Field-grade atomic clocks capable of primary standard performance in compact physics packages would be of significant value in applications ranging from network synchronization to inertial navigation. A coherent-population-trapping clock featuring laser-cooled ${}^{87}\mathrm{Rb}$ atoms and pulsed Ramsey interrogation is a strong candidate for this technology if the frequency biases can be minimized and controlled. Here we characterize the light shift in a cold-atom coherent-population-trapping clock, explaining observed shifts in terms of phase shifts that arise during the formation of dark-state coherences combined with optical-pumping effects caused by unwanted incoherent light in the interrogation spectrum. Measurements are compared with existing and new theoretical treatments, and a laser configuration is identified that would reduce clock frequency uncertainty from light shifts to a fractional frequency level of $\Delta \nu /\nu =4\times {10}^{-14}$ per 100 kHz of laser frequency uncertainty.

Highly charged states created through multiple ionization of gases are shown to enhance terahertz (THz) generation by intense, single- or two-color femtosecond laser pulses. A one-dimensional, nonpropagating fluid model reveals the main conversion processes up to ${10}^{17}\mathrm{W}{\mathrm{cm}}^{-2}$ laser intensities, namely, ionization-induced photocurrents and plasma current oscillations. For increasing intensities, we demonstrate a cyclic growth in the THz signal associated with the different binding energies of argon and helium. This behavior is confirmed by direct particle-in-cell and unidirectional pulse propagation simulations. Changes in the forward and backward THz spectra owing to multiple ionization are discussed.

With the development of quantum-information theory, there has been a flurry of investigations of quantum non-Markovian dynamics, and several significant measures for such dynamics have been proposed from various perspectives, such as the breakdown of dynamical divisibility, increase in the distinguishability between quantum states, increase in correlations between the system and an arbitrary ancillary, and so on. Motivated by the idea of exploiting the information content of parameters encoded in initial states, we propose a conceptually simple and physically intuitive characterization for non-Markovianity with the help of a quantum-Fisher-information matrix. The basic features are illustrated through several examples, and relations with other approaches are elucidated. A hierarchial aspect of quantum non-Markovianity is revealed.

We study the geometric phase of a two-level system under the presence of a structured environment, particularly analyzing its correction with the ohmicity parameter $s$ and the onset of non-Markovianity. We first examine the system coupled to a set of harmonic oscillators and study the decoherence factor as function of the environment's ohmicity parameter. Second, we propose the two-level system coupled to a nonequilibrium environment, and show that these environments display non-Markovian effects for all values of the ohmicity parameter. The geometric phase of the two-level system is therefore computed under the presence of both types of environment. The correction to the unitary geometric phase is analyzed in both the Markovian and non-Markovian regimes. Under Markovian environments, the correction induced on the system's phase is mainly ruled by the coupling constant between the system and the environment, while in the non-Markovian regime, memory effects seem to trigger a significant correction to the unitary geometric phase. The result is significant to the quantum information processing based on the geometric phase in quantum open systems.

We theoretically study operations with a four-level superconducting circuit as a two-qubit system. Using a mapping on a two-qubit system, we show how to implement iswap gates and Hadamard gates through pulses on transitions between particular pairs of energy levels. Our approach allows one to prepare pure two-qubit entangled states with desired form of reduced density matrices of the same purity and, in particular, arbitrary identical reduced states of qubits. We propose using schemes for the Hadamard gate and two-qubit entangled states with identical reduced density matrices in order to verify $logN$ inequalities for Shannon and Rényi entropies for the considered noncomposite quantum system.

The $k$-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of $k$-nonseparability of $n$-partite quantum states from an information perspective and obtain some $k$-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many $k$-nonseparable states, and their advantages over an important and well-known $k$-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.

We observe the microwave transitions of calcium from the $4snf$ states to the $4s(n+1)d,4sng,4snh,4sni$, and $4snk$ states for $18\le n\le 23$ using delayed field ionization as the state selective detection technique. The observed intervals between the $\ell \ge 5$ states can be analyzed to extract the ${\mathrm{Ca}}^{+}$ ionic dipole $\left({\alpha }_d\right)$ and quadrupole $\left({\alpha }_q\right)$ polarizabilities using two nonadiabatic core polarization models. Using these two models we determine the ionic dipole and quadrupole polarizabilities to be $75.3a_0^3<{\alpha }_d<76.9a_0^3$ and $206a_0^5<{\alpha }_q<1590a_0^5$, respectively.

We report the results of a theoretical investigation of the electronic structure of the ${\mathrm{ThF}}^{+}$ cation, which is one of the most interesting systems to search for the electron electric dipole moment $\left(e\mathrm{EDM}\right)$ [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013)] and other effects of violation of time reversal (T) and spatial parity (P) symmetries in fundamental interactions. For the working ${}^3{\Delta }_1$ state we find a quite high value of the effective electric field acting on unpaired electrons (37.3 GV/cm). The field will be required to interpret the experiment planned on ${\mathrm{ThF}}^{+}$ in terms of the $e\mathrm{EDM}$. Within the concept of atoms in compounds [A. V. Titov, Y. V. Lomachuk, and L. V. Skripnikov, Phys. Rev. A 90, 052522 (2014)], we compare the ${\mathrm{ThF}}^{+}$ electronic structure with that of ThO. Also, we calculate other parameters of T,P-odd interactions: $W_{T,P}$, which is needed for interpretation of the experiment in terms of the dimensionless constant $k_{T,P}$ characterizing the strength of the $T,P$-odd pseudoscalar-scalar electron-nucleus neutral current interaction (50 kHz); and $W_M$, which is required to search for the ${}^{229}\mathrm{Th}$ nuclear magnetic quadrupole moment in ${}^{229}{\mathrm{ThF}}^{+}$ (0.88 $\frac{{10}^{33}\mathrm{Hz}}{e{\mathrm{cm}}^2})$. A number of properties which can be measured are also calculated: the hyperfine structure constant, molecule-frame dipole moment, and $g$ factor.

The Coulomb explosion of small cluster beams can be used to measure the dwell time of fragments traversing amorphous films. Therefore, the thickness of thin films can be obtained with the so-called Coulomb depth profiling technique using relatively high cluster energies where the fragments are fully ionized after breakup. Here we demonstrate the applicability of Coulomb depth profiling technique at lower cluster energies where neutralization and wake effects come into play. To that end, we investigated 50–200 keV/u ${{\mathrm{H}}_2}^{+}$ molecular ions impinging on a 10 nm ${\mathrm{TiO}}_2$ film and measured the energy of the backscattered ${\mathrm{H}}^{+}$ fragments with high-energy resolution. The effect of the neutralization of the ${\mathrm{H}}^{+}$ fragments along the incoming trajectory before the backscattering collision is clearly observed at lower energies through the decrease of the energy broadening due to the Coulomb explosion. The reduced values of the Coulomb explosion combined with full Monte Carlo simulations provide compatible results with those obtained at higher cluster energies where neutralization is less important. The results are corroborated by electron microscopy measurements.

Wave-function microscopy images for Stark resonance states of H atoms are simulated using the quantum-mechanical formalism developed previously. Spatial distributions of ejected electron current densities are compared with experiment, and a good agreement is shown. The nonzero values of minima in the experimentally observed electron current distributions are reproduced by convoluting the theoretical current distribution with an instrumental function representing uncertainties in the position. Our relative strengths of the ejected electron current densities differ from those calculated with the wave packet propagation technique. We show that for the full convergence of the calculation, the distance between the ionized atom and the detector should exceed $10\mu \mathrm{m}$.

The adiabatic strong-field approximation is used to study ionization yields as a function of the angle between the polarization of the external field and molecular axis for ${\mathrm{CO}}_2$, CO, and OCS molecules. We find that orbital distortion plays an important role in explaining positions and relative strengths of extrema in the yields for both polar and nonpolar molecules, even for molecules with low polarizabilities and at low laser intensities. In particular, we show that for ${\mathrm{CO}}_2$ the maximum in the ionization yield shifts towards the experimentally measured maximum when accounting for orbital distortion. For the CO molecule, not only is the preferred direction of ionization correctly predicted by the theory, but also the ratio between yields for orientations with the electric field pointing towards C and O ends, respectively. For OCS we find that ionization is more probable when the laser field points from the O end towards the S end than when the field points in the opposite direction.

We study the collisionless spin dynamics of a harmonically trapped Fermi gas in a magnetic field gradient. In the absence of interactions, the system evolution is periodic: the magnetization develops twists, which evolve into a longitudinal polarization. Recurrences follow. For weak interaction, the exchange interactions lead to beats in these oscillations. We present an array of analytic and numerical techniques for studying this physics.

We investigate both theoretically and experimentally strong correlations in macroscopic (bright) quantum states of light generated via unseeded parametric down-conversion and four-wave mixing. The states generated this way contain only quantum noise, without a classical component, and are referred to as bright squeezed vacuum (BSV). Their important advantage is the multimode structure, which offers a larger capacity for the encoding of quantum information. For the theoretical description of these states and their correlation features we introduce a generalized fully analytical approach, based on the concept of independent collective (Schmidt) modes and valid for the cases of both weak and strong nonlinear interaction. In experiment, we generate states of macroscopic BSV with up to ${10}^{10}$ photons per mode and examine large photon-number spatial correlations that are found to be very well described by our theoretical approach.

For Doppler-broadened media operating under double-double electromagnetically induced transparency (EIT) conditions, we devise a scheme to control and reduce the probe-field group velocity at the center of the second transparency window. We derive numerical and approximate analytical solutions for the width of EIT windows and for the group velocities of the probe field at the two distinct transparency windows, and we show that the group velocities of the probe field can be lowered by judiciously choosing the physical parameters of the system. Our modeling enables us to identify three signal-field strength regimes (with a signal-field strength always higher than the probe-field strength), quantified by the Rabi frequency, for slowing the probe field. These three regimes correspond to a weak signal field, with the probe-field group velocity and transparency-window width both smaller for the second window compared to the first window, a medium-strength signal field, with a probe-field group velocity smaller in the second window than in the first window but with larger transparency-window width for the second window, and the strong signal field, with both group velocity and transparency-window width larger for the second window. Our scheme exploits the fact that the second transparency window is sensitive to a temperature-controlled signal-field nonlinearity, whereas the first transparency window is insensitive to this nonlinearity.

We determine the dispersion of the third-order polarizability of small donor-acceptor substituted organic molecules using wavelength-dependent degenerate four-wave mixing experiments in solutions with varying concentrations. We find that donor-acceptor–substituted molecules that are characterized by extremely efficient off-resonant nonlinearities also have a correspondingly high two-photon absorption cross section. The width and shape of the first two-photon resonance for these noncentrosymmetric molecules follows what is expected from their longest wavelength absorption peak, and the observed two-photon absorption cross sections are record high when compared to the available literature data, the size of the molecule, and the fundamental limit for two-photon absorption to the lowest excited state, which is essentially determined by the number of conjugated electrons and the excited-state energies. The two-photon absorption of the smallest molecule, which only has 16 electrons in its conjugated system, is one order of magnitude larger than for the molecule called AF-50, a reference molecule for two-photon absorption [O.-K. Kim et al., Chem. Mater. 12, 284 (2000)].

The physics of many materials is modeled by quantum many-body systems with local interactions. If the model of the system is sensitive to noise from the environment, or small perturbations to the original interactions, it will not properly model the robustness of the real physical system it aims to describe, or be useful when engineering novel systems for quantum information processing. We show that local observables and correlation functions of local Liouvillians are stable to local perturbations if the dynamics is rapidly mixing and has a unique fixed point. No other condition is required.

The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite-dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete-time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a superoperator (quantum channel) in each time step followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the part of the Hilbert space explored by the system, then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work shows that the expected return time is a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state.

We derive the structure of Landau-Zener-Stückelberg-Majorana (LZSM) interference patterns for a qubit that experiences quantum dissipation and is additionally subjected to time-periodic but otherwise general driving. A spin-boson Hamiltonian serves as the model, which we treat with a Bloch-Redfield master equation in the Floquet basis. It predicts resonance peaks whose form depends significantly on the operator through which the qubit couples to the bath. The Fourier transforms of the LZSM patterns exhibit arc structures which reflect the shape of the driving. These features are captured by an effective time-independent Bloch equation which provides an analytical solution. Moreover, we determine the decay of these arcs as a function of dissipation strength and temperature.

We introduce an efficient scheme for quantum state transfer that uses a parity-based mirror inversion technique. We design efficient circuits for implementing mirror inversion in Ising ${\mathit{\sigma }}_{\mathbf{X}}{\mathit{\sigma }}_{\mathbf{X}}$ and ${\mathit{\sigma }}_{\mathbf{Y}}{\mathit{\sigma }}_{\mathbf{Y}}$ coupled systems and show how to analytically solve for system parameters to implement the operation in these systems. The key feature of our scheme is a three-qubit parity gate, which we design as a two-control one-target qubit gate. The parity gate operation is implemented by only varying a single control parameter of the system Hamiltonian and the difficulty of implementing this gate is equivalent to that of a controlled-not gate in a two-qubit system. By applying a sequence of $N+1$ parity-based controlled-unitary operations between nearest-neighbor qubits, where all qubits in an $N$-qubit chain function either as controls or targets, we are able to reverse the order of all qubits along the array. These operations are accomplished by varying only a single control parameter per data qubit. The control parameter depends on the physical system under consideration and on the choice of the designer. Since every qubit participates in the mirror-inversion process functioning either as a control or target, all nearest-neighbor couplings are used. Therefore, we do not need additional measures to cancel the effect of any unwanted interactions and the quantum cost of our scheme does not increase in systems that do not have the ability shut off couplings. Moreover, our scheme does not require additional ancillas, nor does it use a pre-engineered mirror-periodic Hamiltonian to govern the evolution of the system. Using our mirror inversion scheme, we also show how to implement a swap gate between two arbitrary remote qubits, move a block of qubits, and implement efficient computing between two remote qubits in nearest-neighbor layouts.