We show that the $s$-wave-scattering resonances induced by dipolar interactions in polar molecular gases have a universal large and positive effective range, which is very different from Feshbach resonances previously realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequences in many-body physics. At a high-temperature regime, a positive effective range gives rise to a stronger repulsive interaction energy for positive scattering length, and a weaker attractive interaction energy for negative scattering length. At low temperatures, we study a polaron problem formed by a single-impurity molecule, and we find that the polaron binding energy increases at the BEC side and decreases at the BCS side. All these effects are opposite to narrow Feshbach resonances, where the effective range is negative.

An anomalous light shift in the precession of a ground-state Zeeman coherence is observed: The Larmor frequency increases with the strength of a drive that is blue (red) detuned from a transition out of the lower (upper) energy level. Our measurements are made on ${}^{85}\mathrm{Rb}$ atoms traversing an optical cavity containing a few photons; shifts as large as 1$\%$ per photon are recorded. The anomalous shift arises from an accumulation of phase driven by quantum jumps. It is stochastic and accompanied by broadening.

We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104, 240401 (2010)]. The theory of contextual values is a principled approach to the generalized measurement of observables. It extends the well-established theory of generalized state measurements by bridging the gap between partial state collapse and the observables that represent physically relevant information about the system. To emphasize the general utility of the concept, we first construct the full theory of contextual values within an operational formulation of classical probability theory, paying special attention to observable construction, detector coupling, generalized measurement, and measurement disturbance. We then extend the results to quantum probability theory built as a superstructure on the classical theory, pointing out both the classical correspondences to and the full quantum generalizations of both Lüder's rule and the Aharonov-Bergmann-Lebowitz rule in the process. As such, our treatment doubles as a self-contained pedagogical introduction to the essential components of the operational formulations for both classical and quantum probability theory. We find in both cases that the contextual values of a system observable form a generalized spectrum that is associated with the independent outcomes of a partially correlated and generally ambiguous detector; the eigenvalues are a special case when the detector is perfectly correlated and unambiguous. To illustrate the approach, we apply the technique to both a classical example of marble color detection and a quantum example of polarization detection. For the quantum example we detail two devices: Fresnel reflection from a glass coverslip, and continuous beam displacement from a calcite crystal. We also analyze the three-box paradox to demonstrate that no negative probabilities are necessary in its analysis. Finally, we provide a derivation of the quantum weak value as a limit point of a pre- and postselected conditioned average and provide sufficient conditions for the derivation to hold.

In this study, we explicitly calculate information and fidelity of an $r$-rank projective measurement on a completely unknown state in a $d$-dimensional Hilbert space. We also show a tradeoff between information and fidelity at the level of a single outcome and discuss the efficiency of measurement with respect to fidelity.

The relationship between orientation-to-alignment conversion (a form of atomic polarization evolution induced by an electric field) and the phenomenon of spin squeezing is demonstrated. A “stretched” state of an atom or molecule with maximum angular-momentum projection along the quantization axis possesses orientation and is a quantum-mechanical minimum-uncertainty state, where the product of the equal uncertainties of the angular-momentum projections on two orthogonal directions transverse to the quantization axis is the minimum allowed by the uncertainty relation. Application of an electric field for a short time induces orientation-to-alignment conversion and produces a spin-squeezed state, in which the quantum state essentially remains a minimum-uncertainty state, but the uncertainties of the angular-momentum projections on the orthogonal directions are unequal. This property can be visualized using the angular-momentum probability surfaces, where the radius of the surface is given by the probability of measuring the maximum angular-momentum projection in that direction. Brief remarks are also given concerning collective-spin squeezing and quantum nondemolition measurements.

In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying it, we obtain indecomposable optimal witnesses that have no spanning property. These also provide examples that support a recent conjecture saying that the so-called structural physical approximations to optimal positive maps (optimal entanglement witnesses) give entanglement breaking maps (separable states).

We present a theoretical analysis of methods to synthesize entangled states of two superconducting resonators. These methods use experimentally demonstrated interactions of resonators with artificial atoms and offer efficient routes to generate nonclassical states. We analyze physical implementations, energy level structure, and the effects of decoherence through detailed dynamical simulations.

By using the Rashba Hamiltonian, the evolution of entanglement of two spin-$\frac{1}{2}$ charged particles in a homogeneous electric field is investigated. It is shown that Bell states become disentangled within finite time and there exist unentangled spin states that stay unentangled during evolution. The correlations among spin-spin, momentum-momentum, and spin-momentum entanglements are discussed in detail. Moreover, a state is constructed to illustrate the fact that spin-momentum entanglement is solely a dynamical effect that can arise without any entanglement of the other degree of freedom. The results are also extended to the mixed states where Werner states are treated.

We investigate an extended version of the quantum Ising model which includes beyond-nearest-neighbor interactions and an additional site-dependent longitudinal magnetic field. Treating the interaction exactly and using perturbation theory in the longitudinal field, we calculate the energy spectrum and find that the presence of beyond-nearest-neighbor interactions enhances the minimum gap between the ground state and the first excited state, irrespective of the nature of decay of these interactions along the chain. The longitudinal field adds a correction to this gap that is independent of the number of qubits. We discuss the application of our model to implementing specific instances of three-satisfiability problems (Exact Cover) and make a connection to a chain of flux qubits.

Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (ELOCC) are studied. We propose an alternative method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground-state local convertibility in the one-dimensional transverse field Ising model, $XY$ model and $XXZ$ model. It is found that the ELOCC convertibility suddenly changes at the phase transition points. In the transverse field Ising model the ELOCC convertibility between the first-excited state and the ground state are also distinct for different phases. The relation between the order of quantum phase transitions and the local convertibility is discussed.

We introduce a symmetrization technique that can be used as an extra step in some continuous-variable quantum key distribution protocols. By randomizing the data in phase space, one can dramatically simplify the security analysis of the protocols, in particular in the case of collective attacks. The main application of this procedure concerns protocols with postselection, for which security was established only against Gaussian attacks until now. Here, we prove that under some experimentally verifiable conditions, Gaussian attacks are optimal among all collective attacks.

The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. In the present work, we used configuration interaction $+$ coupled-cluster method to evaluate polarizabilities of the $6s^2{}^1{S}_0$ and $6s6p{}^3{P}_0$ states of the Tl${}^{+}$ ion; we find ${\alpha }_0{(}^1{S}_0)=19.6$ a.u. and ${\alpha }_0{(}^3{P}_0)=21.4$ a.u. The resulting BBR shift of the $6s6p{}^3{P}_0-6s^2{}^1{S}_0$ Tl${}^{+}$ transition at 300 K is $\Delta {\nu }_{\mathrm{BBR}}=-0.0157\left(16\right)$ Hz. This result demonstrates that near cancellation of the ${}^1{S}_0$ and ${}^3{P}_0$ state polarizabilities in divalent B${}^{+}$, Al${}^{+}$, and In${}^{+}$ ions of group IIIB [M. S. Safronova et al., Phys. Rev. Lett. 107, 143006 (2011)] continues for much heavier Tl${}^{+}$, leading to anomalously small BBR shift for this system. This calculation demonstrates that the BBR contribution to the fractional frequency uncertainty of the Tl${}^{+}$ frequency standard at 300 K is $1\times {10}^{-18}$. We find that Tl${}^{+}$ has the smallest fractional BBR shift among all present or proposed frequency standards with the exception of Al${}^{+}$.

Differential cross sections for xenon are presented for low-energy ($e$,2$e$) measurements under doubly symmetric kinematics, for incident energies between 5 and 40 eV above the ionization threshold. A range of geometries were investigated from coplanar through to the perpendicular plane, with the outgoing electrons having equal energies and angles. The cross sections were monitored as the geometry changed, in order to identify the evolution of the observed structures. The data for an excess energy of 10 eV are compared to theory, and significant differences are found. Further calculations are required to aid in interpretation of the full range of cross sections that have been measured.

Ion emissions from clusters in intense ultrashort laser fields have been studied predominantly using time-of-flight (TOF) spectroscopy so far. Assuming atomic ion emission, arrival time signal is converted to a charge-integrated kinetic-energy spectrum. We present here a Thomson parabola spectrum that decrypts the charge-integrated energy distribution to the charge-resolved kinetic-energy spectra (CRKES). TOF measurements compare well with the spectrum generated by encrypting back the CRKES. A quantitative measure of ionization probabilities of Ar${}_{36000}$ clusters to varied charge states at $7\times {10}^{15}$ W cm${}^{-2}$ is compared with three-dimensional microscopic particle-in-cell simulations. A good agreement between these detailed measurements and the simulations shows the possibility for the retrieval of charge distribution within a nanocluster.

We investigate picosecond cooperative emission in an ensemble of rubidium atoms coherently excited by 100-fs laser pulses that are three-photon resonant to the $6P$-$5S$ transition. The emitted 420-nm light is recorded by a streak camera with 2-ps resolution. The resultant pulse shape shows ringing typical for superradiance in extended sample. The pulse shape is measured as a function of input power and is compared to the solutions of Maxwell-Bloch equations. The observed superradiance, which is in the low-excitation regime, is found to be closely related to optical precursor behavior.

We obtain a generalization of the nonrelativistic space-translation transformation to the Dirac equation in the case of a unidirectional laser pulse. This is achieved in a quantum-mechanical representation connected to the standard Dirac representation by a unitary operator $T$ transforming the Foldy-Wouthuysen free-particle basis into the Volkov spinor basis. We show that a solution of the transformed Dirac equation containing initially low momenta $p$ ($p/mc\ll 1)$ will maintain this property at all times, no matter how intense the field or how rapidly it varies (within present experimental capabilities). As a consequence, the transformed four-component equation propagates independently electron and positron wave packets, and in fact the latter are propagated via two two-component Pauli equations, one for the electron, the other for the positron. These we shall denote as the Pauli low-momentum regime (LMR) equations, equivalent to the Dirac equation for the laser field. Successive levels of dynamical accuracy appear depending on how accurately the operator $T$ is approximated. At the level of accuracy considered in this paper, the Pauli LMR equations contain no spin matrices and are in fact two-component Schrödinger equations containing generalized time-dependent potentials. The effects of spin are nevertheless included in the theory because, in the calculation of observables which are formulated in the laboratory frame, use is made of the spin-dependent transformation operator $T$. In addition, the nonrelativistic limit of our results reproduces known results for the laboratory frame with spin included. We show that in intense laser pulses the generalized potentials can undergo extreme distortion from their unperturbed form. The Pauli LMR equation for the electron is applicable to one-electron atoms of small nuclear charge$(\alpha Z\ll 1)$ interacting with lasers of all intensities and frequencies $\omega \ll m{c}^2.$

We consider the phenomenon of spin-pattern formation reported in recent experiments in spin-2 rubidium condensate [J. Kronjäger, C. Becker, P. Soltan-Panahi, K. Bongs, and K. Sengstock, Phys. Rev. Lett. 105, 090402 (2010)]. To understand the mechanism underlying the process and explain the parameters such as pattern period and growth rate, we employ the Bogoliubov–de Gennes equations and an alternative method based on energy conservation and the uncertainty principle. While the two methods agree in the spin-1 case, only the second method can provide analytical results in the spin-2 case. Using these results, we explain the occurrence of two regimes, the spin-dominated and the Zeeman-dominated, with the prevalence of spin-wave modes and quadrupole modes, respectively. We obtain very good agreement between theory and experiment for the pattern period and growth rate over several orders of magnitude of the magnetic field strength.

We propose a method for controlling the atomic currents of a two-component Bose-Einstein condensate in a double well by applying an external field to the atoms in one of the potential wells. We study the ground-state properties of the system and show that the directions of spin currents and net-particle tunneling can be manipulated by adiabatically varying the coupling strength between the atoms and the field. This system can be used to study spin and tunneling phenomena across a wide range of interaction parameters. In addition, spin-squeezed states can be generated. It is useful for quantum information processing and quantum metrology.

Inspired by the recent creation of a honeycomb optical lattice and the realization of a Mott-insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, Floquet theory may be applied to derive a time-independent Hamiltonian. In this effective description, the hopping parameters are renormalized by a Bessel function, which depends on the shaking direction, amplitude, and frequency. Consequently, the hopping parameters can vanish and even change sign, in an anisotropic manner, thus yielding different band structures. Here, we study the merging and the alignment of Dirac points and dimensional crossovers from the two-dimensional system to one-dimensional chains and zero-dimensional dimers. We also consider next-nearest-neighbor hopping, which breaks the particle-hole symmetry and leads to a metallic phase when it becomes dominant over the nearest-neighbor hopping. Furthermore, we include weak repulsive on-site interactions and find the density profiles for different values of the hopping parameters and interactions, both in a homogeneous system and in the presence of a trapping potential. Our results may be experimentally observed by use of momentum-resolved Raman spectroscopy.

We systematically study stationary light pulses formed in cold atomic media based on the effect of electromagnetically induced transparency (EIT) with counterpropagating laser fields. In contrast to hot media, the formation of stationary light in cold media is not straightforward. Detrimental coherences of high spatial frequencies can be excited which are naturally suppressed in hot media. We demonstrate numerically that these excitations prevent the formation of stationary light in cold media. We further present numerical and experimental results which show that these excitations can be dynamically suppressed in a medium of nonstationary atoms by reducing the width of the EIT transparency window below the typical Doppler shifts present in the medium. This provides an increased interaction time of the light pulses with the medium and enhances the efficiency of nonlinear optical interactions.