We consider the qubit initial-state preparation due to the nonselective measurements on an overcomplete basis, when the number of outcomes $N=3$. To be specific, we have chosen the dephasing model and applied the conditions for a post-measurement state to ensure a gradual coherence enhancement at the initial stage of the system evolution. It is shown that contrary to the von Neumann–Lüders projection scheme with $N=2$, the most mixed post-measurement state of the qubit in the general case can depend on the bath temperature. This remarkable feature allows one to consider a “temperature-controlled” initial purification of the open quantum system. We also consider some kinds of the repeated nonselective measurements from the viewpoint of an eventual system purification and analyze the important peculiarities of such schemes.

A distinguishing feature of protective measurement is the possibility of obtaining information about expectation values while making the disturbance of the initial state arbitrarily small. Quantifying this state disturbance is of paramount importance. Here we derive exact and perturbative expressions for the state disturbance and the faithfulness of the measurement outcome in a model describing a spin-1/2 particle protectively measured by an inhomogeneous magnetic field. We determine constraints on the experimentally required field strengths from bounds imposed on the allowable state disturbance. We also demonstrate that the protective measurement may produce an incorrect result even when the particle's spin state is unaffected by the measurement, and show that successive measurements using multiple magnetic fields produce the same state disturbance as a single measurement involving a superposition of these fields. Our results supply comprehensive understanding of a paradigmatic model for protective measurement, may aid the experimental implementation of the measurement scheme, and illustrate fundamental properties of protective measurements.

Although much work has been devoted to multivalued quantum logic synthesis, the question of whether multivalued quantum circuits are more efficient than conventional binary quantum circuits is still open. This article is devoted to the optimization of generic multivalued quantum circuits. Multivalued quantum Shannon decompositions are improved so that the circuits obtained are asymptotically optimal for all dimensionality $d$. The syntheses of uniformly multifold controlled $R_y$ rotations are also optimized to make the circuits further simplified. Moreover, the theoretical lower bound of complexity for multivalued quantum circuits is investigated, and a quantity known as the efficiency index is proposed to evaluate the efficiency of the synthesis of various quantum circuits. The algorithm for qudit circuits given here is an efficient synthesis routine which produces improved results for all dimensionality $d$, whether the number of qudits $n$ is small or large. The two facts, the leading factor of the lower bound of complexity for qudit circuits is small by a factor of $d-1$ in comparison to that for qubit circuits and the asymptotic efficiency index is increased with an increase of dimensionality $d$, reveal the potential advantage of qudit circuits over generic qubit circuits. Generic $n$-qudit circuits with $d\ge 5$ and generic two-ququart circuits synthesized by the algorithm given here are practical circuits which are more efficient than the most efficient qubit circuits.

The thin sample method is often used to experimentally determine ionization cross sections, especially when focusing on the low overvoltage region. The simplicity of the formalism involved in this method is very appealing, but some experimental complications arise in the preparation of thin films. In this work, a thick sample method was used to measure the $\text{Si}-K$ x-ray production cross section by electron impact. The good agreement between the results obtained and the values reported in the literature validates the method and the parameters used. The advantages and disadvantages of the method are discussed and its application is extended to the determination of Si multiple-ionization cross sections, where the very low emission rates (around two orders of magnitude lower than the single-ionization case) make the use of the thin sample method impracticable.

Following Marx et al. [Phys. Rev. Lett. 111, 243007 (2013)], we discuss the measurement and manipulation of the temperature of cold CO molecules in a microchip environment. In particular, we present a model to explain the observed and calculated velocity distributions. We also show that a translational temperature can be extracted directly from the measurements. Finally, we discuss the conditions needed for an effective adiabatic cooling of the molecular ensemble trapped on the microchip.

Driven optical lattices permit the engineering of effective dynamics with well-controllable tunneling properties. By specifically designing polychromatic driving forces, we describe how an optimal realization of a tunable Chern insulator can be achieved with a system of interacting particles on a shaken hexagonal lattice. Its implementation does not require shallow lattices and favors the study of strongly correlated phases with nontrivial topology.

We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of ${}^6\mathrm{Li}$ atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the Bardeen-Cooper-Schrieffer and unitary regimes. We disagree with the QMC results in the Bose-Einstein condensate regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure the equation of state in the crossover regime for a gas with equal numbers of the two fermion spin states.

We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $\mu \mathrm{Gal}$ ($1\mu \mathrm{Gal}={10}^{-8}\mathrm{m}/{\mathrm{s}}^2$). We also show that this effect is not compensated when averaging over the two directions of the Raman wave vector $k$. This thus constitutes a limit to the rejection efficiency of the $k$-reversal technique. Our analysis allows us to separate this effect from the effect of the finite speed of light, which we find in perfect agreement with expected values. This study highlights the benefit of chirping symmetrically the two Raman lasers.

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level $\mathsf{V}$ and $\mathrm{\Lambda }$ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

We consider the optical generation and characterization of entanglement in atomic ensembles under nonuniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of nonuniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the average total spin remains large, and the detection does not resolve single spins. Furthermore, we derive an analytic formula for determining the observable entanglement in the case, of relevance in practice, where the ensemble-mode coupling differs between state generation and measurement.

We generalize a nonclassicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2012)], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving a contradiction with the classical description in terms of a probability distribution in phase space. As opposed to the previous work, we generalize the test to include states without rotational symmetry in phase space. Furthermore, we compare the performance of the nonclassicality test with classical tomography methods based on the inverse Radon transform, which can also be used to establish the quantum nature of a physical system. In particular, we consider a nonclassicality test based on the so-called filtered back-projection formula. We show that the general nonclassicality test is conceptually simpler, requires less assumptions on the system, and is statistically more reliable than the tests based on the filtered back-projection formula. As a specific example, we derive the optimal test for quadrature squeezed single-photon states and show that the efficiency of the test does not change with the degree of squeezing.

The ability to convert quantum states from microwave photons to optical photons is important for hybrid system approaches to quantum information processing. We report the up-conversion of a microwave signal into the optical telecommunications wavelength band using erbium dopants in a yttrium orthosilicate crystal via stimulated Raman scattering. The microwaves were applied to the sample using a three-dimensional copper loop-gap resonator and the coupling and signal optical fields were single passed. The conversion efficiency was low, in agreement with a theoretical analysis, but can be significantly enhanced with an optical resonator.

If a single-mode nonclassical light is combined with the vacuum on a beam splitter, then the output state is entangled. As proposed in [Phys. Rev. Lett. 94, 173602 (2005)], by measuring this output-state entanglement for a balanced lossless beam splitter, one can quantify the input-state nonclassicality. These measures of nonclassicality (referred to as entanglement potentials) can be based, in principle, on various entanglement measures, leading to the negativity (NP) and concurrence (CP) potentials, and the potential for the relative entropy of entanglement (REEP). We search for the maximal relative nonclassicality, which can be achieved by comparing two entanglement measures for (i) arbitrary two-qubit states and (ii) those which can be generated from a photon-number qubit via a balanced lossless beam splitter, where the qubit basis states are the vacuum and single-photon states. Surprisingly, we find that the maximal relative nonclassicality, measured by the REEP for a given value of the NP, can be increased (if $\mathrm{NP}<0.527$) by using either a tunable beam splitter or by amplitude damping of the output state of the balanced beam splitter. We also show that the maximal relative nonclassicality, measured by the NP for a given value of the REEP, can be increased by phase damping (dephasing). Note that the entanglement itself is not increased by these losses (since they act locally), but the possible ratios of different measures are affected. Moreover, we show that partially dephased states can be more nonclassical than both pure states and completely dephased states, by comparing the NP for a given value of the REEP. Thus, one can conclude that not all standard entanglement measures can be used as entanglement potentials. Alternatively, one can infer that a single balanced lossless beam splitter is not always transferring the whole nonclassicality of its input state into the entanglement of its output modes. The application of a lossy beam splitter can solve this problem, at least for the cases analyzed in this paper.

An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors but is both time consuming (when one wants to learn only a few key parameters) and usually inaccurate without resources such as perfect state preparation and measurement, which might not be available. With the goal of efficiently and accurately estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge key systematic parameters (specifically, amplitude and off-resonance errors) in a universal single-qubit gate set with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling, and do so without entanglement and entirely within a single-qubit Hilbert space. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins et al., New J. Phys. 11, 073023 (2009)].

To investigate how a temporally ordered gate sequence can be parallelized in adiabatic implementations of quantum computation, we modify adiabatic gate teleportation, a model of quantum computation proposed by Bacon and Flammia [Phys. Rev. Lett. 103, 120504 (2009)], to a form deterministically simulating parallelized gate teleportation, which is achievable only by postselection. We introduce a twisted Heisenberg-type interaction Hamiltonian, a Heisenberg-type spin interaction where the coordinates of the second qubit are twisted according to a unitary gate. We develop parallelizable adiabatic gate teleportation (PAGT) where a sequence of unitary gates is performed in a single step of the adiabatic process. In PAGT, numeric calculations suggest the necessary time for the adiabatic evolution implementing a sequence of $L$ unitary gates increases at most as $O\left(L^5\right)$. However, we show that it has the interesting property that it can map the temporal order of gates to the spatial order of interactions specified by the final Hamiltonian. Using this property, we present a controlled-PAGT scheme to manipulate the order of gates by a control qubit. In the controlled-PAGT scheme, two differently ordered sequential unitary gates $FG$ and $GF$ are coherently performed depending on the state of a control qubit by simultaneously applying the twisted Heisenberg-type interaction Hamiltonians implementing unitary gates $F$ and $G$. We investigate why the twisted Heisenberg-type interaction Hamiltonian allows PAGT. We show that the twisted Heisenberg-type interaction Hamiltonian has an ability to perform a transposed unitary gate by just modifying the space ordering of the final Hamiltonian implementing a unitary gate in adiabatic gate teleportation. The dynamics generated by the time-reversed Hamiltonian represented by the transposed unitary gate enables deterministic simulation of a postselected event of parallelized gate teleportation in adiabatic implementation.

The electron emission from the uracil molecule induced by fast proton impact has been investigated using the classical-trajectory Monte Carlo (CTMC) method. Applying the independent-particle model, the full three-body dynamics of the projectile, an active electron, and the molecule core is considered. The interactions with the molecule core are described by a multicenter potential built from screened atomic potentials. Double and single differential, as well as total ionization cross sections are calculated and compared with the predictions of the first Born approximation with correct boundary conditions (CB1), the continuum-distorted-wave–eikonal-initial-state (CDW-EIS) approach, as well as the combined classical-trajectory Monte Carlo–classical over-the-barrier (CTMC-COB) model. The effect of the molecular treatment of the ionization by the multicenter potential is analyzed by simplified CTMC calculations in which the ionization cross section of the uracil is determined as a linear combination of the contributions of the constituent atoms of the molecule.

For the single differential cross section (SDCS) for hydrogen ionization by electron impact ($e$-H problem), we propose a correction to the flux formula given by R. Peterkop [Theory of Ionization of Atoms by Electron Impact (Colorado Associated University Press, Boulder, 1977)]. The modification is based on an alternative way of defining the kinetic energy fraction, using Bohm's definition of velocities instead of the usual asymptotic kinematical, or geometrical, approximation. It turns out that the solution-dependent, modified energy fraction is equally related to the components of the probability flux. Compared to what is usually observed, the correction yields a finite and well-behaved SDCS value in the asymmetrical situation where one of the continuum electrons carries all the energy while the other has zero energy. We also discuss, within the $S$-wave model of the $e-\mathrm{H}$ ionization process, the continuity of the SDCS derivative at the equal energy sharing point, a property not so clearly observed in published benchmark results obtained with integral and $S$-matrix formulas with unequal final states.

Linear polarization of bremsstrahlung x rays produced in collisions of longitudinally polarized 2.1-MeV electrons with gold atoms was studied using the Compton scattering technique. We observed that the angle of x-ray polarization is strongly correlated with the incoming electron polarization. This correlation reveals the dominance of the spin-orbit interaction in bremsstrahlung and indicates a striking effect of the electron spin on the electron motion in a strong Coulomb field. The results confirm the validity of the theoretical predictions in a computationally challenging energy regime.

We theoretically investigate the dynamical phase diagram of a one-dimensional chain of laser-excited two-species Rydberg atoms. The existence of a variety of unique dynamical phases in the experimentally achievable parameter region is predicted under the mean-field approximation, and the change in those phases when the effect of the next-nearest-neighbor interaction is included is further discussed. In particular, we find that the com-petition of the strong Rydberg-Rydberg interactions and the optical excitation imbalance can lead to the presence of complex multiple chaotic phases, which are highly sensitive to the initial Rydberg-state population and the strength of the next-nearest-neighbor interactions.