In the context of the development of new sources of strong laser pulses in the mid-infrared region new nonperturbative methods for analysis of strong-laser-field induced or assisted atomic and molecular processes are welcome. We formulate such a theory of above-threshold ionization by a strong low-frequency laser pulse. We call this theory the low-frequency approximation (LFA). A detailed derivation of the LFA, both for short and long laser pulses, is given. As an example the LFA is applied to the analysis of recently discovered low-energy structures in the above-threshold ionization spectra of atoms ionized by long-wavelength laser pulses. It was found that these low-energy structures are caused by the forward soft recollision of the ionized electrons with the parent ion which is enhanced by the Coulomb effect.

Atomic ionization by intense mid-infrared (mid-IR) pulses produces low-electron-energy features that the strong-field approximation, which is expected to be valid in the tunneling ionization regime characterized by small Keldysh parameters $\left(\gamma \ll 1\right)$, cannot describe. These features include the low-energy structure (LES), the very-low-energy structure (VLES), and the more recently found zero-energy structure (ZES). They result from the interplay between the laser electric field and the atomic Coulomb field which controls the low-energy spectrum also for small $\gamma$. In the present joint experimental and theoretical study we investigate the vectorial momentum spectrum of photoelectrons emitted from an Ar gas target at very low energies. Using a reaction microscope optimized for the detection of very-low-energy electrons, we have performed a thorough study of the three-dimensional momentum spectrum well below 1 eV. Our measurements are complemented by quantum and classical simulations, which allow for an interpretation of the LES and VLES and of the ZES in terms of two-dimensional Coulomb focusing and recapture into Rydberg states, respectively.

We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e., low-frequency squeezing), (2) two-mode squeezed optical vacuum (i.e., high-frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.

We study two species of particles in two dimensions interacting by isotropic short-range potentials with the interspecies potential fine-tuned to a $p$-wave resonance. Their universal low-energy physics can be extracted by analyzing a properly constructed low-energy effective field theory with the renormalization group method. Consequently, a three-body system consisting of two particles of one species and one of the other is shown to exhibit the super Efimov effect, the emergence of an infinite tower of three-body bound states with orbital angular momentum $\ell =\pm 1$ whose binding energies obey a doubly exponential scaling, when the two particles are heavier than the other by a mass ratio greater than 4.034 04 for identical bosons and 2.414 21 for identical fermions. With increasing the mass ratio, the super Efimov spectrum becomes denser which would make its experimental observation easier. We also point out that the Born-Oppenheimer approximation is incapable of reproducing the super Efimov effect, the universal low-energy asymptotic scaling of the spectrum.

We investigate the metastability of a ferromagnetic spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional rotating ring trap by solving the spin-1 Gross-Pitaevskii equation. We find analytical solutions that exhibit spin textures. By performing linear stability analysis, it is shown that the solutions can become metastable states. We also find that the number of Nambu-Goldstone modes changes at a certain rotation velocity without changing the continuous symmetry of the order parameter.

We propose a method of joint interrogation in a single atom interferometer which overcomes the dead time between consecutive measurements in standard cold atomic fountains. The joint operation enables for a faster averaging of the Dick effect associated with the local oscillator noise in clocks and with vibration noise in cold atom inertial sensors. Such an operation allows one to achieve the lowest stability limit due to atom shot noise. We demonstrate a multiple joint operation in which up to five clouds of atoms are interrogated simultaneously in a single setup. The essential feature of multiple joint operation, demonstrated here for a microwave Ramsey interrogation, can be generalized to go beyond the current stability limit associated with dead times in present-day cold atom interferometer inertial sensors.

We present a generalized theory based on one-dimensional Maxwell-Bloch equations to study the amplification process of an inner-shell photoionization-pumped atomic x-ray laser. Focusing an x-ray free-electron laser beam in an elongated neon-gas target results in a strong exponential amplification of $K\alpha$ fluorescence, as recently demonstrated [N. Rohringer et al., Nature (London) 481, 488 (2012); C. Weninger et al., Phys. Rev. Lett. 111, 233902 (2013)]. Here, we present an in-depth theoretical study of the amplification process that goes beyond the previous theory based on a rate-equation approach. We study the evolution of the pulse characteristics during the amplification process for transform-limited Gaussian and broadband self-amplified spontaneous-emission pump pulses. We discuss the impact of the gain-dependent group velocity on the emitted x-ray radiation and the resulting gain-guiding effects. A thorough analysis of the spectral and temporal properties of the emitted radiation is presented, including higher-order field-correlation functions, to characterize the ensemble of emitted x-ray pulses.

For a system of two spatially separated qubits (two-level atoms) coupled to a one-dimensional waveguide we have described the time evolution of singly or doubly excited states of the atomic subsystem. When the interatomic distance $l$ takes special (“resonant” or “antiresonant”) values, the singly excited system of resonant atoms can form metastable (dark) states. If $l$ slightly deviates from one of the special values or the atomic frequencies do not coincide, the dark states slowly decay and we have calculated the decay rate. Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay but, with a finite probability, can evolve (with the emission of a single photon) to one of the metastable singly excited states. Metastable states of pairs of qubits may find applications (e.g., as memory elements) in information processing or as detectors sensitive to external perturbations.

We report an experimental demonstration of entangling two separable photonic ququarts using linear optical elements. Each ququart is implemented by using the dichotomic spatial and polarization modes of a single photon. By interfering two independent ququarts at a polarizing beam splitter, we experimentally generate entangled ququarts.

The photon-number statistics from resonance fluorescence of a two-level atom near a metal nanosphere driven by a laser field with finite bandwidth is studied theoretically. Our analysis shows that all interesting physics here takes place in a small area around the nanosphere where the near field and the atom-nanosphere coupling essentially affect the radiative properties of the atom. Computer modeling estimates this area roughly as $r\le 2a$ $(r$ is the distance from the center of the nanosphere to the atom), with $a$ being the radius of the nanosphere. At the larger distances, the influence of the nanoparticle vanishes and the atom tends to behave similarly to that in free space. It is shown that the distribution function $p(n,T)$ of the emission probability of $n$ photons in a given time interval $T$ in steady-state resonance fluorescence drastically depends on the atom location around the nanosphere for $r\le 2a$, featuring a characteristic twist in the ridgelike dependence and a convergence time of up to $9\mu \text{s}$, two orders of magnitude slower than for the atom in free space. At large distances, the distribution converges to a Gaussian one, as for the atom in free space. The typical convergence time scale at large distances $r>2a$ tends to the convergence time of the atom in free space. There are also two areas symmetrical around the nanosphere in which $\Omega \sim \gamma$ and the convergence time goes to zero. This behavior is determined by the interplay of the radiative and nonradiative decay rates of the atom due to the coupling with the metal nanosphere and by the near-field intensity. Additional parameters are the normalized laser frequency detuning from the atomic resonance and the bandwidth of the incoming laser field.

Propagation of a two-photon pulse in a waveguide coupled to a two-level system (TLS) is studied. The pulse is formed by two spatially separated identical wave packets. A set of equations governing the dynamics of the photon distribution in the configuration-momentum space is derived and solved. It is shown that the distribution function can be negative, which manifests its quasiprobability nature. A spectrum of the reflected light is found to be narrower than that of the transmitted light that features a pronounced filtering effect. Average numbers of the transmitted and reflected photons and their variances are shown to be dependent not only on the pulse widths and the light-TLS interaction but also on the pulse separation that can serve as an effective controlling parameter. Our approach is generalized for the case of an $n$-photon Fock state.

We present a criterion that determines whether a fermionic state is a convex combination of pure Gaussian states. This criterion is complete and characterizes the set of convex-Gaussian states from the inside. If a state passes a program it is a convex-Gaussian state and any convex-Gaussian state can be approximated with arbitrary precision by states passing the criterion. The criterion is presented in the form of a sequence of solvable semidefinite programs. It is also complementary to the one developed by de Melo, Ćwikliński, and Terhal, which aims at characterizing the set of convex-Gaussian states from the outside. Here we present an explicit proof that criterion by de Melo et al. is complete by estimating a distance between an $n$-extendible state, a state that passes the criterion, to the set of convex-Gaussian states.

We propose a two-step approach to realize a multiqubit phase gate in circuit QED beyond the rotating-wave approximation. The multiqubit gate can be implemented in a few nanoseconds, which is much faster than that under the rotating-wave approximation. Also the operation time of the gate is independent of the number of qubits. Due to the absence of the resonator degree of freedom in the effective Hamiltonian, our scheme is insensitive to the initial state of the resonator and immune to the leakage of photons. Numerical simulation shows that the scheme is robust against the main decoherence sources.

We present spectra of ultracold ${}^7\mathrm{Li}{}^{85}\mathrm{Rb}$ molecules in their electronic ground state formed by spontaneous decay of weakly bound photoassociated molecules. Beginning with atoms in a dual-species magneto-optical trap, weakly bound molecules are formed in the 4(1) electronic state, which corresponds to the $B^1\Pi$ state at short range. These molecules spontaneously decay to the electronic ground state and we use resonantly enhanced multiphoton ionization to determine the vibrational population distribution in the electronic ground states after spontaneous emission. Many of the observed lines from the spectra are consistent with transitions from the $X^1{\Sigma }^{+}$ ground electronic state to either the $B^1\Pi$ or the $D^1\Pi$ electronic state that has been previously observed, with levels possibly as low as $X^1{\Sigma }^{+}(v^{\prime \prime }=2)$ being populated. We do not observe decay to weakly bound vibrational levels of the $X^1{\Sigma }^{+}$ or $a^3{\Sigma }^{+}$ electronic state in the spectra. We also deduce a lower bound of $3900 \mathrm{cm}{}^{-1}$ for the dissociation energy of the $\mathrm{LiRb}{}^{+}$ molecular ion.

Fully relativistic calculations are presented for the double $K$-shell photoionization cross section for several neutral medium-$Z$ atoms, from magnesium ($Z=10$) up to silver ($Z=47$). The calculations take into account all multipoles of the absorbed photon as well as the retardation of the electron-electron interaction. The approach is based on the partial-wave representation of the Dirac continuum states and uses the Green's-function technique to represent the full Dirac spectrum of intermediate states. The method is strictly gauge invariant, which is used as an independent cross-check of the computational procedure. The calculated ratios of the double-to-single $K$-shell ionization cross sections are compared with the experimental data and with previous computations.

We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices, and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential decay of the vortex number is quantitatively well described by a rate equation consisting of one-body and two-body decay terms. In our measurement, we find that the local two-body decay rate is closely proportional to $T^2/\mu$, where $T$ is the temperature and $\mu$ is the chemical potential.

We discuss singularities in the spectrum of driven many-body spin systems. In contrast to undriven models, the driving allows us to control the geometry of the quasienergy landscape. As a consequence, one can engineer singularities in the density of quasienergy states by tuning an external control. We show that the density of levels exhibits logarithmic divergences at the saddle points, while jumps are due to local minima of the quasienergy landscape. We discuss the characteristic signatures of these divergences in observables such as the magnetization, which should be measurable with current technology.

We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.

The relativistic coupled-clusters method combined with the generalized relativistic effective core potential approach and nonvariational one-center restoration technique is applied to evaluation of parameters of the spin-rotational effective Hamiltonian in lead monofluoride to study the effects of violation of time-reversal invariance $\left(T\right)$ and space parity $\left(P\right)$ in PbF. The obtained hyperfine structure constants, $A_{\left|\right|}=9942$ MHz and $A_{\perp }=-7174$ MHz, are stable with respect to the improvement of the correlation treatment, and they are in very good agreement with the experimental data, $A_{\left|\right|}=10147$ MHz and $A_{\perp }=-7264$ MHz [R. J. Mawhorter, B. S. Murphy, A. L. Baum, T. J. Sears, T. Yang, P. M. Rupasinghe, C. P. McRaven, N. E. Shafer-Ray, L. D. Alphei, and J.-U. Grabow, Phys. Rev. A 84, 022508 (2011); A. N. Petrov, L. V. Skripnikov, A. V. Titov, and R. J. Mawhorter, Phys. Rev. A 88, 010501(R) (2013)]. This is essential to the important task of verifying the value of effective electric field $E_{\mathrm{eff}}=40$ GV/cm, the parameter of $P$-odd interaction $W_P=-1213$ Hz, and the parameter of $T,P$-odd pseudoscalar-scalar electron-nucleus interaction $W_{T,P}=91$ kHz, which are of primary interest in the Brief Report.

We study a method of generating Bell inequalities by using group actions of single-generator Abelian groups. Two parties, Alice and Bob, each make one of $M$ possible measurements on a system, with each measurement having $K$ possible outcomes. The probabilities for the outcomes of these measurements are $P(a_j=k,b_{j^{\prime }}=k^{\prime })$, where $j,j^{\prime }\in \{1,2,...,M\}$ and $k,k^{\prime }\in \{0,1,...,K-1\}$. The sums of some subsets of these probabilities have upper bounds when the probabilities result from a local, realistic theory that can be violated if the probabilities come from quantum mechanics. In our case the subsets of probabilities are generated by a group action, in particular, a representation of a single-generator group acting on product states in a tensor-product Hilbert space. We show how this works for several cases, including $M=2$, $K=3$, and general $M$, $K=2$. We also discuss the resulting inequalities in terms of nonlocal games.