We investigate the dynamics of a two-mode laser system by extending the two-mode Tavis-Cummings model with dissipative channels and incoherent pumping and by applying the mean-field approximation in the thermodynamic limit. To this end we analytically calculate up to four possible nonequilibrium steady states (fixed points) and determine the corresponding complex phase diagram. Various possible phases are distinguished by the actual number of fixed points and their stability. In addition, we apply three time-delayed Pyragas feedback control schemes. Depending on the time delay and the strength of the control term, this can lead to the stabilization of unstable fixed points or to the selection of a particular cavity mode that is macroscopically occupied.

The theoretical basis leading to the creation of a light field with a hexagonal honeycomb structure resembling graphene is considered along with its experimental realization and its interaction with atoms. It is argued that associated with such a light field is an optical dipole potential which leads to the diffraction of the atoms, but the details depend on whether the transverse spread of the atomic wave packet is larger than the transverse dimensions of the optical lattice (resonant Kapitza-Dirac effect) or smaller (optical Stern-Gerlach effect). Another effect in this context involves the creation of gauge fields due to the Berry phase acquired by the atom moving in the light field. The experimental realization of the light field with a honeycomb hexagonal structure is described using holographic methods and we proceed to explore the atom diffraction in the Kapitza-Dirac regime as well as the optical Stern-Gerlach regime, leading to momentum distributions with characteristic but different hexagonal structures. The artificial gauge fields too are shown to have the same hexagonal spatial structure and their magnitude can be significantly large. The effects are discussed with reference to typical parameters for the atoms and the fields.

Conventional theoretical approaches to model strong field phenomena driven by plasmonic fields are based on the length gauge formulation of the laser-matter coupling. Obviously, from the physical point of view, there exists no preferable gauge and, consequently, the predictions and outcomes should be independent of this choice. The use of the length gauge is mainly due to the fact that the quantity obtained from finite-element simulations of plasmonic fields is the plasmonic enhanced laser electric field rather than the laser vector potential. We develop, from first principles, the velocity gauge formulation of the problem and we apply it to the high-order-harmonic generation (HHG) in atoms. A comparison to the results obtained with the length gauge is made. As expected, it is analytically and numerically demonstrated that both gauges give equivalent descriptions of the emitted HHG spectra resulting from the interaction of a spatially inhomogeneous field and the single active electron model of the helium atom. We discuss, however, advantages and disadvantages of using different gauges in terms of numerical efficiency, which turns out to be very different. In order to understand it, we analyze the quantum mechanical results using time-frequency Gabor distributions. This analysis, combined with classical calculations based on solutions of the Newton equation, yields important physical insight into the electronic quantum paths underlying the dynamics of the harmonic generation process. The results obtained in this way also allow us to assess the quality of the quantum approaches in both gauges and put stringent limits on the numerical parameters required for a desired accuracy.

We investigate the propagation of microwave photons in a one-dimensional open waveguide interacting with a number of artificial atoms (qubits). Within the formalism of projection operators and a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme for the calculation of the transmission and reflection factors of the microwave signal in a waveguide which contains an arbitrary number $N$ of noninteracting qubits. We considered in detail the resonances and photon-mediated entanglement for two and three qubits in a chain. We showed that in the non-Markovian case the resonance widths, which define the decay rates of the entangled state, can be much smaller than the decay width of an individual qubit. It is also shown that for identical qubits in the long-wavelength limit a coherent superradiant state is formed with the width being equal to the sum of the widths of spontaneous transitions of $N$ individual qubits. The results obtained in the paper are of general nature and can be applied to any type of qubits. The specific properties of the qubit are only encoded in the two parameters: the qubit energy $\mathrm{\Omega }$ and the rate of spontaneous emission $\mathrm{\Gamma }$.

Quantum routers are the necessary elements of the quantum information network, and thus their routing capabilities are particularly important. With the atomic mirrors robustly controlling the reflected or transmitted coefficient of the waveguide photon, we show that a two-level atom can be served as an ideal quantum router to redirect a single photon from the input waveguide into the output waveguides (OWGs) with designable probabilities, e.g., $100\%$ for one OWG, $1/2$ to one of the two OWGs, and $1/3$ to one of the three OWGs, etc.. The influence of the atomic dissipations on the routing capability is also discussed.

We propose a protocol to probe the ultrafast evolution and dephasing of coherent electronic excitation in molecules in the time domain by the intrinsic streaking field generated by the molecule itself. Coherent electronic motion in the endohedral fullerene ${\mathrm{Ne}@\mathrm{C}}_{60}$ is initiated by a moderately intense femtosecond UV-visible pulse leading to coherent oscillations of the molecular dipole moment that persist after the end of the laser pulse. The resulting time-dependent molecular near field is probed through the momentum modulation of photoemission from the central neon atom by a time-delayed attosecond XUV pulse. Our ab initio time-dependent density functional theory and classical trajectory simulations predict that this self-streaking signal accurately traces the molecular dipole oscillations in real time. We discuss the underlying processes and give an analytical model that captures the essence of our ab initio simulations.

When a quantum system interacts with its environment it may incur in decoherence. Quantum erasure makes it possible to restore coherence in a system by gaining information about its environment, but measuring the whole of it may be prohibitive: Realistically, one might be forced to address only an accessible subspace and neglect the rest. In such a case, under what conditions will quantum erasure still be effective? In this work we compute analytically the largest recoverable coherence of a random qubit plus environment state and we show that it approaches 100% with overwhelmingly high probability as long as the dimension of the accessible subspace of the environment is larger than $\sqrt{D}$, where $D$ is the dimension of the whole environment. Additionally, we find a sharp transition between a linear behavior and a power-law behavior as soon as the dimension of the inaccessible environment exceeds the dimension of the accessible one. Our results imply that the typical states of a qubit plus environment system admit a measurement spanning only about $\sqrt{D}$ degrees of freedom, any outcome of which projects the qubit on a maximally coherent state. This suggests, for instance, that in the dynamics of open quantum systems, if the interactions are known, it would in principle be possible to gain sufficient information and restore coherence in a qubit by dealing with a fraction of the physical resources.

The preparation of a quantum degenerate gas of heteronuclear molecules has been an outstanding challenge. We use path-integral quantum Monte Carlo simulations to understand the role of interactions and finite temperature effects in the protocol currently employed to adiabatically prepare a low-entropy gas of polar molecules in a lattice starting from an ultracold Bose-Fermi mixture. We find that interspecies interactions affect the final temperature of the mixture after the adiabatic loading procedure and detrimentally limit the molecular peak filling. Our conclusions are in agreement with recent experimental measurements [Moses et al., Science 350, 659 (2015)] and therefore are of immediate relevance for the myriad experiments that aim to form molecules from dual-species atomic gases.

We study the origin of the cusp structure in the transverse or lateral electron momentum distribution (TEMD) for the process of tunneling ionization driven by a linearly polarized laser pulse. We show that the appearance of the cusp in the TEMD can be explained as follows. Projection on the set of the Coulomb scattering states leads to the appearance of elementary cusps which have a simple structure as functions of the lateral momentum. This structure is independent of the detailed dynamics of the ionization process and can be described analytically. These elementary cusps can be used to describe the cusp structure in TEMD.

When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.

The dyadic Green's function of the inhomogeneous vector Helmholtz equation describes the field pattern of a single frequency point source. It appears in the mathematical description of many areas of electromagnetism and optics including both classical and quantum, linear and nonlinear optics, dispersion forces (such as the Casimir and Casimir-Polder forces), and in the dynamics of trapped atoms and molecules. Here we compute the Green's function for a layered topological insulator. Via the magnetoelectric effect, topological insulators are able to mix the electric $\mathbf{E}$ and magnetic induction $\mathbf{B}$ fields and, hence, one finds that the TE and TM polarizations mix on reflection from or transmission through an interface. This leads to unusual field patterns close to the surface of a topological insulator.

We derive the explicit expression for the Casimir energy between a sphere and a one-dimensional grating in terms of the sphere and grating reflection matrices. This expression is valid for arbitrary materials, sphere radius, and grating geometric parameters. We then numerically calculate the Casimir energy between a metallic (gold) sphere and a dielectric (fused silica) lamellar grating at room temperature, and we explore its dependence on the sphere radius, grating-sphere separation, and lateral displacement. We quantitatively investigate the geometrical dependence of the interaction, which is sensitive to the grating height and filling factor, and we show how the sphere can be used as a local sensor of the Casimir force geometric features. Toward that end, we mostly concentrate on separations and sphere radii of the same order of the grating parameters (here of the order of $1 \mu \text{m}$). We also investigate the lateral component of the Casimir force, resulting from the absence of translational invariance. We compare our results with those obtained within the proximity force approximation (PFA). When applied to the sphere only, the PFA overestimates the strength of the attractive interaction, and we find that the discrepancy is larger in the sphere-grating than in the sphere-plane geometry. On the other hand, when the PFA is applied to both the sphere and the grating, it provides a better estimate of the exact results, simply because the effect of a single grating is underestimated, thus leading to a partial compensation of errors.

We present a Heisenberg-picture approach to the electric dipole interaction of two generally nonidentical atoms, one of which is initially excited, and address the question of whether the dependence of the interaction energy on the interatomic separation $r$ is purely monotonic or is sinusoidally modulated as it falls off with $r$. We derive energies of both types and associate them with different model assumptions and physical effects. The sinusoidally modulated form is the interaction energy involved in reversible exchange of excitation (“pendulation”). The monotonic form characterizes an energy shift associated with effectively irreversible (Förster) excitation transfer.

We present an analytic Bogoliubov description of a Bose-Einstein condensate of polar molecules trapped in a quasi-two-dimensional geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and static structure factors. This method can be applied to any homogeneous, two-component system with linear coupling and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. The nature of these instabilities is clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave responses in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\mathrm{\Lambda }$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\mathrm{\Sigma }$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.

The experimental realization of lattices with Chern bands in ultracold-atom and photonic systems has motivated the study of time-dependent phenomena, such as spatial propagation, in lattices with nontrivial topology. We study the dynamics of Gaussian wave packets on the Haldane honeycomb Chern-band lattice model, in the presence of a harmonic trap. We focus on the transverse response to a force, which is due partly to the Berry curvature and partly to the transverse component of the energy band curvature. We evaluate the accuracy of a semiclassical description, which treats the wave packet as a point particle in both real and momentum space, in reproducing the motion of a realistic wave packet with finite extent. We find that, in order to accurately capture the wave-packet dynamics, the extent of the wave packet in momentum space needs to be taken into account: The dynamics is sensitive to the interplay of band dispersion and Berry curvature over the finite region of momentum (reciprocal) space where the wave packet has support. Moreover, if the wave packet is prepared with a finite initial momentum, the semiclassical analysis reproduces its motion as long as it has a large overlap with the eigenstates of a single band. The semiclassical description generally improves with increasing real-space size of the wave packet, as long as the external conditions (e.g., external force) remain uniform throughout the spatial extent of the wave packet.

The electronic, rotational, and vibrational components of the ultrafast optical nonlinearity in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are measured directly and absolutely at intensities up to the ionization threshold of $\sim {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. As the most basic nonlinear interactions of the simplest molecules exposed to high fields, these results constitute a benchmark for high-field laser-matter theory and simulation.

Studying time-dependent behavior in lasers is analytically difficult due to the saturating nonlinearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time and space in conventional finite-difference time-domain approaches. We describe here an efficient spectral method to overcome these shortcomings in complex lasers of arbitrary shape, gain medium distribution, and pumping profile. We apply this approach to a quasidegenerate two-mode laser in different dynamical regimes and compare the results in the long-time limit to the steady-state ab initio laser theory (SALT), which is also built on a spectral method but makes a more specific ansatz about the long-time dynamical evolution of the semiclassical laser equations. Analyzing a parameter regime outside the known domain of validity of the stationary inversion approximation, we find that for only a narrow regime of pump powers the inversion is not stationary, and that this, as pump power is further increased, triggers a synchronization transition upon which the inversion becomes stationary again. We provide a detailed analysis of mode synchronization (also known as cooperative frequency locking), revealing interesting dynamical features of such a laser system in the vicinity of the synchronization threshold.

The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high-fidelity single-qubit gates for the hyperfine qubit of a ${}^{171}\text{Yb}^{+}$ ion trapped in a microfabricated surface-electrode ion trap. Gate error is characterized using a randomized benchmarking protocol and an average error per randomized Clifford group gate of $3.6\left(3\right)\times {10}^{-4}$ is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length.

We report a point-particle ponderomotive model of a Dirac electron oscillating in a high-frequency field. Starting from the Dirac Lagrangian density, we derive a reduced phase-space Lagrangian that describes the relativistic time-averaged dynamics of such a particle in a geometrical-optics laser pulse propagating in vacuum. The pulse is allowed to have an arbitrarily large amplitude provided that radiation damping and pair production are negligible. The model captures the Bargmann-Michel-Telegdi (BMT) spin dynamics, the Stern-Gerlach spin-orbital coupling, the conventional ponderomotive forces, and the interaction with large-scale background fields (if any). Agreement with the BMT spin precession equation is shown numerically. The commonly known theory in which ponderomotive effects are incorporated in the particle effective mass is reproduced as a special case when the spin-orbital coupling is negligible. This model could be useful for studying laser-plasma interactions in relativistic spin-$1/2$ plasmas.