We show how slow-light pulse delays in realistic electromagnetically-induced-transparency (EIT) media can be determined directly from static transmission spectra. Using only the measured EIT linewidth and off-resonant transmission, the absolute delay of a slow-light pulse in an optically thick, power-broadened medium can be simply and accurately determined, while capturing more complex optical pumping behavior.

The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133902 (2008)]. The uniformity is broken at subwavelength scale, where the system may exhibit strong stratification of local field and dipole polarization, with the strata period being much shorter than the incident wavelength. In this paper, we further develop and advance that theory for the most fundamental case of one-dimensional arrays, and study nanoscale excitation of so-called “locsitons” (local field excitations) and their standing waves (strata) that result in size-related resonances and related large field enhancement in finite arrays of atoms. The locsitons may have a whole spectrum of spatial frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic domains, to supershort waves, with neighboring atoms alternating their polarizations, which are reminiscent of antiferromagnetic spin patterns. Of great interest is the different kind of “hybrid” mode of excitation, greatly departing from any magnetic analogies. We also study differences between Ising-type near-neighbor approximation and the case where each atom interacts with all other atoms in the array. We find an infinite number of “exponential eigenmodes” in the lossless system in the latter case. At certain “magic” numbers of atoms in the array, the system may exhibit self-induced (but linear in the field) cancellation of resonant local-field suppression. We also studied nonlinear modes of locsitons and found optical bistability and hysteresis in an infinite array for the simplest modes.

By performing two-wave mixing experiments in a liquid-crystal light valve, optical pulses are slowed down to group velocities as slow as a few tenths of mm/s, corresponding to a very large group index. We present experiments and model of the slow-light process occurring in the liquid-crystal light valve, showing that this is characterized by multiple-beam diffraction in the Raman-Nath regime. Depending on the initial frequency detuning between pump and signal, the different output order beams are distinguished by different group delays. The group delay can be tuned by changing the main parameters of the experiment: the detuning between the pump and the input wave packet, the strength of the nonlinearity, and the intensity of the pump beam.

We demonstrate compact optical wavelength conversion architecture for picosecond laser pulses and data streams within photonic band gap waveguides. These multimode waveguides are seeded with resonantly driven, inhomogeneously broadened, distributions of quantum dots whose optical transition center frequency is placed near a sharp discontinuity in the local (electromagnetic) density of states (LDOS). This discontinuity is provided by a cutoff in one of the waveguide modes. Wavelength conversion of an optical pulse propagating in the single-mode spectral range of the waveguide, near the LDOS jump, is provided by a steady-state holding field with frequency matched to the center frequency of the quantum dot distribution. In the absence of an incident laser pulse, the holding field is absorbed by the quantum dots. When the incident pulse intensity is sufficient to cause population inversion of a suitable fraction of the quantum dots, the holding field is amplified and the incident pulse profile is imprinted on to the holding field, leading to wavelength conversion in the range of 3–20 nm at wavelengths near $1.5\mu \text{m}$. Larger wavelength shifts typically require higher power levels for operation (milliwatt scale) but enable conversion of shorter (picosecond) pulses. Small wavelength shifts typically require narrower distribution of quantum dot resonance frequencies. Using finite-difference time-domain simulations, we show that an optical pulse (Gaussian in time) can create another equivalent optical pulse with either higher or lower center frequency inside the photonic band gap of the structure. Optical pulses of a given center frequency can also be selectively amplified or absorbed depending on the coincident arrival of another laser pulse with different center frequency, enabling all-optical logic operations within a multiwavelength-channel optical circuit.

We consider dynamics of a slowly time-dependent Dicke model, which represents a many-body generalization of the Landau-Zener model. In particular, the model describes narrow Feshbach resonance passage in an ultracold gas of Fermi atoms. Adiabaticity is destroyed when a parameter crosses a critical value, even at very slow sweeping rates of a parameter. The dynamics crucially depends on direction of the sweep. We apply our recent analysis (A. P. Itin and P. Törmä, e-print arXiv:0901.4778) to the “inverse” sweep through the resonance, corresponding (in a context of Feshbach resonance passage) to dissociation of molecules. On a level of the mean-field approximation, the dynamics is equivalent to a molecular condensate formation from Bose atoms within a two-mode model. Mapping the system to a Painlevé equation allows us to calculate deviation from adiabaticity at very slow sweeps analytically.

In this paper we propose a probabilistic method which allows an unambiguous modification of two nonorthogonal quantum states. We experimentally implement this protocol by using two-photon polarization states generated in the process of spontaneous parametric down conversion. In the experiment, for codifying initial quantum states, we consider single-photon states and heralded detection. We show that the application of this protocol to entangled states allows a fine control of the amount of entanglement of the initial state.

The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the “relative entropy of entanglement” (REE) in the one-energy-excitation manifold of the reduced $\text{TLS}+\text{HO}$ system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.

Explicit expressions for the concurrence of all positive and trace-preserving (“stochastic”) one-qubit maps are presented. Our method allows to construct the relevant convex roof patterns. We conclude that two-component optimal decompositions always exist. Our results can be transferred to $2\times n$-quantum systems providing the concurrence for all rank-two density operators, as well as lower and upper bounds for their entanglement of formation. We apply these results to a study of the entanglement entropy of one-qubit stochastic maps which preserve axial symmetry. Using analytic and numeric results we analyze the bifurcation patterns appearing in the convex roof of optimal decompositions and give results for the one-shot (Holevo-Schumacher-Westmoreland) capacity of those maps.

We study the time evolution of decoherence factor of two spin qubits and qutrits coupled to an $XY$ spin chain with Dzyaloshinsky-Moriya (DM) interaction environment. The dynamical process of the decoherence is numerically and analytically investigated. We find that the DM interaction can enhance slightly the decay of the decoherence factor in the weak-coupling region. However, in the strong-coupling region, the decoherence factor is very sensitive to the DM interaction.

We report the observation of dipole-forbidden, but quadrupole-allowed, one-photon transitions to high-Rydberg states in Rb. Using pulsed uv excitation of ultracold atoms in a magneto-optical trap, we excite $5s\to nd$ transitions over a range of principal quantum numbers $n=27–59$. Compared to dipole-allowed (E1) transitions from $5s\to np$, these E2 transitions are weaker by a factor of approximately 2000. We also report measurements of the anomalous $n{p}_{3/2}:n{p}_{1/2}$ fine-structure transition strength ratio for $n=28–75$. Both results are in agreement with theoretical predictions.

We use the $4s{\left[3/2\right]}_2^o$ metastable state of atomic argon created by charge-transfer collisions between a 5 keV ${\text{Ar}}^{+}$ beam and K vapor to perform laser scaled-energy Stark photoabsorption and recurrence spectroscopy of even-parity Rydberg states, detected by field ionization and forced autoionization, in a region of the spectrum that contains two distinct perturbations. We apply a uniform electric field that changes with the frequency of the laser to maintain a constant scaled energy relative to the first ionization limit of the atom, associated with the ion core in a ${{}^{2}P}_{3/2}$ configuration. Local perturbations to the Rydberg series $\left(15\le n\le 28\right)$ occur due to $n^{\prime }=8$ and 10 Stark states that belong to the series converging to the second ionization threshold with the ion core in a ${{}^{2}P}_{1/2}$ configuration. The resulting absorption spectra show multielectron effects due to configuration interaction and angular momentum coupling. These effects have dynamical implications in the recurrence spectrum. In particular, the variations in the Stark structure of the absorption spectrum result in a recurrence spectrum that shows two prominent multielectron features. One is the presence of recurrence peaks with scaled actions less than that of the hydrogenic primitive orbit. We attribute this to excitation in which both the ion core and the Rydberg electron absorb energy during photoexcitation. The second multielectron effect observed is recurrence peaks that occur at the sum of scaled actions of the primitive orbit (and its repetitions) associated with the pair of perturbations and a hydrogenic closed classical orbit. We attribute these peaks to core-changing inelastic scattering of the Rydberg electron with the ionic core due to angular momentum coupling. For comparison, we measured the regular autoionizing Rydberg series of argon between the first and second ionization thresholds, where no perturbing resonances exist.

A comprehensive theoretical and experimental investigation of the triple differential cross sections arising from the electron-impact ionization of molecular hydrogen is made, at an incident electron energy of 35.4 eV, for cases where the outgoing electrons have equal and unequal energies, and for a range of experimental geometries. Generally, good agreement is found between two theoretical approaches and experiment, with the best agreement arising for intermediate geometries with large gun angles and for the perpendicular geometry.

We investigate high-order harmonic generation (HHG) in a thin macroscopic medium by solving Maxwell’s equation using microscopic single-atom induced dipole moment calculated from the recently developed quantitative rescattering (QRS) theory. We show that macroscopic HHG yields calculated from QRS compared well with those obtained from solving the single-atom time-dependent Schrödinger equation but with great saving of computer time. We also show that macroscopic HHG can be expressed as a product of a “macroscopic wave packet” and the photorecombination cross section of the target gas. The latter enables us to extract target structure from the experimentally measured HHG spectra, thus paves the way to use few-cycle infrared lasers for time-resolved chemical imaging of transient molecules with few-femtosecond temporal resolution.

Ionization and fragmentation of ${\text{C}}_{60}$ fullerenes are studied by time-of-flight mass spectrometry, in elliptically polarized femtosecond laser fields at 797 nm of intensities $I_0=\left(0.5–4.3\right)\times {10}^{14}\text{W}{\text{cm}}^{-2}$. Xe atoms serve as a test case. We derive a qualitative theory describing such polarization studies. It turns out that polarization dependence can very sensitively distinguish single active electron (SAE) and multiple active electrons dynamics. In the case of Xe a clear signature of SAE dynamics is observed, with very pronounced changes in the ion yield as a function of ellipticity, indicative of $\mathcal{N}=5–8$ and 18–22 photon processes for ${\text{Xe}}^{+}$ and ${\text{Xe}}^{2+}$, respectively. In contrast, only a moderate polarization dependence is observed in the ${\text{C}}_{60}$ case, although at least 5 $h\nu$ photons at 797 nm are needed to generate $\text{C}_{60}{}^{+}$ and additional 11 for $\text{C}_{60}{}^{2+}$. At lower intensities, a moderate reduction in the ion yield for circular polarization establishes a two-photon SAE absorption process, connected with the key role of the lowest unoccupied molecular orbital $\left(\text{LUMO}\right)+1\left(t_{1g}\right)$ as “doorway state.” The absence of any polarization effect at 399 nm corroborates this finding. At high intensities enhanced fragmentation is observed, which is tentatively attributed to returning loops of electron trajectories by the combined action of the $\text{C}_{60}{}^{+}$ field and the circularly polarized laser field—in contrast to conventional wisdom that linear polarization should lead to an enhanced recolliding electron yield. No sign of a pronounced multiphoton polarization signature with five and more photons is seen for ${\text{C}}_{60}$ which would be predicted by the SAE picture—although the slopes of the ion yield as a function of intensity are given by the corresponding power laws $\propto I_0^{\mathcal{N}}$. This is taken as clear evidence of multielectron dynamics after reaching the doorway state.

We discuss specific features of the electrodynamic characteristics of quantum systems within the framework of models that include a phenomenological description of the relaxation processes. As is shown by W. E. Lamb, Jr., R. R. Schlicher, and M. O. Scully [Phys. Rev. A 36, 2763 (1987)], the use of phenomenological relaxation operators, which adequately describe the attenuation of eigenvibrations of a quantum system, may lead to incorrect solutions in the presence of external electromagnetic fields determined by the vector potential for different resonance processes. This incorrectness can be eliminated by giving a gauge-invariant form to the relaxation operator. Lamb, Jr., et al. proposed the corresponding gauge-invariant modification for the Weisskopf-Wigner relaxation operator, which is introduced directly into the Schrödinger equation within the framework of the two-level approximation. In the present paper, this problem is studied for the von Neumann equation supplemented by a relaxation operator. First, we show that the solution of the equation for the density matrix with the relaxation operator correctly obtained “from the first principles” has properties that ensure gauge invariance for the observables. Second, we propose a common recipe for transformation of the phenomenological relaxation operator into the correct (gauge-invariant) form in the density-matrix equations for a multilevel system. Also, we discuss the methods of elimination of other inaccuracies (not related to the gauge-invariance problem) which arise if the electrodynamic response of a dissipative quantum system is calculated within the framework of simplified relaxation models (first of all, the model corresponding to constant relaxation rates of coherences in quantum transitions). Examples illustrating the correctness of the results obtained within the framework of the proposed methods in contrast to inaccuracy of the results of the standard calculation techniques are given.

We present the semiclassical laser-field-induced surface-hopping method for the simulation and control of coupled electron-nuclear dynamics in complex molecular systems including all degrees of freedom. Our approach is based on the Wigner representation of quantum mechanics. The combination of the molecular dynamics “on the fly” employing quantum initial conditions with the surface-hopping procedure allows for the treatment of the electronic transitions induced by the laser field. Our semiclassical approach reproduced accurately exact quantum dynamics in a two-electronic-state model system. We demonstrate the scope of our method on the example of the optimal pump-dump control of the trans-cis isomerization of a prototypical Schiff base molecular switch. Our results show that selective photochemistry can be achieved by shaped laser pulses which open new dynamical pathways by suppressing the isomerization through the conical intersections between electronic states.

A necessary condition for the existence of a skyrmion in two-component Bose-Einstein condensates with SU(2) symmetry was recently provided by two of the authors [I. F. Herbut and M. Oshikawa, Phys. Rev. Lett. 97, 080403 (2006)], by mapping the problem to a classical particle in a potential subject to time-dependent dissipation. Here we further elaborate this approach. For two classes of models, we demonstrate the existence of the critical dissipation strength above which the skyrmion solution does not exist. Furthermore, we discuss the local stability of the skyrmion solution by considering the second-order variation. A sufficient condition for the local stability is given in terms of the ground-state energy of a one-dimensional quantum-mechanical Hamiltonian. This condition requires a minimum number of bosons, for a certain class of the trap potential. In the optimal case, the minimum number of bosons can be as small $\sim {10}^4$.

We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second-order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first-order processes versus the slower second-order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. Fölling et al., Nature (London) 448, 1029 (2007); S. Trotzky et al., Science 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic ground states by adiabatic tuning of the superlattice parameters.

We investigate the lifetime of angular momentum in an ultracold strongly interacting Fermi gas, confined in a trap with controllable ellipticity. To determine the angular momentum we measure the precession of the radial quadrupole mode. We find that in the vicinity of a Feshbach resonance, the deeply hydrodynamic behavior in the normal phase leads to a very long lifetime of the angular momentum. Furthermore, we examine the dependence of the decay rate of the angular momentum on the ellipticity of the trapping potential and the interaction strength. The results are in general agreement with the theoretically expected behavior for a Boltzmann gas.