It is well known that a field’s quantum noise can have a profound effect on the fluctuations of laser-induced fluorescence (LIF). However, though previous studies have led to a good understanding of this process in the case of stationary fields, many of the important applications of LIF employ some form of laser modulation, yielding a field of nonstationary stochastic character. Here, we discuss the results from numerical experiments that examine the influence of a nonstationary field on the LIF noise. Specifically, we consider a phase-diffusion field and LIF from a beam of alkali-metal-like atoms with ground and excited-state Zeeman splitting when the field undergoes deterministic frequency modulation. Our computational results show that deterministic modulation at high Fourier frequencies (i.e., 10 MHz) can significantly increase the LIF noise at low Fourier frequencies (e.g., 1 Hz), and that the amount of LIF noise amplification depends on a complicated interplay among the laser’s linewidth, the modulation frequency, the modulation index, and the multilevel atomic system’s energy-level spacing. Interestingly, we find that certain values of the atom’s Zeeman splitting significantly decrease the magnitude of LIF noise.

The process of Raman photoassociation of a trapped atomic condensate to form condensed molecules has been labeled superchemistry because it can occur at 0 K and experiences coherent bosonic stimulation. We show here that the differences from ordinary chemical processes go even deeper, with the conversion rates depending on the quantum state of the reactants, as expressed by the Wigner function. We consider different initial quantum states of the trapped atomic condensate and different forms of the confining potentials, demonstrating the importance of the quantum statistics and the extra degrees of freedom which massive particles and trapping potentials make available over the analogous optical process of second-harmonic generation. We show that both mean-field analyses and quantum calculations using an inappropriate initial condition can make inaccurate predictions for a given system. This is possible whether using a spatially dependent analysis or a zero-dimensional approach as commonly used in quantum optics.

The dynamical behavior of entanglement for excitons in two quantum dots placed in a cavity driven by a broadband squeezed vacuum is studied in the low exciton density regime. It is found that the excitons in two quantum dots can evolve into a pure entangled state only when the dissipation of the cavity and exciton modes is negligible. When the injected field into the cavity is a squeezed vacuum, the excitons will be in a two-mode Gaussian entangled mixed state even in the long time limit. Analytical expressions are derived, showing the dependence of the entanglement property of the excitons in two quantum dots on the squeezing properties of the initial state prepared in the cavity and the strength of two-photon correlations of the squeezed vacuum injected into the cavity.

A parametrization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parametrization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under local unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parametrization.

We study the communication capacities of bosonic broadband channels in the presence of different sources of noise. In particular we analyze lossy channels in the presence of white noise and thermal bath. In this context, we provide a solution for the entanglement-assisted capacity and upper and lower bounds for the classical and quantum capacities.

Reversible state transformations under entanglement nonincreasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end more powerful versions of state transformations (or reducibilities), namely, LOCCq (asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC (asymptotic LOCC with catalysis) have been considered in the literature. In this paper we show that LOCCq state transformations are only as powerful as asymptotic LOCC state transformations for multipartite pure states. The basic tool we use is multipartite entanglement gambling: Any pure multipartite entangled state can be transformed to an Einstein-Podolsky-Rosen pair shared by some pair of parties and any irreducible m-party pure state $(m>~2)$ can be used to create any other state (pure or mixed) using LOCC. We consider applications of multipartite entanglement gambling to multipartite distillability and to characterizations of multipartite minimal entanglement generating sets. We briefly consider generalizations of this result to mixed states by defining the class of cat-distillable states, i.e., states from which cat states $(|0^{\otimes m}〉+|1^{\otimes m}〉)$ may be distilled.

We investigate radiation-imprisonment (RI) phenomena in a system of cold atoms trapped in magneto-optical traps (MOTs) when cooling lasers are switched off for a short period. The problem is formulated within the framework of the Streater-Cooper-Sandle equation that belongs to the Markov class and accounts for photon frequency redistribution in multiple scattering processes. On the basis of a semiclassical approach, we derive explicit analytical solutions for the spectral problem of the RI equation neglecting Doppler effects. The analysis reveals peculiarities in emission profiles under initial partial saturation of the resonance transition by the probe laser pulse. Comparison between theoretical and experimental data on effective radiative lifetimes obtained in Cs and Rb MOTs confirms the validity of the discussed nonstationary model of RI in cold samples. For small detunings, the Streater-Cooper-Sandle equation agrees with the experimental data, while in the case of large detunings, the theory does not agree, probably due to non-Markovian effects.

We investigate systems of identical bosons with the focus on two-body correlations and attractive finite-range potentials. We use a hyperspherical adiabatic method and apply a Faddeev type of decomposition of the wave function. We discuss the structure of a condensate as a function of particle number and scattering length. We establish universal scaling relations for the critical effective radial potentials for distances where the average distance between particle pairs is larger than the interaction range. The correlations in the wave function restore the large-distance mean-field behavior with the correct two-body interaction. We discuss various processes limiting the stability of condensates. With correlations we confirm that macroscopic tunneling dominates when the trap length is about half of the particle number times the scattering length.

We show that subfemtosecond pulse train with large pulse spacing can be generated by using three correlated Raman generators between three Raman levels with strong molecular modulation to control the generation and propagation of the cascade stimulated Raman sidebands. For three Raman generators based on the fundamental rotational and vibrational Raman transitions $(v=0,J=0\mathrm{}\leftrightarrow v=0,J=2\mathrm{}\leftrightarrow v=1,J=0\mathrm{}\leftrightarrow v=0,J=0)$ in molecular hydrogen, a train of subfemtosecond pulses with a pulse spacing of 379.9 fs and pulse width down to 0.26 fs can be generated.

We have demonstrated the generation of a highly coherent x-ray laser at 13.9 nm by an oscillator-amplifier configuration with two targets. In the oscillator-amplifier configuration, a seed x-ray laser beam from one target is injected into a plasma amplifier at another target. When the propagation of the x-ray laser beam is not affected by refraction in the amplifier, a highly coherent x-ray laser beam with small divergence of 0.2 mrad is generated. The observed divergence is close to the diffraction limited value, and this beam has full spatial coherence.

Some $\mathrm{PT}$-symmetric non-Hermitian Hamiltonians have only real eigenvalues. There is numerical evidence that the associated $\mathrm{PT}$-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the states is positive definite only if a recently introduced “charge operator” is included in its definition. A simple derivation of the conjectured completeness and orthonormality relations is given. It exploits the fact that $\mathrm{PT}$ symmetry provides a link between the eigenstates of the Hamiltonian and those of its adjoint, forming a dual pair of bases. The charge operator emerges naturally upon expressing the properties of the dual bases in terms of one basis only, and it is shown to be a function of the Hamiltonian.

We derive a semiclassical approximation for the coherent state propagator $〈z^{″}|e^{-iHt/ħ}|z^{\prime }〉$ using a path integral formulation in which the intermediate coherent states can have arbitrary widths. Our semiclassical formula involves complex trajectories of the smoothed Hamiltonian $\mathcal{H}\mathrm{}(q,p,b)=〈z|Ĥ|z〉$ where b, the width of the coherent state $|z〉,$ is a free function that can be chosen conveniently. The generality of this formalism enables us to derive a semiclassical approximation which contains, as particular cases, other similar approximations known in the literature, providing a natural link between them. We present numerical results showing that the semiclassical propagation can be very sensitive to the choice of b and we suggest an energy dependent value ${b=b}_E$ that results in considerable improvement over other choices. This value for the width will be generally different from the widths ${\sigma }^{\prime }$ or ${\sigma }^{″}$ of the initial and final states $|z^{\prime }〉$ and $|z^{″}〉.$

Quantum-mechanical calculations of muon transfer between muonic hydrogen and an oxygen nuclei for s waves and collision energies in the range ${10}^{-3}–{10}^3\mathrm{eV}$ are presented. Close-coupling time-independent Schrödinger equations, written in terms of hyperspherical elliptic coordinates, were integrated along the hyperradius to obtain the partial and total muon-transfer probabilities. The results show the expected Wigner-Bethe threshold behavior up to collision energies of the order of ${10}^{-2}\mathrm{eV}$ and pronounced maxima at ${10}^2\mathrm{eV}$ which can be interpreted in terms of crossings between potential energy curves corresponding to the entrance channel state $(\mu {p)}_{1s}+\mathrm{O}$ and two product channels which asymptotically correlate to $p+(\mathrm{O}\mu {)}_{n=5,6\mathrm{}}.$ The population of the final states with different orbital angular momenta is found to be essentially independent of energy in the range considered in this work. This can be attributed to a strong selection rule for the conservation of the quantum number associated with one of the elliptic hyperangles.

The van der Waals coefficients $C_6,$ $C_8,$ and $C_{10}$ for H and He interactions with the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are determined from oscillator strength sum rules. The oscillator strengths were computed using a combination of ab initio and semiempirical methods. The dispersion parameters generally agree with close to exact variational calculations for Li-H and Li-He at the 0.1% level of accuracy. For larger systems, there is agreement with relativistic many-body perturbation theory estimates of $C_6$ at the 1% level. These validations for selected systems attest to the reliability of the present dispersion parameters. About half the present parameters lie within the recommended bounds of the Standard and Certain compilation [J. Chem. Phys. 83, 3002 (1985)].

The elaborate linkage pattern of the interaction Hamiltonian descriptive of pulsed laser interaction of elliptically polarized light with a degenerate two-level system can, for coherent excitation, be reduced to sets of independent pairs of coupled two-state equations by means of the Morris-Shore transformation [Phys. Rev. A 27, 906 (1983)]. By extending the earlier defining work, which dealt only with time-independent interactions, to consider various pulse shapes, one can obtain exact analytic solutions to various multilevel linkages. We use these to find the conditions on the interaction parameters (e.g., the ellipticity) leading to various population transfer schemes, for example, to achieve either population inversion or orientation. We illustrate these with the M and W linkages amongst magnetic sublevels of $J=1\mathrm{}$ or $J=2\mathrm{}$ excited by elliptically polarized light.

The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $〈\delta N_0^2〉\sim N^{22/15}$ and the fluctuations vanish when temperature approaches the BEC critical temperature.

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel, uniform, static electric, and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.

We consider the problem of communicating quantum states by simultaneously making use of a noiseless classical channel, a noiseless quantum channel, and shared entanglement. We specifically study the version of the problem in which the sender is given knowledge of the state to be communicated. In this setting, a trade-off arises between the three resources, some portions of which have been investigated previously in the contexts of the quantum-classical trade-off in data compression, remote state preparation, and superdense coding of quantum states, each of which amounts to allowing just two out of these three resources. We present a formula for the triple resource trade-off that reduces its calculation to evaluating the data compression trade-off formula. In the process, we also construct protocols achieving all the optimal points. These turn out to be achievable by trade-off coding and suitable time sharing between optimal protocols for cases involving two resources out of the three mentioned above.

We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi and S. Lloyd, e-print quant-ph/0305013. The quantum state space $\mathcal{H}$ encoding information decomposes into irreducible sectors and subsystems associated with the group of available evolutions. If this group coincides with the unitary part of the group algebra $C\mathcal{K}$ of some group $\mathcal{K}$ then universal control is achievable over the K-irreducible components of $\mathcal{H}.$ This general strategy is applied to different kinds of bosonic systems. We first consider massive bosons in a double well and show how to achieve universal control over all finite-dimensional Fock sectors. We then discuss a multimode massless case giving the conditions for generating the whole infinite-dimensional multimode Heisenberg-Weyl enveloping algebra. Finally we show how to use an auxiliary bosonic mode coupled to finite-dimensional systems to generate high-order nonlinearities needed for universal control.

We study the quantum adiabatic evolution algorithm with different evolution paths that correspond to different control Hamiltonians $H\left(\tau \right)$ sampled from a random ensemble. The algorithm is applied to a random binary optimization problem where the cost function is symmetric with respect to the permutation of individual bits. We investigate the method proposed by Farhi et al. when different evolution paths preserve the bit symmetry of the control Hamiltonians $H\left(\tau \right)$ and are generated by an ensemble of random $8\times 8$ matrices. In this case, the algorithm dynamics is completely described in terms of the motion of a spin-n/2 system. We show that different evolution paths can be parametrized by a small number of independent parameters that are expansion coefficients of $H\left(\tau \right)$ in a certain universal set of operators. One of these operators is responsible for avoiding the tunnelling for the spin-n/2 system and the corresponding coefficient determines the algorithm complexity for a given problem instance. We show that any problem instance can be solved in polynomial time by applying one of the two universal path modifications (due to the possible reflection symmetry of the problem). We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin $n/2\mathrm{}$ and provide a complete characterization of such paths.