We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the qubit-oscillator coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive qubit readout is possible. If several qubits are coupled to one resonator, an effective qubit-qubit interaction of Ising type emerges, whereas RWA leads to isotropic $XY$ interaction. This impacts on the entanglement characteristics of the qubits.

Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one’s measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely, the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.

We demonstrate that the precessional frequencies of vortices in Bose-Einstein condensates (BECs) are determined by a conservation law and not by the lowest-lying excitation energy mode. We determine the precessional frequency for a single off-axis vortex and vortex lattices in BECs using the continuity equation and solve this self-consistently with the time-independent Hartree-Fock-Bogoliubov equations in the rotating frame. We find agreement with zero-temperature calculations (Bogoliubov approximation) and a smooth variation in the precession frequency as the temperature is increased. Time-dependent solutions confirm the validity of these predictions.

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and ${\text{Be}}^{+}$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground-state energies $-7.47806032391010\left(32\right)$ and $-14.32476317679043\left(22\right)$ of Li and ${\text{Be}}^{+}$, correspondingly, are the most accurate to date. When small basis set is considered, explicitly correlated exponential functions are much more effective. With only 128 functions we obtained about ${10}^{-9}$ relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.

We explore the effects of microwave laser fields on spin-changing transitions in collisions of polar molecules in a ${}^2\Sigma$ electronic state with atoms in the presence of a static magnetic field. We use the dressed-state formalism of quantum optics to describe the interaction of the radiation field with the collision complex and perform rigorous scattering calculations to study spin-changing transitions in collisions of CaH molecules with He atoms at temperatures below 1 K. Our calculations demonstrate that collision-induced spin relaxation of ${}^2\Sigma$ molecules is enhanced near avoided crossings between different Zeeman levels. We show that the positions of the avoided crossings can be modified by varying the frequency and the intensity of the microwave laser field and discuss the mechanisms of microwave field control of spin-dependent interactions in cold open-shell molecules.

We present an experimental and theoretical study of a scalar atomic magnetometer using an oscillating field-driven Zeeman resonance in a high-density optically pumped potassium vapor. We describe an experimental implementation of an atomic gradiometer with a noise level below $10\text{fT}{\text{Hz}}^{-1/2}$, fractional field sensitivity below ${10}^{-9}{\text{Hz}}^{-1/2}$, and an active measurement volume of about $1.5{\text{cm}}^3$. We show that the fundamental field sensitivity of a scalar magnetometer is determined by the rate of alkali-metal spin-exchange collisions even though the resonance linewidth can be made much smaller than the spin-exchange rate by pumping most atoms into a stretched spin state.

We examine very high energy Compton scattering on bound electrons, comparing cross sections obtained using relativistic impulse approximation (RIA) to the extreme relativistic (ER) limit of the exact Coulomb (EC) results for the $1s$ electron. For this purpose, in the case of an initial bound $s$ state, we establish analytic expressions, valid within RIA, for the triply differential cross section (TDCS), corresponding to the detection of photons and electrons in coincidence, and for the ER limit of TDCS and of photon double-differential cross section (DDCS). We find that the RIA-ER expression for DDCS is the product of a simple factor, depending only on the ratio of initial and final photon frequencies, and a function of a single kinematic variable. Since the same structure is displayed by the EC-ER cross section, we present a compact representation of the ER results, in which the main differences between RIA-ER and EC-ER are displayed as a shift of the peak position of the frequency distribution and an asymmetry about that position. The comparison shows to what extent RIA, which becomes exact for vanishing nuclear charge $Z$, remains a good approximation for low and medium values of $Z$ in the peak region of high-energy Compton scattering.

We study a gas of ultracold atoms resonantly driven into a strongly interacting Rydberg state. The long-distance behavior of the spatially frozen effective pseudospin system is determined by a set of dimensionless parameters, and we find that the experimental data exhibit algebraic scaling laws for the excitation dynamics and the saturation of Rydberg excitation. Mean-field calculations as well as numerical simulations provide an excellent agreement with the experimental finding and are evidence for universality in a strongly interacting frozen Rydberg gas.

The radio-frequency spectrum of the fermions in the unitary limit at finite temperatures is characterized by the sum-rule relations. We consider a simple picture where the atoms are removed by radio-frequency excitations from the strongly interacting states into a state of negligible interaction. We calculate the moments of the response function in the range of temperature $0.08{ϵ}_F<T<0.8{ϵ}_F$ using auxiliary field Monte Carlo technique in which continuum auxiliary fields with a density-dependent shift are used. We estimate the effects of superfluid pairing from the clock shift. We find a qualitative agreement with the pairing gap–pseudogap transition behavior. We also find within the quasiparticle picture that in order for the gap to come into quantitative agreement with the previously known value at $T=0$, the effective mass has to be $m^{\ast }\sim 1.43m$. Finally, we discuss implications for the adiabatic sweep of the resonant magnetic field.

The applicability of the so-called truncated Wigner approximation $\left(-W\right)$ is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. First, what class of multitime averages the $-W$ approximates and, second, how to proceed if the average in question does not belong to this class. To answer the first question, we develop a (in principle, exact) path-integral approach in phase space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The $-W$ equations emerge as an approximation within these path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages, Kubo’s renowned formula relating the linear-response function to two-time commutators suffices. The $-W$ is directly generalized to the response properties of the system allowing one to calculate approximate time normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.

The results of enhanced high-order harmonic generation (HHG) in laser-produced plasmas using a two-color laser pump (98% of 800 nm and 2% of 400 nm) are presented. Even (up to the 38th order) and odd (up to the 45th order) harmonics of 800 nm radiation were generated in the case of a two-color orthogonal polarization pump of various plasmas. The comparison between HHGs using parallel and orthogonally polarized 400 and 800 nm radiations showed better conversion efficiency for the latter case. We have also used circularly polarized 800 nm pump for second-harmonic generation and HHG. We also present the results of the influence of the chirp and phase modulation of the fundamental radiation in laser plasma on the spectral properties of odd and even harmonics.

We analyze a system of fermionic ${}^6\text{L}\text{i}$ atoms in an optical trap and show that an atom “on demand” can be prepared with ultrahigh fidelity, exceeding 0.999 98. This process can be scaled to many sites in parallel, providing a realistic method to initialize $N$ qubits at ultrahigh fidelity for quantum computing. We also show how efficient quantum gate operation can be implemented in this system and how spatially resolved single-atom detection can be performed.

We calculate the cross sections for scattering of a neutral ytterbium atom with its positive ion at energies up to 30 eV. We identify peaks in the forward direction as arising from elastic collisions and those in the backward direction as from charge transfer. We show that the total cross section follows a semiclassical expression over a large range of energies and that the resonant charge transfer may be characterized by four energy regimes: an $s$-wave regime at ultralow energies, a modified Langevin regime at low energy, a Langevin regime at medium energy, and an “exchange” regime at high energy. We find large variations between the different isotopes for the two lowest-energy regimes and very little variation for the two highest-energy regimes. Our results are consistent with recent measurements.

Several recent papers have shown that some forms of dispersion cancellation have classical analogs and that some aspects of nonlocal two-photon interferometry are consistent with local realistic models. It is noted here that the classical analogs only apply to local dispersion cancellation experiments [A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 68, 2421 (1992)] and that nonlocal dispersion cancellation [J. D. Franson, Phys. Rev. A 45, 3126 (1992)] is inconsistent with any classical field theory and has no classical analog. The local models that have been suggested for two-photon interferometry are shown to be local but not realistic if the spatial extent of the interferometers is taken into account. It is the inability of classical models to describe all of the relevant aspects of these experiments that distinguishes between quantum and classical physics, which is also the case in Bell’s inequality.

We point out a symmetry exhibited by pairs of entangled states and discuss its possible applications in quantum information. More specifically, we consider quadripartite systems prepared in bipartite product states of the form $|\Psi ⟩={|\psi ⟩}_{12}\otimes {|\psi ⟩}_{34}$ and let the uncorrelated subsystems 14 and 23 interact by a given unitary $U_{14}\otimes U_{23}$ describing two bilinear interactions: we show that entanglement between the noninteracting subsystems 12 and 34 may lead to invariance of $|\Psi ⟩$ under the action of the unitary, i.e., make $|\Psi ⟩$ an eigenstate of $U_{14}\otimes U_{23}$. We call this phenomenon entanglement induced transparency and investigate its occurrence both in continuous variable and qubit systems. We also discuss its possible applications to bath engineering, double swapping and remote inversion.

Dür [Phys. Rev. Lett. 87, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the same Bell inequality if and only if $N\ge 6$ [Phys. Rev. A 79, 032309 (2009)]. On the other hand, it has been also shown that the states which Dür considered violate Bell inequalities different from the inequality for $N\ge 6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with $M$ settings of the measuring apparatus for sufficiently large $M$, we prove that there exists an $N$-qubit bound entangled state violating the $M$-setting Bell inequality if and only if $N\ge 4$.

Edge states lying at the edge of positive-partial-transpose- (PPT-) entangled states have a very intriguing existence and their detection is equally interesting. We present here a witness for detection of edge states. We then compare between our proposed witness operator and the witness operator proposed by Lewenstein et al. [Phys. Rev. A 62, 052310 (2000)] in terms of the efficiency in the detection of PPT entangled states. In this regard we show that this operator is finer than the operator of Lewenstein et al. in some restrictions. We also discuss about its experimental realization via Gell-Mann matrices.

We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single negative power of all distances can be obtained from the second-order differential equation in $r$, the distance between nuclei. For particular values of nonlinear parameters corresponding to the James-Coolidge basis, we find a fully analytic expression. For integrals with arbitrary powers of all distances, we construct recursion relations which starts from the master integral. The presented approach opens a window for the high-precision calculations of relativistic effects in diatomic molecules.

The total and partial photodissociation cross sections of the molecular ion ${\text{HeH}}^{+}$ are computed by time-dependent methods for fragmentation into the excited shells $n=1,2,3$ up to a photon energy of 40 eV. ${{}^1\Sigma }^{+}$ and ${}^1\Pi$ states are considered for parallel and perpendicular transitions for different initial rotational or vibrational excitations. Nonadiabatic radial and rotational couplings are taken into account. The results from coupled-channel equations are compared with the Born-Oppenheimer approximation. A time-dependent calculation with a femtosecond laser pulse is carried out to simulate a recent crossed beam photodissociation imaging experiment with vacuum ultraviolet free-electron laser [H. B. Pedersen et al., Phys. Rev. Lett. 98, 223202 (2007)]. The dominance of photodissociation perpendicular to the photon polarization is confirmed.