We study the nondemolition mapping of collective quantum coherence onto a cavity light field in a superradiant, cold-atom ${}^{87}$Rb Raman laser. We show theoretically that the fundamental precision of the mapping is near the standard quantum limit on phase estimation for a coherent spin state, $\Delta \varphi =1/\sqrt{N}$, where $N$ is the number of atoms. The associated characteristic measurement time scale ${\tau }_W\propto 1/N$ is collectively enhanced. The nondemolition nature of the measurement is characterized by only 0.5 photon recoils deposited per atom due to optical repumping in a time ${\tau }_W$. We experimentally realize conditional Ramsey spectroscopy in our superradiant Raman laser, compare the results to the predicted precision, and study the mapping in the presence of decoherence, far from the steady-state conditions previously considered. Finally, we demonstrate a hybrid mode of operation in which the laser is repeatedly toggled between active and passive sensing.

We employ a dressed-state approach to perform a study on the behavior of the uncertainty principle for a system in a heated cavity. We find, in a small cavity for a given temperature, an oscillatory behavior of the momentum-coordinate product $\left(\Delta p\right)\left(\Delta q\right)$, which attains periodically finite absolute minimum (maximum) values, no matter how large the elapsed time is. This behavior is in sharp contrast to what happens in free space, where the product $\left(\Delta p\right)\left(\Delta q\right)$ tends asymptotically, for each temperature, to a constant value, independent of time.

Utilizing operational dynamic modeling [D. I. Bondar et al., Phys. Rev. Lett. 109, 190403 (2012)], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities are also revealed, including the nonexistence of the free particle and ambiguity in defining potential forces. Non-Hermitian mechanics is shown to have the same problems. This work compromises a popular belief that finite-dimensional mechanics is a straightforward discretization of the corresponding infinite-dimensional formulation.

In the present work, we explore the thermal entanglement between spin and orbital angular momentum in a rare-earth ion. A witness, based on the magnetic susceptibility and capable of revealing entanglement between these two angular momenta of different nature, is introduced. We found entanglement temperatures of 322 K for promethium and 715 K for samarium. These high temperatures make interesting the use of rare-earth in applications of quantum-information processes at room temperature.

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.

Using resonant two-step laser excitation of trapped ${}^{232}$Th${}^{+}$ ions, we observe 43 previously unknown energy levels within the energy range from $7.3$ to $8.3$ eV. The high density of states promises a strongly enhanced electronic bridge excitation of the ${}^{229m}$Th nuclear state that is expected in this energy range. From the observation of resonantly enhanced three-photon ionization of Th${}^{+}$, the second ionization potential of thorium can be inferred to lie within the range between 11.9 and 12.3 eV. Pulsed laser radiation in a wide wavelength range from 237 to 289 nm is found to provide efficient photodissociation of molecular ions that are formed in reactions of Th${}^{+}$ with impurities in the buffer gas, leading to a significantly increased storage time for Th${}^{+}$ in the ion trap.

A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are defined using the results of ab initio calculations of the diagonal and nondiagonal matrix elements of the one-loop QED operator with H-like wave functions. The model operator can be easily included in any calculations based on the Dirac-Coulomb-Breit Hamiltonian. The efficiency of the method is demonstrated by comparison of the model QED operator results for the Lamb shifts in many-electron atoms and ions with exact QED calculations.

We numerically model the dissociation dynamics of the noble-gas dimer ions He${}_2^{+}$, Ne${}_2^{+}$, Ar${}_2^{+}$, Kr${}_2^{+}$, and Xe${}_2^{+}$ in ultrashort pump and probe laser pulses of different wavelengths. Our calculations reveal a distinguished “gap” in the kinetic energy spectra, observed experimentally for the Ar${}_2$ dimer [J. Wu et al., Phys. Rev. Lett. 110, 033005 (2013)], for all noble-gas dimers for appropriate wavelength combinations. This striking phenomenon can be explained by the dissociation of dimer ions on dipole-coupled Born-Oppenheimer adiabatic potential curves. Comparing pump-probe-pulse-delay-dependent kinetic-energy-release spectra for different noble-gas dimer cations of increasing mass, we discuss increasingly prominent (i) fine-structure effects in and (ii) classical aspects of the nuclear vibrational motion.

Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second order in the random potential strength and obtain analytic results for the disorder ensemble averages of both the condensate and the superfluid depletion, the equation of state, and the sound velocity. For a pure contact interaction and a vanishing correlation length, we reproduce the seminal results of Huang and Meng, which were originally derived within a Bogoliubov theory around a disorder-averaged background field. For dipolar interaction and isotropic Lorentzian-correlated disorder, we obtain results which are qualitatively similar to the case of an isotropic Gaussian-correlated disorder. In the case of an anisotropic disorder, the physical observables show characteristic anisotropies which arise from the formation of fragmented dipolar condensates in the local minima of the disorder potential.

We consider, within the classical theory of electromagnetic coherence, the spectral coherence properties of a field emanating from an aperture in a blackbody cavity. Spatial coherence and polarization are assessed both in the aperture and in its far zone. We derive an expression for the full $3\times 3$ cross-spectral density matrix of the field in the opening and discuss the validity of some related results given in the literature. The aperture field serves as a finite, planar secondary source whose transverse coherence length is found to be of the order of the wavelength and which is unpolarized in the three-dimensional sense. The far field is obtained by propagating each of the three source-field components separately, resulting in the evaluation of the far-field spatial coherence in any pair of directions, paraxial or nonparaxial. We show that in the paraxial case, the coherence properties coincide with those obtained for a planar, secondary source which is spatially $\delta$-correlated and unpolarized. The results can find applications in the modeling of thermal sources and in the propagation of natural light fields.

We propose a scheme to generate (3+1)-dimensional slow-light Airy wave packets in a resonant $\Lambda$-type three-level atomic gas via electromagnetically induced transparency. We show that in the absence of dispersion the Airy wave packets formed by a probe field consist of two Airy wave packets accelerated in transverse directions and a longitudinal Gaussian pulse with a constant propagating velocity lowered to ${10}^{-5}c$ ($c$ is the light speed in vacuum). We also show that in the presence of dispersion it is possible to generate another type of slow-light Airy wave packet consisting of two Airy beams in transverse directions and an Airy wave packet in the longitudinal direction. In this case, the longitudinal velocity of the Airy wave packet can be further reduced during propagation. Additionally, we further show that the transverse accelerations (or bending) of the both types of slow-light Airy wave packets can be completely eliminated and the motional trajectories of them can be actively manipulated and controlled by using a Stern-Gerlach gradient magnetic field.

The quantum dynamics of arbitrary $N$-level systems, including dissipative systems, are modeled exactly here by the dynamics of classical coupled oscillators. A one-to-one correspondence is established between the quantum states and the positions of the oscillators. Quantum coherence, expectation values, and measurement probabilities for system observables can therefore be realized from the corresponding classical states. Although the well-known equivalence [SU(2), SO(3) homomorphism] of two-level quantum dynamics to a rotation in real, physical space cannot be generalized to arbitrary $N$-level systems, the representation of quantum dynamics by a system of coupled harmonic oscillators in one physical dimension $is$ general for any $N$. The time evolution of an $N$-level system [generated by a complex element of the SU($N$) group], is first represented as the rotation of a real state vector in (unphysical) hyperspace, as previously known for density matrix states and also extended here to include Schrödinger states. The resulting rotor in $n$ Euclidean dimensions [the rotation group SO($n$)] is then mapped directly to $n$ oscillators in one physical dimension, which significantly reduces the level of abstraction required to visualize quantum dynamics compared to vector models or generalized Bloch spheres in higher dimensions. The number of such oscillators needed to represent $N$-level systems scales as $N^2$ for the density matrix formalism but increases only linearly with $N$ for Schrödinger states. Values for the classical coupling constants are readily derived from the system Hamiltonian, allowing construction of classical mechanical systems that provide insight into the dynamics of abstract quantum systems (new dynamical invariants) as well as a metric for characterizing the interface between quantum and classical mechanics. A distinctive attribute of the quantum-classical connection as presented here is the necessity for both positive and negative couplings and, in the case of dissipative systems, antisymmetric couplings.

The question of testing the nonlocality of a single photon has raised much debate over the last years. The controversy is intimately related to the issue of providing a common reference frame for the observers to perform their local measurements. Here we address this point by presenting a simple scheme for demonstrating the nonlocality of a single photon which does not require a shared reference frame. Specifically, Bell inequality violation can be obtained with certainty with unaligned devices, even if the relative frame fluctuates between each experimental run of the Bell test. Our scheme appears feasible with current technology and may simplify the realization of quantum communication protocols based on single-photon entanglement.

An experimental demonstration of two-qutrit state tomography via one-qutrit symmetric informationally complete positive operator-valued measure (SIC-POVM) is presented. A two-qutrit state is encoded in the transversal paths of a spontaneous parametric down-converted photon pair. A spatial light modulator allows us to implement the necessary 81 POVM elements to reconstruct the state. The quality of the reconstruction is evaluated by comparing independent measurements with the predicted results calculated with the reconstructed state. Entanglement in the system is calculated via negativity and generalized robustness from the two-qutrit reconstructed density operator.

We propose an alternative technique for numerically renormalizing quantum field theories based on their Hamiltonian formulation. This method is nonperturbative in nature and, therefore, exact to all orders. It does not require any correlation functions or Feynman diagrams. We illustrate this method for a model Yukawa-like theory describing the interaction of electrons and positrons with model photons in one spatial dimension. We show that, after mass renormalization of the fermionic and bosonic single-particle states, all other states in the Fock space have finite energies, which are independent of the momentum cutoff.

The traditional quantum adiabatic condition is viewed as a first-order approximation to guarantee the adiabatic evolution. However, its application may lead to inconsistency in certain cases. Here, based on the Green's function and partial resummarization method, we derive a more powerful adiabatic condition. This adiabatic condition bears a clear physical sense and is free of the former inconsistency. The methods we adopt in this paper also provide a natural framework to discuss adiabaticity in more general settings.

A relativistic description of the Kapitza-Dirac effect in the so-called Bragg regime with two and three interacting photons is presented by investigating both numerical and perturbative solutions of the Dirac equation in momentum space. We demonstrate that spin flips can be observed in the two-photon and the three-photon Kapitza-Dirac effects for certain parameters. During the interaction with the laser field the electron's spin is rotated, and we give explicit expressions for the rotation axis and the rotation angle. The off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not exactly fulfilled, is described by a generalized Rabi theory. We also analyze the in-field quantum dynamics as obtained from the numerical solution of the Dirac equation.

We investigate the superadditivity property of quantum-correlating power (QCP), which is the power of generating quantum correlation by a local quantum channel. We prove that, when two local quantum channels are used in parallel, the QCP of the composed channel is no less than the sum of QCP of the two channels. For local channels with zero QCP, the superactivation of QCP is a fairly common effect, and it is proven to exist widely except for the trivial case where both of the channels are completely decohering channels or unitary operators. For general quantum channels, we show that the (not-so-common) additivity of QCP can be observed for the situation where a measuring-and-preparing channel is used together with a completely decohering channel.

We investigate the loss of nonclassicality and non-Gaussianity of a single-mode state of the radiation field in contact with a thermal reservoir. The damped density matrix for a Fock-diagonal input is written using the Weyl expansion of the density operator. Analysis of the evolution of the quasiprobability densities reveals the existence of two successive characteristic times of the reservoir which are sufficient to assure the positivity of the Wigner function and, respectively, of the $P$ representation. We examine the time evolution of non-Gaussianity using three recently introduced distance-type measures. They are based on the Hilbert-Schmidt metric, the relative entropy, and the Bures metric. Specifically, for an $M$-photon-added thermal state, we obtain a compact analytic formula of the time-dependent density matrix that is used to evaluate and compare the three non-Gaussianity measures. We find a good consistency of these measures on the sets of damped states. The explicit damped quasiprobability densities are shown to support our general findings regarding the loss of negativities of Wigner and $P$ functions during decoherence. Finally, we point out that Gaussification of the attenuated field mode is accompanied by a nonmonotonic evolution of the von Neumann entropy of its state conditioned by the initial value of the mean photon number.

Parity-nonconservation (PNC) amplitudes are calculated for the 7$s$-6$d_{3/2}$ transitions of the francium isoelectronic sequence (Fr, Ra${}^{+}$, Ac${}^{2+}$, Th${}^{3+}$, Pa${}^{4+}$, U${}^{5+}$, and Np${}^{6+}$) and for the 6$s$-5$d_{3/2}$ transitions of the cesium isoelectronic sequence (Cs, Ba${}^{+}$, La${}^{2+}$, Ce${}^{3+}$, and Pr${}^{4+}$). We show in particular that isotopes of La${}^{2+}$, Ac${}^{2+}$, and Th${}^{3+}$ ions have strong potential in the search for new physics beyond the standard model: The PNC amplitudes are large, the calculations are accurate, and the nuclei are practically stable. In addition, ${}^{232}$Th${}^{3+}$ ions have recently been trapped and cooled [Campbell et al., Phys. Rev. Lett. 102, 233004 (2009)]. We also extend previous works by calculating the $s$-$s$ PNC transitions in Ra${}^{+}$ and Ba${}^{+}$ and provide calculations of several energy levels, and electric dipole and quadrupole transition amplitudes for the Fr-like actinide ions.