Laser-induced fluorescence to the electronic ground state $\left(X\right)1^1{\Sigma }^{+}$ of LiNa has been recorded by a Fourier-transform spectrometer. Optical excitations of the LiNa molecules into the $\left(A\right)2{}^1{\Sigma }^{+}$ state were performed with different dye lasers. The spectra showed fluorescence progressions up to $v^{\prime \prime }=44$ of the singlet ground state covering 99.9$\%$ of the potential well. However, searches for fluorescence into the triplet ground state $\left(a\right)1{}^3{\Sigma }^{+}$ induced by spin-orbit coupling in the excited system $\left(b\right)1^3\Pi$–$\left(A\right)2{}^1{\Sigma }^{+}$ were not successful. The potential energy curve of the singlet ground state was determined by direct potential fits with a data set of about 8200 assigned lines using two distinct analytical potential representations. In addition, the isotopologue ${}^6\text{Li}{}^{23}\text{Na}$ was studied for a possible need of Born-Oppenheimer corrections by simultaneous fits of both observed isotopologues from ${}^6$Li and ${}^7$Li. Finally, new data on Feshbach resonances from cold-atom experiments at Heidelberg were included for improving the potential description around the dissociation energy for both electronic states $\left(X\right)1{}^1{\Sigma }^{+}$ and $\left(a\right)1{}^3{\Sigma }^{+}$ of the atom-pair ground-state asymptote.

We have observed 26 interspecies Feshbach resonances at fields up to 2050 G in ultracold ${}^6\text{Li}+{}^{23}\text{Na}$ mixtures for different spin-state combinations. Applying the asymptotic bound-state model to assign the resonances, we found that most resonances have $d$-wave character. This analysis serves as guidance for a coupled-channel calculation, which uses modified interaction potentials to describe the positions of the Feshbach resonances well within the experimental uncertainty and to calculate their widths. The scattering length derived from the improved interaction potentials is experimentally confirmed and deviates from previously reported values in sign and magnitude. We give prospects for ${}^7\text{Li}+{}^{23}\text{Na}$ and predict broad Feshbach resonances suitable for tuning.

We have measured the evolution with depth $z$ of the vicinage effect and Coulomb explosion for H${}_2{}^{+}$ and H${}_3{}^{+}$ molecular ions traversing thick, uniform amorphous targets of Si${}_3$N${}_4$ and SiO${}_2$. High depth resolution is achieved by scanning the energy per nucleus of the incoming molecules $E_b$ around the energy $E_R$ corresponding to narrow resonances in the cross sections of ${}^{18}$O${(p,\alpha )}^{15}$N at 151 keV and in ${}^{15}$N${(p,\alpha \gamma )}^{12}$C at 429 keV. The corresponding reaction yield $Y\left(E_b\right)$ is, to first order, inversely proportional to the stopping force $S_{\mathrm{mol}}$ on the molecular fragments, giving a direct image of the evolution of the vicinage effect and Coulomb explosion with $z$. At the target surface, the vicinage effect enhances the stopping force on the molecules by a factor $\chi >1$. As they penetrate the matter, the distance between the molecule nuclei increases, as a consequence of Coulomb explosion and multiple scattering lateral displacement, and the vicinage effect decreases with depth $z$. The experiment yields information on the screened Coulomb repulsive potential via the repulsion velocity $V^{\lim }$ observed at large $z$, where the distances $R_{ij}$ between the molecule nuclei are large compared to the adiabatic cutoff $R_{\mathrm{ad}}$ (no vicinage effect). We show that the first order view, that $Y\left(Eb\right)$ $\propto S_{\mathrm{mol}}^{-1}$, is profoundly modified by the energy fluctuations induced by the Coulomb explosion and lateral multiple scattering. Our observations are satisfactorily reproduced when modeled using a dynamic screening radius $r_s$ in the range $R_{\mathrm{ad}}$ (for H${}_3{}^{+}$) to $2R_{\mathrm{ad}}$ (for H${}_2{}^{+}$) for the Coulomb explosion and the evolution with $R_{ij}$ of $\chi$ given by the dielectric model for the interaction of the exploding molecules with the target electron gas.

In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the discrete self-trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from quantum information theory, i.e., the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero-temperature case, but considers thermal effects as well.

A laser pulse propagating through the atmosphere self-focuses due to the nonlinear index of refraction modifications from the instantaneous electronic and delayed rotational responses of the air molecules. If the pulse power is sufficient, the focused pulse intensity can surpass the ionization threshold, resulting in a plasma filament. The balance between defocusing due to plasma refraction and focusing due to the instantaneous and delayed responses results in extended propagation at high intensities. Because the rotational response induced by the first pulse (the pump pulse) is periodic in time, owing to quantum-mechanical discreteness of the rotational eigenfrequencies of the molecules, a subsequent laser pulse (the probe pulse), delayed at the recurrence period, experiences a propagating wake of index modification left behind by the previous pulse. Here, we present propagation simulations based on a recent experiment [Varma et al. (unpublished)] showing that axial extension of the plasma filament and probe pulse shaping imposed by the molecular alignment wake are sensitive to probe delay changes of as little as 10 fs.

We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU$\left(N\right)$ Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing $N$ for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all $N$, fixing the initial entropy, or for all $N\lesssim 20$ (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.

We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Rényi entropy, particularly in the case of coarse-grained measurements. We then sharpen a Heisenberg-like uncertainty relation derived previously in [Europhys. Lett. 97, 38003 (2012)] that uses variances and reduces to the usual one in the case of infinite precision measurements. Our sharpened uncertainty relation is meaningful for any amount of coarse graining. That is, there is always a nontrivial uncertainty relation for coarse-grained measurement of the noncommuting observables, even in the limit of extremely large coarse graining.

We report a study of the intensity and time dependence of scintillation produced by weak $\alpha$-particle sources in superfluid helium in the presence of an electric field (0–45 kV/cm) in the temperature range of 0.2 to 1.1 K at the saturated vapor pressure. Both the prompt and the delayed components of the scintillation exhibit a reduction in intensity with the application of an electric field. The reduction in the intensity of the prompt component is well approximated by a linear dependence on the electric field strength with a reduction of 15$\%$ at 45 kV/cm. When analyzed using the Kramers theory of columnar recombination, this electric field dependence leads to the conclusion that roughly 40$\%$ of the scintillation results from species formed from atoms originally promoted to excited states and 60$\%$ from excimers created by ionization and subsequent recombination with the charges initially having a cylindrical Gaussian distribution about the $\alpha$ track of 60 nm radius. The intensity of the delayed component of the scintillation has a stronger dependence on the electric field strength and on temperature. The implications of these data on the mechanisms affecting scintillation in liquid helium are discussed.

Dynamics of electron capture and excitation processes in collisions of H${}^{+}$ with the excited He(2 ${}^{1,3}{L}_m$) atom ($L$ $=$ $S$,$P$) has been studied by using the full quantum-mechanical molecular orbital close-coupling (QMOCC) method with ab initio determined molecular states. 38 singlet and 37 triplet molecular states of the HeH${}^{+}$ system, that asymptotically correlate to the $n$ $=$ 1–4 projectile and target atomic states, have been included in the expansion basis. The shell- and state-selective electron capture and excitation cross sections have been calculated in the 0.01–6 keV/u energy range up to the $n$ $=$ 4 shell and their energy behavior discussed on the basis of identified reaction mechanisms.

Repulsive interactions between particles on a lattice may lead to bound states, so called doublons. Such states may be created by dynamically tuning the interaction strength, e.g. using a Feshbach resonance, from attraction to repulsion. We study the doublon production efficiency as a function of the tuning rate at which the on-site interaction is varied. An expectation based on the Landau-Zener law suggests that exponentially few doublons are created in the adiabatic limit. Contrary to such an expectation, we found that the number of produced doublons scales as a power law of the tuning rate with the exponent dependent on the dimensionality of the lattice. The physical reason for this anomaly is the effective decoupling of doublons from the two-particle continuum for center-of-mass momenta close to the corners of the Brillouin zone. The study of doublon production may be a sensitive tool to extract detailed information about the band structure.

It is generally believed that a dilute spin-$\frac{1}{2}$ Fermi gas with repulsive interactions can undergo a ferromagnetic phase transition to a spin-polarized state at a critical gas parameter ${\left(k_{\mathrm{F}}a\right)}_c$. Previous theoretical predictions of the ferromagnetic phase transition have been based on the perturbation theory, which treats the gas parameter as a small number. On the other hand, Belitz, Kirkpatrick, and Vojta (BKV) have argued that the phase transition in clean itinerant ferromagnets is generically of first order at low temperatures, due to the correlation effects that lead to a nonanalytic term in the free energy. The second-order perturbation theory predicts a first-order phase transition at ${\left(k_{\mathrm{F}}a\right)}_c=1.054$, consistent with the BKV argument. However, since the critical gas parameter is expected to be of order $O\left(1\right)$, perturbative predictions may be unreliable. In this paper we study the nonperturbative effects on the ferromagnetic phase transition by summing the particle-particle ladder diagrams to all orders in the gas parameter. We consider a universal repulsive Fermi gas where the effective range effects can be neglected, which can be realized in a two-component Fermi gas of ${}^6$Li atoms by using a nonadiabatic field switch to the upper branch of a Feshbach resonance with a positive $s$-wave scattering length. Our theory predicts a second-order phase transition, which indicates that ferromagnetic transition in dilute Fermi gases is possibly a counterexample to the BKV argument. The predicted critical gas parameter ${\left(k_{\mathrm{F}}a\right)}_c=0.858$ is in good agreement with the recent quantum Monte Carlo result ${\left(k_{\mathrm{F}}a\right)}_c=0.86$ for a nearly zero-range potential [S. Pilati et al., Phys. Rev. Lett. 105, 030405 (2010)]. We also compare the spin susceptibility with the quantum Monte Carlo result and find good agreement.

Prime factorization is an outstanding problem in arithmetic with important consequences in a variety of fields, most notably cryptography. Here I employ the intriguing analogy between prime factorization and optical interferometry in order to obtain analytic expressions for closely related functions, including the number of distinct prime factors.

A representation of the phase observable in terms of a positive-operator-valued measure for an arbitrary quantum system with a finite Hilbert space is consistently defined. The phase for systems with rational relations between the energy eigenvalue differences is treated explicitly and the phase in the case of the irrational relations is obtained as a well-defined limit of the rational approximations.

Zheng et al. [Zheng, Gao, Ye, and Zhang, Phys. Rev. A 83, 061401(R) (2011)] have measured a strong linear pressure dependence of the nuclear relaxation rate of ${}^3$He in glass cells typically used to generate and/or store polarized ${}^3$He at room and cryogenic temperatures. Their interpretation is that this linear dependence is a general characteristic of paramagnetic wall relaxation, and they offer a theoretical explanation of the effect based on diffusion theory in the bulk with an incorrect boundary condition. We question the physical basis of the boundary condition and suggest some alternate explanations of the observations. Numerous previous studies support a broadly valid pressure-independent model for wall relaxation.

We analyze quantum computation using quantum information stored on two component Bose-Einstein condensates (BECs). We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two-qubit gate operations that can be performed at a time reduced by a factor of $N$, where $N$ is the number of bosons in the BEC. We illustrate the scheme by an application to Grover's algorithm, and discuss possible experimental implementations and decoherence effects.

We calculate the ground state and simulate the dynamics of a finite chain of spins with Ising nearest-neighbor interactions and a Dicke collective spin interaction with a single-mode cavity field. We recover the signatures of first- and second-order phase transitions predicted by mean-field theory, and for small chains, we find significant and nontrivial finite-size effects. Below the first-order phase transition, even quite large spin chains of 30–40 spins give rise to a mean photon number and number fluctuations significantly above the mean-field vacuum result. Near the second-order phase critical point, our calculations reveal photon number fluctuations that grow beyond Poisson statistics with the size of the spin chain. We simulate the stochastic evolution of the system when the cavity output field is subject to homodyne detection. For an initial state close to the first-order phase-transition the random character of the measurement process causes a measurement-induced symmetry breaking in the system. This symmetry breaking occurs on the time scale needed for an observer to gather sufficient information to distinguish between the two possible (mean-field) symmetry-broken states.

We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurement-induced nonlocality, namely, it is the maximal entropy increase after the locally invariant measurements. The relative entropy of nonlocality is upper bounded by the entropy of the measured subsystem. We establish a relationship between the relative entropy of nonlocality and the geometric nonlocality based on the Hilbert-Schmidt norm, and show that it is equal to the maximal distillable entanglement. Several trade-off relations are obtained for tripartite pure states. We also give explicit expressions for the relative entropy of nonlocality for Bell-diagonal states.

We study scalability of quantum computing based on nanomechanical resonators (NAMRs), including the consequences of the effective next-nearest-neighbor spin-spin couplings induced by the NAMRs, NAMR frequency errors, and NAMR-spin coupling errors on the scalability of quantum computing based on NAMRs. We show the fidelity change of the quantum operation due to these errors numerically. Switchable interactions between NAMRs can be achieved by adding control gates. Based on this modification, we present a method to perfectly avoid the next-nearest-neighbor spin-spin couplings and compensate for the negative effects due to the frequency errors and spin coupling errors.

The spectrum of a random laser (RL) may appear either as a set of sharp resonances or as a smooth line superimposed on the fluorescence. Recently, Leonetti, Conti, and Lopez [Nat. Photonics 5, 615 (2011)] accounted for this duality with the onset of a mode-locked regime that is triggered by the increase of both the number of activated modes and of the intermode interaction and is accompanied by a pulse shortening. Here we report an extensive review of the experimental approach used by Leonetti et al., including the sample preparation and the particulars of the setup. Here we describe also the way in which our approach allows us either to set the degree of interaction between modes or to have a certain degree of control over the effective set of resonances brought to lasing. Moreover we report an investigation on the spatial properties of the RL which brings further confirmation of the synchronization picture, whose physical origin is deepened.