We present theoretical studies of high-order-harmonic generation (HHG) produced by nonhomogeneous fields resulting from the illumination of plasmonic nanostructures with a short laser pulse. We show that both the inhomogeneity of the local fields and the confinement of the electron movement play an important role in the HHG process and lead to the generation of even harmonics and a significantly increased cutoff, more pronounced for the longer-wavelength cases studied. In order to understand and characterize the new HHG features, we employ two different approaches: the numerical solution of the time-dependent Schrödinger equation and the semiclassical approach known as the strong-field approximation (SFA). Both approaches predict comparable results and show the new features, but by using the semiclassical arguments behind the SFA and time-frequency analysis tools, we are able to fully understand the reasons for the cutoff extension.

We develop a rigorous, mathematically consistent description of $\mathrm{PT}$-symmetric optical systems by using second quantization. We demonstrate the possibility of significant spontaneous generation of photons in $\mathrm{PT}$-symmetric systems. Further, we show the emergence of Hanbury Brown–Twiss correlations in spontaneous generation. We show that the spontaneous generation determines decisively the nonclassical nature of fields in $\mathrm{PT}$-symmetric systems. Our work can be applied to other systems, such as plasmonic structures, where losses are compensated by gain mechanisms.

One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particlelike $or$ a wavelike behavior, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.

An entanglement-generating protocol is described for two qubits coupled to a cavity field in the bad-cavity limit. By measuring the amplitude of a field transmitted through the cavity, an entangled spin-singlet state can be established probabilistically. Both fundamental limitations and practical measurement schemes are discussed, and the influence of dissipative processes and inhomogeneities in the qubits are analyzed. The measurement-based protocol provides criteria for selecting states with an infidelity scaling linearly with the qubit-decoherence rate.

The van der Waals complex of the helium dimer has a binding energy of $\sim$10${}^{-7}$ eV and a bond distance of $\sim$52 Å. Our ab initio electronic structure calculations show that in an ac electric field of $\approx$$5.614\times {10}^{19}$ W/cm${}^2$ with a high photon energy ($\approx$108 eV), stable He${}_2$ molecules with a binding energy of 12.5 eV, which are much stronger than conventional molecular hydrogen bonds, are produced. The chemical bond distance of He${}_2$ produced by the strong laser field is equal to $2.01$ Å. The strength of the chemical bond of He${}_2$ is reflected in more than 4500 rovibrational bound states. The strongly bound He${}_2$ is aligned by the linear polarized field, like in other diatomic molecules. However, it is shown that the mechanism of the alignment of the He${}_2$ molecule produced by light differs from the usual alignment mechanism of real molecules. Our results indicate the possibility of producing unusual chemical species, and perhaps chemical reactions that differ from what we know today, in the presence of strong electromagnetic radiation.

The Gunnarsson-Lundqvist (GL) theorem of density functional theory states that there is a one-to-one relationship between the density of the lowest nondegenerate excited state of a given symmetry and the external potential. As a consequence, knowledge of this excited state density determines the external potential uniquely. [The GL theorem is the equivalent for such excited states of the Hohenberg-Kohn (HK) theorem for nondegenerate ground states.] For other excited states, there is no equivalent of the GL or HK theorem. For these states, there thus exist multiple potentials that generate the excited-state density. We show, by example, the satisfaction that the GL theorem holds and the multiplicity of potentials for excited states.

Single charge transfer in low-energy ${\mathrm{Na}}^{+}+{}^{87}\mathrm{Rb}(5s,5p)$ collisions is investigated using magneto-optically trapped Rb atoms and high-resolution recoil-ion momentum spectroscopy. The three-dimensional reconstruction of the recoil-ion momentum provides accurate relative cross sections for the active channels along with their associated distributions in projectile scattering angle. The measurements are accompanied by molecular close-coupling calculations. The predicted diffractionlike oscillations in angular distributions are clearly resolved by the experiment. An excellent agreement is found between the present molecular calculations and the experimental data.

We demonstrate one-dimensional robust Raman cooling in a three-level $\Lambda$-type atom, where the velocity-selective transfer is carried out by a STIRAP pulse. In contrast to the standard Raman method, the excitation profile is insensitive to variations in the pulse duration, whereas its position and width are nevertheless under control. Two different cooling variants are examined and we show that subrecoil temperatures are attainable in both cases.

If a quantum mechanical particle passes a spatially finite region of a purely time-dependent potential, coherent emission and absorption of energy take place. Due to Zeeman interaction, this situation can be realized with neutrons crossing an oscillating magnetic field. We solve the corresponding Schrödinger equation for fields consisting of an arbitrary number of frequencies and measure the calculated transition amplitudes for the quantized energy transfer by means of time-dependent neutron interferometry. Investigating the interferometer contrast for magnetic signals consisting of a high number of modes whose phases are randomly distributed shows that noise fields and therefore decoherence processes can be modeled in this calculation as well.

We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect, but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling reminiscent of Bloch oscillations.

We report on measurements of splitting Bose-Einstein condensates (BEC) by using a time-dependent optical lattice potential. First, we demonstrate the division of a BEC into a set of equally populated components by means of time-dependent control of Landau-Zener tunneling in a vertical lattice potential. Next, we apply time-dependent optical Bragg mirrors to a BEC oscillating in a harmonic trap. We demonstrate high-order Bragg reflection of the condensate due to multiphoton Raman transitions, where the depth of the optical lattice potential allows for a choice of the order of the transition. Finally, a combination of multiple Bragg reflections and Landau-Zener tunneling allows for the generation of macroscopic arrays of condensates with potential applications in atom optics and atom interferometry.

The quantum dynamics of an ultracold diatomic molecule tunneling and diffusing in a one-dimensional optical lattice exhibits unusual features. While it is known that the process of quantum tunneling through potential barriers can break up a bound-state molecule into a pair of dissociated atoms, interference and reassociation produce intricate patterns in the time-evolving site-dependent probability distribution for finding atoms and bound-state molecules. We find that the bound-state molecule is unusually resilient against break up at ultralow binding energy $E_b$ ($E_b$ much smaller than the barrier height of the lattice potential). After an initial transient, the bound-state molecule spreads with a width that grows as the square root of time. Surprisingly, the width of the probability of finding dissociated atoms does not increase with time as a power law.

We study the influence of population imbalance on the pairing, spin, and density instabilities of a two-component ideal Fermi gas after a sudden quench of interactions near a Feshbach resonance. Over a large region of parameters the pairing instability is dominated by finite-momentum pairing, suggesting the possibility of observing Fulde-Ferrell-Larkin-Ovchinnikov–like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the Bardeen-Cooper-Schrieffer side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the Bose-Einstein-condensate side of the resonance, the pairing instability is present for scattering lengths larger than a critical value that is only weakly dependent on population imbalance and always smaller than the scattering length at which the Stoner-like spin instability occurs.

We experimentally demonstrate the importance of two-photon symmetry for the propagation of spatial quantum correlations in a multiple-scattering disordered system. Two distinguishable entangled photons with tunable spatial exchange symmetry are sent through the scattering medium. The two photons are observed to have an ensemble-averaged tendency to cluster together (bosonic symmetry) or to avoid each other (fermionic symmetry). An intermediate degree of clustering is observed for anyonic exchange symmetry.

We consider the nonlinear Schrödinger flow past a dynamic obstacle, where the obstacle itself is a localized solitary wave coupled to the fluid. This is achieved in a cross-phase coupled nonlinear Schrödinger system. Similar to an immobile obstacle, we find three distinct dynamical regimes of sub-, trans-, and supercritical flow. We determine the phase diagram and show that the subcritical speed, below which a superfluid flow is possible, depends on the cross coupling and thus on the backaction of the fluid on the obstacle. The time dynamics of the cross-phase coupled system is analyzed numerically and we use the developed hydrodynamic model to interpret the results.

We study wave propagation in linear arrays composed of pairs of conjugate waveguides with balanced gain and loss, that is, arrays of $\mathcal{PT}$-symmetric couplers, where the linear spectrum is known to feature high-frequency and low-frequency branches. We introduce a domain wall by switching the gain and loss in half of the array and analyze the scattering of linear waves on this defect. The analysis reveals two major effects: amplification of both reflected and transmitted waves and excitation of the reflected and transmitted low-frequency and high-frequency waves by the incident high-frequency and low-frequency waves, respectively.

Single-step implementations of multiqubit gates are generally believed to provide a simpler design, a faster operation, and a lower decoherence. For three coupled qubits interacting with a photon field, a realizable scheme for a single-step Toffoli gate is investigated. We find that the three-qubit system can be described by four effective modified Jaynes-Cummings models in the states of two control qubits. Within the rotating-wave approximation, the modified Jaynes-Cummings models are shown to be reduced to the conventional Jaynes-Cummings models with renormalized couplings between qubits and photon fields. A single-step Toffoli gate is shown to be realizable with tuning of the four characteristic oscillation periods that satisfy a commensurate condition. Possible values of the system parameters are estimated for a single-step Toffoli gate. Further, we discuss our single-step Toffoli-gate operation errors due to imperfections in the system parameters; numerical calculations show that a Toffoli gate with high fidelity can be obtained by adjusting pairs of the photon-qubit and qubit-qubit coupling strengths. In addition, a decoherence effect on the Toffoli-gate operation due to a thermal reservoir is discussed.

We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO presents two ${\chi }^{\left(2\right)}$-level oscillation thresholds that are therefore much lower than for a ${\chi }^{\left(3\right)}$ OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a ${\chi }^{\left(2\right)}$ cascaded device also has potential applications in frequency conversion to far-infrared regimes. But, most importantly, it can generate novel multipartite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian and therefore not describable by any semiclassical model. In this paper, we derive quantum stochastic equations in the positive-$P$ representation and undertake an analysis of steady-state and dynamical properties of this system.

A scheme to squeeze the center-of-mass motional quadratures of a quantum mechanical oscillator below its standard quantum limit is proposed and analyzed theoretically. It relies on the dipole-dipole coupling between a magnetic dipole mounted on the tip of a cantilever to equally oriented dipoles located on a mesoscopic tuning fork. We also investigate the influence of several sources of noise on the achievable squeezing, including classical noise in the driving fork and the clamping noise in the oscillator. A detection of the state of the cantilever based on state transfer to a light field is considered. We investigate possible limitations of that scheme.