By comparison with the solution of the time-dependent Schrödinger equation we explore the validity of the two-step semiclassical model for strong-field ionization in elliptically polarized laser pulses. We find that the discrepancy between the two-step model and the quantum theory correlates with situations where the ensemble average of the force deviates considerably from the force calculated at the average position of the trajectories of the ensemble. We identify the general trends for the applicability of the semiclassical model in terms of intensity, ellipticity, and wavelength of the laser pulse, and in terms of the properties of the atomic potential.

Employing a recently developed method that is numerically accurate within a model space simulating the real-time dynamics of few-body systems interacting with macroscopic environmental quantum fields, we analyze the full dynamics of an atomic system coupled to a continuum light field with a gapped spectral density. This is a situation encountered, for example, in the radiation field in a photonic crystal, whose analysis has so far been confined to limiting cases due to the lack of suitable numerical techniques. We show that both atomic population and coherence dynamics can drastically deviate from the results predicted when using the rotating-wave approximation, particularly in the strong-coupling regime. Experimental conditions required to observe these corrections are also discussed.

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy.

We revisit the theory of tunnel-coupled atomic quasicondensates in double-well elongated traps at finite temperatures. Using the functional-integral approach, we calculate the relative-phase correlation function beyond the harmonic limit of small fluctuations of the relative phase and its conjugate relative-density variable. We show that the thermal fluctuations of the relative phase between the two quasicondensates decrease the frequency of Josephson oscillations and even wash out these oscillations for small values of the tunnel coupling.

We present a theoretical study of the transient absorption of an ultrafast, extreme ultraviolet (XUV) pulse in the presence of an infrared (IR) control pulse in a macroscopic three-level helium gas. We concentrate on cases in which the IR pulse is shorter than the XUV pulse and induces transient transparency and amplification of the XUV light via coherent control. We give a time-dependent picture of the absorption process through the time dependence of the populations and relative coherences of the three states. We show that the XUV absorption can be dynamically changed into emission via phase control of the XUV-resonant $2p$ state through IR-induced coupling between the $2p$ and the $2s$ states. This can lead to compression and amplification of the XUV pulse when propagating through a laser-dressed macroscopic medium. We discuss the influence of atomic decoherence times on the XUV reshaping and show that fast decoherence means that the laser dressing acts more like a passive transmission window and less like a dynamical redistribution of energy.

We analyze the dynamics of a chain of singly charged ions confined in a linear Paul trap and which couple with the mode of a high-finesse optical resonator. In these settings the ions interact via the Coulomb repulsion and are subject to the mechanical forces due to scattering of cavity photons. We show that the interplay of these interactions can give rise to bistable equilibrium configurations, into which the chain can be cooled by cavity-enhanced photon scattering. We characterize the resulting equilibrium structures by determining the stationary state in the semiclassical limit for both cavity field and crystal motion. The mean occupation of the vibrational modes at steady state is evaluated, showing that the vibrational modes coupled to the cavity can be simultaneously cooled to low occupation numbers. It is also found that at steady state the vibrations are entangled with the cavity field fluctuations. The entanglement is quantified by means of the logarithmic negativity. The spectrum of the light at the cavity output is evaluated and the features signaling entanglement are identified.

Photons with complex spatial mode structures open up possibilities for new fundamental high-dimensional quantum experiments and for novel quantum information tasks. Here we show entanglement of photons with complex vortex and singularity patterns called Ince-Gauss modes. In these modes, the position and number of singularities vary depending on the mode parameters. We verify two-dimensional and three-dimensional entanglement of Ince-Gauss modes. By measuring one photon and thereby defining its singularity pattern, we nonlocally steer the singularity structure of its entangled partner, while the initial singularity structure of the photons is undefined. In addition we measure an Ince-Gauss specific quantum-correlation function with possible use in future quantum communication protocols.

We evaluated the static and dynamic polarizabilities of the $5s^2{}^1{S}_0$ and $5s5p{}^3{P}_0^o$ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5s^2{}^1{S}_0-5s5p{}^3{P}_0^o$ dc Stark shift measurement $\Delta \alpha =247.379\left(7\right)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1$\%$ uncertainty; $-$0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7$\%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.

Long-range states of diatomic molecules have average values of internuclear separations $\langle R\rangle$ at least one order of magnitude larger than the equilibrium value of $R$. For example, the helium dimer ${{}^4\mathrm{He}}_2$ has a single bound state with $\langle R\rangle$ of about 50 Å. We show that the properties of these states, such as $\langle R\rangle$, the dissociation energy, or the $s$-wave scattering length, can be related by simple, yet very accurate, formulas if a potential-energy curve is known. By examining a range of ab initio and empirical helium dimer potentials as well as scaling these potentials, we found that the formulas remain accurate, even if very approximate potentials were used. In addition to ${{}^4\mathrm{He}}_2$, we present results for ${{}^9\mathrm{Be}}_2,{{}^{20}\mathrm{Ne}}_2$, and KRb.

We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including ball and shell formations and axially or radially separated states, with a marked sensitivity to the potential perturbations and the relative atom number in each species. Incorporation of linear trap perturbations, albeit weak, are found to be essential to match the range of equilibrium density profiles observed in a recent ${}^{87}$Rb-${}^{133}$Cs Bose-Einstein condensate experiment [McCarron et al., Phys. Rev. A 84, 011603(R) (2011)]. Our analysis of this experiment demonstrates that sensitivity to linear trap perturbations is likely to be an important factor in interpreting the results of similar experiments in the future.

We consider the effects of experimental imperfections on the problem of estimation-based feedback control of a trapped particle undergoing continuous position measurement. These limitations violate the assumption that the estimator (i.e., filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We quantify the parameter regimes for stable cooling and show that the control scheme is robust to detector inefficiency, time delay, technical noise, and miscalibrated parameters. We apply these results to the specific context of a weakly-interacting Bose-Einstein condensate (BEC). Given that this system has previously been shown to be less stable than a feedback-cooled BEC with strong interatomic interactions, this result shows that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback.

We consider the scattering of an atom by a sequence of two near-resonant standing light waves, each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves, within the rotating wave approximation, the adiabatic approximation applied to the atomic center-of-mass motion, and a smooth turning on and off of the interaction, the dynamical phase cancels out and the final state of the atom differs from the initial one only by the sum of the two Berry phases accumulated in the two interaction regions. This phase depends on the position of the atom in a way such that the wave packet emerging from the scattering region will focus, which constitutes a method to observe the Berry phase without resorting to interferometric methods.

We consider the phase-transition-like behavior in the Rabi model containing a single two-level system, or qubit, and a single harmonic oscillator. The system experiences a sudden transition from an uncorrelated state to an increasingly correlated one as the qubit-oscillator coupling strength is varied and increased past a critical point. This singular behavior occurs in the limit where the oscillator's frequency is much lower than the qubit's frequency; away from this limit one obtains a finite-width transition region. By analyzing the energy-level structure, the value of the oscillator field and its squeezing and the qubit-oscillator correlation, we gain insight into the nature of the transition and the associated critical behavior.

We study theoretically and experimentally the combined effects of polarization-selective optical feedback and of crossed-polarization reinjection in a vertical-cavity surface-emitting laser. We show that the application of polarization-selective optical feedback, which induces an effective dichroism in the system, allows one to generate a robust and regular square-wave output signal in each polarization component. The period of the square-wave signal is determined by twice the reinjection delay. We analyze the regularity of the induced modulation as a function of laser bias current, dichroism, and of the levels and delays of reinjection and feedback, thus revealing the robustness of the square-wave emission in the parameter space. We also show that the feedback is more effective when acting on the long-wavelength polarization mode, which can be traced to the asymmetry of the bistable region of the vertical-cavity surface-emitting lasers for low dichroism.

Tests of local position invariance (LPI) made by comparing the relative redshift of atomic clocks based on different atoms have been carried out for a variety of pairs of atomic species. In most cases, several absolute frequency measurements per year are used to look for an annual signal, resulting in tests that can span on order of a decade. By using the output of continuously running clocks, we carry out LPI tests with comparable or higher precision after less than 1.5 years. These include new measurements of the difference in redshift anomalies $\beta$ for hyperfine transitions in ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ and in ${}^1\mathrm{H}$ and ${}^{133}\mathrm{Cs}$ and a measurement comparing ${}^{87}\mathrm{Rb}$ and ${}^1\mathrm{H}$, resulting in a stringent limit on LPI, ${\beta }_{\mathrm{Rb}}-{\beta }_{\mathrm{H}}=\left(-2.7\pm 4.9\right)\times {10}^{-7}$. The method of making these measurements for continuous clocks is discussed.

We demonstrate a $p$-wave optical Feshbach resonance (OFR) using purely long-range molecular states of a fermionic isotope of ytterbium ${}^{171}$Yb, following the proposition made by K. Goyal et al. [Phys. Rev. A 82, 062704 (2010)]. The $p$-wave OFR is clearly observed as a modification of a photoassociation rate for atomic ensembles at about 5 $\mu$K. A scattering phase shift variation of $\delta \eta =0.022$ rad is observed with an atom loss rate coefficient $K=28.0\times {10}^{-12}$ cm${}^3$/s.

We reduce the necessary and sufficient biseparable conditions of four-qubit cluster diagonal states to concise forms. Only 4 out of the 15 parameters are proved to be relevant in specifying the genuine entanglement of the states. Using the relative entropy of entanglement as entanglement measure, we analytically find the genuine entanglement of all the four-qubit cluster diagonal states. The formulas for the genuine entanglement are of five kinds, for seven different parameter regions of genuinely entangled states.

We develop the theory to describe the generation of entangled-photon pairs in the parametrically induced transparency regime in an ensemble of $\Lambda$ atoms. A highly effective conversion of the monochromatic drive field into entangled-photon pairs is predicted. In the suggested regime, the generation of entangled photons has some advantages as compared to the well-known methods, such as a narrow frequency band and a low threshold for the drive power. The two-mode squeezed vacuum generation is thorouhly investigated.

Understanding fault-tolerant properties of quantum circuits is important for designing large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the relationship between properties such as the noise model, encoding scheme, and threshold value. For general noisy circuits, these simulations quickly become intractable in the size of the encoded circuit. We introduce a general theoretical method for approximating a noise process by one that allows for efficient Monte Carlo simulation of properties of encoded circuits. The approximation is as close to the original process as possible without overestimating its ability to preserve quantum information, a key property for obtaining honest estimates of threshold values. We numerically illustrate the method with various physically relevant noise models.

We propose the generalized controlled $X$ (gcx) gate as the two-qudit elementary gate, and based on Cartan decomposition, we also give the one-qudit elementary gates. Then we discuss the physical implementation of these elementary gates and show that it is feasible with current technology. With these elementary gates many important qudit quantum gates can be synthesized conveniently. We provide efficient methods for the synthesis of various kinds of controlled qudit gates and greatly simplify the synthesis of existing generic multi-valued quantum circuits. Moreover, we generalize the quantum Shannon decomposition (QSD), the most powerful technique for the synthesis of generic qubit circuits, to the qudit case. A comparison of ququart ($d=4$) circuits and qubit circuits reveals that using ququart circuits may have an advantage over the qubit circuits in the synthesis of quantum circuits.