Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and its properties are reported. The relationship between the Thomas-Fermi theory as a density functional and the theory as a potential functional is derived. The properties of several recent semiclassical potential functionals are explored, especially regarding their approach to the large particle number and classical continuum limits. The lack of ambiguity in the energy density of potential functional approximations is demonstrated. The density-density response function of the semiclassical approximation is calculated and shown to violate a key symmetry condition.

Experiments have shown that positrons can attach to molecules via vibrational Feshbach resonances. This leads to increased annihilation rates, the magnitudes of which depend upon molecular structure. Presented here is a simplified rate-equation model to describe the competition between annihilation while the positron is attached to the molecule, positron ejection from the entrance state, and diffusion of the vibrational energy to multimode states followed by similar ejection due to vibrational deexcitation. The latter ejection process can involve vibrations more strongly coupled to the positron continuum, producing suppression of the annihilation, or those more weakly coupled to the continuum, resulting in enhanced annihilation rates. This model elucidates the role that mode coupling can play in determining resonant annihilation amplitudes. Simple limits are obtained and compared with experimental results for selected molecules.

We analyze the influence of dipole-dipole interactions between Rydberg atoms on the generation of Abelian artificial gauge potentials and fields. When two Rydberg atoms are driven by a uniform laser field, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole and van der Waals interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion.

We report a computational investigation of positron scattering by pyrimidine (C${}_4$H${}_4$N${}_2$) in the gas phase. Integral and differential cross sections have been calculated over a broad energy range by employing two distinct ab initio quantum scattering methods: the $R$-matrix method and a corrected form of the independent-atom representation, at low and high energies, respectively. Since pyrimidine is a strong polar molecule further dipole-induced excitations have been calculated in the framework of the first Born approximation. Good agreement is found between the different computational models and fair agreement is found with prior experimental results.

We recently used a compact Penning trap to capture and isolate highly charged ions extracted from an electron beam ion trap (EBIT) at the National Institute of Standards and Technology. Isolated charge states of highly stripped argon and neon ions with total charge $Q\ge 10$, extracted at energies of up to $4\times {10}^{3}Q$ eV, are captured in a trap with well depths of $\approx (4–12)Q$ eV. Here we discuss in detail the process to optimize velocity tuning, capture, and storage of highly charged ions in a unitary Penning trap designed to provide easy radial access for atomic or laser beams in charge exchange or spectroscopic experiments, such as those of interest for proposed studies of one-electron ions in Rydberg states or optical transitions of metastable states in multiply charged ions. Under near-optimal conditions, ions captured and isolated in such rare-earth Penning traps can be characterized by an initial energy distribution that is $\approx 60$ times narrower than typically found in an EBIT. This reduction in thermal energy is obtained passively, without the application of any active cooling scheme in the ion-capture trap.

We study the connection between the semiclassical phase space of the Bose-Hubbard dimer and inherently quantum phenomena in this model, such as entanglement and dissipation-induced coherence. Near the semiclassical self-trapping fixed points, the dynamics of Einstein-Podolski-Rosen (EPR) entanglement and condensate fraction consists of beats among just three eigenstates. Since persistent EPR entangled states arise only in the neighborhood of these fixed points, our analysis explains essentially all of the entanglement dynamics in the system. We derive accurate analytical approximations by expanding about the strong-coupling limit; surprisingly, their realm of validity is nearly the entire parameter space for which the self-trapping fixed points exist. Finally, we show significant enhancement of entanglement can be produced by applying localized dissipation.

We have studied the coherent evolution of ultracold atomic rubidium clouds subjected to a microwave field driving Rabi oscillations between the stretched states of the $F=1$ and $F=2$ hyperfine levels. A phase winding of the two-level system pseudospin vector is encountered for elongated samples of atoms exposed to an axial magnetic-field gradient and can be observed directly in state-selective absorption imaging. When dispersively recording the sample-integrated spin population during the Rabi drive, we observe a damped oscillation directly related to the magnetic-field gradient, which we quantify using a simple dephasing model. By analyzing such dispersively acquired data from millimeter sized atomic samples, we demonstrate that field gradients can be determined with an accuracy of $\sim 25$ nT/mm. The dispersive probing of inhomogeneously broadened Rabi oscillations in prolate samples opens up a path to gradiometry with bandwidths in the kilohertz domain.

We study the transverse-field Ising model with infinite-range coupling and spontaneous emission on every site. We find that there is spin squeezing in steady state due to the presence of the transverse field. This means that there is still entanglement, despite the decoherence from spontaneous emission. We analytically calculate fluctuations beyond mean-field theory using a phase-space approach, which involves converting the master equation into a Fokker-Planck equation for the Wigner function. Our calculations are relevant to current experiments with trapped ions.

We study the full field and frequency filtered output photon statistics of a resonator in thermal equilibrium with a bath and containing an arbitrarily large quartic nonlinearity. According to the general theory of photodetection, we derive general input-output relations valid for the ultra-anharmonic regime, where the nonlinearity becomes comparable to the energy of the resonator, and show how the emission properties are modified as compared to the generally assumed simple anharmonic regime. We analyze the impact of the nonlinearity on the full statistics of the emission, $g^{\left(2\right)}$, and its spectral properties. In particular, we derive a semianalytical expression for the frequency resolved two-photon correlations or two-photon spectrum of the system in terms of the master-equation coefficients and density matrix. This provides a very clear insight into the level structure and emission possibilities of the system.

We study the long-range quantum correlations in the anisotropic $XY$ model. By first examining the thermodynamic limit, we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Furthermore, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite-size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A 77, 062516 (2008)] to evaluate the ground-state static electric dipole polarizabilities ($\alpha$s) of several atomic systems. In this work, we have incorporated a class of higher-order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracies of $\alpha$s. We also calculate the ground state $\alpha$s of the inert gas atoms and several isoelectronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computations of the unperturbed single and doubl coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher-order correlation effects for the accurate determination of ($\alpha$s) of the systems that we have considered.

Electron-impact theoretical cross sections and rate coefficients for vibrational excitation of vibrationally excited H${}_2$ molecules, occurring through the H${}_2^{-}$ resonant species in the ${}^2{\Sigma }_g^{+}$ Rydberg-excited electronic state, are presented. The cross sections are calculated as functions of the incident electron energy by adopting the local-complex-potential model for resonant collisions and by using ab initio calculated molecular potentials and resonance widths. The calculations have been extended to all possible vibrational transitions linking all 15 vibrational levels of the electronic ground state of the H${}_2$ molecule. The corresponding rate coefficients are also obtained as a function of the electron temperature by assuming a Maxwellian electron energy distribution function, and a simple analytical expression is derived. Finally, the present rate coefficients for the transitions starting from the lowest vibrational level of the H${}_2$ molecule are compared with those for the process involving the $X^2{\Sigma }_u^{+}$ resonant state of the H${}_2^{-}$ molecular ion.

An x-ray pulse-shaping scheme is put forward for imprinting an optical frequency comb onto the radiation emitted on a driven x-ray transition, thus producing an x-ray frequency comb. A four-level system is used to describe the level structure of $N$ ions driven by narrow-bandwidth x rays, an optical auxiliary laser, and an optical frequency comb. By including many-particle enhancement of the emitted resonance fluorescence, a spectrum is predicted consisting of equally spaced narrow lines which are centered on an x-ray transition energy and separated by the same tooth spacing as the driving optical frequency comb. Given an x-ray reference frequency, our comb could be employed to determine an unknown x-ray frequency. While relying on the quality of the light fields used to drive the ensemble of ions, the model has validity at energies from the 100 eV to the keV range.

We consider the quasi-one-dimensional (quasi-1D) system realized by an array of weakly coupled parallel one-dimensional “tubes” in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin-orbit coupling (SOC), and an $s$-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature ($T=0$) Bogoliubov–de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes and show that the $T=0$ phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with nonzero center-of-mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center-of-mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the three-dimensional and 1D systems and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one dimensional. We also find evidence of the existence of a Zeeman-tuned topological quantum phase transition (TQPT) within the FFLO phase itself and, for large values of the Zeeman field and small SOC, the TQPT gives rise to a topologically distinct FFLO phase.

We present a systematic analysis of coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator. Depending on the elementary particles comprising the composite particles, we gauge the resemblance between this eigenstate and traditional coherent states through typical measures of nonclassicality, such as quadrature variances and Mandel's $Q$ parameter. Furthermore, we show that the eigenstate of the coboson annihilation operator is useful in estimating the maximum eigenvalue of the coboson number operator.

We report on an experimental realization of unidirectional transporting island structures in an otherwise chaotic phase space of the $\delta$-kicked rotor system. Using a Bose-Einstein condensate as a source of ultracold atoms, we employ asymmetric phase modulation in the kicks, with the narrow momentum distribution of the atoms allowing us to address individual island structures. We observe quantum ratchet behavior in this system, with clear directed momentum current in the absence of a directional force, which we characterize and connect to $\epsilon$-classical theory.

We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very diverse quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. Starting from the composite fermionization regime, in which the interactions between both components are large and neither gas is phase coherent, our results show that a phase-separated state can be reached by increasing the interaction in one of the species. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting one is expelled to the edges of the trap. The crossover is sharp, as can be witnessed in the system's energy and in the occupation of the lowest natural orbital of the weakly interacting species. We show that such a transition is a few-atom effect which disappears for a large population imbalance.

We investigate the quantum fluctuation effects in the vicinity of the critical point of a $p$-orbital bosonic system in a square optical lattice using the Wilsonian renormalization group, where the $p$-orbital bosons condense at nonzero momenta and display rich phases including both time-reversal symmetry invariant and broken Bose-Einstein condensation states. The one-loop renormalization-group analysis generates corrections to the mean-field phase boundaries. We also show the quantum fluctuations in the $p$-orbital system tend to induce the ordered phase but not destroy it via the Coleman-Weinberg mechanism, which is qualitatively different from the ordinary quantum fluctuation corrections to the mean-field phase boundaries in $s$-orbital systems. Finally, we discuss the observation of these phenomena in the realistic experiment.

Coherent population trapping (CPT) and electromagnetically induced transparency in atoms have garnered enormous attention because of their conceptual novelty in quantum optics and potential applications in quantum information processing. Here, we show that CPT can occur in buckminsterfullerene ${\mathrm{C}}_{60}$. If we radiate ${\mathrm{C}}_{60}$ with a cw coupling field first and then with a weak probe field, ${\mathrm{C}}_{60}$ becomes much less absorptive. Turning off the coupling field restores the absorptive nature. Using two coupling pulses, we can prepare ${\mathrm{C}}_{60}$ in a dark state, which is transparent to the probe field. Such a dark state sensitively depends on the laser field amplitude, pulse durations, time delay between two coupling pulses, and laser chirps. Too strong fields refill the ground state, while too long durations overshoot the population and become less effective. There is an optimal delay between two pulses. By employing the first-principles method and solving the Liouville equation dynamically, we scan the vast laser parameter space and find a practical path to coherent population trapping in ${\mathrm{C}}_{60}$, which is of great importance for future experimental investigations.

We provide a theoretical treatment of the quantum backaction of Larmor frequency measurements on a spinor Bose-Einstein condensate by an off-resonant light field. Two main results are presented; the first is a “quantum jump” operator description that reflects the abrupt change in the spin state of the atoms when a single photon is counted at a photodiode. The second is the derivation of a conditional stochastic master equation relating the evolution of the condensate density matrix to the measurement record. We provide a few examples of the application of this formalism and comment on its application to metrology.