While the microscopic origins of radio-frequency (rf) heating of simultaneously stored, charged particles in a Paul trap are not yet understood in detail, a universal heating curve [J. D. Tarnas, Y. S. Nam, and R. Blümel, Phys. Rev. A 88, 041401 (2013)] was recently discovered that collapses scaled rf heating data onto a single universal curve. Based on a simple analytical mean-field theory, we derive an analytical expression for the universal heating curve, which is in excellent agreement with numerical data. We find that for spherical clouds the universal curve depends only on a single scaling parameter, $\lambda ={\left[q(N-1)\right]}^{2/3}/T$, where $N$ is the number of trapped particles, $q$ is the Paul-trap control parameter, and $T$ is the temperature.

The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length and time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the Zaremba-Nikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further shows reconnections to be insensitive to the inhomogeneity in the background density.

Dissipation is introduced to a strongly interacting ultracold bosonic gas in the Mott-insulator regime of a three-dimensional spin-dependent optical lattice. A weakly interacting superfluid comprised of atoms in a state that does not experience the lattice potential acts as a dissipative bath coupled to the lattice atoms via collisions. Lattice atoms are excited to a higher-energy band via Bragg transitions, and the resulting bath-induced decay is measured using the atomic quasimomentum distribution. A competing but slower intrinsic decay mechanism arising from collisions between lattice atoms is also investigated. The measured bath-induced decay rate is compared with the predictions of a weakly interacting model with no free parameters. The presence of intrinsic decay, which cannot be accommodated within this framework, signals that strong interactions may play a central role in the lattice-atom dynamics.

We study theoretically the propagation of large-wave-vector waves (volume plasmon polaritons) in multilayer hyperbolic metamaterials with two levels of structuring. We show that when the parameters of a subwavelength metal-dielectric multilayer (substructure) are modulated (superstructured) on a larger, wavelength scale, the propagation of volume plasmon polaritons in the resulting multiscale hyperbolic metamaterials is subject to photonic-band-gap phenomena. A great degree of control over such plasmons can be exerted by varying the superstructure geometry. When this geometry is periodic, stop bands due to Bragg reflection form within the volume plasmonic band. When a cavity layer is introduced in an otherwise periodic superstructure, resonance peaks of the Fabry-Pérot nature are present within the stop bands. More complicated superstructure geometries are also considered. For example, fractal Cantor-like multiscale metamaterials are found to exhibit characteristic self-similar spectral signatures in the volume plasmonic band. Multiscale hyperbolic metamaterials are shown to be a promising platform for large-wave-vector bulk plasmonic waves, whether they are considered for use as a kind of information carrier or for far-field subwavelength imaging.

We investigate the rich physics of photonic molecule lasers using a non-Hermitian dimer model. We show that several interesting features, predicted recently using a rigorous steady-state ab initio laser theory (SALT), can be captured by this toy model. In particular, we demonstrate the central role played by exceptional points (EPs) in both pump-selective lasing and laser self-termination phenomena. Due to its transparent mathematical structure, our model provides a lucid understanding for how different physical parameters (optical loss, modal coupling between microcavities, and pump profiles) affect the lasing action. Interestingly, our analysis also confirms that, for frequency mismatched cavities, operation in the proximity of exceptional points (without actually crossing the square root singularities) can still lead to laser self-termination. We confirm this latter prediction for two coupled slab cavities using scattering matrix analysis and SALT technique. In addition, we employ our model to investigate the pump-controlled lasing action and we show that emission patterns are governed by the locations of exceptional points in the gain space. Finally we extend these results to multicavity photonic molecules, where we found the existence of higher-order EPs and pump-induced localization.

In a recent experiment by Yamazaki et al. [Phys. Rev. A 87, 010704(R) (2013)], a $p$-wave optical Feshbach resonance in fermionic ${}^{171}\mathrm{Yb}$ atoms using purely long-range molecular excited states has been demonstrated. We show theoretically that, if two purely long-range excited states of ${}^{171}\mathrm{Yb}$ are coupled to the ground-state continuum of scattering states with two lasers, then it is possible to significantly suppress photoassociative atom loss by a dark resonance in the excited states. We present a general theoretical framework for creating a dark state in an electronically excited molecular potential for the purpose of increasing the efficiency of the optical Feshbach resonance. This can be accomplished by properly adjusting the relative intensity, phase, polarizations, and frequency detunings of two lasers. We present selected numerical results for atom-loss spectra and $p$-wave elastic- and inelastic-scattering cross sections of ${}^{171}\mathrm{Yb}$ atoms to illustrate the effects of the molecular dark state on the optical Feshbach resonance.

The efficient production of very-high-$n$, $n\sim 300$, quasi-one-dimensional (quasi-1D) strontium Rydberg atoms through three-photon excitation of extreme Stark states in the presence of a weak dc field is demonstrated using a crossed laser-atom beam geometry. Strongly polarized quasi-1D states with large permanent dipole moments $\sim 1.2n^2$ a.u. can be created in the beam at densities ($\sim {10}^6$ cm${}^{-3}$) where dipole blockade effects should become important. A further advantage of three-photon excitation is that the product $F$ states are sensitive to the presence of external fields, allowing stray fields to be reduced to very small values. The experimental data are analyzed using quantum calculations based on a two-active-electron model together with classical trajectory Monte Carlo simulations. These allow determination of the atomic dipole moments and confirm that stray fields can be reduced to $\le 25\mu$V cm${}^{-1}$.

We study the properties of an atomic Bose–Einstein condensate produced in an optical-box potential, using high-resolution Bragg spectroscopy. For a range of box sizes, up to $70\mu$m, we directly observe Heisenberg-limited momentum uncertainty of the condensed atoms. We measure the condensate interaction energy with a precision of $k_{\mathrm{B}}\times 100$ pK and study, both experimentally and numerically, the dynamics of its free expansion upon release from the box potential. All our measurements are in good agreement with theoretical expectations for a perfectly homogeneous condensate of spatial extent equal to the size of the box, which also establishes the uniformity of our optical-box system on a sub-nK energy scale.

We investigate the superfluid phases of a Rashba spin-orbit-coupled Bose-Einstein condensate residing on a two-dimensional square optical lattice in the presence of an effective Zeeman field $\Omega$. At a critical value $\Omega ={\Omega }_c$, the single-particle spectrum $E_{\mathbf{k}}$ changes from having a set of four degenerate minima to a single minimum at $\mathbf{k}=0$, corresponding to condensation at finite or zero momentum, respectively. We describe this quantum phase transition and the symmetry breaking of the condensate phases. We use the Bogoliubov theory to treat the superfluid phases and determine the phase diagram, the excitation spectrum, and the sound velocity of the phonon excitations. A dynamically unstable superfluid regime occurring when $\Omega$ is close to ${\Omega }_c$ is analytically identified and the behavior of the condensate quantum depletion is discussed. Moreover, we show that there are two types of roton excitations occurring in the $\Omega <{\Omega }_c$ regime and obtain explicit values for the corresponding energy gaps.

We present a theoretical study of the quantum Zeno effect in a driven superconducting charge qubit strongly and ultrastrongly coupled to a transmission line resonator. Using the dressed-state approach, we predict the different dynamics behaviors of the dressed qubit subjected to two opposite projection measurements. We show that, for very frequent measurements, the survival probability of the initial state is of exponential form and the Zeno time of the dressed qubit can be several orders of magnitude longer than that of the bare qubit. For slowly repeated measurements, the detuning of the driving field has significant impact on the measurement dynamics, and by choosing appropriate parameters for the dressed qubit, the Zeno effect can occur in the nonresonant coupling case. Such a Zeno effect is excluded from a usual two-level system.

The derivative-expansion approach to the calculation of the interaction between two surfaces is a generalization of the proximity force approximation, a technique in widespread use in different areas of physics. The derivative expansion has so far been applied to seemingly unrelated problems in different areas; it is our principal aim here to present the approach in its full generality. To that end, we introduce a unified setting, which is independent of any particular application, provide a formal derivation of the derivative expansion in that general setting, and study some of its properties. With a view toward the possible application of the derivative expansion to other areas, like nuclear and colloidal physics, we also discuss the relation between the derivative expansion and some time-honored uncontrolled approximations used in these contexts. By putting them under similar terms as in the derivative expansion, we believe that the path is open to the calculation of next-to-leading-order corrections also for these contexts. We also review some results obtained within the derivative expansion, by applying it to different concrete examples and highlighting some important points.

We explore the possibility of using “weak” measurements to carry out quantum state tomography via numerical simulations. Given a fixed number of copies of identically prepared states of a qubit, we perform state tomography using weak as well as projective measurements. Due to the collapse of the state after measurement, we cannot reuse the state after a projective measurement. If the coupling strength between the quantum system and the measurement device is made weaker, the disturbance caused to the state can be lowered. This then allows us to reuse the same member of the ensemble for further measurements and thus extract more information from the system. However, this happens at the cost of getting imprecise information from the first measurement. We implement this scheme for a single qubit and show that under certain circumstances, it can outperform the projective measurement-based tomography scheme. This opens up the possibility of new ways of extracting information from quantum ensembles. We study the efficacy of this scheme for different coupling strengths and different ensemble sizes.

Tree size ($\mathrm{TS}$) is an interesting measure of complexity for multiqubit states: not only is it in principle computable, but one can obtain lower bounds for it. In this way, it has been possible to identify families of states whose complexity scales superpolynomially in the number of qubits. With the goal of progressing in the systematic study of the mathematical property of $\mathrm{TS}$, in this work we characterize the tree size of pure states for the case where the number of qubits is small, namely, 3 or 4. The study of three qubits does not hold great surprises, insofar as the structure of entanglement is rather simple; the maximal $\mathrm{TS}$ is found to be 8, reached for instance by the $|W\rangle$ state. The study of four qubits yields several insights: in particular, the most economic description of a state is found not to be recursive. The maximal $\mathrm{TS}$ is found to be 16, reached for instance by a state called $|{\Psi }^{\left(4\right)}\rangle$ which was already discussed in the context of four-photon down-conversion experiments. We also find that the states with maximal tree size form a set of zero measure: a smoothed version of tree size over a neighborhood of a state ($\epsilon$-TS) reduces the maximal values to 6 and 14, respectively. Finally, we introduce a notion of tree size for mixed states and discuss it for a one-parameter family of states.

We report on large-scale and critically evaluated ab initio multiconfiguration Dirac-Hartree-Fock calculations of the wavelength and transition rate of the “coronal,” $M1$ transition $4f{}^2{F}_{5/2}^o$–${}^2{F}_{7/2}^o$ in Ag-like ions. The transition between these two fine-structure levels, which makes up the ground term for $Z\ge 62$ in the isoelectronic sequence, has recently been observed in ${\mathrm{Yb}}^{23+}$ and ${\mathrm{W}}^{27+}$, where the latter could be of great importance for fusion plasma diagnostics. We present values for all members of the sequence between $Z=50$ and 94, which are supported by excellent agreement with values from recent experiments. The importance of including core-valence correlation with the $n=3$ shell in the theoretical model is emphasized. The results show close-to-spectroscopic accuracy for these forbidden lines.

The Casimir force between two objects is notoriously difficult to calculate in anything other than parallel-plate geometries due to its nonadditive nature. This means that for more complicated, realistic geometries one usually has to resort to approaches such as making the crude proximity force approximation (PFA). Another issue with calculation of Casimir forces in real-world situations (such as with realistic materials) is that there are continuing doubts about the status of Lifshitz's original treatment as a true quantum theory. Here we demonstrate an alternative approach to the calculation of Casimir forces for arbitrary geometries which sidesteps both of these problems. Our calculations are based upon a Born expansion of the Green's function of the quantized electromagnetic vacuum field, interpreted as multiple scattering, with the relevant coupling strength being the difference in the dielectric functions of the various materials involved. This allows one to consider arbitrary geometries in single or multiple scattering simply by integrating over the desired shape, meaning that extension beyond the PFA is trivial. This work is mostly dedicated to illustration of the method by reproduction of known parallel-slab results—a process that turns out to be nontrivial and provides several useful insights. We also present a short example of calculation of the Casimir energy for a more complicated geometry; namely, that of two finite slabs.

We study the classical electromagnetic radiation due to the presence of a dipole layer on a plane that performs a bounded motion along its normal direction, to the first nontrivial order in the amplitude of that motion. We show that the total emitted power may be written in terms of the dipole layer autocorrelation function. We then apply the general expression for the emitted power to cases where the dipole layer models the presence of patch potentials, comparing the magnitude of the emitted radiation with that coming from the quantum vacuum in the presence of a moving perfect conductor (dynamical Casimir effect).

In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); A. K. Bhatia, Phys. Rev. A 86, 032709 (2012); A. K. Bhatia, Phys. Rev. A 87, 042705 (2013)] electron-H, $-{\mathrm{He}}^{+}$, and $-{\mathrm{Li}}^{2+}$ $P$-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet $D$-wave scattering in the elastic region. The long-range correlations are included in the Schrödinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated $D$-wave and previously calculated $S$-wave continuum functions, photoionization of singlet and triplet $P$ states of He and ${\mathrm{Li}}^{+}$ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.

Molecular fragmentation leading to the formation of negatively and positively charged hydrogen ions in 7-keV ${OH}^{+}$ + Ar collisions is investigated experimentally. The most striking finding is that negative and positive hydrogen ions are emitted with very similar angular dependences. Also, the kinetic energy distribution of the $H^{+}$ fragment shows strong similarities with that of the ejected $H^{-}$ ion. The kinematics of the emitted H core is found to be essentially driven by its scattering on the atomic target. However, in addition to this binary-encounter process, dissociative electronic excitation of the molecular projectile has to be invoked to explain the observed fragmentation patterns. Though the electron capture process is complex, it is shown that the relative population of the different final charge states of the outgoing fragments can be described by simple statistical laws.

We present an analytic model for the description of above-threshold ionization (ATI) of an atom by an intense, linearly polarized short laser pulse. Our treatment is based upon a description of ATI by an infinitely long train of short laser pulses whereupon we take the limit that the time interval between pulses becomes infinite. In the quasiclassical approximation, we provide detailed quantum-mechanical derivations, within the time-dependent effective range (TDER) model, of the closed-form formulas for the differential probability $\mathcal{P}\left(\mathbf{p}\right)$ of ATI by an intense, short laser pulse that were presented briefly by Frolov et al. [Phys. Rev. Lett. 108, 213002 (2012)] and that were used to describe key features of the high-energy part of ATI spectra for H and He atoms in an intense, few-cycle laser pulse, using a phenomenological generalization of the physically transparent TDER results to the case of real atoms. Moreover, we extend these results here to the case of an electron bound initially in a $p$ state; we also take into account multiple-return electron trajectories. The ATI amplitude in our approach is given by a coherent sum of partial amplitudes describing ionization by neighboring optical cycles near the peak of the intensity envelope of a short laser pulse. These results provide an analytical explanation of key features in short-pulse ATI spectra, such as the left-right asymmetry in the ionized electron angular distribution, the multiplateau structures, and both large-scale and fine-scale oscillation patterns resulting from quantum interferences of electron trajectories. Our results show that the shape of the ATI spectrum in the middle part of the ATI plateau is sensitive to the spatial symmetry of the initial bound state of the active electron. This sensitivity originates from the contributions of multiple-return electron trajectories. Our analytic results are shown to be in good agreement with results of numerical solutions of the time-dependent Schrödinger equation for He and Ar atoms. Comparison of our results with those of quantitative rescattering theory is also discussed.