We have precisely measured the frequencies of 12 transitions of the ${\nu }_2$ fundamental band of ${\mathrm{H}}_3^{+}$ molecular ion. Their absorption spectra are observed using a precision tunable difference frequency generation (DFG) source and a direct current discharge tube with ion concentration modulation scheme. Accurate calibration of the DFG frequency by an optical frequency comb and an iodine-stabilized laser enables us to measure the transition frequencies to an accuracy one order of magnitude better than that achieved in the previous results.

We study the formation and collision-aided decay of an ultracold atomic Bose-Einstein condensate in the first excited band of a double-well two-dimensional optical lattice with weak harmonic confinement in the perpendicular $z$ direction. This lattice geometry is based on an experiment by Wirth et al. [Nat. Phys. 7, 147 (2010)]. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding model with that obtained numerically using a plane-wave basis. We find the tight-binding model to be in quantitative agreement for the lowest two bands, in qualitative agreement for the next two bands, and inadequate for even higher excited bands. The bandwidths of the excited bands are much larger than the harmonic-oscillator energy spacing in the $z$ direction. We then study the thermodynamics of a noninteracting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature $T_c$ as functions of the lattice parameters. For typical atom numbers, the critical energy $k_B{T}_c$, with $k_B$ the Boltzmann constant, is larger than the excited bandwidths and harmonic-oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of the lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used tight-binding wave functions for the lowest four bands and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but close to the critical temperature, it stays smaller than the tunneling rate between the $s$ and $p$ orbitals in adjacent wells.

We study the efficiency of different two-photon states of light to induce the simultaneous excitation of two atoms of different kinds when the sum of the energies of the two photons matches the sum of the energies of the two atomic transitions, while no photons are resonant with each individual transition. We find that entangled two-photon states produced by an atomic cascade are indeed capable of enhancing by a large factor the simultaneous excitation probability as compared to uncorrelated photons, as predicted some years ago by Muthukrishnan et al., but that several unentangled, separable, correlated states, produced either by an atomic cascade or parametric down-conversion, or even appropriate combinations of coherent states, have comparable efficiencies. We show that the key ingredient for the increase of simultaneous excitation probability is the presence of strong frequency anticorrelation and neither time correlation nor time-frequency entanglement.

We present an analytical theory describing a phenomenon of enhanced backscattering corresponding to the spatial refocussing of a spreadout correlated wave packet due to a brief interaction with a disordered potential. Our theory is validated by numerical simulations and explains the physics observed in recent experiments on cold atom transport in disorder.

We investigate the thermodynamics of one-dimensional (1D) Bose gases in the strongly correlated regime. To this end, we prepare ensembles of independent 1D Bose gases in a two-dimensional optical lattice and perform high-resolution in situ imaging of the column-integrated density distribution. Using an inverse Abel transformation we derive effective one-dimensional line-density profiles and compare them to exact theoretical models. The high resolution allows for a direct thermometry of the trapped ensembles. The knowledge about the temperature enables us to extract thermodynamic equations of state such as the phase-space density, the entropy per particle, and the local pair-correlation function.

We show that in device-independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise security. We show that a combined attack exploiting test sample and measurement choices compromises the security even with a linear-size test sample and otherwise device-independent security considerations. We explicitly derive the sample size needed to retrieve security as a function of the randomness quality. We demonstrate that exploiting features of genuinely higher-dimensional systems, one can reduce this weakness and provide device-independent security more robust against weak randomness sources.

One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a graph containing a marked site. In many physical implementations, however, one might expect to have multiple particles. In interacting bosonic systems at zero temperature, the dynamics is well described by a discrete nonlinear Schrödinger equation. We investigate the role of nonlinearity in determining the efficiency of the spatial search algorithm within the quantum walk model, for the complete graph. The analytical calculations reveal that the nonlinear search time scales with the size of the search space $N$ like $\sqrt{N}$, equivalent to the linear case, though with a different overall constant. The results indicate that interacting Bose-Einstein condensates at zero temperature could be natural systems for implementation of the quantum search algorithm.

There exist memoryless zero-capacity quantum channels that when used jointly result in a channel with positive capacity. This phenomenon is called superactivation. Making use of Parrondo's paradox, we exhibit examples of the superactivation-like effect for the capacity of classical communication channels as well as quantum and private capacity of quantum channels with memory. There are several ingredients necessary for superactivation of quantum capacity to occur in the memoryless case. The first one is the requirement for the quantum channels which are suitable for superactivation to come from two distinct families: binding entanglement channels and erasure channels. The second one is the ability to utilize inputs which are entangled across the uses of the channels. Our construction uses a single family of erasure channels with classical memory to achieve the same superactivation-like effect for quantum capacity without any of the ingredients above.

The influence of hyperfine interactions on the tune-out wavelengths of the ${}^{39}$K, ${}^{40}$K, and ${}^{41}$K isotopes of the potassium atom was investigated. The hyperfine interaction of the $4s_{1/2}$ ground state results in a shift and splitting of the primary tune-out wavelength near 769 nm. The $4s_{1/2}$ state hyperfine splittings of the primary tune-out wavelength were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0009, 0.0026, and 0.0005 nm for ${}^{39}$K, ${}^{40}$K, and ${}^{41}$K, respectively. The hyperfine splitting of the $n{p}_J$ levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the $4p_{J,F}$ states. The hyperfine Stark shift for the ground states of all three isotopes was also computed, and the value for ${}^{39}$K was found to be compatible with the previous experiments and the most recent calculation using relativistic many-body perturbation theory.

Momentum imaging measurements from two experiments are presented and interpreted with the aid of ab initio theoretical calculations to describe the dissociative electron attachment (DEA) dynamics of CO${}_2$. The dynamics of the transient negative ions of CO${}_2^{-}$ involve several conical intersections taking part in mechanisms that have only recently been understood. We address the problem of how the 4-eV ${}^2{\Pi }_u$ shape resonance in CO${}_2$ proceeds to dissociate to CO(${}^1{\Sigma }^{+}$) $+$ O${}^{-}$(${}^{2}P$) by DEA.

The photoelectron velocity-map image technique was employed to examine the one-photon detachment of Cu monomer and dimer anions using a linearly polarized infrared femtosecond laser. While the photoelectron angular distribution (PAD) in a single-photon detachment experiment of Cu${}^{-}$ shows no dependence on photon energy, the dimer anion PAD does show a strong dependence on photon energy. As the laser wavelength increases from 532 to 817 nm, the photoelectron angular distributions of the main one-photon detachment channel of the prominent detachment channel of Cu${}_2$${}^{-}$ changes its direction from parallel to the direction of polarization for the 532-nm laser to perpendicular to the direction of polarization for the 817-nm laser. Based upon a numerical analysis of the anisotropy parameters, the relative contributions of the $s$, $p$, and $d$ orbitals are obtained. The fully occupied $d$ orbitals contribute less to the detachment amplitude. The contribution of the $p$ waves to the detachment amplitude increases with the photon energy, while that of $s$ waves decreases, which is in agreement with the prediction of the Wigner threshold law. The relative contributions of the different partial waves, $s$ and $p$, to the detachment amplitude are altered by the excess energy of the detached electron, resulting in the determined shape of the photoelectron angular distributions. Our one-photon photodetachment experiments on the energy-dependent angular distributions of the copper anionic dimers indicate that $s$-$p$ coupling is important to the photodetachment of copper dimer anions, especially at increased photon energies.

We study quantum mechanically the influence of an external laser field on the antihydrogen ($\overline{\mathrm{H}}$) formation cross sections in ground and excited states (2$s$,2$p$) via the three-body recombination process inside a dense plasma of antiprotons and positrons, supposed to be the most efficient mechanism for cold and trapped antihydrogen. The plasma screening is considered in the framework of a Debye- Hückel potential. The laser polarization is chosen to be parallel to the incident momentum of the passive positron. The modifications due to the presence of the laser field are found to be quite significant both quantitatively and qualitatively for all the states. In the presence of a laser, the $\overline{\mathrm{H}}$ formation cross sections are found to be suppressed significantly with respect to the field-free situation particularly in the ground state, while the excited state cross sections are in general enhanced at very low incident energies but are again suppressed at higher energies except for some special cases. The sensitivity of the formation cross sections with respect to the Debye length are also studied both in the laser-assisted and in the field-free situations. At very low incident energies, the ground state multiphoton formation is found to enhance with the increase in Debye screening, while the reverse is true for the excited states. These findings should have important implications for future $\overline{\mathrm{H}}$ studies.

We study the dynamics of a nondegenerate, harmonically trapped Fermi gas following a sudden ramp of the spin-orbit coupling strength using a Boltzmann equation approach. In the absence of interactions and a Zeeman field, we solve the spin-orbit-coupled Boltzmann equation analytically and derive expressions for the phase-space and temporal dynamics of an arbitrary initial spin state. For a fully spin-polarized initial state, the total magnetization exhibits collapse and revival dynamics in time with a period set by the trapping potential. In real space, this corresponds to oscillations between a fully polarized state and a spin helix. To make predictions relevant to current experiments on spin-orbit-coupled Fermi gases, we then numerically study the dynamics in the presence of an additional momentum-independent Zeeman field. We find that the spin helix is robust for weak magnetic fields but disappears for stronger field strengths. Finally, we explore the spin dynamics in the presence of interactions and find that weak interactions enhance the amplitude of the spin helix.

We propose a method to generate and detect large quantum superposition states and arbitrary Fock states for the oscillational mode of an optically levitated nanocrystal diamond. The nonlinear interaction required for the generation of non-Gaussian quantum states is enabled through the spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond. The proposed method allows the generation of large superpositions of nanoparticles with millions of atoms and the observation of the associated spatial quantum interference under reasonable experimental conditions.

We propose an experimentally feasible scheme to prepare tripartite continuous-variable entanglement with the spatial degrees of freedom of photons. The scheme relies on postselection upon the state obtained when one photon of an entangled pair produced by spontaneous parametric down-conversion interferes with a single photon on a 50:50 beam splitter. We show that the presence of genuine tripartite entanglement can be detected by the van Loock–Furusawa criterion.

We analyze the distortion of the molecular frame photoelectron angular distributions of H${}_2$${}^{+}$ ionized by a strong, circularly polarized infrared laser field using classical trajectory Monte Carlo simulations. We find that the nonisotropic field of the molecular ion rotates the final electron momenta. The degree of distortion from the strong-field approximation's predictions is thereby sensitive to the field strength and the internuclear distance but, counterintuitively, does not necessarily decrease for high field strengths. Furthermore, the distortion also depends crucially on the initial momentum of the classical electron after tunneling, while the exact shape of the ionization rate seems to be less important. A trajectory analysis within our simple model allows us to interpret recent experimental results.

We report an experimental and theoretical study of single-molecule inner-shell photoemission measured over an extended range of photon energies. The vibrational intensity ratios $I(\nu =1)/I(\nu =0)$ from the C $1s$ photoelectron spectra of carbon monoxide, although mostly determined by the bond length change upon ionization, are shown to be affected also by photoelectron recoil and by scattering from the neighboring oxygen atom. Static-exchange density functional theory (DFT) is used to encompass all these effects in a unified theoretical treatment. The ab initio calculations show that the vibrational ratio as a function of the photoelectron momentum is sensitive to both the ground-state internuclear distance and its contraction upon photoionization. We present a proof-of-principle application of DFT calculations as a quantitative structural analysis tool for extracting the dynamic and static molecular geometry parameters simultaneously.

Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these systems provide a realization of a single-component one-dimensional Fermi gas with a generalized contact interaction. Using an exact duality between one-dimensional Fermi and Bose gases, we show that when the dipole moment is strong enough, bound many-body states exist, and we calculate the critical coupling strength for the emergence of these states. At higher densities, the Hartree–Fock approximation is accurate, and by combining the two approaches we determine the structure of the phase diagram. The many-body bound states should be accessible in future experiments with ultracold polar molecules.

Landau levels (LLs) are broadened in the presence of a periodic potential, forming a barrier for accurate simulation of the fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight-binding lattice if a particular form of long-range hopping is introduced [Kapit and Mueller, Phys. Rev. Lett. 105, 215303 (2010)]. In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are infinitely many long-range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wave functions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restores the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wave functions is as large as the space spanned by continuum wave functions, and we find the constraints on the magnetic field for this condition to be satisfied. Finally, using these constraints and the first Chern numbers, we identify the bands of the Hofstadter butterfly that correspond to continuum LLs.

We study the non-Markovian effect on the dynamics of the quantum Fisher information (QFI) by exactly solving a model consisting of a qubit system subjects to a zero-temperature reservoir for two different non-Markovian conditions: a high-$Q$ cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap, respectively. The phenomenon that the QFI, namely, the precision of estimation, changes dramatically with the environment structure and is affected by the environment memory effects. We find that revivals and retardation of QFI loss may occur by adjusting the cavity-qubit detuning, in the first case, while partial QFI trapping occurs in nonideal photonic band gaps and the decreasing gap width seriously destroys coherence, thus reducing the precision of estimation. These features make the qubit system in non-Markovian environments a good candidate for implementation of quantum optics schemes and information with high precision.