field is placed, whose temporal shape is modulated, for example, as a binary sequence of distinguishable high and low values of the amplitude. The resulting distortion of the vacuum state reflecting this information propagates then to a second location, where this digital signal can be read off sequentially by a static electric field pulse. If this second field is supercritical, it can create electron-positron pairs from the manipulated vacuum state. The original information transported by the vacuum mode is then imprinted on the temporal behavior of the created particle yield for a selected energy.

Manipulation of the Vacuum to Control Its Field-Induced Decay.

It has long been predicted that permanent electron-positron pairs can be created from the quantum vacuum at those spatial regions where an external electric field exceeds a supercritical value. By solving the Dirac equation numerically, we show that the yield of the created positrons at targeted energies can be controlled via a second (subcritical) electric field that is placed far outside the creation zone. This is a clear indication of the nonlocal character of the pair-creation process, as the second field can be placed at distant spatial regions that are never visited by the created positrons. This counterintuitive phenomenon can be understood in terms of a dressing of the vacuum state long before the particles are actually created. We present an analytical expression for the spectrum of the created particles that describes all quantitative features of this dressing and predicts how the second field can be used to increase as well as decrease the electron-positron yield for desired energies.

Superposition principle for the simultaneous optimization of collective responses.

We study the dynamics of sets of independent systems, all of which are coupled to the same time-dependent external force. Using optimal control theory, we compute the most efficient temporal pulse shape for this force that can maximize simultaneously the collective response of these systems. This response can be a weighted sum of all amplitudes at the final interaction time. Remarkably, it turns out that for certain systems this optimal force for the collective response can be related to the individual forces that would optimize each system separately. We illustrate this superposition principle for the simultaneous optimization of collective responses with numerical and also analytical solutions for sets of damped linear and nonlinear oscillators. We also apply this principle to predict the optimal temporal profile of a laser pulse that can maximize the final macroscopic polarization (total dipole moment) of a set of quantum mechanical two-level atoms.

Applications of the first digit law to measure correlations.

The quasiempirical Benford law predicts that the distribution of the first significant digit of random numbers obtained from mixed probability distributions is surprisingly meaningful and reveals some universal behavior. We generalize this finding to examine the joint first-digit probability of a pair of two random numbers and show that undetectable correlations by means of the usual covariance-based measure can be identified in the statistics of the corresponding first digits. We illustrate this new measure by analyzing the correlations and anticorrelations of the positions of two interacting particles in their quantum mechanical ground state. This suggests that by using this measure, the presence or absence of correlations can be determined even if only the first digit of noisy experimental data can be measured accurately.

Noncompeting channel approach to pair creation in supercritical fields.

The Dirac and Klein-Gordon equations are solved on a space-time grid to study the strong-field induced pair creation process for bosons and fermions from the vacuum. If the external field is sufficiently strong to induce bound states that are embedded in the negative energy continuum, a complex scaling technique of the Hamiltonian can predict the longtime behavior of the dynamics. In the case of multiple bound states this technique predicts the occurrence of a new collective time scale. The longtime behavior of the pair creation is not determined by a single (most important) channel, but collectively by the sum of all individual widths of the embedded states.

Magnetic control of the pair creation in spatially localized supercritical fields.

We examine the impact of a perpendicular magnetic field on the creation mechanism of electron-positron pairs in a supercritical static electric field, where both fields are localized along the direction of the electric field. In the case where the spatial extent of the magnetic field exceeds that of the electric field, quantum field theoretical simulations based on the Dirac equation predict a suppression of pair creation even if the electric field is supercritical. Furthermore, an arbitrarily small magnetic field outside the interaction zone can bring the creation process even to a complete halt, if it is sufficiently extended. The mechanism for this magnetically induced complete shutoff can be associated with a reopening of the mass gap and the emergence of electrically dressed Landau levels.

Space-time resolved approach for interacting quantum field theories.

An alternative approach to the usual perturbative S-matrix evaluation of quantum field theories is presented which is nonperturbative and provides full space-time resolution. We study the dynamical development of the force between two fermion wave packets for the Yukawa system. The spatial distribution of the virtual bosons that act as mediators of the force can be analyzed along with the fermionic densities. Using a potential function for the fermion-fermion interaction is a good approximation to the field theoretical calculations when the Fock space is restricted to only one boson, but in the full quantum field theory the fermion-fermion force is enhanced by higher-order multiboson processes. Furthermore, the normally attractive fermion-fermion Yukawa force can, in principle, be manipulated to even be repulsive if the momentum modes available to the virtual bosons are restricted.

Impact of large-angle scattering on diffusively backscattered halos.

We discuss the impact of large-angle scattering events in highly forward-scattering media on the spatial distribution of the diffusively reflected light. We show that, even for highly forward-scattering media, the reflected light near the incident beam axis is strongly dependent on the small number of large-angle scattering events. Reliable modeling of near-axis reflection thus requires accurate knowledge of the scattering phase function's behavior at large angles.

Nonperturbative retrieval of the scattering strength in one-dimensional media.

We examine several approaches on how to use the transmission and reflection amplitudes as functions of the modulation frequency of the laser's intensity to reconstruct the position-dependent scattering coefficient for a simple turbid medium. We explore the region where the contrast between the coefficient and its spatially averaged value is large enough such that perturbative methods fail. We show that in the case of a transillumination geometry, the knowledge of the transmission profile alone is not sufficient for unique image reconstruction, whereas the reflection spectrum allows for a complete inversion. We demonstrate the invertibility for media sampled at only a few positions.

Light scattering regimes along the optical axis in turbid media.

We inject an angularly collimated laser beam into a scattering medium of a nondairy creamer-water solution and examine the distribution of the scattered light along the optical axis as a function of the source-detector spacing. The experimental and simulated data obtained from a Monte Carlo simulation suggest four regimes characterizing the transition from unscattered to diffusive light. We compare the data also with theoretical predictions based on a first-order scattering theory for regions close to the source, and with diffusionlike theories for larger source-detector spacings. We demonstrate the impact of the measurement process and the effect of the unavoidable absorption of photons by the detection fiber on the light distribution inside the medium. We show that the range of validity of these theories can depend on the experimental parameters such as the diameter and acceptance angle of the detection fiber.

Velocity half-sphere model for multiple light scattering in turbid media.

We extend the traditional diffusion theory by distinguishing between the energy radiance in the forward and backward directions at each point in space. This approach leads to a new effective source for the diffusion equation that is nonzero for an anisotropic light source. It differs significantly from the diffusion theory for short source-detector spacings. We derive an analytical solution for the two lowest-order velocity moments of the radiance.

Creation dynamics of bound States in supercritical fields.

Using space-time resolved solutions to relativistic quantum field theory, we analyze the electron-positron creation process from vacuum in the long-time regime in which multiple pairs are produced. We find that for a supercritical potential of finite extension, the time dependence of the production rate of pairs is described by four distinct regimes that have their direct counterparts in the time evolved spatial density of the particles. These regimes include the shape-invariant birth process, an entanglement-induced reduction of interference, a recurrent Pauli suppression of pair production induced by electron-potential scattering, and finally a production halt associated with a population of supercritical and a partial population of subcritical bound states.

Generalized diffusion solution for light scattering from anisotropic sources.

The traditional diffusion theory, often used for isotropic sources, becomes inaccurate at short source-detector spacings and cannot be applied to media with large absorption or with small scattering strengths. We show that for any type of source anisotropy, a Green's-function-based procedure can remove these limitations. The accuracy of the new approach is examined through a comparison with the numerical solution to the radiative transfer equation.

Effect of eigenmodes on the optical transmission through one-dimensional random media.

Using the transfer matrix method as well as numerical solutions to the one-dimensional wave equation derived from the Maxwell equations, we study the transition from a photonic crystal with a finite size to a random dielectric medium. We examine the validity of the Kronig-Penney model for a finite size crystal and analyze the spatial structure of the eigenmodes as the crystal is made more irregular.

Determination of g and mu using multiply scattered light in turbid media.

We propose an inversion scheme to reconstruct the scattering coefficient mu and the anisotropy factor g that characterize the optical properties of a turbid medium. It is based on a theory for the scattering of light inside the medium from an angularly collimated light source. We demonstrate the feasibility of this method using light scattering data obtained from a Monte Carlo simulation.

Relativistic electron localization and the lack of Zitterbewegung.

Using space-time resolved solutions to relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum. For early times the entangled electron-positron wave function can be obtained analytically. We show that there are, in principle, no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also find that quantum field theory prohibits the occurrence of Zitterbewegung for an electron.

Klein paradox in spatial and temporal resolution.

Based on spatially and temporally resolved numerical solutions to the relativistic quantum field equations, we provide a resolution to the controversial issue of how an incoming electron scatters off a supercritical potential step and how the electron-positron pair production is affected by this collision. The treatment of the problem as a correlated three-particle problem suggests revealing insight into the process.

Bridging the microscopic and macroscopic theories for light reflected from disordered plane-parallel dielectric slabs.

For a system of randomly arranged plane-parallel dielectric layers with randomly varying index of refraction and width, we compare the reflection coefficient derived from the Maxwell equations with that of the Boltzmann theory. For a strictly monochromatic field this coefficient is an oscillatory function of the laser frequency. We show how suitable frequency or ensemble averaging permits a comparison of the two theories. The calculation of the usual Boltzmann scattering coefficient from microscopic parameters can be improved to permit a better agreement with the exact Maxwell data.