We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. Höltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer-gas atoms, our model allows us to investigate the influence of nonhomogeneous buffer-gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile, and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (forced sympathetic cooling).

By using a sum-rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a one-dimensional (1D) harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized in the high-temperature collisionless regime by a beating signal of two different frequencies (${\omega }_z$ and $3{\omega }_z$), while in the high-temperature collisional regime, the excitation consists of a single frequency ($\sqrt{7}{\omega }_z$). This behavior differs from the case of the lowest breathing mode whose excitation consists of a single frequency ($2{\omega }_z$) in both regimes. Our predictions for the dipole compression mode open promising perspectives for the experimental investigation of collisional effects in 1D configurations.

We develop an approach to enable the full-wave simulation of stimulated Brillouin scattering and related phenomena in a frequency-domain, finite-element environment. The method uses transformation-optics techniques to implement a time-harmonic coordinate transform that reconciles the different frames of reference used by electromagnetic and mechanical finite-element solvers. We show how this strategy can be successfully applied to bulk and guided systems, comparing the results with the predictions of established theory.

We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of preferred phases when two micromasers are coupled together. Using perturbation theory, we show that the behavior of the phase distribution is strongly dependent on exactly how the oscillators are coupled. In the quantum regime where photon occupation numbers are low we find that, although synchronization effects are rather weak, they are nevertheless significantly stronger than expected from a semiclassical description of the phase dynamics. We also compare the behavior of the phase distribution with the mutual information of the two oscillators and show that they can behave in rather different ways.

A new theory-independent noncontextuality inequality is presented [R. Kunjwal and R. W. Spekkens, Phys. Rev. Lett. 115, 110403 (2015)] based on a Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing noncontextuality inequalities, we show that such result can be generalized from a KS set to the noncontextuality inequalities not only for a state-independent scenario but also for a state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.

The phase-space description of bosonic quantum systems has numerous applications in such fields as quantum optics, trapped ultracold atoms, and transport phenomena. Extension of this description to the case of fermionic systems leads to formal Grassmann phase-space quasiprobability distributions and master equations. The latter are usually considered as not possessing probabilistic interpretation and as not directly computationally accessible. Here, we describe how to construct $c$-number interpretations of Grassmann phase-space representations and their master equations. As a specific example, the Grassmann $B$ representation is considered. We discuss how to introduce $c$-number probability distributions on Grassmann algebra and how to integrate them. A measure of size and proximity is defined for Grassmann numbers, and the Grassmann derivatives are introduced which are based on infinitesimal variations of function arguments. An example of $c$-number interpretation of formal Grassmann equations is presented.

The nonlinear Compton scattering rate in a rotating electric field is explicitly calculated. For this purpose, an approximate solution to the Klein-Gordon equation in the presence of a rotating electric field is applied. An analytical expression for the emission rate is obtained, as well as a simplified approximation adequate for implementation in kinetic codes. The spectrum is numerically calculated for present-day optical and x-ray laser parameters. The results are compared to the standard Volkov-Ritus rate for a particle in a plane wave, which is commonly assumed to be valid for a rotating electric field under certain conditions. Substantial deviations between the two models, in both the radiated power and the spectral shape, are demonstrated. First, the typical number of photons participating in the scattering process is much smaller compared to the Volkov-Ritus rate, resulting in up to an order of magnitude lower emitted power. Furthermore, our model predicts a discrete harmonic spectrum for electrons with low asymptotic momentum compared to the field amplitude. This discrete structure is a clear imprint of the electric field frequency, as opposed to the Volkov-Ritus rate, which reduces to the constant crossed field rate for the physical conditions under consideration. Our model predictions can be tested with present-day laser facilities.

Quantum information processing provides remarkable advantages over its classical counterpart. Quantum optical systems have been proved to be sufficient for realizing general quantum tasks, which, however, often rely on single-photon sources. In practice, imperfect single-photon sources, such as a weak-coherent-state source, are used instead, which will inevitably limit the power in demonstrating quantum effects. For instance, with imperfect photon sources, the key rate of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol will be very low, which fortunately can be resolved by utilizing the decoy-state method. As a generalization, we investigate an efficient way to simulate single photons with imperfect ones to an arbitrary desired accuracy when the number of photonic inputs is small. Based on this simulator, we can thus replace the tasks that involve only a few single-photon inputs with the ones that make use of only imperfect photon sources. In addition, our method also provides a quantum simulator to quantum computation based on quantum optics. In the main context, we take a phase-randomized coherent state as an example for analysis. A general photon source applies similarly and may provide some further advantages for certain tasks.

We propose a scheme for frequency-domain quantum computation (FDQC) in which the errors due to crosstalk are suppressed using extra physical systems coupled to a cavity. FDQC is a promising method to realize large-scale quantum computation, but crosstalk is a major problem. When physical systems employed as qubits satisfy specific resonance conditions, gate errors due to crosstalk increase. In our scheme, the errors are suppressed by controlling the resonance conditions using extra physical systems.

We propose schemes of controlled-Z and controlled-not gates with ultracold neutral atoms based on deterministic phase accumulation during double adiabatic passage of the Stark-tuned Förster resonance of Rydberg states. The effect of deterministic phase accumulation during double adiabatic passage in a two-level quantum system has been analyzed in detail. Adiabatic rapid passage using nonlinearly chirped pulses with rectangle intensity profile has been discussed. Nonlinear time dependence of the energy detuning from the Förster resonance is used to achieve a high fidelity of population transfer between Rydberg states. Fidelity of two-qubit gates has been studied with an example of the $90S+96S\to 90P+95P$ Stark-tuned Förster resonance in Cs Rydberg atoms.

Simulating unitary dynamics unavailable in nature by finite perturbative expansion of its Hamiltonian is a straightforward and intuitive approach which often fails when continuous-variable systems are considered. We propose a solution to this problem, which lies in constructing these expansions from suitably bounded operators. We demonstrate this by suggesting an elementary bounded gate based on Rabi coupling and showing its optimality and suitability for approximations of unitary operators.

We present the first spectroscopic studies of the $C{}^1{\mathrm{\Sigma }}^{+}$ electronic state and the $A{}^1{\mathrm{\Sigma }}^{+}$–$b{}^3{\mathrm{\Pi }}_{0^{+}}$ complex in ${}^7\mathrm{Li}-{}^{85}\mathrm{Rb}$. Using resonantly enhanced, two-photon ionization, we observed $v=7$, 9, 12, 13, and 26–45 of the $C{}^1{\mathrm{\Sigma }}^{+}$ state. We augment the REMPI data with a form of depletion spectra in regions of dense spectral lines. The $A{}^1{\mathrm{\Sigma }}^{+}$–$b{}^3{\mathrm{\Pi }}_{0^{+}}$ complex was observed with depletion spectroscopy, depleting to vibrational levels $v=0\to 29$ of the $A{}^1{\mathrm{\Sigma }}^{+}$ state and $v=8\to 18$ of the $b{}^3{\mathrm{\Pi }}_{0^{+}}$ state. For all three series, we determine the term energy and vibrational constants. Finally, we outline several possible future projects based on the data presented here.

We simulate a one-dimensional fermionic optical lattice to analyze heating due to nonadiabatic lattice loading. Our simulations reveal that, similar to the bosonic case, density redistribution effects are the major cause of heating in harmonic traps. We suggest protocols to modulate the local-density distribution during the process of lattice loading in order to reduce the excess energy. Our numerical results confirm that linear interpolation of the trapping potential and/or the interaction strength is an efficient method of doing so, bearing practical applications relevant to experiments.

Photoinduced dynamics of a weakly bound triatomic molecule $\mathrm{He}{{\mathrm{H}}_2}^{+}$ exposed to electromagnetic radiation is investigated by time-dependent quantum wave-packet propagation. Adopting a two-dimensional linear H-H-He model, the three lowest-lying potential energy surfaces (PESs) and corresponding dipole moment surfaces are constructed. One of the two characteristic excited PESs of $\mathrm{He}{{\mathrm{H}}_2}^{+}$ leads to the charge-transfer reaction ${{\mathrm{H}}_2}^{+}+\mathrm{He}\to {\mathrm{H}}_2+\mathrm{H}{\mathrm{e}}^{+}$ and the other corresponds to the first excited state of ${{\mathrm{H}}_2}^{+}$ perturbed by the presence of He. When $\mathrm{He}{{\mathrm{H}}_2}^{+}$ is exposed to a femtosecond intense ultraviolet light pulse ($I=4\times {10}^{14}\mathrm{W}\mathrm{c}{\mathrm{m}}^{-2}, \lambda =400\mathrm{nm}$), both of the two excited PESs are found to be coupled with the light field and a variety of reaction pathways become opened so that HeH, $\mathrm{He}{\mathrm{H}}^{+}, {\mathrm{H}}_2,{{\mathrm{H}}_2}^{+},\mathrm{H},{\mathrm{H}}^{+}$, He, and $\mathrm{H}{\mathrm{e}}^{+}$ are produced. Simulations also show that the anharmonic coupling between the two stretching vibrational modes in $\mathrm{He}{{\mathrm{H}}_2}^{+}$ leads to the stabilization of the ${{\mathrm{H}}_2}^{+}$ moiety against the decomposition into $\mathrm{H}+{\mathrm{H}}^{+}$ compared with bare ${{\mathrm{H}}_2}^{+}$. The theoretical findings of the formation of $\mathrm{He}{\mathrm{H}}^{+}$ composed of the most abundant elements in the universe are also discussed in view of the theoretical modeling of the chemical reactions proceeding in the primordial gas and in the interstellar medium.

Atom interferometers are a useful tool for precision measurements of fundamental physical phenomena, ranging from the local gravitational-field strength to the atomic fine-structure constant. In such experiments, it is desirable to implement a high-momentum-transfer “beam splitter,” which may be achieved by inducing quantum resonance in a finite-temperature laser-driven atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration and derive an $\epsilon$-classical model for the dynamics of the gas atoms which is capable of reproducing quantum resonant behavior for both zero-temperature and finite-temperature noninteracting gases. We show that this model agrees well with the fully quantum treatment of the system over a time scale set by the choice of experimental parameters. We also show that this model is capable of correctly treating the time-reversal mechanism necessary for implementing an interferometer with this physical configuration and that it explains an unexpected universality in the dynamics.

We obtain the exact analytical self-similar bright-, dark-, and kink-solitary-wave solutions of the nonlinear Schrödinger equation with localized inhomogeneous cubic-quintic nonlinearity by employing a similarity transformation. This equation could be a model equation of stable pulse propagation beyond ultrashort range in optical fiber communication systems in inhomogeneous media. We have investigated that the self-similar bright- and dark-solitary-wave solitons show interesting compression and amplification features that can be controlled by suitably changing the phase modulation parameter and consequently varying the nonlinear parameter. We unearth a surprising connection between optical self-similar localized waves in graded-index inhomogeneous media and solitons in homogeneous media with the same type of cubic-quintic nonlinearity. Finally, the stability of the solutions is discussed numerically under finite initial perturbations.

We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest nonvanishing terms of the wave function near the singularity, it is possible to infer the structure of the Bohmian streamlines. Conversely, starting from a map of the electron's Bohmian velocities, we demonstrate that it is possible to derive the form of the electron's wave function near the singularity. We outline a procedure that could yield an experimental method to determine the main parameters of the electron's wave function close to a singularity.

In this paper, we show that the polarization-entangled photon pairs can be generated using spontaneous parametric down conversion in a dual periodically poled planar waveguide. The proposed configuration is shown to have efficiencies higher than in the case of bulk crystals with the possibility of ease of collection, like in channel waveguides, with the additional feature of wavelength tunability. We also show that the planar waveguide configuration permits the generation of hyperentanglement in polarization and path degree of freedom, which is not possible in case of channel waveguide. The proposed design should find applications in quantum information processing using integrated quantum optics.