Multiphoton transition probability can be manipulated by tailoring the ultrashort laser pulses. In this paper, we theoretically and experimentally investigate the influence of the absorption bandwidth and line shape on the coherent control of two-photon transitions in two-level system by manipulating the femtosecond laser pulse with the $\pi$ spectral phase step. A coherent feature with a coherent peak and two coherent dips can be achieved if the absorption bandwidth is less than twice of the laser spectral bandwidth. The absorption bandwidth decides the coherent peak or dip intensity, and the absorption line shape affects the symmetry of the two coherent dips.

We study the phonon fluxes emitted when the condensate velocity crosses the speed of sound, i.e., in backgrounds which are analogous to that of a black hole. We focus on elongated one-dimensional condensates and on stationary flows. Our theoretical analysis and numerical results are based on the Bogoliubov–de Gennes equation without further approximation. The spectral properties of the fluxes and of the long distance density-density correlations are obtained, both with and without an initial temperature. In realistic conditions, we show that the condensate temperature dominates the fluxes and thus hides the presence of the spontaneous emission (the Hawking effect). We also explain why the temperature amplifies the long distance correlations which are intrinsic to this effect. This confirms that the correlation pattern offers a neat signature of the Hawking effect. Optimal conditions for observing the pattern are discussed, as well as correlation patterns associated with scattering of classical waves. Flows associated with white holes are also considered.

Long-baseline laser-interferometer gravitational-wave (GW) detectors are operating at a factor of $\sim 10$ (in amplitude) above the standard quantum limit (SQL) within a broad frequency band (in the sense that $\Delta f\sim f$). Such a low-noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of $\sim 200$. This result, along with the prospect for further improvements, heralds the possibility of experimentally probing macroscopic quantum mechanics (MQM)—quantum mechanical behavior of objects in the realm of everyday experience—using GW detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer’s classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum-state preparation and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses and the performance of the planned Advanced LIGO interferometers in quantum-state preparation.

We present a combined experimental and theoretical study of angular momentum depolarization in cold collisions of ${}^{2}P$ atoms in the presence of an external magnetic field. We show that collision-induced Zeeman relaxation of $\text{Ga}\left({{}^{2}P}_{1/2}\right)$ and $\text{In}\left({{}^{2}P}_{1/2}\right)$ atoms in cold ${}^4\text{H}\text{e}$ gas is dramatically suppressed compared to atoms in ${{}^{2}P}_{3/2}$ states. Using rigorous quantum-scattering calculations based on ab initio interaction potentials, we demonstrate that Zeeman transitions in collisions of atoms in ${{}^{2}P}_{1/2}$ electronic states occur via couplings to the ${{}^{2}P}_{3/2}$ state induced by the anisotropy of the interaction potential. Our results suggest the feasibility of sympathetic cooling and magnetic trapping of ${{}^{2}P}_{1/2}$-state atoms, such as halogens, thereby opening up exciting areas of research in precision spectroscopy and cold-controlled chemistry.

We show that the recently measured magnetic field dependence of three-body loss in a three-component mixture of ultracold ${}^6\text{L}\text{i}$ atoms [T. B. Ottenstein et al., Phys. Rev. Lett. 101, 203202 (2008); J. H. Huckans et al., Phys. Rev. Lett. 102, 165302 (2009)] can be explained by the presence of a universal trimer state. Previous work suggested a universal trimer state as a probable explanation, yet it failed to get good agreement between theory and experiment over the whole range of magnetic fields. For our description we adapt the theory of Braaten and Hammer [Phys. Rep. 428, 259 (2006)] for three identical bosons to the case of three distinguishable fermions by combining the three scattering lengths $a_{12}$, $a_{23}$, and $a_{13}$ between the three components to an effective interaction parameter $a_m$. We show that taking into account a magnetic field variation in the lifetime of the trimer state is essential to obtain a complete understanding of the observed decay rates.

The influence of the modification of the free vacuum on the quantum Zeno and anti-Zeno effects, as well as the Lamb (energy) shift of a multilevel atom, is studied. A unitary transformation method has been used to include the counter-rotating terms and to obtain the ground state of the whole Hamiltonian. The anti-Zeno effect is recovered if the modified density of states (DOS) has a dip near the transition frequency. The modification of DOS by a dip or a peak will change the Lamb shift compared with that in the free vacuum. Together with our unitary transformation method, there are three different methods to obtain the change in the Lamb shift. Using our method we investigate the change in the Lamb shift and obtain a formula for the change, which is the same as obtained with the method of Louisell [Quantum Statistical Properties of Radiation (Wiley, New York, 1973)] but different from the method of Cohen-Tannoudji et al. [Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992), pp. 317 and 417]. The correctness of the Lamb shift formulas obtained by the three methods can be easily testified experimentally.

We present two ready-to-use numerical algorithms to evaluate convex-roof extensions of arbitrary pure-state entanglement monotones. Their implementation leaves the user merely with the task of calculating derivatives of the respective pure-state measure. We provide numerical tests of the algorithms and demonstrate their good convergence properties. We further employ them in order to investigate the entanglement in particular few-spins systems at finite temperature. Namely, we consider ferromagnetic Heisenberg exchange-coupled spin-$\frac{1}{2}$ rings subject to an inhomogeneous in-plane field geometry obeying full rotational symmetry around the axis perpendicular to the ring through its center. We demonstrate that highly entangled states can be obtained in these systems at sufficiently low temperatures and by tuning the strength of a magnetic field configuration to an optimal value which is identified numerically.

We present a multipartite entanglement measure for $N$-qudit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for an important class of $N$-qutrit pure states, namely, general GHZ states. We prove that this measure possesses all the essential and many desirable properties expected of a good entanglement measure, including monotonicity. We also discuss the feasibility of the experimental evaluation of this measure for an $N$-qutrit system.

The constrained-search formulation gives valuable insights into the fundamentals of density functional theory. It provides exact results and bounds on the ground- and excited-state density functionals. An important advantage of the theory is that it gives guidance in the construction of functionals. Here we engage the constrained-search formulation to explore issues associated with the functional behavior of “stretched bonds” in molecular hydrogen. A constrained search is performed with familiar valence-bond wave functions ordinarily used to describe molecular hydrogen. The effective, one-electron hamiltonian is determined. Analysis of the functional suggests the need to construct different functionals for the same density and to allow a competition among these functionals. As a result the correlation energy functional is composed explicitly of energy gaps from the different functionals.

We have carried out a comprehensive study of electron-impact on AlH molecule using the $R$-matrix method. Elastic (integrated and differential), momentum-transfer, excitation, and ionization cross sections along with rate coefficients have been presented at various levels of approximation. The target states are represented by including correlations via a configuration-interaction technique. The results of the static-exchange, one-state, and 20-state close-coupling approximations are presented. Our study has detected Feshbach and core-excited shape resonances in 20-state model. We detect a stable bound state of ${\text{AlH}}^{-}$ having configuration $1{\sigma }^{2}2{\sigma }^{2}3{\sigma }^{2}4{\sigma }^{2}1{\pi }^{4}5{\sigma }^{2}2\pi$ with a vertical electronic affinity value of 0.22 eV which is in good agreement with the estimated experimental value of about 0.15 eV. The ionization cross sections are calculated in binary-encounter-Bethe model in which Hartree-Fock molecular orbitals are used to calculate kinetic and binding energies of the occupied molecular orbitals.

The valence photoelectron spectrum of ${\text{Sb}}_4$ clusters and the following fragmentation patterns have been studied using synchrotron radiation and electron-ion coincidence technique. An experimental photoelectron spectrum of the $5t_2$ ionization of ${\text{Sb}}_4$ is presented. Theoretical molecular calculations, together with the existing data on the noble gas xenon, were used to describe the experimental results. The bonding properties of the molecular orbitals involved are used to qualitatively describe the dissociation process.

Inhomogeneous broadening of energy levels is one of the principal limiting factors for achieving “slow” or “stationary” light in solid-state media by means of electromagnetically induced transparency, a quantum version of stimulated Raman adiabatic passage (STIRAP). Stark-shift-chirped rapid adiabatic-passage (SCRAP) has been shown to be far less sensitive to inhomogeneous broadening than STIRAP, a population transfer technique to which it is closely related. We further optimize the pulses used in SCRAP to be even less sensitive to inhomogeneous broadening in a $\Lambda$-type three-level system. The optimized pulses perform at a higher fidelity than the standard Gaussian pulses for a wide range of detunings (i.e., large inhomogeneous broadening).

The transfer of spin angular momentum from photons to small particles is a key experiment of quantum physics. The particles rotate clockwise or counterclockwise depending on the polarization of the light beam which holds them in an optical trap. We show that even perfectly disk shaped particles will in general not rotate with a constant angular speed. The particles will periodically accelerate and decelerate their rotational motion due to a varying spin angular momentum transfer from the light. Using the Poincaré sphere we derive the equation of motion of a birefringent plate and verify the results by measuring the time dependent rotation of small crystals of $\text{Hg}\left(\text{I}\right)$ iodide and 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) in the trap of polarized optical tweezers. For small ellipticities of the polarized light in the tweezers the plate stops in a fixed orientation relative to the axes of the light ellipse. We discuss the origin of this halt and propose an application of small birefringent plates as self-adjusting optical retarders in micro-optics.

We present an experimental test of quantum contextuality by using two-photon product states. The experimental results show that the noncontextual hidden-variable theories are violated by nonentangled states in spite of the local hidden-variable theories can be violated or not. We find that the Hong-Ou-Mandel-type quantum interference effect causes the quantum contextuality.

Neutron time-of-flight interferometry assumes the validity of the classical time-of-flight expression in the interpretation of time-of-flight data and simultaneously assumes that the incident neutrons are de Broglie wave packets obeying the laws of quantum mechanics. A quantum-mechanical treatment of time of flight as an expected value of an appropriate time-of-arrival operator for a given initial wave-packet state shows that the size of the initial wave packet introduces measurable quantum corrections to the expected classical time of flight. Our results provide concrete testable predictions that may clarify the status of time as a quantum-dynamical observable.

Phase reversal occurs in the propagation of an electromagnetic wave in a negatively refracting medium or a phase-conjugate interface. Here we report the experimental observation of phase-reversal diffraction without the above devices. Our experimental results and theoretical analysis demonstrate that phase-reversal diffraction can be formed through the first-order field correlation of chaotic light. The experimental realization is similar to the phase-reversal behavior in negatively refracting media.

Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory, and the configuration-interaction technique. We consider $\left(P,T\right)$-odd interactions, which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, $\left(P,T\right)$-odd electron-nucleon interaction, and electron electric dipole moment. Interpretation of an experimental constraint of a permanent electric dipole moment of ${}^{199}\text{H}\text{g}$ [W. C. Griffith, M. D. Swallows, T. H. Loftus, M. V. Romalis, B. R. Heckel, and E. N. Fortson, Phys. Rev. Lett. 102, 101601 (2009)] is discussed.

We present energy loss measurements of protons and deuterons down to velocities of 0.1 a.u. in very thin polycrystalline Cu and Ag foils, using the transmission technique. As in previous experiments in Au, a transition between two energy loss regimes is observed, i.e., from a stopping due to the excitation of only the free conduction band electrons at the lowest velocities, to a slowing down with the participation of both the free electrons and the loosely bound $d$ electrons. This transition causes a change of the slope in the energy loss versus ion velocity curve at a characteristic threshold velocity related to the binding energy of the $d$ electrons. As shown by model calculations these threshold velocities for Cu and Ag are shifted according to their density of states distributions.

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasiperiodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the noncommensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly, we find that a perturbative treatment in both cases, weak and strong disorders, gives a good description at all frequencies. In particular, we find that the infrared-absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected since for other quantities, like the conductivity in one-dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems and, in particular, the effect of the harmonic trap.