We present a study of Sisyphus cooling of molecules: The scattering of a single photon removes a substantial amount of the molecular kinetic energy and an optical pumping step allows one to repeat the process. A review of the produced cold molecules so far indicates that the method can be implemented for most of them, making it a promising method able to produce a large sample of molecules at sub-mK temperatures. Considerations of the required experimental parameters, for instance the laser power and linewidth or the trap anisotropy and dimensionality, are given. Rate equations, as well as scattering and dipolar forces, are solved using kinetic Monte Carlo methods for several lasers and several levels. For NH molecules, such detailed simulation predicts a 1000-fold temperature reduction and an increase of the phase-space density by a factor of 10${}^7$. Even in the case of molecules with both low Franck-Condon coefficients and a nonclosed pumping scheme, 60% of trapped molecules can be cooled from 100 mK to sub-mK temperatures in a few seconds. Additionally, these methods can be applied to continuously decelerate and cool a molecular beam.

We present an analytically exactly solvable two-state quantum model, in which the coupling has a hyperbolic-tangent temporal shape and the frequency detuning is constant. The exact solution is expressed in terms of associated Legendre functions. An interesting feature of this model is that the excitation probability does not vanish, except for zero pulse area or zero detuning; this feature is attributed to the asymmetric pulse shape. Two limiting cases are considered. When the coupling rises very slowly, it is nearly linear and the tanh model reduces to the shark model introduced earlier. When the coupling rises very quickly, the tanh model reduces to the Rabi model, which assumes a rectangular pulse shape and hence a sudden switch on. Because of its practical significance, we have elaborated the asymptotics of the solution in the Rabi limit, and we have derived the next terms in the asymptotic expansion, which deliver the corrections to the amplitude and the phase of the Rabi oscillations due to the finite rise time of the coupling.

At large anisotropies, the spectrum of the Heisenberg XXZ spin chain separates into “bands” with energies largely determined by the number of domain walls. The band structure is richer with open-boundary conditions: there are more bands and the bands develop intricate fine structures. We characterize and explain these structures and substructures in the open-boundary chain. The fine structures are explained using degenerate perturbation theory. We also present some dynamical consequences of these subband structures, through explicit time evolution of the wave function from initial states motivated by the fine-structure analysis.

We study the Josephson oscillation and self-trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of ${}^{52}$Cr atoms polarized along the symmetry axis of an axially symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length $a$) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large numbers of atoms, whereas self-trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self-trapping towards Josephson oscillation. We consider a simple two-mode description for a qualitative understanding of the dynamics.

Dispersion management of periodically alternating fiber sections with opposite signs of two leading dispersion terms is applied for the regeneration of self-accelerating truncated Airy pulses. It is demonstrated that for such a dispersion management scheme, the direction of the acceleration of the pulse is reversed twice within each period. In this scheme the system features light hot spots in the center of each fiber section, where the energy of the light pulse is tightly focused in a short temporal slot. Comprehensive numerical studies demonstrate a long-lasting propagation also under the influence of a strong fiber Kerr nonlinearity.

A strong photon-photon nonlinear interaction is a necessary condition for a photon blockade. Moreover, this nonlinearity can also result in a bistable behavior in the cavity field. We analyze the relation between the detecting field and the photon blockade in a superconducting circuit-QED system, and show that a photon blockade cannot occur when the detecting field is in the bistable regime. This photon blockade is the microwave-photonics analog of the Coulomb blockade. We further demonstrate that the photon transmission through such a system can be controlled (from photon blockade to transparency) by the detecting field. Numerical calculations show that our proposal is experimentally realizable with current technology.

We study the quantum state of phonons propagating on top of a fluid of light coherently generated in a planar microcavity device by a quasiresonant incident laser beam. In the steady state under a monochromatic pump, because of the finite radiative lifetime of photons, a sizable incoherent population of low-frequency phonons is predicted to appear. Their mean occupation number differs from a Planck distribution and is independent of the photon lifetime. When the photon fluid is subjected to a sudden change of its parameters, additional phonon pairs are created in the fluid with remarkable two-mode squeezing and entanglement properties. Schemes to assess the nonseparability of the phonon state from measurements of the correlation functions of the emitted light are discussed.

The radial degrees of freedom of the biphoton states that are produced in spontaneous parametric down-conversion (SPDC) in the Laguerre-Gaussian (LG) basis are investigated, theoretically and experimentally. We calculated the theoretical azimuthal Schmidt numbers for different combinations of radial indices and found that a larger azimuthal Schmidt number is obtained for higher radial indices of the signal and idler beams. Moreover, larger azimuthal Schmidt numbers are also obtained when the difference between the two radial indices increases. Comparing these theoretical predictions with the azimuthal Schmidt numbers obtained from experimentally measurements, we found good agreement. Experimentally we demonstrated that it is possible to obtain a threefold increase in the azimuthal Schmidt number while maintaining a reasonable coincidence count rate by using LG modes with slightly larger radial indices.

Second-harmonic generation from incoherent conical beams is investigated. A theoretical description of an incoherent conical beam is provided. It is demonstrated that in the case of noncollinear phase matching, the spectrum of the second-harmonic beam narrows with the propagation in a nonlinear crystal. A simplified experiment with two intersecting fundamental beams is described. Numerical simulations of the nonlinear coupling equations are performed and good agreement with the theory is obtained.

We propose and investigate a family of nonlinear metamaterials in which light rays propagate just in one direction—one-way propagation. Furthermore, we argue how such nonlinear media could provide an analog model for investigating the Born-Infeld Lagrangian in the realm of fields larger than its scale field.

Based on results well known in the mathematics literature but not yet common knowledge in the physics literature, we conduct a study on three-fermionic systems with six, seven, eight, and nine single-particle states. Via introducing special polynomial invariants playing the role of entanglement measures the structure of the stochastic local operations and classical communication (SLOCC) entanglement classes is investigated. The SLOCC classes of the six- and seven-dimensional cases can elegantly be described by special subconfigurations of the Fano plane. Some special embedded systems containing distinguishable constituents are arising naturally in our formalism, namely, three-qubits and three-qutrits. In particular, the three fundamental invariants $I_6$, $I_9$, and $I_{12}$ of the three-qutrits system are shown to arise as special cases of the four fundamental invariants of three-fermions with nine single-particle states.

We present a theoretical scheme to study optical cavity quantum electrodynamics using dark-state polaritons. Exploiting the highly tunable lifetimes of the photons in the form of cavity dark-state polaritons, we push the strong coupling of single optical photons to an effective two-level emitter in a Rydberg-blockade atomic ensemble to an unprecedented regime. The resulting Jaynes–Cummings model with extremely strong coupling is of fundamental interest. We discuss applications in controlled quantum Rabi oscillation, nonlinear spectroscopy of the Jaynes-Cummings ladder, as well as the generation of nonclassical states, all based on light-matter interactions in the optical domain.

Despite all the complexity of the underlying nonlinear physics, the filamentation of ultrashort optical field wave forms is shown to obey a set of physically transparent scaling laws. This scaling is applicable within a remarkably broad range of laser powers, pulse widths, gas pressures, and propagation paths, suggesting specific recipes for the power scaling of filamentation-based pulse compression.

We develop a full quantum-optical approach for optical self-feedback of a microcavity laser. These miniaturized devices work in a regime between the quantum and classical limit and are test beds for the differences between a quantized theory of optical self-feedback and the corresponding semiclassical theory. The light intensity and photon statistics are investigated with and without an external feedback: We show that in the low-gain limit, where relaxation oscillations do not appear, the recently observed photon bunching in a quantum-dot microcavity laser with optical feedback can be accounted for only by the fully quantized model. By providing a description of laser devices with feedback in the quantum limit, we reveal insights into the origin of bunching in quantized and semiclassical models.

We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patterns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic preparation of their ground states.

Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated code words with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent-state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations [passive linear optics: beam splitters and phase shifters; second-order nonlinear optics (or active linear optics): squeezers, along with homodyne or heterodyne detection measurements] and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communication, one has to incorporate non-Gaussian, i.e., third- or higher-order nonlinear operations in the receiver. Finally we compare our Gaussian receiver limit with experimentally feasible non-Gaussian receivers and show that in the regime of low received photon flux, it is possible to overcome the Gaussian receiver limit by relatively simple non-Gaussian receivers based on photon counting.

We describe high-order-harmonic generation (HHG) within the adiabatic strong-field approximation (ASFA) where the ground state and its energy adiabatically follows the instantaneous external field and within the Stark-shift-corrected SFA (SSFA), where only the energy shift is accounted for. We show that the molecular polarizability reflects the significance of field-induced orbital distortion in the HHG process. We show that for CO${}_2$, which possesses a relatively low polarizability, the two-center interference minimum can be clearly seen in both the ASFA and the SSFA. This finding is in agreement with experimental data at large wavelength. Moreover, we introduce a method for analyzing the recombination events. This method relies on averaging the recombination matrix elements weighted with the photon emission probability of each harmonic. In the case of CO${}_2$ this method confirms that the interference minimum is determined by recombination to the two O atoms. We use the example of N${}_2$O, which has a moderate polarizability, to show that the number of centers taking part in the creation of the interference minimum may change depending on the intensity. Finally, we show that in the short-pulse limit, the minimum in the HHG spectrum from oriented N${}_2$O strongly depends on the molecular orientation and carrier-envelope phase.

It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and where to target stable Kerr frequency combs in the parameter space defined by the frequency detuning and the pump power is provided. Moreover, the work presented also includes the organization of various dynamical regimes in terms of bifurcation points of higher codimension in regions of parameter space that were previously unexplored in the Lugiato-Lefever equation. We discuss different dynamical instabilities such as oscillations and chaotic regimes.

We use a fiber-based double-slit Young interferometer for studying the far-field spatial distribution of the two-photon coincidence rate (coincidence pattern) for various quantum states with different degree of spatial entanglement. The realized experimental approach allows us to characterize coincidence patterns for different states without any modifications of the setup. Measurements were carried out with path-entangled and separable states. The dependence of the coincidence pattern on the phase of the interferometer for superposition and separable states was studied. The results have implications for using of nonclassical light in multiphoton imaging, quantum lithography, and studies of phase decoherence.

We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as the sum of a projection onto the local conserved charges of the system and a projection onto the nonlocal ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit, although we find no indications that the eigenstate thermalization hypothesis applies.