The complementarity between time and energy, as well as between an angle and a component of angular momentum, is described at three different layers of understanding. The phenomena of super-resolution are readily apparent in the quantum phase representation which also reveals that entanglement is not required. We modify Schwinger's harmonic oscillator model of angular momentum to include the case of photons. Therein, the quantum angle measurement is shown to be equivalent to the measurement of the relative phase between the two oscillators. Two reasonable ways of dealing with degeneracy are shown to correspond to a conditional measurement which takes a snapshot in absolute time (corresponding to adding probability amplitudes) and a marginal measurement which takes an average in absolute time (corresponding to adding probabilities). The sense in which distinguishability is a “matter of how long we look” is discussed and the meaning of the general theory is illustrated by taking the two oscillators to be circularly polarized photons. It is shown that an odd number of $x$-polarized photons will never have an angle in correspondence with the $y$ axis, but an even number of $x$-polarized photons always can! The behavior of an $x$-polarized coherent state is examined and the snapshot angular distributions are seen to evolve into two counter-rotating peaks resulting in considerable correspondence with the $y$ axis at the time for which a classical linear polarization vector would shrink to zero length. We also demonstrate how the probability distribution of absolute time (herein a measurable quantity, rather than just a parameter) has an influence on how these snapshot angular distributions evolve into a quantum version of the polarization ellipse.

In this work we use the classical trajectory Monte Carlo method within an eight-electron scheme to theoretically study photonic spectra that follow charge-exchange processes between highly charged ions of charge states 10+, 17+, 18+, and 36+ with neutral argon. The energy range considered is 18 eV/amu to 4 keV/amu, covering typical electron beam ion traps and solar wind energies. The role played by multiple electron capture processes for the different collision systems under consideration is explicitly analyzed and its contribution separated as arising from radiative decay and autoionizing multiple capture. For the present collision systems we find that multiple electron capture is responsible for 50%–60% of the resulting x-ray spectra. The present results are of direct relevance to the astrophysical program.

Vortices are an inherent property of the velocity fields of complex, time-dependent, Schrödinger wave functions $\psi$ occurring where both the real and the imaginary parts of $\psi$ vanish. They have been known since the early work of Dirac on magnetic monopoles and have frequently been studied theoretically. The possibility of observing them by exploiting an “imaging theorem” that relates atomic wave functions to measured electron momentum distributions has recently been proposed. Using the Coulomb-Born approximation, we examine ionization of a $K$-shell electron of a model carbon atom by fast electron impact. For an incident electron energy of 1801.2 eV and a scattering angle of $4^{\circ }$, we find a vortex in the velocity field associated with a zero in the ionization $T$-matrix element and hence in the triply differential cross section, and we obtain a segment of the vortex line. Angular momentum transfer is essential to produce the vortex in the velocity field and the corresponding zero in the ionization $T$-matrix element and in the triply differential cross section.

Kelvin probe force microscopy at normal pressure was performed by two different groups on the same Au-coated planar sample used to measure the Casimir interaction in a sphere-plane geometry. The obtained voltage distribution was used to calculate the separation dependence of the electrostatic pressure $P_{\mathrm{res}}\left(D\right)$ in the configuration of the Casimir experiments. In the calculation it was assumed that the potential distribution in the sphere has the same statistical properties as the measured one, and that there are no correlation effects on the potential distributions due to the presence of the other surface. The result of this calculation, using the currently available knowledge, is that $P_{\mathrm{res}}\left(D\right)$ does not explain the magnitude or the separation dependence of the difference $\Delta P\left(D\right)$ between the measured Casimir pressure and the one calculated using a Drude model for the electromagnetic response of Au. We discuss in the conclusions the points which have to be checked out by future work, including the influence of pressure and a more accurate determination of the patch distribution, in order to confirm these results.

The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions and initial states the system does not evolve to an orthogonal quantum state. Here, we ask what proportion of quantum states evolve to nearly orthogonal systems as a function of the dimensionality of the Hilbert space of the system, and numerically study the evolution of quantum states in low-dimensional Hilbert spaces. We find that, as well as the speed of dynamical evolution, the level of maximum distinguishability depends critically on the Hamiltonian of the system.

We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short-lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Waals interaction range with perspectives for entangling atoms in separate ensembles.

Experimental implementation of the surface code will be a significant milestone for quantum computing. We develop a circuit and a decoder targeted for near-term implementation of a distance-3 surface code. We simulate the code under amplitude and phase damping and compare the threshold to a Pauli-twirl approximation. We find that the approximation yields a pessimistic threshold estimate. From numerical Monte Carlo simulations, we identify the gate and measurement speeds required to achieve reliable error correction. For superconductor devices, a qubit encoded in a 17-qubit surface code demonstrates a lower error rate than an unencoded qubit assuming gate times of 5–40 ns and $T_1$ times of at least 1–2 $\mu \mathrm{s}$. If $T_1\ge 10$ ns, the difference is significant and can be experimentally measured, allowing near-term implementation and verification of a small surface code. For ion trap devices, gates times of 1 $\mu \mathrm{s}$ and $T_1\ge 40$ ms admit measurable differences in error rate.

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\widehat{H}\left(t\right)=\widehat{A}+\widehat{B}t+\widehat{C}/t$, where $t$ is time and $\widehat{A},\widehat{B},\widehat{C}$ are Hermitian $N\times N$ matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at $t\to -\infty$. This allows one to continue such solutions analytically to $t\to +\infty$, and connect their asymptotic behavior at $t\to -\infty$ and $t\to +\infty$. This property becomes particularly useful when a model shows additional discrete symmetries. In particular, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.

Measurements of hyperfine polarization quantum beats are used to determine the magnetic dipole (A) and electric quadrupole (B) coupling constants in the excited atomic Cs $8p{}^2{P}_{3/2}$ level. The experimental approach is a combination of pulsed optical pumping and time-delayed stimulated-emission probing of the excited level. From the measured evolution of the atomic linear polarization degree as a function of probe delay time, we determine the hyperfine coupling constants $A=7.42\left(6\right)$ MHz and $B=0.14\left(29\right)$ MHz.

We demonstrate an efficient scheme for controlling the tunneling ionization of a ${{\mathrm{H}}_2}^{+}$ molecular ion. Our scheme is based on the idea that the tunneling ionization rate is highly dependent on the instantaneous magnitude of the electric field. By manipulating the relative phase of the synthesized 5-fs, 790–395-nm laser field, the fragments yielded by the tunneling ionization show a large asymmetry relative to the laser polarization. We find that the time-dependent ionization rate is sharply peaked near the antinodes of the synthesized field. Most importantly, the critical internuclear distances at which the tunneling ionization rate is enhanced depend on the field strength of the antinodes. It is well explained by tracing the laser-driven motion of the electron in the field-dressed double well potential.

Near-threshold photodissociation of ${\mathrm{Br}}_2$ from a supersonic beam produces slow bromine atoms that are trapped in the magnetic-field minimum formed between two opposing permanent magnets. Here we quantify the dominant trap-loss rate due to collisions with two sources of residual gas: the background limited by the vacuum chamber base pressure and the carrier gas during the supersonic gas pulse. The loss rate due to collisions with residual Ar in the background follows pseudo-first-order kinetics and the bimolecular rate coefficient for collisional loss from the trap is determined by measurement of this rate as a function of the background Ar pressure. This rate coefficient is smaller than the total elastic collision rate coefficient, as it only samples those collisions that lead to trap loss, and is determined to be $\langle \nu \sigma \rangle =(1.12\pm 0.09)\times {10}^{-9}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. The calculated differential cross section can be used with this value to estimate a trap depth of $293\pm 24\mathrm{mK}$. Carrier-gas collisions occur only during the tail of the supersonic beam pulse. Using the differential cross section verified by the background-gas collision measurements provides an estimate of the peak molecular-beam density of $(3.0\pm 0.3)\times {10}^{13}{\mathrm{cm}}^{-3}$, in good agreement with the prediction of a simple supersonic expansion model. Finally, we estimate the trap-loss rate due to Majorana transitions to be negligible, owing to the relatively large trapped-atom phase-space volume.

We demonstrate that memory in an $N$-qubit system subjected to decoherence, is a potential resource for the slowdown of the entanglement decay. We show that this effect can be used to retain the sub-shot-noise sensitivity of the parameter estimation in quantum interferometry. We calculate quantum Fisher information, which sets the ultimate bound for the precision of the estimation. We also derive the sensitivity of such a noisy interferometer, when the phase is either estimated from the measurements of the population imbalance or from the one-body density.

In this paper, we study an extended bosonic t-J model in an optical lattice, which describes two-component hard-core bosons with nearest-neighbor pseudospin interactions and, also, inter- and intraspecies dipole-dipole interactions. In particular, we focus on the case in which two-component hard-core bosons have antiparallel polarized dipoles with each other. The global phase diagram is studied by means of the Gutzwiller variational method and also quantum Monte Carlo (QMC) simulations. Both calculations show that a striped solid order, besides a checkerboard one, appears as a result of the dipole-dipole interactions. By QMC, we find that two kinds of supersolids (SSs) form, i.e., checkerboard SS and striped SS, and we also verify the existence of an exotic phase between the striped solid and the checkerboard SS. Finally, by QMC, we study the t-J-like model, which was recently realized experimentally by A. de Paz et al. [Phys. Rev. Lett. 111, 185305 (2013)].

We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.

I investigate the extent to which the description of quantum systems by Gibbs states can be justified purely on the basis of tomographic data, without recourse to theoretical concepts such as infinite ensembles, environments, or information or to the systems' dynamics. I show that the use of Gibbs states amounts to a relevance hypothesis, which I spell out in detail. This hypothesis can be subjected to statistical hypothesis testing and hence assessed on the basis of the experimental data.

A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system. When the physical model is the Heisenberg ferromagnet in the absence of an external magnetic field, the corresponding ground space contains all permutation-invariant states. We use techniques from combinatorics and operator theory to construct families of permutation-invariant quantum codes. These codes have length proportional to $t^2$; one family of codes perfectly corrects arbitrary weight $t$ errors, while the other family of codes approximately correct $t$ spontaneous decay errors. The analysis of our codes' performance with respect to spontaneous decay errors utilizes elementary matrix analysis, where we revisit and extend the quantum error correction criterion of Knill and Laflamme, and Leung, Chuang, Nielsen and Yamamoto.

Spin-1 systems, in comparison to spin-$\frac{1}{2}$ systems, offer a better security for encoding and transferring quantum information, primarily due to their larger Hilbert spaces. Superconducting artificial atoms possess multiple energy levels, thereby being capable of emulating higher-spin systems. Here I consider a one-dimensional lattice of nearest-neighbor-coupled superconducting transmon systems, and devise a scheme to transfer an arbitrary qutrit state (a state encoded in a three-level quantum system) across the chain. I assume adjustable couplings between adjacent transmons, derive an analytic constraint for the control pulse, and show how to satisfy the constraint to achieve a high-fidelity state transfer under current experimental conditions. My protocol thus enables enhanced quantum communication and information processing with promising superconducting qutrits.

A generalized formulation is presented for determining the saturation thresholds for optical processes excited by ultrafast pulses based on the pulse area of the excitation pulse. It is demonstrated that the threshold of driving-pulse intensity for absorption and fluorescence saturation in a two-level system is inversely proportional to the square of the duration of the excitation pulse. These results are obtained from both a simplified analytical solution assuming a Gaussian excitation pulse shape and a detailed numerical calculation based on density-matrix equations. The calculation is generalized further to obtain the saturation condition for a two-photon Raman process by defining a two-photon pulse area both analytically and numerically. These results not only provide predictive capabilities for determining thresholds of signal saturation using ultrashort durations with arbitrary pulse shapes and durations but also open up possibilities for predetermining the threshold intensities of various resonant nonlinear processes.