We present an analytical description of phase-matched second-harmonic generation in photonic crystal waveguides in the presence of loss. In particular, we investigate the case where the second-harmonic modes suffer from radiative losses. We use the adjoint field formalism to develop a coupled-mode theory that uses the quasinormal Bloch modes as the basis for modal expansion. To test our analytical description numerically, we propose a design in a lithium niobate photonic crystal slab waveguide, where a slow-light mode at the fundamental harmonic frequency is phase matched to a leaky mode at the second-harmonic frequency. The results of the numerical experiment agree with our analytical predictions.

Testing the spatial variation of the fine-structure constant $\alpha$ indicated by Webb et al. [J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, and M. B. Bainbridge, Phys. Rev. Lett. 107, 191101 (2011)] with terrestrial laboratory atomic measurements requires at least $\dot{\alpha }/\alpha \sim {10}^{-19}{\text{yr}}^{-1}$ sensitivity. We conduct a systematic search of atomic systems for such a test that have all features of the best optical clock transitions leading to the possibility of the frequency measurements with fractional accuracy on the level of ${10}^{-18}$ or better and have a factor of 100 extra enhancement of $\alpha$ variation in comparison to experimental frequency ratio measurement accuracy. We identify the pair of actinide ${\mathrm{Cf}}^{15+}$ and ${\mathrm{Es}}^{16+}$ ions as the best system for a test of spatial $\alpha$-variation hypothesis as it satisfies both of these requirements and has sufficiently simple electronic structure to allow for high-precision predictions of all atomic properties required for rapid experimental progress.

We control the relative coupling strength of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions with the cycles for the two cases ${180}^{\circ }$ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum simulation and quantum control. Using the standing-wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.

A two-dimensional dipolar Fermi gas in a harmonic trap under rotation is studied by solving ab initio Kohn-Sham equations. The physical parameters used match those of an ultracold gas of fermionic ${}^{23}\text{Na}{}^{40}\text{K}$ molecules, a prototypical system of strongly interacting dipolar quantum matter, which was created very recently. We find that, as the critical rotational frequency is approached and the system collapses into the lowest Landau level, an array of tightly packed quantum vortices develops, in spite of the nonsuperfluid character of the system. In this state the system loses axial symmetry and the fermionic cloud boundaries assume an almost perfect square shape. At higher values of the filling factor the vortex lattice disappears, while the system still exhibits square-shaped boundaries. At lower values of the filling factor the fermions become instead localized in a Wigner cluster structure.

In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analyzing the effects on communication when the parties have partial knowledge about the transformation relating their frames, when the transformation is either a rotation or a pure boost. This then enables us to investigate how the efficiency of communication is affected due to partially correlated inertial reference frames related by an arbitrary Lorentz transformation. Furthermore, we show how the results of previous studies where reference frames are completely uncorrelated are recovered from our results in appropriate limits.

Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the minimum energy gap encountered during the dynamics. Unfortunately, the direct calculation of the gap is strongly limited by the exponential growth in the dimensionality of the Hilbert space associated to the quantum system. Although many special-purpose methods have been devised to reduce the effective dimensionality, they are strongly limited to particular classes of problems with evident symmetries. Moreover, little is known about the computational power of adiabatic quantum optimizers in real-world conditions. Here we propose and implement a general purposes reduction method that does not rely on any explicit symmetry and which requires, under certain general conditions, only a polynomial amount of classical resources. Thanks to this method, we are able to analyze the performance of “nonideal” quantum adiabatic optimizers to solve the well-known Grover problem, namely the search of target entries in an unsorted database, in the presence of discrete local defects. In this case, we show that adiabatic quantum optimization, even if affected by random noise, is still potentially faster than any classical algorithm.

We consider the task of deterministically entangling two remote qubits using joint measurement and feedback, but no directly entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Finally, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.

Fragmentation of gas-phase chloro- and bromoacetic acid samples, particularly its dependency on the atomic site of the initial core ionization, was studied in photoelectron-photoion-photoion coincidence (PEPIPICO) measurements. The fragmentation was investigated after ionizing carbon $1s$ and bromine $3d$ or chlorine $2p$ core orbitals. It was observed that the samples had many similar fragmentation pathways and that their relative weights depended strongly on the initial ionization site. Additional Auger PEPIPICO measurements revealed a clear dependence of fragment pair intensities on the kinetic energy of the emitted Auger electrons. The modeled and measured Auger electron spectra indicated that the average internal energy of the molecule was larger following the carbon $1s$ core-hole decay than after the decay of the halogen core hole. This difference in the internal energies was found to be the source of the site-dependent photofragmentation behavior.

We present theory and calculations of a real-time-domain interferometry for the photodetachment dynamics of negative ions in the presence of a single-cycle terahertz pulse. The photoelectron can follow two or more classical trajectories to arrive at a detector simultaneously allowing the electron waves to interfere quantum mechanically. Both the in-phase and antiphase oscillations can be observed in the photoelectron interferences from negative hydrogen and fluorine ions depending on the pulse strength and the observing angle. Especially, a temporal-caustic bifurcation is observed when the detection angle is not in line with the pulse polarization direction. Similar interferences and bifurcations are also expected in the angle-resolved energy spectrum, as a result of its approximate equivalence with the time-dependent electron flux at large distances.

We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a multi-Dirac-point system. We find that the quantum Hall effects present different features with the change in relative strengths of several perturbations. Namely, the quantum spin Hall effect can be induced by gauge-field-dressed next-nearest-neighbor hopping, which, together with a Zeeman field, can induce the quantum anomalous Hall effect characterized by different Chern numbers. Furthermore, we find that the edge states of the multi-Dirac-point system represent very different features for different boundary geometries, in contrast with the generic two-Dirac-point system. Our study extends the borders of the field of quantum Hall effects in a honeycomb optical lattice with multivalley degrees of freedom.

We study the spreading of density-density correlations and the Loschmidt echo, after different sudden quenches in an interacting one-dimensional Bose gas on a lattice, also in the presence of a superimposed aperiodic potential. We use a time dependent Bogoliubov approach to calculate the evolution of the correlation functions and employ the linked cluster expansion to derive the Loschmidt echo.

We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in one dimension (1D), 2D, and 3D by a careful study of the ideal gas limit. Numerical benchmarking in 1D shows that the ideal gas results carry over unchanged into the weakly interacting gas. The optimum high-energy cutoff is in general shown to depend strongly on the observable in question (e.g., energy, density fluctuations, phase coherence length, condensate fraction). This explains the wide range of past results. A consistent classical field representation with less than 10% deviation in all typical observables can be given for systems at temperatures below $0.0064$ degeneracy temperature in 1D, and $0.49$ critical temperature in 3D. Surprisingly, this is not possible for the two-dimensional ideal gas even at zero temperature because mean density, density fluctuations, and energy cannot be simultaneously matched to the quantum results.

We study the quantum transport of multiphoton Fock states in one-dimensional Bose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose an optical scheme to probe the underlying many-body states of the system by analyzing the properties of the transmitted light using scattering theory. To this end, we employ the Lippmann-Schwinger formalism within which an analytical form of the scattering matrix can be found. The latter is evaluated explicitly for the two-particle, two-site case which we use to study the resonance properties of two-photon scattering, as well as the scattering probabilities and the second-order intensity correlations of the transmitted light. The results indicate that the underlying structure of the many-body states of the model in question can be directly inferred from the physical properties of the transported photons in its QCA realization. We find that a fully resonant two-photon scattering scenario allows a faithful characterization of the underlying many-body states, unlike in the coherent driving scenario usually employed in quantum master-equation treatments. The effects of losses in the cavities, as well as the incoming photons' pulse shapes and initial correlations, are studied and analyzed. Our method is general and can be applied to probe the structure of any many-body bosonic model amenable to a QCA implementation, including the Jaynes-Cummings-Hubbard model, the extended Bose-Hubbard model, as well as a whole range of spin models.

Analytic expressions for the electric and magnetic fields of an ultrashort, tightly focused, linearly polarized laser pulse are derived, to lowest order of a truncated power-series expansion, from vector and scalar potentials. Clear steps are described for the analytic and numerical evaluation of higher-order terms in the series, to any desired accuracy.

We employ doubly resonant two-photon excitation into the $74S$ Rydberg state to spectroscopically measure the dynamic scalar polarizability, ${\alpha }_0$, and tensor polarizability, ${\alpha }_2$, of rubidium $5P_{3/2}$. A cavity-generated 1064-nm optical lattice allows us to reach intensities near $2\times {10}^{11}\mathrm{W}/{\mathrm{m}}^2$, where the atom field is larger than the hyperfine interaction, and magnetic sublevels are well resolved. In the evaluation of the data we use a self-referencing method that renders the polarizability measurement largely free from the intensity calibration of the laser light field. We obtain experimental values ${\alpha }_0=-1149(\pm 2.5\%)$ and ${\alpha }_2=563(\pm 4.2\%)$, in atomic units. Methods and results are supported by simulations. The results provide an experimental test of atomic-structure calculations used to determine systematic shifts in atomic clocks and to interpret fundamental-physics experiments.

We characterize the pointer states generated by the master equation of quantum Brownian motion and derive stochastic equations for the dynamics of their trajectories in phase space. Our method is based on a Poissonian unraveling of the master equation whose deterministic part exhibits soliton-like solutions that can be identified with the pointer states. In the semiclassical limit, their equations of motion in phase space turn into those of classical diffusion, yielding a clear picture of the quantum-classical transition induced by environmental decoherence.

We characterize the set of generalized quantum measurements that can be decomposed into a continuous measurement process using a stream of probe qubits and a tunable interaction Hamiltonian. Each probe in the stream interacts weakly with the target quantum system and then is measured projectively in a standard basis. This measurement result is used in a closed feedback loop to tune the interaction Hamiltonian for the next probe. The resulting evolution is a stochastic process with the structure of a one-dimensional random walk. To maintain this structure and require that at long times the measurement outcomes be independent of the path, the allowed interaction Hamiltonians must lie in a restricted set such that the Hamiltonian terms on the target system form a finite-dimensional Jordan algebra. This algebraic structure of the interaction Hamiltonians yields a large class of generalized measurements that can be continuously performed by our scheme and we fully describe this set.

We investigate two interacting open quantum systems whose time evolutions are governed by Markovian master equations. We show a class of coupled systems whose interaction leaves invariant the steady state of one of the systems, i.e., only one of the reduced steady states is sensitive to the interactions. A detailed proof with the help of the Trotter product formula is presented. We apply this general statement to a few models, one of which is the optomechanical coupling model where an optical cavity is coupled to a small mechanical oscillator.