We analyze a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC crossover. Using a quasiparticle random-phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC, respectively, we show that the single-particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, we can use these prominent effects to systematically probe the strongly interacting Fermi gas.

Information recycling has been shown to improve the sensitivity of atom interferometers by exploiting atom-light entanglement. In this Rapid Communication, we apply information recycling to an interferometer where the input quantum state has been partially transferred from some donor system. We demonstrate that when the quantum state of this donor system is from a particular class of number-correlated Heisenberg-limited states, information recycling yields a Heisenberg-limited phase measurement. Crucially, this result holds irrespective of the fraction of the quantum state transferred to the interferometer input and also for a general class of number-conserving quantum-state-transfer processes, including ones that destroy the first-order phase coherence between the branches of the interferometer. This result could have significant applications in Heisenberg-limited atom interferometry, where the quantum state is transferred from a Heisenberg-limited photon source, and in optical interferometry where the loss can be monitored.

Light's wave-particle duality is at the heart of quantum mechanics and can be well illustrated by Wheeler's delayed-choice experiment: The choice of inserting or removing the second classical (quantum) beam splitter in a Mach-Zehnder interferometer determines the classical (quantum) wave-particle behavior of a photon. In this paper, we report our experiment on directly observing simultaneous wave and particle behavior in a narrowband single-photon wave packet by classically inserting or removing the second beam splitter when part of the wave packet passes through it. Our experiment demonstrates that the produced wave-particle state can be utilized in encoding quantum information.

We present the entropic uncertainty relations for multiple measurement settings which demonstrate the uncertainty principle of quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory, and can be proven by a unified method. Our results recover some well known entropic uncertainty relations for two observables, which show the uncertainties about the outcomes of two incompatible measurements. The bounds of those relations which quantify the extent of the uncertainty take concise forms and are easy to calculate. Those uncertainty relations might play important roles in the foundations of quantum theory. Potential experimental demonstration of those entropic uncertainty relations is discussed.

We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that in both cases, for an appropriate choice of the modulation parameters, the state amplitudes in a generic $n$-excitation subspace obey the same equations of motion that can be obtained from a static non-Hermitian Jaynes-Cummings Hamiltonian with $\mathcal{PT}$ symmetry, that is with an imaginary coupling constant. This gives further support to recent results showing the possible physical interest of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians. We also generalize the well-known diagonalization of the Jaynes-Cummings Hamiltonian to the non-Hermitian case in terms of pseudobosons and pseudofermions, and discuss relevant mathematical and physical aspects.

The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As a straightforward application, we show how to use the stability of driven non-Hermitian two-level systems (0 dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity–time reversal symmetry is also briefly discussed.

Indirect control of qubits by a quantum actuator has been proposed as an appealing strategy to manipulate qubits that couple only weakly to external fields. While universal quantum control can be easily achieved when the actuator-qubit coupling is anisotropic, the efficiency of this approach is less clear. Here we analyze the time efficiency of quantum actuator control. We describe a strategy to find time-optimal control sequences by the quantum actuator and compare their gate times with direct driving, identifying regimes where the actuator control performs faster. As a paradigmatic example, we focus on a specific implementation based on the nitrogen-vacancy center electronic spin in diamond (the actuator) and nearby ${}^{13}\mathrm{C}$ nuclear spins (the qubits).

This paper presents a numerical convergence study of a hyperspherical-harmonics expansion for binding energies of a system of $4\le N\le 728$ helium atoms using a phenomenological soft attractive two-body He-He potential and a repulsive three-body force aimed at compensating for the absence of the two-body repulsive core. Earlier calculations with such a potential have shown an improved convergence when $N$ increases from four to six. The present study reveals that the improved convergence occurs only for a limited range of $N$ determined by the range of the three-body repulsion. For a soft repulsive three-body force, the convergence is fast for $N\le 20$, while for a short-range three-body repulsion it deteriorates at $N\ge 10$. The reasons for this deterioration are discussed. The range of the three-body force also determines the binding energy behavior with $N$, and it is also responsible for binding the excited states. The long-range force binds all first excited $0^{+}$ states but strongly underbinds the systems of $N$ helium atoms at large $N$. The short-range force does not bind the first $0^{+}$ states for $A\le 7$ but gives better predictions of binding energies as compared to the calculations of other authors though overestimating them. Some options to improve both the description of the binding energies and the convergence of the hyperspherical-harmonics expansion using phenomenological forces are discussed. It is pointed out that a fast convergence is very much needed for the reliable predictions of states with nonzero angular momentum, examples of which are also given.

We have studied theoretical photoelectron-momentum distributions of ${\mathrm{C}}_{60}$ using time-dependent density functional theory (TDDFT) in real time and including a self-interaction correction. Our calculations furthermore account for a proper orientation averaging allowing a direct comparison with experimental results. To illustrate the capabilities of this direct (microscopic and time-dependent) approach, two very different photo-excitation conditions are considered: excitation with a high-frequency XUV light at 20 eV and with a low-frequency IR femtosecond pulse at 1.55 eV. The interaction with the XUV light leads to one-photon transitions and a linear ionization regime. In that situation, the spectrum of occupied single-electron states in ${\mathrm{C}}_{60}$ is directly mapped to the photoelectron spectrum. On the contrary, the IR pulse leads to multiphoton ionization in which only the two least-bound states contribute to the process. In both dynamical regimes (mono- and multiphoton), calculated and experimental angle-resolved photoelectron spectra compare reasonably well. The observed discrepancies can be understood by the theoretical underestimation of higher-order many-body interaction processes such as electron-electron scattering and by the fact that experiments are performed at finite temperature. These results pave the way to a multiscale description of the ${\mathrm{C}}_{60}$ ionization mechanisms that is required to render justice to the variety of processes observed experimentally for fullerene molecules.

In this work, the controversy between the interpretations of recent measurements on dense aluminum plasma created with the Linac coherent light source (LCLS) x-ray free electron laser (FEL) and the Orion laser has been addressed. In both kinds of experiments, heliumlike and hydrogenlike spectral lines are used for plasma diagnostics. However, there exist no precise theoretical calculations for He-like ions within a dense plasma environment. The strong need for an accurate theoretical estimate for spectral properties of He-like ions in a strongly coupled plasma environment leads us to perform ab initio calculations in the framework of the Rayleigh-Ritz variation principle in Hylleraas coordinates where an ion-sphere potential is used. An approach to resolve the long-drawn problem of numerical instability for evaluating two-electron integrals with an extended basis inside a finite domain is presented here. The present values of electron densities corresponding to the disappearance of different spectral lines obtained within the framework of an ion-sphere potential show excellent agreement with Orion laser experiments in Al plasma and with recent theories. Moreover, this method is extended to predict the critical plasma densities at which the spectral lines of H-like and He-like carbon and argon ions disappear. Incidental degeneracy and level-crossing phenomena are being reported for two-electron ions embedded in strongly coupled plasma. Thermodynamic pressure experienced by the ions in their respective ground states inside the ion spheres is also reported.

The nuclear electric quadrupole moment (NQM) of gold is reviewed by means of the molecular method and data from as many as 15 linear systems. The electric-field gradients (EFGs) used to this end were obtained with the Dirac-Coulomb Hamiltonian and coupled-cluster theory, CCSD(T) and CCSD-T, by means of an augmented relativistic basis set for gold. The direct approach was found to be inadequate for the diatomic molecules investigated, which is probably due to improper treatment of the static electron correlation. However, these effects are much less relevant for $\mathrm{OCAu}X$ ($X=\mathrm{F},\mathrm{Cl},\mathrm{Br}$, and $\mathrm{I}$) complexes. Thus, the indirect version of the molecular method is preferred in this case. Hence, a NQM value of 515(15) mb is determined for ${}^{197}\mathrm{Au}$ from linear regressions performed with the best EFGs determined for ten of these systems.

We present a detailed analysis of the time-scaled coordinate approach and its implementation for solving the time-dependent Schrödinger equation describing the interaction of atoms or molecules with radiation pulses. We investigate and discuss the performance of multiresolution schemes for the treatment of the squeezing around the origin of the bound part of the scaled wave packet. When the wave packet is expressed in terms of $B$ splines, we consider two different types of breakpoint sequences: an exponential sequence with a constant density and an initially uniform sequence with a density of points around the origin that increases with time. These two multiresolution schemes are tested in the case of a one-dimensional Gaussian potential and for atomic hydrogen. In the latter case, we also use Sturmian functions to describe the scaled wave packet and discuss a multiresolution scheme which consists of working in a Sturmian basis characterized by a set of nonlinear parameters. Regarding the continuum part of the scaled wave packet, we show explicitly that, for large times, the group velocity of each ionized wave packet goes to zero while its dispersion is suppressed, thereby explaining why, eventually, the scaled wave packet associated with the ejected electrons becomes stationary. Finally, we show that only the lowest scaled bound states can be removed from the total scaled wave packet once the interaction with the pulse has ceased.

Two-photon ionization of an alkali-metal atom in the presence of a uniform electric field is investigated using a standardized form of the local-frame-transformation and generalized quantum defect theory. The relevant long-range quantum defect parameters in the combined Coulombic plus Stark potential are calculated with eigenchannel $R$-matrix theory applied in the downstream parabolic coordinate $\eta$. The present formulation permits us to express the corresponding microscopy observables through the local frame transformation, and it gives a critical test of the accuracy of the Harmin-Fano theory.

Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultracold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional-ground-state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground-state cooling schemes for single ${}^{25}{\mathrm{Mg}}^{+}$ ions and sympathetic ground-state cooling of ${}^{24}{\mathrm{MgH}}^{+}$. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground-state cooling outside the Lamb-Dicke regime.

Laser-induced impulsive alignment of symmetric linear molecules leads to time-dependent observables which are analyzed in terms of their spectral components. Signals appear as sums over positive integers $\ell$ of periodic components $A_{2\ell }\left(t\right)$ with periods ${\tau }_{2\ell }={\left(2\ell c{B}_0\right)}^{-1}$, where $B_0$ is the rotational constant in wave number units. Within each period ${\tau }_{2\ell }$, four fractional revivals at times $n{\tau }_{2\ell }/4$ $(n=0,1,2,3)$ exhibit constant successive phase shifts ${(-1)}^{\ell +p}\pi /2$ depending on the even-odd parity $(p=0,1)$ of the initial rotational states. This analysis gives a comprehensive account of the so-called high-order revivals usually discussed in terms of fractional revivals within the period ${\tau }_2$ of the average value $\langle {cos}_{\vartheta }^2\rangle \left(t\right)$ of ${cos}^2\left(\vartheta \right)$, where $\vartheta$ is the angle between the molecular axis and the alignment direction. These considerations are illustrated by experiments and numerical calculations of laser-induced impulsive alignment and tunnel ionization of ${\text{CO}}_2$ molecules for which calculated ionization yields of fixed-in-space molecules are available.

It is known that a semiclassical analysis is not always adequate for atomtronics devices, but that a fully quantum analysis is often necessary to make reliable predictions. While small numbers of atoms at a small number of sites are tractable using the density matrix, a fully quantum analysis is often not straightforward as the system becomes larger. We show that the fully quantum positive-P representation is then a viable calculational tool. We postulate an atomtronic phase gate consisting of four wells in a Bose-Hubbard configuration, for which the semiclassical dynamics are controllable using the phase of the atomic mode in one of the wells. We show that the quantum predictions of the positive-P representation for the performance of this device have little relation to those found semiclassically, and that the performance depends markedly on the actual quantum states of the initially occupied modes. We find that initial coherent states lead to closest to classical dynamics, but that initial Fock states give results that are quite different. A fully quantum analysis also opens the door for deeply quantum atomtronics, in which properties such as entanglement and Einstein-Podolsky-Rosen steering become valuable technical attributes of a device.

Wheeler's delayed-choice experiment highlights strange features of quantum theory such as pre-sensing of the experimental setup by the quantum object and the role of time. A recent proposal for such an experiment with an interferometer having a quantum beam splitter (QBS) [R. Ionicioiu and D. R. Terno, Phys. Rev. Lett. 107, 230406 (2011)] and its subsequent experimental implementations through photonics and NMR have produced results including the modification in the concept of complementarity. Here we propose a matter-wave Mach-Zehnder-Bragg cavity-QED interferometric setup with final QBS engineered through a cavity field that is taken initially in the superposition of zero and one photon. The setup operates through first-order off-resonant Bragg diffraction of the neutral atoms from the cavity fields with the matter wave's particle (wave) nature marked through the absence (presence) of a photon in the final cavity. The proposal, addressing the issue through atomic de Broglie waves, can be executed within the present cavity-QED experimental scenario with appreciable success probability and fidelity.

We consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.

A pulse of matter waves may dramatically change its shape when traversing an absorbing barrier with time-dependent transparency. Here we show that this effect can be utilized for controlled manipulation of spatially localized quantum states. In particular, in the context of atom-optics experiments, we explicitly demonstrate how the proposed approach can be used to generate spatially shifted, split, squeezed, and cooled atomic wave packets. We expect our work to be useful in devising new interference experiments with atoms and molecules and, more generally, to enable new ways of coherent control of matter waves.

We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in Soltan-Panahi et al. [Nat. Phys. 8, 71 (2012)]. Theoretically, the origin of this effect is not understood. We perform numerical simulations of an extended single-band Bose-Hubbard model adapted to the experimental parameters employing the multilayer multiconfiguration time-dependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory in the relevant parameter range, within the extended single-band Bose-Hubbard model. Beyond this, we provide a detailed analysis of correlation effects correcting the mean-field result. These have the potential to induce asymmetries in single shot time-of-flight measurements, but we find no indication of the patterns characteristic of the twisted superfluid. We comment on the restrictions of our model and possible extensions.