We study the equilibrium current density profiles of harmonically trapped ultracold Fermi gases in quantum Hall-like states that appear when the quasi-two-dimensional trap is set in fast rotation. The density profile of the gas (in the rotating reference frame) consists of incompressible strips of constant quantized density separated by compressible regions in which the density varies. Remarkably, we find that the atomic currents flow in opposite directions in the compressible and incompressible regions—a prediction that should be amenable to experimental verification.

We analyze theoretically the dynamics of an atomic double-well system with a single ion trapped in its center. We find that the atomic tunneling rate between the wells depends both on the spin of the ion via the short-range spin-dependent atom-ion scattering length and on its motional state with tunneling rates reaching hundreds of hertz. A protocol is presented that could transport an atom from one well to the other, depending on the motional (Fock) state of the ion within a few milliseconds. This phonon-atom coupling is of interest for creating atom-ion entangled states and may form a building block in constructing a hybrid atom-ion quantum simulator. We also analyze the effect of imperfect ground-state cooling of the ion and the role of micromotion when the ion is trapped in a Paul trap. Due to the strong nonlinearities in the atom-ion interaction, the micromotion can cause couplings to high-energy atom-ion scattering states, preventing accurate state preparation and complicating the double-well dynamics. We conclude that the effects of micromotion can be reduced by choosing ion-atom combinations with a large mass ratio and by choosing large interwell distances. The proposed double-well system may be realized in an experiment by combining either optical traps or magnetic microtraps for atoms with ion trapping technology.

We study, in the framework of open quantum systems, the time evolution of a circularly accelerated two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields. We find that both the spontaneous transition rates and the geometric phase for a circularly accelerated atom do not exhibit a clear sign of thermal radiation characterized by the Planckian factor in contrast to the linear acceleration case. The spontaneous transition rates and effective temperature of the atom are examined in detail in the ultrarelativistic limit and are shown to be always larger than those in the linear acceleration case with the same proper acceleration. Unlike the effective temperature, the geometric phase is dependent on the initial atomic states. We show that when the polar angle in Bloch sphere, $\theta$, that characterizes the initial state of the atom equals $\pi /2$, the geometric phases acquired due to circular and linear acceleration are the same. However, for a generic state with an arbitrary $\theta$, the phase will be in general different, and then we demonstrate in the ultrarelativistic limit that the geometric phase acquired for the atom in circular motion is always larger than that in linear acceleration with same proper acceleration for $\theta \in (0,\frac{\pi }{2})\cup (\frac{\pi }{2},\pi )$.

Differential elastic electron-scattering cross sections of pyrimidine were absolutely measured for electron energies from 20 eV to 1 keV in the angular range between 5° and 135°. The present results agree with the data of other groups within the experimental uncertainties at scattering angles below 75° while considerable differences among the data were found at higher scattering angles. The experimental values were compared to theoretical values calculated using the modified independent-atom model. The theoretical values reproduce the angular dependence of the experimental differential elastic scattering cross sections qualitatively well for electron energies above 60 eV. The sum of the integral elastic scattering cross sections, obtained by the integration of the differential elastic scattering cross sections, and ionization cross sections predicted by the binary-encounter-Bethe model agree with the previously measured total electron-scattering cross sections of pyrimidine to within 8%.

We calculate the ground state of a Bose gas trapped on a two-leg ladder where Raman-induced hopping mimics the effect of a large magnetic field. In the mean-field limit, where there are large numbers of particles per site, this maps onto a uniformly frustrated two-leg ladder classical spin model. The net particle current always vanishes in the ground state, but generically there is a finite “chiral current,” corresponding to equal and opposite flow on the two legs. We vary the strength of the hopping across the rungs of the ladder and the interaction between the bosons. We find the following three phases. (1) A “saturated chiral current phase” (SCCP), where the density is uniform and the chiral current is simply related to the strength of the magnetic field. In this state the only broken symmetry is the U(1) condensate phase. (2) A “biased ladder phase” (BLP), where the density is higher on one leg than the other. The fluid velocity is higher on the lower density leg, so the net current is zero. In addition to the U(1) condensate phase, this has a broken $Z_2$ reflection symmetry. (3) A “modulated density phase” (MDP), where the atomic density is modulated along the ladder. In addition to the U(1) condensate phase, this has a second broken U(1) symmetry corresponding to translations of the density wave. We further study the fluctuations of the condensate in the BLP, finding a roton-maxon-like excitation spectrum. Decreasing the hopping along the rungs softens the spectrum. As the energy of the “roton” reaches to zero, the BLP becomes unstable. We describe the experimental signatures of these phases, including the response to changing the frequency of the Raman transition.

We present a computable criterion for completely classifying multiqubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multiqubit systems are locally unitarily equivalent or not. Once a positive answer is obtained, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states.

Implementing nonlocal unitary operators is an important and hard question in quantum computing and cryptography. We show that any bipartite nonlocal unitary operator of Schmidt rank three on the $(d_A\times d_B)$-dimensional system is locally equivalent to a controlled unitary when $d_A$ is at most three. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank $r=\min \{d_A^2,d_B\}$. We further show that stochastic-equivalent nonlocal unitary operators are indeed locally equivalent, and propose a sufficient condition on which nonlocal and controlled unitary operators are locally equivalent. We also provide the solution to a special case of a conjecture on the ranks of multipartite quantum states.

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.

A time-bin qubit is a promising candidate qubit for advanced quantum information processing systems operating over optical fibers or integrated quantum photonic circuits. However, the single- and two-qubit operations of time-bin qubits have been largely unexplored compared with those of polarization qubits. Here, I present a simple scheme for implementing a basic two-qubit operation, namely an “entangling” operation of two independent time-bin qubits, based on Hong-Ou-Mandel quantum interference in a high-speed $2\times 2$ optical switch. With the proposed scheme, the formation of a time-bin entanglement was confirmed experimentally.

We examine fully differential cross sections for 176 eV electron-impact dissociative excitation-ionization of orientated $D_2$ for transitions to final ion states $2s{\sigma }_g$, $2p{\sigma }_u$, and $2p{\pi }_u$. In previous work [Phys. Rev. A 88, 062705 (2013)], we calculated these cross sections using the molecular four-body distorted wave (M4DW) method with the ground-state $D_2$ wave function being approximated by a product of two Dyson 1$s$-type orbitals. The theoretical results were compared with experimental measurements for five different orientations of the target molecule (four in the scattering plane and one perpendicular to the scattering plane). For the unresolved $2s{\sigma }_g+2p{\pi }_u$ final states, good agreement with experiment was found for two of the five measured orientations, and for the $2p{\sigma }_u$ final state, good agreement was found for three of the five orientations. However, theory was a factor of 200 smaller than experiment for the $2p{\sigma }_u$ state. In this paper, we investigate the importance of the approximation for the molecular ground-state wave function by repeating the M4DW calculation using a better variational wave function for the ground state.

The $B$-spline $R$-matrix-with-pseudostates (BSR) method is employed to treat electron collisions with nitrogen atoms. Predictions for elastic scattering, excitation, and ionization are presented for all transitions between the lowest 21 states of nitrogen in the energy range from threshold to 120 eV. The structure description has been further improved compared to a previous BSR calculation by Tayal and Zatsarinny [J. Phys. B 38, 3631 (2005)]. This change in the structure model, together with the inclusion of a large number of pseudostates in the close-coupling expansion, has a major influence on the theoretical predictions, especially at intermediate energies, where many of the excitation cross sections are reduced significantly. Ionization cross sections for the ground and metastable initial states are also provided. Finally, we carry out an accurate ab initio treatment of the prominent shape resonance just above the elastic threshold.

Various total cross sections for scattering of electrons by phosphorous triflouride (${\mathrm{PF}}_3$) using the $R$-matrix method for incident energies from 0.1$–$15 eV and using spherical complex optical potential formalism beyond ionization threshold of target to 5000 eV are reported. We performed close-coupling calculations using static exchange plus polarization model. We employed different target models in order to study their relative dependence on the total cross sections. Three important structures are revealed in the total-cross-section curve: one that corresponds to the Ramsauer-Townsend minimum at 0.33 eV, the second is a strong maximum of 100 Å${}^2$ at 1 eV, the third is around 11 eV corresponding to negative ion formation as predicted by earlier study. The total ionization cross sections are computed using the complex scattering potential ionization contribution method and the binary encounter Bethe method. The electronic-excitation cross sections, momentum-transfer cross sections, and differential and ionization cross sections are our maiden efforts for this system. We have compared our total-cross-section results with available theoretical and experimental results.

In this article, we consider the monopole excitations of a harmonically trapped Bose gas in the vicinity of the Tonks-Girardeau limit. Using Girardeau's Fermi-Bose duality and subsequently an effective fermion-fermion odd-wave interaction, we obtain the dominant correction to the scale-invariance-protected value of the excitation frequency, for microscopically small excitation amplitudes. We produce a series of diffusion Monte Carlo results that confirm our analytic prediction for three particles. And less expectedly, our result stands in excellent agreement with the result of a hydrodynamic simulation (with the Lieb-Liniger equation of state as an input) of the microscopically large but macroscopically small excitations. We also show that the frequency we obtain coincides with the upper bound derived by Menotti and Stringari using sum rules. Surprisingly, however, we found that the usually successful hydrodynamic perturbation theory predicts a shift that is $9/4$ higher than its ab initio numerical counterpart. We conjecture that the sharp boundary of the cloud in local density approximation—characterized by an infinite density gradient—renders the perturbation inapplicable. All our results also directly apply to the three-dimensional $p$-wave-interacting waveguide-confined fermions.

We use permutation-group methods plus SU(3) group-theoretic methods to determine the action of a three-channel passive optical interferometer on controllably delayed single-photon pulse inputs to each channel. Permutation-group techniques allow us to relate directly expressions for rates and, in particular, investigate symmetries in the coincidence landscape. These techniques extend the traditional Hong-Ou-Mandel effect analysis for two-channel interferometry to valleys and plateaus in three-channel interferometry. Our group-theoretic approach is intuitively appealing because the calculus of Wigner D functions partially accounts for permutational symmetries and directly reveals the connections among D functions, partial distinguishability, and immanants.

We present an all-optical control device in which coupling a weak control optical field into a high-$Q$ lithium niobate whispering-gallery-mode microcavity decouples it from a signal field due to nonlinear optical interactions. This results in switching and modulation of the signal with low-power control pulses. In the quantum limit, the underlying nonlinear-optical process corresponds to the quantum Zeno blockade. Its “interaction-free” nature effectively alleviates loss and decoherence for the signal waves. This work therefore presents experimental progress towards acquiring large phase shifts with few photons or even at the single-photon level.

Cavity optomechanical systems are approaching a strong-coupling regime where the coherent dynamics of nanomechanical resonators can be manipulated and controlled by optical fields at the single-photon level. Here we propose an interferometric scheme able to detect optomechanical coherent interaction at the single-photon level which is experimentally feasible with state-of-the-art devices.

We propose a flexible numerical framework for extracting the energy spectra and photon transfer dynamics of a unit kagome cell with disordered cavity-cavity couplings under realistic experimental conditions. A projected-entangled pair state (PEPS) Ansatz to the many-photon wave function allows us to gain a detailed understanding of the effects of undesirable disorder in fabricating well-controlled and scalable photonic quantum simulators. The correlation functions associated with the propagation of two-photon excitations reveal intriguing interference patterns peculiar to the kagome geometry and promise at the same time a highly tunable quantum interferometry device with a signature for the formation of resonant or Fabry-Peŕot-like transmission of photons. Our results justify the use of the proposed PEPS technique for addressing the role of disorder in such quantum simulators in the microwave regime and promises sophisticated numerical machinery for yet further explorations of the scalability of the resulting kagome arrays. The introduced methodology and the physical results may also pave the way for unraveling exotic phases of correlated light on a kagome geometry.

For the last few years, our group has calculated cross sections for electron-impact ionization of molecules using the molecular three-body distorted-wave approximation coupled with the orientation-averaged molecular orbital (OAMO) approximation. This approximation was very successful for calculating ionization cross sections for hydrogen molecules and to a lesser extent nitrogen molecules. Recently we used the approximation to calculate single ionization cross sections for the $1t_2$ state of methane (CH${}_4$) and we found major discrepancies with the experimental data. Here we investigate the validity of the OAMO approximation by calculating cross sections that have been properly averaged over all molecular orientations. These calculations with proper averages are in much better agreement with experiment than the OAMO calculations.