Quantum mechanical interference effects in the line broadening of intrashell transitions are investigated for dense plasma conditions. Simulations that involved $LSJ$-split level structure and intermediate coupling discovered unexpected strong line narrowing for intrashell transitions $L$-$L$ while $M$-$L$ transitions remained practically unaffected by interference effects. This behavior allows a robust study of line narrowing in dense plasmas. Simulations are carried out for XUV transitions of aluminum that have recently been observed in experiments with the FLASH free-electron laser in Hamburg irradiating solid aluminum samples with intensities greater than ${10}^{16}$ W/cm${}^2$. We explore the advantageous case of Al that allows, first, simultaneous observation of $M$-$L$ transitions and $L$-$L$ intrashell transitions with high-resolution grating spectrometers and, second, has a convenient threshold to study interference effects at densities much below solid. Finally, we present simulations at near solid density where the line emission transforms into a quasicontinuum.

When attempting to split a coherent noninteracting atomic cloud by bifurcating the initial trap into two well-separated wells, slow adiabatic following is unstable with respect to any slight trap asymmetry, and the matter wave “collapses” to the well with the lowest energy. A generic fast chopping splits the wave but it also excites it. Shortcuts to adiabaticity engineered to speed up the unperturbed adiabatic process through nonadiabatic transients provide, instead, quiet and robust balanced splitting. For a Bose-Einstein condensate in the mean-field limit, the interatomic interaction makes the splitting, adiabatic or via shortcuts, more stable with respect to trap asymmetry. Simple formulas are provided to distinguish different regimes.

We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-range Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and study the resulting spectrum as a function of the interparticle interaction strength. Both the attractive and repulsive systems are analyzed. We study the impact of the potential's range on the ground-state energy. We also explicitly verify by a variational treatment that in the zero-range limit the positive $\delta$ potential in two dimensions only reproduces the noninteracting results, if the Hilbert space in not truncated, and demonstrate that an extremely large Hilbert space is required to approach the ground state when one is to tackle the limit of zero-range interaction numerically. Finally, we establish and discuss the connection between our finite-range treatment and regularized zero-range results from the literature. The present results indicate that a finite-range interparticle potential is numerically amenable for treating the statics and the nonequilibrium dynamics of interacting many-particle systems (bosons) in two dimensions.

The nonlinear dynamics of the photon number in an optical cavity filled with a cigar-shaped Bose-Einstein condensate is investigated. We find that the way of adding the field is crucial to the switching close to the critical transition point. If the pump field is changed abruptly, the system may jump from one branch to the other even if the pump field intensity has not reached the critical transition point yet. This behavior is similar to the anomalous switching in the dispersive optical bistability.

We propose a quantum nondemolition (QND) readout scheme for a superconducting artificial atom coupled to a resonator in a circuit QED architecture, for which we estimate a very high measurement fidelity without Purcell effect limitations. The device consists of two transmons coupled by a large inductance, giving rise to a diamond-shaped artificial atom with a logical qubit and an ancilla qubit interacting through a cross-Kerr-like term. The ancilla is strongly coupled to a transmission line resonator. Depending on the qubit state, the ancilla is resonantly or dispersively coupled to the resonator, leading to a large contrast in the transmitted microwave signal amplitude. This original method can be implemented with a state-of-the-art Josephson parametric amplifier, leading to QND measurements in a few tens of nanoseconds with fidelity as large as 99.9$\%$.

We theoretically analyze the efficiency of a protocol for creating mesoscopic superpositions of ion chains, described in Baltrusch et al. [Phys. Rev. A 84, 063821 (2011)], as a function of the temperature of the crystal. The protocol makes use of state-dependent forces, so that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. Ion Coulomb crystals are well isolated from the external environment and should therefore experience a coherent, unitary evolution, which follows the quench and generates structural Schrödinger-cat-like states. The temperature of the chain, however, introduces a statistical uncertainty in the final state. We characterize the quantum state of the crystal by means of the visibility of Ramsey interferometry performed on one ion of the chain and determine its decay as a function of the crystal's initial temperature. This analysis allows one to determine the conditions on the chain's initial state in order to efficiently perform the protocol.

Quantum input-output response analysis is a useful method for modeling the dynamics of complex quantum networks, such as those for communication or quantum control via cascade connections. Non-Markovian effects are expected to be important in networks realized using mesoscopic circuits, but such effects have not yet been studied. Here we extend the Markovian input-output network formalism to non-Markovian networks. The general formalism can be applied to various examples: (i) we show how non-Markovian coherent feedback can reduce the speed of decoherence for an atom in an optical cavity; (ii) we examine the effect of finite-cavity bandwidths in a superconducting circuit.

We investigate the performance of a streamlined version of Shor's algorithm in which the quantum Fourier transform is replaced by a banded version that, for each qubit, retains only coupling to its $b$ nearest neighbors. Defining the performance $P(n,b)$ of the $n$-qubit algorithm for bandwidth $b$ as the ratio of the success rates of Shor's algorithm equipped with the banded and the full-bandwidth ($b=n-1$) versions of the quantum Fourier transform, our numerical simulations show that $P(n,b)\approx \exp [-{\phi }_{\max }^2(n,b)/100]$ for $n<n_t\left(b\right)$ (nonexponential regime) and $P(n,b)\approx 2^{-{\xi }_b(n-8)}$ for $n>n_t\left(b\right)$ (exponential regime), where $n_t\left(b\right)$, the location of the transition, is approximately given by $n_t\left(b\right)\approx b+5.9+\sqrt{7.7(b+2)-47}$ for $b\gtrsim 8$, ${\phi }_{\max }(n,b)=2\pi [2^{-b-1}(n-b-2)+2^{-n}]$, and ${\xi }_b\approx 1.1\times 2^{-2b}$. Analytically we obtain $P(n,b)\approx \exp [-{\phi }_{\max }^2(n,b)/64]$ for $n<n_t\left(b\right)$ and $P(n,b)\approx 2^{-{\xi }_b^{\left(a\right)}n}$ for $n>n_t\left(b\right)$, where ${\xi }_b^{\left(a\right)}\approx \frac{{\pi }^2}{12\ln \left(2\right)}\times 2^{-2b}\approx 1.19\times 2^{-2b}$. Thus, our analytical results predict the ${\phi }_{\max }^2$ scaling ($n<n_t$) and the $2^{-2b}$ scaling ($n>n_t$) of the data perfectly. In addition, in the large-$n$ regime, the prefactor in ${\xi }_b^{\left(a\right)}$ is close to the results of our numerical simulations, and in the low-$n$ regime, the numerical scaling factor in our analytical result is within a factor 2 of its numerical value. As an example we show that $b=8$ is sufficient for factoring RSA-2048 with a 95$\%$ success rate.

Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.

Transitions between high Rydberg states of ${}^{133}$Cs atoms have been studied by high-resolution millimeter-wave spectroscopy of an ultracold sample. The spectroscopic measurements were performed after releasing the atoms from a magneto-optical trap. Switching off all trapping fields and compensating the stray electric and magnetic fields to below 1 mV/cm and 2 mG, respectively, prior to the spectroscopic measurement enabled the recording of millimeter-wave spectra of Rydberg states with principal quantum number beyond $n=100$ under conditions where the inhomogeneous broadening by stray fields is minimal and no dephasing of the Rydberg-atom sample can be detected over measurement times up to 60 $\mu$s. The Fourier-transform-limited line widths of better than 20 kHz enabled the observation of the hyperfine structure of $nS$ and $nP$ Rydberg states of Cs beyond $n=90$. The analysis of the line shapes of transitions to Rydberg states with $n\approx 230$ indicated that field inhomogeneities across the atomic sample represent the dominant cause of spectral broadening at high $n$ values. The analysis also revealed that the initial polarization of the atomic sample ($F=4$, $M_F=4$) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.

We apply a fundamental definition of time delay, as the difference between the time a particle spends within a finite region of a potential and the time a free particle spends in the same region, to determine results for photoionization of an electron by an extreme ultraviolet laser field using numerical simulations on a grid. Our numerical results are in good agreement with those of the Wigner-Smith time delay, obtained as the derivative of the phase shift of the scattering wave packet with respect to its energy, for the short-range Yukawa potential. In the case of the Coulomb potential we obtain time delays for any finite region, while—as expected—the results do not converge as the size of the region increases towards infinity. The impact of an ultrashort near-infrared probe pulse on the time delay introduced here is analyzed for both the Yukawa and the Coulomb potential and is found to be small for intensities below ${10}^{13}$ W/cm${}^2$.

Radiation pressure effects recently observed by Smeenk et al. [C. Smeenk, L. Arissian, B. Zhou, A. Mysyrowicz, D. M. Villeneuve, A. Staudte, and P. B. Corkum, Phys. Rev. Lett. 106, 193002 (2011)] in atomic ionization by circularly polarized light are readily explained by the relativistic strong-field approximation (RSFA). The physical picture that emerges is determined by linear and angular momentum properties of the photons required for ionization, and it is largely independent of the atom being ionized. Radiation pressure follows from linear momenta carried by photons, and the angular momenta of the photons require the photoelectron to be in a circular orbit around the remnant ion. Two special features of the Smeenk et al. experiments are highlighted by the analysis. One is that this is the first verification of true relativistic effects in ionization. The other is that the circular trajectory picture from the RSFA analysis directly contradicts the physical picture that emerges from the length gauge. This is an exceptionally striking example of gauge-dependent differences in physical interpretations. Nevertheless, the distribution of momentum found by the Smeenk et al. experiments is accurately predicted by the RSFA. Results herein provide a universal theory to which the analysis of Titi and Drake [A. S. Titi and G. W. F. Drake, Phys. Rev. A 85, 041404(R) (2012)] represents an approximation. The physical properties of ionization by circularly polarized light also cast doubt on some predictions of rescattering theory.

We have performed laser cooling of Mg${}^{+}$ ions confined in a Penning trap. The externally produced ions were captured in flight, stored, and laser cooled. Laser-induced fluorescence was observed perpendicular to the cooling laser axis. Optical detection down to the single-ion level together with the electronic detection of the ion oscillations inside the Penning trap have been used to acquire information on the ion storage time, ion number, and ion temperature. Evidence for the formation of ion crystals has been observed. These investigations are an important prerequisite for the sympathetic cooling of simultaneously stored highly charged ions and the precision laser spectroscopy of forbidden transitions in these.

While the Gross-Pitaevskii equation is well established as the canonical dynamical description of atomic Bose-Einstein condensates (BECs) at zero temperature, describing the dynamics of BECs at finite temperatures remains a difficult theoretical problem, particularly when considering low-temperature, nonequilibrium systems in which depletion of the condensate occurs dynamically as a result of external driving. In this paper, we describe a fully time-dependent numerical implementation of a second-order, number-conserving description of finite-temperature BEC dynamics. This description consists of equations of motion describing the coupled dynamics of the condensate and noncondensate fractions in a self-consistent manner, and is ideally suited for the study of low-temperature, nonequilibrium, driven systems. The $\delta$-kicked-rotor BEC provides a prototypical example of such a system, and we demonstrate the efficacy of our numerical implementation by investigating its dynamics at finite temperature. We demonstrate that the qualitative features of the system dynamics at zero temperature are generally preserved at finite temperatures, and predict a quantitative finite-temperature shift of resonance frequencies which would be relevant for, and could be verified by, future experiments.

We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable $s$-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly confined axial direction can be significant when the two-body binding energy becomes comparable to or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings provide a proper description for a quasi-two-dimensional Fermi gas under spin-orbit coupling, and are helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.

We investigate topological aspects of subnanometer electron vortex beams upon elastic propagation through atomic scattering potentials. Two main aspects can be distinguished: (i) significantly reduced delocalization compared to a similar nonvortex beam if the beam centers on an atomic column and (ii) site symmetry dependent splitting of higher-order vortex beams. Furthermore, the results provide insight into the complex vortex line fabric within the elastically scattered wave containing characteristic vortex loops predominantly attached to atomic columns and characteristic twists of vortex lines around atomic columns.

Autler-Townes (AT) splitting is observed in ultracold cesium Rydberg gases. Frequency and power of the laser field coupling $6S$${}_{1/2}$ and $6P$${}_{3/2}$ levels are tuned to influence the population redistribution of $6P$${}_{3/2}$ and $nS$ levels excited by another light. The profile of AT spectroscopy is measured experimentally and compared with the theoretical simulation considering the estimated large dephasing rates caused by interaction between Rydberg atoms, which demonstrates that splitting and profile of AT spectra are strongly dependent on the interaction between Rydberg atoms. Rabi frequency of the coupling laser and transition dipole moment of $6S$${}_{1/2}\to$ $6P$${}_{3/2}$ are deduced via fitting the measured space variation of two splitting peaks, which is consistent with theoretical calculations.

We prove that a unitary matrix has an exact representation over the Clifford+$T$ gate set with local ancillas if and only if its entries are in the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$. Moreover, we show that one ancilla always suffices. These facts were conjectured by Kliuchnikov, Maslov, and Mosca. We obtain an algorithm for synthesizing a exact Clifford+$T$ circuit from any such $n$-qubit operator. We also characterize the Clifford+$T$ operators that can be represented without ancillas.

The five longest tune-out wavelengths for the potassium atom are determined using a relativistic structure model which treats the atom as consisting of a single valence electron moving outside a closed shell core. The importance of various terms in the dynamic polarizability in the vicinity of the $4p_J$, $5p_J$, and $6p_J$ transitions are discussed.

Auger decay including direct double processes of Ar $2p^{-1}$ hole levels is investigated in the framework of perturbation theory implemented by distorted wave approximation with balanced large-scale configuration interaction among the successive ions being taken into account. The complex transition amplitude obtained from the second perturbation theory for the direct double Auger decay (DAD) is decomposed into approximate formulas according to two generally agreed mechanisms of shake-off and knock-out. Practical computations showed that the knock-out condition is fulfilled and thus justified such a decomposition treatment of knock-out mechanism. The contribution to the DAD probability from knock-out mechanism is larger than shake-off by an order of magnitude and therefore the former is dominant. The interference effect between the knock-out and shake-off mechanisms should be trivial and neglecting it we obtained a branching ratio of 12.0$\%$ for the direct DAD into triply charged states of Ar${}^{3+}$. By including cascade double decay, a total branching ratio of 14.9$\%$ is obtained. Our result explained recent experimental results on the branching ratio into triply charged ion, and should be useful for further detailed experimental investigations.