We calculate the index of refraction of sodium matter waves propagating through a gas of nitrogen molecules. We use a recent ab initio potential for the ground state of the NaN${}_2$ van der Waals complex to perform quantal close-coupling calculations and compute the index of refraction as a function of the projectile velocity. We obtain good agreement with the available experimental data. We show that the refractive index contains glory oscillations but that they are damped by the averaging over the thermal motion of the N${}_2$ molecules. These oscillations appear at lower temperatures and projectile velocity. We also investigate the behavior of the refractive index at low temperature and low projectile velocity to show its dependence on the rotational state of N${}_2$ and discuss the advantage of using diatomic molecules as projectiles.

Charge asymmetric dissociation into ${\mathrm{C}}^{2+}+\mathrm{O}$ following ionization of a CO${}^{+}$ molecular-ion beam with intense ultrashort (7–40-fs) laser pulses is studied using a coincidence three-dimensional momentum imaging method. The data suggest that allowing the molecule enough time to stretch within a laser pulse such that it ionizes beyond the curve crossings of the ${\mathrm{C}}^{2+}+\mathrm{O}$ and ${\mathrm{C}}^{+}+{\mathrm{O}}^{+}$ potentials enhances the otherwise hard-to-reach charge asymmetric dissociation channel.

Considering an electron interacting with an atomic or molecular potential and an external static electric field, one usually focuses on narrow resonances at negative energies originating from the bound states in the absence of the field; we call them tunneling states (TSs). Meanwhile, there also exist relatively broad resonances at positive energies having no counterparts in the absence of the field; we call them static-field-induced states (SFISs). In this paper, the recently developed weak-field asymptotic theory of TSs [O. I. Tolstikhin et al., Phys. Rev. A 84, 053423 (2011)] is extended to SFISs. An asymptotic quantization condition defining the energies of SFISs in an arbitrary potential in the three-dimensional case is derived. The parabolic scattering amplitudes appearing in this quantization condition are defined. The theory is illustrated by calculations for the zero-range and Coulomb potentials. The SFISs in these potentials are found and their energies are shown to be in good agreement with the asymptotic results over a wide interval of the values of the field.

With the help of the solution of the time-dependent Schrödinger equation in momentum space, we study the above-threshold ionization spectrum resulting from the interaction of atomic hydrogen with an infrared and XUV short laser pulses. Our calculations are based on a model where the kernel of the nonlocal Coulomb potential is replaced by a finite sum of $N$ symmetric separable potentials, each of them supporting one bound state of atomic hydrogen. Here, we consider only the case of $1s$, $2s$, and $2p$ states. Thus, the theory fully accounting for the important $1s–2p$ transition, explains the photoelectron spectrum as well as the total ionization probability for the resonant case. We compared the results given by our theory with the numerical solutions of the time-dependent Schrödinger equation.

Atomic ionization by strong and ultrashort laser pulses with frequencies in the midinfrared spectral region have revealed novel features such as the low-energy structures. We have performed fully three-dimensional quantum dynamical as well as classical trajectory Monte Carlo simulations for pulses with wavelengths from $\lambda =2000$ to 6000 nm. Furthermore, we apply distorted-wave quantum approximations. This allows to explore the quantum-classical correspondence as well as the (non) perturbative character of the ionization dynamics driven by long-wavelength pulses. We observe surprisingly rich structures in the differential energy and angular momentum distribution which sensitively depend on $\lambda$, the pulse duration ${\tau }_p$, and the carrier-envelope phase ${\varphi }_{\mathrm{CEP}}$.

We derive the normal modes for a rotating Coulomb ion crystal in a Penning trap, quantize the motional degrees of freedom, and illustrate how they can be driven by a spin-dependent optical dipole force to create a quantum spin simulator on a triangular lattice with hundreds of spins. The analysis for the axial modes (oscillations perpendicular to the two-dimensional crystal plane) follow a standard normal-mode analysis, while the remaining planar modes are more complicated to analyze because they have velocity-dependent forces in the rotating frame. After quantizing the normal modes into phonons, we illustrate some of the different spin-spin interactions that can be generated by entangling the motional degrees of freedom with the spin degrees of freedom via a spin-dependent optical dipole force. In addition to the well-known power-law dependence of the spin-spin interactions when driving the axial modes blue of the phonon band, we notice certain parameter regimes in which the level of frustration between the spins can be engineered by driving the axial or planar phonon modes at different frequencies. These systems may allow for the analog simulation of quantum spin glasses with large numbers of spins.

We develop an interferometric technique for making time-resolved measurements of field-quadrature operators for nonequilibrium ultracold bosons in optical lattices. The technique exploits the internal state structure of magnetic atoms to create two subsystems of atoms in different spin states and lattice sites. A Feshbach resonance turns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state, while atoms in the other subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms are obtained by detecting relative spin populations. The technique can provide quadrature measurements for a variety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems with tunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special case of a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables and their fluctuations. As a second application, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling ${\overline{n}}^{-3/2}$ in the mean number of atoms per lattice site, and standard quantum limit scaling $M^{-1/2}$ in the number of lattice sites. In our analysis, we require $M\gg 1$ and for realistic systems $\overline{n}$ is small, and therefore the scaling in total atom number $N=\overline{n}M$ is below the Heisenberg limit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies should be possible in this system.

The concept of quantum revivals is extended to many-body systems and the implications of traversing a quantum phase transition are explored. By analyzing two different models, the vibron model for the bending of polyatomic molecules and the Dicke model for a quantum radiation field interacting with a system of two-level atoms, we show evidence of revival behavior for wave packets centered around energy levels as low as the fundamental state. Away from criticality, revival times exhibit smooth, nonsingular behavior and are proportional to the system size. Upon approaching a quantum critical point, they diverge as a power law and scale with the system size, although the scaling is no longer linear.

We experimentally study the scattering of guided matter waves on an amplitude-modulated optical lattice. We observe different types of frequency-dependent dips in the asymptotic output density distribution. Their positions are compared quantitatively with numerical simulations. A semiclassical model that combines local Floquet-Bloch bands analysis and Landau-Zener transitions provides a simple picture of the observed phenomena in terms of elementary Floquet photon absorption-emission processes and envelope-induced reflections. Finally, we propose and demonstrate the use of this technique with a bichromatic modulation to design a tunable subrecoil velocity filter. Such a filter can be transposed to all species since it does not rely on a specific internal level configuration of the atoms.

The dynamics, appearing after a quantum quench, of a trapped, spin-orbit coupled, dilute atomic gas is studied. The characteristics of the evolution is greatly influenced by the symmetries of the system, and we especially compare evolution for an isotropic Rashba coupling and for an anisotropic spin-orbit coupling. As we make the spin-orbit coupling anisotropic, we break the rotational symmetry and the underlying classical model becomes chaotic; the quantum dynamics is affected accordingly. Within experimentally relevant time scales and parameters, the system thermalizes in a quantum sense. The corresponding equilibration time is found to agree with the Ehrenfest time, i.e., we numerically verify a $\sim \ln \left({\hslash }^{-1}\right)$ scaling. Upon thermalization, we find that the equilibrated distributions show examples of quantum scars distinguished by accumulation of atomic density for certain energies. At shorter time scales, we discuss nonadiabatic effects deriving from the spin-orbit-coupled induced Dirac point. In the vicinity of the Dirac point, spin fluctuations are large and, even at short times, a semiclassical analysis fails.

We examine the dependence of the Gaussian-Lévy transition in random lasers on the disorder strength, through experimental and theoretical studies. Experiments are performed on samples whose disorder strength varied over almost an order of magnitude. It is found that the Lévy regime is easily accessed under low excitation when the disorder is weak, compared to the energetically expensive transition in strong disorder. Besides, under conditions of weak disorder, the transition energy is mildly dependent on the disorder strength. The Gaussian-Lévy transition also progresses rapidly in weakly scattering samples. In the theoretical investigation, we employ an analytical-numerical method to estimate the parameters of intensity statistics in random lasers. A Monte Carlo simulation is implemented to accurately calculate the excitation region of the random laser, yielding the ${\ell }_g$ and the geometric features of this region. The aspect ratio of this pumped region allows us to further analytically calculate the scale parameter $\langle L\rangle$ of a photon diffusing out of the amplifying region, thereby providing the power-law exponent $\mu$, which allows us to trace the Gaussian-Lévy transition. We find an excellent agreement between the experimental and the theoretical results on the Gaussian-Lévy transition with regard to the location and the rate of transition as a function of the disorder strength.

Two phenomena can affect the transmission of a probe field through an absorbing medium in the presence of an additional field: electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS). Being able to discriminate between the two is important for various practical applications. Here we present an experimental investigation into a method that allows for such a disambiguation as proposed by Anisimov, Dowling, and Sanders in Phys. Rev. Lett. 107, 163604 (2011). We apply the proposed test based on Akaike's information criterion to a coherently driven ensemble of cold cesium atoms and find a good agreement with theoretical predictions, therefore demonstrating the suitability of the method. Beyond the applicability of the test, our results demonstrate that the transition features are highly sensitive to the properties of the medium under study, potentially providing a practical characterizing tool for complex systems.

We consider an optomechanical double-ended cavity under the action of a coupling laser and a probe laser in an electromagnetically induced transparency configuration. It is shown how the group delay and advance of the probe field can be controlled by the power of the coupling field. In contrast to single-ended cavities, which only allow for superluminal propagation, the possibility of both superluminal and subluminal propagation regimes is found. The magnitudes of the group delay and the advance are calculated to be $\sim$1 ms and about $-2$ s, respectively, at a very low pumping power of a few microwatts. In addition, the interaction of the optomechanical cavity with a time-dependent probe field is investigated for controlled excitations of mirror vibrations.

I make evident a method for broadband spectral-phase control of light pulses produced in high-order harmonic generation (HHG). Using a feedback loop scheme, I demonstrate that a broad spectral region of the HHG output field can be coherently added to the intense infrared driving pulse with optimal attenuation and time delay parameters to control the phase of the HHG field generated in a second interaction region. I provide computational evidence of the control scheme by considering an optimal flattening of the spectral phase for the production of isolated attosecond pulses. This is proven by considering different spectral widths and for several central photon energies, such as 36 eV, 70 eV, and 120 eV. An iterative procedure of the method allows one to obtain single pulses with less than 1.2 cycles at a central photon energy of 36 eV. This control scheme is a fundamental tool that can be implemented for amplitude and phase shaping of any suitable spectral region in HHG.

In a recent article [Phys. Rev. A 86, 024302 (2012)], the authors have derived some hierarchy relations between geometric discord and entanglement (measured by negativity and its square). We point out that these results are incorrect and give analytic counterexamples. We also briefly discuss the reason for such violations.

The fine-grained uncertainty relation can be used to discriminate among classical, quantum, and superquantum correlations based on their strength of nonlocality, as has been shown for bipartite and tripartite systems with unbiased measurement settings. Here we consider the situations when two and three parties choose settings with bias for playing certain nonlocal games. We show analytically that while the fine-grained uncertainty principle is still able to distinguish classical, quantum, and superquantum correlations for biased settings corresponding to certain ranges of the biasing parameters, the above-mentioned discrimination is not manifested for all biasing.

We present a unifying framework to the understanding of when and how quantum-mechanical systems become independent of their initial conditions and adapt macroscopic properties (like temperature) of the environment. By viewing this problem from a quantum information theory perspective, we are able to simplify it in a very natural and easy way. We first show that for any interaction between the system and the environment, and almost all initial states of the system, the question of how long the system retains memory of its initial conditions can be answered by studying the temporal evolution of just one special initial state. This special state thereby depends only on our knowledge of macroscopic parameters of the system. We provide a simple entropic inequality for this state that can be used to determine whether most states of the system have or have not become independent of their initial conditions after time $t$. We discuss applications of our entropic criterion to thermalization times in systems with an effective light cone and to quantum memories suffering depolarizing noise. We make a similar statement for almost all initial states of the environment and finally provide a sufficient condition for which a system never thermalizes but remains close to its initial state for all times.

We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is written can be efficiently prepared in a controlled manner. Furthermore, we show how this algorithm is well suited for quantum process tomography, enabling one to perform selective and efficient quantum process tomography.

In this paper we describe a connection between unextendable product bases (UPB) and positive (P) maps which are not completely positive (CP). We show that inner automorphisms of the set of P maps which are not CP produce extremal extensions of these maps that help in entanglement detection. By constructing such an extension of the well-known Choi map, we strengthen its power to unearth positive under partial transpose entangled states. We further show that the class of maps generated from the Choi map via an inner automorphism naturally detects the entanglement of states in the orthogonal complement of certain UPB. This brings out a hitherto undiscovered connection between the Choi map and UPB. We also show that certain other recently considered extremal extensions are obtainable by such extensions of the Choi map.

We investigate multipartite entanglement for composite quantum systems in a pure state. Using the generalized Bloch representation for $n$-qubit states, we express the condition that all $k$-qubit reductions of the whole system are maximally mixed, reflecting maximum bipartite entanglement across all $k$ vs $n-k$ bipartitions. As a special case, we examine the class of balanced pure states, which are constructed from a subset of the Pauli group ${\mathcal{P}}_n$ that is isomorphic to ${\mathbb{Z}}_2^n$. This makes a connection with the theory of quantum error-correcting codes and provides bounds on the largest allowed $k$ for fixed $n$. In particular, the ratio $k/n$ can be lower and upper bounded in the asymptotic regime, implying that there must exist multipartite entangled states with at least $k=\lfloor 0.189n\rfloor$ when $n\to \infty$. We also analyze symmetric states as another natural class of states with high multipartite entanglement and prove that, surprisingly, they cannot have all maximally mixed $k$-qubit reductions with $k>1$. Thus, measured through bipartite entanglement across all bipartitions, symmetric states cannot exhibit large entanglement. However, we show that the permutation symmetry only constrains some components of the generalized Bloch vector, so that very specific patterns in this vector may be allowed even though $k>1$ is forbidden. This is illustrated numerically for a few symmetric states that maximize geometric entanglement, revealing some interesting structures.