We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal, and idler beams resulting from a four-wave mixing process. Due to the high transparency possible between the resonances, these results have applications in the filtering of narrow-band entangled photons and interaction-free measurements.

We study a harmonically trapped Bose-Einstein condensate with dipole-dipole interactions in a regime where a roton spectrum emerges. We show that the roton spectrum is clearly revealed in the static and dynamic structure factors which can be measured using Bragg spectroscopy. We develop and validate a theory based on the local-density approximation for the dynamic structure factor.

We build up a consistent theory of quantum electrodynamics in the presence of macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive and absorbing dielectric medium and formulate the theory in terms of interacting quantum fields. We integrate out the damped polaritons by using diagrammatic techniques and find an exact expression for the displacement-field (photon) propagator in the presence of a dispersive and absorbing dielectric half-space. This offers a route to traceable perturbative calculations of the same kind as in free-space quantum electrodynamics. As a worked-through example, we consider the interaction of a neutral atom with a dispersive and absorbing dielectric half-space. For that, we use the multipolar coupling $\mu ·\mathbf{D}$ of the atomic dipole moment to the electromagnetic displacement field. We apply this formalism to calculate the one-loop correction to the atomic electron propagator and to find the energy-level shift and changes in the spontaneous decay rates for a neutral atom close to an absorptive dielectric mirror.

When visualized as an operation on the Bloch sphere, the qubit $\pi /8$ gate corresponds to 1/8 of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, if it supplements the set of Clifford gates, then universal quantum computation can be achieved. The $\pi /8$ gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit ($d$-level, where $d$ is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three, or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase-damping noise, in complete analogy with the qubit case. Motivated by this and other similarities, we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recently, independent work by Campbell et al. confirmed the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.

The $A^1\Pi -X^1{\Sigma }^{+}$ band system of carbon monoxide, which has been detected in six highly redshifted galaxies ($z=1.6$–2.7), is identified as a probe method to search for possible variations of the proton-electron mass ratio ($\mu$) on cosmological time scales. Laboratory wavelengths of the spectral lines of the $A-X$ ($v$,0) bands for $v=0$–9 have been determined at an accuracy of $\Delta \lambda /\lambda =1.5\times {10}^{-7}$ through VUV Fourier-transform absorption spectroscopy, providing a comprehensive and accurate zero-redshift data set. For the (0,0) and (1,0) bands, two-photon Doppler-free laser spectroscopy has been applied at the $3\times {10}^{-8}$ accuracy level, verifying the absorption data. Sensitivity coefficients $K_{\mu }$ for a varying $\mu$ have been calculated for the CO $A-X$ bands so that an operational method results to search for $\mu$ variation.

We present experimental and theoretical cross sections for positron collisions with ethene molecules. The experimental total cross sections (TCSs) were obtained with a linear transmission technique, for energies from 0.1 eV up to 70 eV. The calculations employed the Schwinger multichannel method and were performed in the static plus polarization approximation for energies up to 10 eV. Our calculated elastic cross sections indicate a Ramsauer-Townsend minimum around 2.8 eV and a virtual state, in agreement with previous calculations by da Silva et al. [Phys. Rev. Lett. 77, 1028 (1996)]. We found reasonable agreement between the calculated elastic integral cross section and the measured total cross section below the positronium formation threshold. The present results are also in quite good agreement with available theoretical and experimental data, although for the experiments this is only true for TCSs above about 7 eV.

Relativistic distorted wave calculations have been carried out to study the electron-impact excitation of Zn and Yb atoms from their ground ${}^1{S}_0$ state which have outer shell configurations 3$d^{10}$4$s^2$ and 4$f^{14}$6$s^2$, respectively. Excitations to the lowest and next-lowest singlet $P$ states viz. (4$s$4$p$, 4$s$5$p$) ${}^1{P}_1$ in Zn and (6$s$6$p$, 6$s$7$p$) ${}^1{P}_1$ in Yb along with the (6$s$5$d$) ${}^1{D}_2$ state in Yb have been considered. Differential and integrated cross section results have been obtained and compared with recent experimental results and theoretical convergent close coupling calculations. In general, good agreement between the theoretical calculations and experimental measurements has been observed.

We construct the effective lowest-band Bose-Hubbard model incorporating interaction-induced on-site correlations. The model is based on ladder operators for local correlated states, which deviate from the usual Wannier creation and annihilation, allowing for a systematic construction of the most appropriate single-band low-energy description in the form of the extended Bose-Hubbard model. A formulation of this model in terms of ladder operators not only naturally contains the previously found effective multibody interactions, but also contains multibody-induced single-particle tunneling, pair tunneling, and nearest-neighbor interaction processes of higher orders. An alternative description of the same model can be formulated in terms of occupation-dependent Bose-Hubbard parameters. These multiparticle effects can be enhanced using Feshbach resonances, leading to corrections which are well within experimental reach and of significance to the phase diagram of ultracold bosonic atoms in an optical lattice. We analyze the energy-reduction mechanism of interacting atoms on a local lattice site and show that this cannot be explained only by a spatial broadening of Wannier orbitals on a single-particle level, which neglects correlations.

Within extended coherent states, a recent exact solution to the quantum Rabi model (QRM) [D. Braak, Phys. Rev. Lett. 107, 100401 (2011)] can be recovered in an alternative simpler and more physical way, without use of any extra conditions. In the same framework, the two-photon QRM is solved exactly by treating extended squeezed states on an equal footing. Concise transcendental functions responsible for the exact solutions are derived. The isolated Juddian solutions are also analytically obtained in terms of degeneracy. Both the extended coherent states and squeezed states employed here are essentially Fock states in the space of the corresponding Bogoliubov operators, which result in free-particle number operators. The present approach can be summarized concisely in a unified way and easily extended to various spin-boson systems with multiple levels, even multiple modes.

We use the generalized rotating-wave approximation approach [Irish, Phys. Rev. Lett. 99, 173601 (2007)] to study single-photon scattering on a two-level system (TLS) with arbitrarily strong coupling to a local mode in a one-dimensional (1D) coupled-resonator array. We obtain the scattering amplitudes by an analytical method, which works well in a broad parameter region, confirmed by independent numerical results. In particular, when the resonator mode is far off resonance with the TLS, our results appear more reasonable than the ones from the standard adiabatic approximation. The approach is further extended to cases with a 1D resonator array strongly coupled to more than one TLS.

We demonstrate the effect of two-center interference on single-photon double ionization [double photoionization (DPI)] of the aligned H${}_2$ molecule when it shrinks or expands from the equilibrium internuclear distance. This interference affects the first stage of the DPI process in which the primary photoelectron is ejected predominantly along the polarization axis of light and its geometrical interference factor is most sensitive to the internuclear distance in the parallel ($\Sigma$) orientation of the internuclear and polarization axes. This effect is responsible for strong modification of the DPI amplitude in the parallel orientation while the corresponding amplitude for the perpendicular ($\Pi$) orientation is rather insensitive to the internuclear distance. The combination of these two factors explains the profound kinetic energy release effect on the fully differential cross sections of DPI of H${}_2$.

Collisions at ultracold temperatures between ${}^1\Sigma$-state diatomic polar molecules in a circularly polarized microwave field are theoretically analyzed. We demonstrate that elastic and inelastic collisions of polar molecules at ultracold temperatures are affected by an external microwave field and that they are enhanced at resonance frequencies. We show that the collision dynamics of polar molecules in a microwave field is largely determined by the long-range dipole-dipole interaction. Through this interaction, two polar molecules can resonantly exchange internal energy by undergoing a transition between neighboring rotational levels. This process may stabilize the system and enable the successive evaporative cooling of molecules. This paper discusses fermionic polar molecules at ultralow temperatures (1 $\mu$K).

Differential cross sections for elastic electron scattering and the excitation of the C-H vibrational modes of isoxazole molecules were measured in the energy range from 2 to 20 eV and over the scattering angle range from 10° to 180°. The cross sections at the scattering angles of and above 90° were accessible with the use of a magnetic angle changer. The differential cross sections were integrated to yield integral and momentum transfer cross sections. The negative ion resonances in the elastic scattering at 2.7 eV and in the vibrational excitation of isoxazole at 5.5 and 10 eV were observed. The present cross sections for elastic scattering are compared with the corresponding results in furan.

Single and double photodetachment of the oxygen anion O${}^{-}$ have been investigated at 41.7  nm (29.8 eV) in a crossed beams experiment using intense photon pulses from a free-electron laser. The ratio of single (O${}^0+e^{-}$) and double (O${}^{+}+2e^{-}$) detachment was determined to be ${\sigma }_{{\mathrm{O}}^0}/{\sigma }_{{\mathrm{O}}^{+}}=4.12\pm$ 0.17 as identified directly from the yield of O${}^0$ and O${}^{+}$ fragments after irradiation. The absolute cross section for the dominating single detachment channel was measured to ${\sigma }_{{\mathrm{O}}^0}=(2.1\pm 0.6)\times {10}^{-19}$ cm${}^2$. Analysis of photoelectrons detected in coincidence with neutral fragments (O${}^0$) suggests that single photodetachment primarily happens via the ground (${}^{3}P$) or lowest excited (${}^{1}D$) state of oxygen. The results demonstrate the feasibility and advantage of crossed beams experiments for complete studies of photodetachment reactions.

We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short-time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing, its scaling with $N$, and the speed of coherent spin formation with simple analytical formulas which successfully describe the numerical Bose-Hubbard results. This method of producing highly squeezed spin states in systems of ultracold atoms is compared to other standard methods in the literature.

Density oscillations of confined one-dimensional Fermi gases of contact repulsive interactions in a continuous space are discussed within Bethe-ansatz-based spin-density-functional theory. The results are compared against the exact analytical and the exact diagonalization method. For an unpolarized system, the number of peaks in the density profiles is doubled, signaling the crossover of the $2k_F$-Friedel to $4k_F$-Wigner oscillations (with $k_{\mathrm{F}}$ being the Fermi wave vector). For both unpolarized and polarized systems, a threshold of the short-range interaction strength can be found where $N_f$-peak Wigner oscillations of a $4k_F$ wave vector appear in the density profile ($N_f$ is the total particle number).

The interference of entangled photon pairs permits the study of the fundamental properties of quantum mechanics. The process is also finding practical applications in optical imaging. The Michelson interferometer provides an elegant means for characterizing the degree of two-photon entanglement, but the technique has not yet been described and analyzed in detail. Here we provide a full description of the interference of collinear down-converted photons in a Michelson interferometer. We explain the basic elements that characterize the interference pattern and complement the theory with experimental measurements. The two-photon Michelson interferometer can be used in quantum optical coherence tomography for dispersion-free imaging and localization.

Analysis on direct transforming the slow light into the stationary light pulse (SLP) is presented. Without the process of turning the slow light into the coherence between the lower levels, the generation of SLP is more efficient. The Maxwell-Liouville equations are employed to study the light pulse dynamics in the samples coherently driven by a bichromatic standing wave. The solution indicates that the forward and backward components of the SLP approach to each other exponentially. Such property is described by introducing a quantity called characteristic length, which appeared to be the ratio of the optical coherence decay rate and the coefficient of the driving term in Maxwell equation. The necessary length for completing the conversion can be estimated as five times the characteristic length. Several materials are analyzed here, including the ${}^{87}$Rb atoms with different densities, Pr${}^{3+}$-doped yttrium orthosilicate (Pr:YSO), and nitrogen-vacancy color centers in diamond (N-V centers). The values of the characteristic length for the corresponding materials are calculated, as well as the necessary length.

For over a century, two rival descriptions of electromagnetic field momentum in matter have coexisted, due to Abraham and Minkowski, respectively. We propose a setup for measuring the difference between Abraham's and Minkowski's predictions in optics. To wit, a setup is proposed in which the transient “Abraham force,” a consequence of the Abraham energy-momentum tensor of 1909, may be measured directly. We show that when a train of short laser pulses is sent through a fiber wound up on a cylindrical drum, the Abraham theory predicts a torque, which, by inserting realistic parameters, is found to be detectable. Indeed, the same torque when calculated with the Minkowski tensor takes the opposite sign. Numerical estimates show that with a typical torsion pendulum setup and standard laser parameters, the angular deflection is in the order of ${10}^{-3}$ rad, which is easily measurable and even visible to the naked eye. Although its prediction is a century old, the Abraham force has proven experimentally elusive, and to our knowledge no macroscopic experimental demonstration of the difference between the predictions of the two mentioned energy-momentum tensors exists at optical frequencies.

The nonlinear Bethe-Heitler process in a bichromatic laser field is investigated using strong-field quantum electrodynamics formalism. The symmetry properties of the angular distributions of the created $e^{-}{e}^{+}$ pairs are analyzed. These properties are shown to be governed by a behavior of the vector potential characterizing the laser field, rather than by the respective electric-field component.