The need to perform quantum state tomography on ever-larger systems has spurred a search for methods that yield good estimates from incomplete data. We study the performance of compressed sensing (CS) and least squares (LS) estimators in a fast protocol based on continuous measurement on an ensemble of cesium atomic spins. They both efficiently reconstruct nearly pure states in the 16-dimensional ground manifold, reaching average fidelities ${\overline{\mathcal{F}}}_{\mathrm{CS}}=0.92$ and ${\overline{\mathcal{F}}}_{\mathrm{LS}}=0.88$ using similar amounts of incomplete data. Surprisingly, the main advantage of CS in our protocol is an increased robustness to experimental imperfections.

High-precision results are reported for the energy levels of the $2{}^{1}S$ and $2{}^{1}P$ states of the beryllium atom. Calculations are performed using fully correlated Gaussian basis sets and taking into account the relativistic, quantum electrodynamics (QED), and finite nuclear mass effects. Theoretical predictions for the ionization potential of the beryllium ground state $75192.699\left(7\right){\mathrm{cm}}^{-1}$ and the $2{}^{1}P\to 2{}^{1}S$ transition energy $42565.441\left(11\right){\mathrm{cm}}^{-1}$ are compared to known but less accurate experimental values. The accuracy of the four-electron computations approaches that achieved for the three-electron atoms, which enables determination of the nuclear charge radii and precision tests of QED.

We investigate the effects of spatial inhomogeneities on the entanglement of modes of strongly correlated systems in the framework of small Fermi-Hubbard chains. We find regimes where entanglement is strongly enhanced by the presence of inhomogeneities. This contrasts with recent reports of entanglement destruction due to inhomogeneities. We further study this phenomenon using concepts of density functional theory and, thus, provide a general recipe for the prediction of entanglement enhancement in nanostructures. We find enhancement of up to $\sim 27\%$, as compared to impurity-free chains.

Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to securely share encryption keys between two parties. Here, we present an approach to high-capacity, high-efficiency QKD by exploiting cross-disciplinary ideas from quantum information theory and the theory of light scattering of aperiodic photonic media. We propose a unique type of entangled-photon source, as well as a physical mechanism for efficiently sharing keys. The key-sharing protocol combines entanglement with the mathematical properties of a recursive sequence to allow a realization of the physical conditions necessary for implementation of the no-cloning principle for QKD, while the source produces entangled photons whose orbital angular momenta (OAM) are in a superposition of Fibonacci numbers. The source is used to implement a particular physical realization of the protocol by randomly encoding the Fibonacci sequence onto entangled OAM states, allowing secure generation of long keys from few photons. Unlike in polarization-based protocols, reference frame alignment is unnecessary, while the required experimental setup is simpler than other OAM-based protocols capable of achieving the same capacity and its complexity grows less rapidly with increasing range of OAM used.

Many-body quantum systems in the ground states have zero-point energy due to the uncertainty relation. In many cases, the system in the ground state accompanies spatially entangled energy density fluctuation via the noncommutativity of the energy density operators, though the total energy takes a fixed value, i.e., the lowest eigenvalue of the Hamiltonian. Quantum energy teleportation (QET) is a protocol for the extraction of the zero-point energy out of one subsystem using information of a remote measurement of another subsystem. From an operational viewpoint of protocol users, QET can be regarded as an effective rapid energy transportation without breaking all physical laws, including causality and local energy conservation. In the protocol, the ground-state entanglement plays a crucial role. In this paper, we show analytically for a general class of spin-chain systems that the entanglement entropy is lower bounded by a positive quadratic function of the teleported energy between the regions of a QET protocol. This supports a general conjecture that ground-state entanglement is an evident physical resource for energy transportation in the context of QET. The result may also deepen our understanding of the energy density fluctuation in condensed-matter systems from a perspective of quantum information theory.

We show that dissipative quantum state preparation processes can be protected against qubit dephasing by interlacing the state preparation control with dynamical decoupling (DD) control consisting of a sequence of short $\pi$ pulses. The inhomogeneous broadening can be suppressed to second order of the pulse interval, and the protection efficiency is nearly independent of the pulse sequence but determined by the average interval between pulses. The DD protection is numerically tested and found to be efficient against inhomogeneous dephasing on two exemplary dissipative state preparation schemes that use collective pumping to realize many-body singlets and linear cluster states, respectively. Numerical simulation also shows that the state preparation can be efficiently protected by $\pi$ pulses with completely random arrival time. Our results make possible the application of these state preparation schemes in inhomogeneously broadened systems. DD protection of state preparation against dynamical noises is also discussed using the example of Gaussian noise with a semiclasscial description.

The ideal Bennett-Brassard 1984 (BB84) quantum-key-distribution protocol is based on the preparation and measurement of qubits in two alternative bases differing by an angle of $\pi /2$. Any real implementation of the protocol, though, will inevitably introduce misalignments in the preparation of the states and in the alignment of the measurement bases with respect to this ideal situation. Various security proofs take into account (at least partially) such errors, i.e., show how Alice and Bob can still distill a secure key in the presence of these imperfections. Here, we consider the complementary problem: How can Eve exploit misalignments to obtain more information about the key than would be possible in an ideal implementation? Specifically, we investigate the effects of misalignment errors on the security of the BB84 protocol in the case of individual attacks, where necessary and sufficient conditions for security are known. Though the effects of these errors are small for expected deviations from the perfect situation, our results nevertheless show that Alice and Bob can incorrectly conclude that they have established a secure key if the inevitable experimental errors in the state preparation and in the alignment of the measurements are not taken into account. This gives further weight to the idea that the formulation and security analysis of any quantum cryptography protocol should be based on realistic assumptions about the properties of the apparatus used. Additionally, we note that BB84 seems more robust against alignment imperfections if both the $x$ and $z$ bases are used to generate the key.

In this paper, we report on relativistic quantum-mechanical calculations of electron-impact linewidths and line shifts in singly ionized strontium ions in ultracold neutral plasmas. We have used the Dirac $R$-matrix methods to solve ($N+1$)-electron colliding systems and to generate the required scattering matrices. Calculated linewidths and line shifts at an electron density ${10}^{17}{\text{cm}}^{-3}$ and electron temperatures (several electronvolts) agree well with other theoretical calculations and are closer to the experimental observations. Our theoretical findings of linewidths and line shifts are almost twice as large as the earlier calculations for the particular selected plasma conditions. This work develops these quantum-mechanical procedures and applies them to the emission from ultracold neutral plasmas.

We have completed a measurement of the Stark shift in ${}^{115}$In within the 410-nm $5P_{1/2}$-$6S_{1/2}$ transition. We measure the Stark shift constant to be $k_S=-122.92\left(33\right)$ kHz/(kV/cm)${}^2$, corresponding to a difference in the $6S_{1/2}$- and $5P_{1/2}$-state polarizabilities, $\Delta {\alpha }_0$ (in atomic units), of $1000.2\pm 2.7a_0^3$. This result is a factor of 30 more precise than previous measurements and is in excellent agreement with a new theoretical value based on an ab initio calculation of the wave functions in this three-valence-electron system. The measurement was performed in an indium atomic-beam apparatus, used a GaN laser diode system, and exploited a FM spectroscopy technique to extract laser transmission spectra under conditions where our interaction region optical depth was typically less than 10${}^{-3}$.

The dynamic dipole polarizabilities for the $3s$ state of the Li atom are computed using Hylleraas and semiempirical approaches. This enables the calculation of the ${}^7$Li($2s\to 3s$) Stark shift at photon wavelengths of 610.5 nm and 735.1 nm. They are calculated to be 834.7(5) and $-686.7\left(25\right)$ $a_0^3$, respectively. The first two tune-out frequencies for the ${}^7$Li($2s$) ground state are determined to be $670.971626\left(1\right)$ nm and $324.192\left(2\right)$ nm, respectively.

We introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers $L$. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\le 2$ Fano-Feshbach resonances in the range $0–1000$ G for the scattering of ${}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}$ in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.

The semiclassical theory of atomic dynamics in a three-dimensional pulsed optical dipole trap formed by superimposed trains of short laser pulses (down to a few fs duration), which is based on a stochastic formulation for the dynamics of an open quantum system, is considered in detail. It covers all key features of the atomic dynamics in the trap, including the dipole-dipole interaction (DDI) between trapped atoms due to the exchange of virtual photons between the atoms. Analytical solutions are obtained for the relaxation and laser Liouvillians, which describe the dissipation and laser excitation in the system, respectively. The probabilities of single-atom and two-atom escapes from the trap are analyzed. As an example, the theory is applied to computer simulation of Rb atoms preliminarily cooled in a magneto-optical trap that are trapped in a femtosecond optical dipole trap (pulse duration 100 fs). Our simulations prove that such a trap effectively confines atoms at the pump laser power in the range from a few mW to several kW. It is also shown that a near-resonant DDI, through which atoms that are closely spaced in the micropotential wells interact with each other, can be significantly increased by illuminating the atoms with a near-resonant probe laser beam. By varying both the parameters of the trap and the intensity of the probe laser field, the role of the DDI in the atomic dynamics in the trap and its influence on the single-atom and two-atom escape rates are clarified in detail.

We show, theoretically and experimentally, that chirped photonic crystals (where the longitudinal modulation period varies along the propagation direction) can provide a substantial spatial (angular) filtering of light beams. The chirped photonic crystals, in gapless configuration, were recorded in a bulk of glass, where the refraction index has been periodically modulated using tightly focused femtosecond laser pulses. The spatial filtering performance has been studied in detail, and the filtering efficiencies up to approximately 50$\%$ have been experimentally demonstrated.

We present a quantum-mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically symmetric stable light fields—the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity, and we discover several compelling features, including nonmonotonic behavior, stable beams with real continuous (noninteger) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may have applications in quantum key distribution, atom trapping, and quantum informatics in general—as the ellipticity opens up an alternative way of navigating the spatial photonic Hilbert space.

We consider excitation of highly charged, hydrogenlike ions by the impact of equivelocity electrons and protons. The kinetic energy of the protons is more than 3 orders of magnitude larger than that of the equivelocity electrons. It is shown, however, that despite this fact, the electrons can be much more effective in inducing excitation at collision velocities (slightly) above the threshold for electron-impact excitation. The basic reason for this is the strong distortion of the motion of the electron by the attractive field of the nucleus of the highly charged ion.

We revisit the process of optical wave thermalization through supercontinuum generation in photonic crystal fibers. We report theoretically and numerically a phenomenon of `truncated thermalization': The incoherent optical wave exhibits an irreversible evolution toward a Rayleigh-Jeans thermodynamic equilibrium state characterized by a compactly supported spectral shape. The theory then reveals the existence of a frequency cut-off which regularizes the ultraviolet catastrophe inherent to ensembles of classical nonlinear waves. This phenomenon sheds new light on the mechanisms underlying the formation of bounded supercontinuum spectra in photonic crystal fibers.

A class of Maxwellian beams, which is an exact solution of the vector wave equation (Helmholtz equation) and Maxwell's equations, is introduced. The solution, termed a quasi-Gaussian electromagnetic (EM) beam, is formed from a superposition of sources and sinks with complex coordinates, and is characterized by an arbitrary waist $w_0$ and a diffraction convergence length known as the Rayleigh range $z_R$. An attractive feature of this beam is the description of strongly focused (or strongly divergent) EM-optical wave fields for $k{w}_0\le 1$, where $k$ is the wave number. A vector wave analysis is developed to determine and compute the spatial Cartesian components of the electric and magnetic fields (valid in the near field and the far field) stemming from Maxwell's vector equations and the Lorenz gauge condition, with particular emphasis on the parameter $k{w}_0$ and the polarization states of the vector potentials used to derive the EM field's components. The results are potentially useful in the study of the axial and/or arbitrary wave scattering, radiation force, and torque in lasers operating with strongly focused (or strongly divergent) beams for particle manipulation in optical tweezers and imaging applications.

We construct a large class of completely positive and trace-preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics for statistical operators characterized by a continuous time evolution interrupted by jumps, randomly distributed in time and described by a quantum channel. The state of the open system is shown to obey a closed evolution equation, given by a master equation with a memory kernel and an inhomogeneous term. The non-Markovianity of the obtained dynamics is explicitly assessed studying the behavior of the distinguishability of two different initial system's states with elapsing time.

Using a phase-detection method to determine the cyclotron frequency of a single trapped ion in a Penning trap allowed us to perform a measurement of the $g$ factor of the bound electron in hydrogenlike ${}^{28}$Si${}^{13+}$ with a statistical uncertainty of $4\times {10}^{-11}$. Furthermore, we reevaluated the image-charge shift as the main source of uncertainty. Our result challenges bound-state quantum-electrodynamical calculations by probing two-loop contributions of order (Z$\alpha$)${}^6$ and paves the way towards a more precise determination of fundamental constants as the electron mass.