We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval $[0,1]$. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.

We present calculations of cross sections for one- and two-electron processes in collisions of ${\mathrm{H}}^{+}$, He${}^{2+}$, and ${\mathrm{C}}^{6+}$ with water molecules in the framework of the Franck-Condon approximation. We employ an independent-electron method and a classical trajectory Monte Carlo approach. Anisotropy effects related to the structure of the target are explicitly incorporated by using a three-center model potential to describe the electron-H${}_2$O${}^{+}$ interaction. We derive scaling laws with respect to the projectile charge. We also estimate cross sections for molecular fragmentation subsequent to electron removal.

Electron elastic total cross sections (TCSs) for ground and excited Mn, Cu, Zn, Ni, Ag, and Cd atoms have been investigated in the electron-impact energy range 0 ⩽ $E$ ⩽ 1 eV. The near-threshold TCSs for both the ground and excited states of these atoms are found to be characterized by Ramsauer-Townsend minima, shape resonances, and extremely sharp resonances corresponding to the formation of stable bound negative ions. The recently developed Regge-pole methodology where the crucial electron-electron correlations are embedded is employed for the calculations. From close scrutiny of the imaginary parts of the complex angular momenta, we conclude that these atoms form stable weakly bound ground and excited negative ions as Regge resonances through slow electron collisions. The extracted electron binding energies from the elastic TCSs of these atoms are contrasted with the available experimental and theoretical values.

Self-acousto-optic Raman-Nath modulation and nonorthogonal transversal modes are found in a broad-area Nd:YAG single-shot laser. The device is free from the thermal-induced effects previously related to orthogonality violation and the acousto-optic modulation comes from a shock wave produced by the discharge of the flash lamps that optically pump the laser. The experimental findings are reproduced by a general model of a class B laser.

We propose a scheme for inducing a blazed transmission grating in a four-level, $N$-type atomic medium under electromagnetically induced transparency (EIT). The blazed grating relies on the giant Kerr nonlinearity that the atomic medium exhibits under EIT. The grating is created using an intensity mask in one of the driving optical fields and only weak fields with intensities below saturation level are involved. Diffraction efficiencies of a resonant probe beam close to $100\%$ are predicted.

Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.

Many theoretical and experimental investigations have concluded that evanescent electromagnetic modes can propagate superluminally. However, in this paper we show that the average energy velocity of evanescent modes inside a cutoff waveguide is always less than or equal to the velocity of light in vacuum, while the instantaneous energy velocity can be superluminal, which does not violate causality according to quantum field theory: the fact that a particle can propagate over a spacelike interval does preserve causality provided that a measurement performed at one point cannot affect another measurement at a point separated from the first with a spacelike interval.

We present a scheme to generate frequency-multiplexed entangled (FME) single photons based on the entanglement between two species in an atomic-mixture ensemble. The atomic ensemble driven by the write and read fields according to a certain timing sequence, the generation of FME single photons can be repeated until success is achieved. The source might have significant applications in wavelength-division-multiplexing quantum key distribution.

We theoretically investigate the light propagation in a cavity optomechanical system with a Bose-Einstein condensate (BEC). It is shown that slow light can easily be realized in this system via a BEC coupled to an optical cavity field. The numerical results further demonstrate that the transmitted probe beam from the cavity can be delayed as much as 0.8 ms by suitably selecting the pump field detuning from the cavity field frequency. The scheme proposed here may have potential applications in telecommunication and interferometry.

We derive an asymptotic formula for the Wigner $9j$ symbol, in the limit of one small and eight large angular momenta, using a gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our factorization eliminates the geometric phases completely, using gauge-invariant noncanonical coordinates, parallel transports of spinors, and quantum rotation matrices. Our derivation generalizes to higher $3\mathit{nj}$ symbols. We display without proof some asymptotic formulas for the $12j$ symbol and the $15j$ symbol in the Appendices. This work contributes an asymptotic formula of the Wigner $9j$ symbol to the quantum theory of angular momentum and serves as an example of a general method for deriving asymptotic formulas for $3\mathit{nj}$ symbols.

We show that the noise spectrum of a parametrically excited nonlinear oscillator can display a fine structure. It emerges from the interplay of the nonequidistance of the oscillator quasienergy levels and quantum heating that accompanies relaxation. The heating leads to a finite-width distribution over the quasienergy, or Floquet states, even for zero temperature of the thermal reservoir coupled to the oscillator. The fine structure is due to transitions from different quasienergy levels, and thus it provides a sensitive tool for studying the distribution. For larger damping, where the fine structure is smeared out, quantum heating can be detected from the characteristic double-peak structure of the spectrum, which results from transitions accompanied by the increase or decrease of the quasienergy.

Open quantum systems interacting with structured environments is important and manifests non-Markovian behavior, which was conventionally studied using a quantum trajectory stochastic method. In this paper, by dividing the effects of the environment into two parts, we propose a deterministic method without using a quantum trajectory. This method is more efficient and accurate than the stochastic method in most Markovian and non-Markovian cases. We also extend this method to the generalized Lindblad master equation.

The search for “a quantum needle in a quantum haystack” is a metaphor for the problem of finding out which one of a permissible set of unitary mappings—the oracles—is implemented by a given black box. Grover’s algorithm solves this problem with quadratic speedup as compared with the analogous search for “a classical needle in a classical haystack.” Since the outcome of Grover’s algorithm is probabilistic—it gives the correct answer with high probability, not with certainty—the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These test states can also be used to realize “a classical search for the quantum needle” which is deterministic—it always gives a definite answer after a finite number of steps—and 3.41 times as fast as the purely classical search. Since the test-state search and Grover’s algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover’s algorithm.

Up to now, the lifetime of experimentally demonstrated entangled states has been limited due to their fragility under decoherence and dissipation. Therefore, they are created under strict isolation conditions. In contrast, new approaches harness the coupling of the system to the environment, which drives the system into the desired state. Following these ideas, we present a robust method for generating steady-state entanglement between two distant atomic ensembles. The proposed scheme relies on the interaction of the two atomic systems with the common vacuum modes of an electromagnetic field which act as an engineered environment. We develop the theoretical framework for two-level systems, including dipole-dipole interactions, and complement it by considering its implementation in multilevel ground states. Based on these results, the realization of entanglement generation by engineered dissipation has been experimentally demonstrated [H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, e-print arXiv:1006.4344].

We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyze the multipartite entanglement properties in the Deutsch-Jozsa, Grover, and Simon algorithms. Our results show that for these algorithms most instances involve multipartite entanglement.

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies $N$, and in the asymptotic limit as $N\to \infty$. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here an adaptive measurement is one in which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite $N$) and the scaling of this error in the asymptotic limit. In the asymptotic limit, it is known analytically (and we verify numerically) that adaptive schemes have no advantage over the optimal fixed local scheme. Here we show moreover that, in this limit, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme except for states with less than 2% mixture. For finite $N$, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme for any degree of mixture.

We discuss the three-body properties of identical bosons exhibiting large scattering length in two spatial dimensions. Within an effective field theory for resonant interactions, we calculate the leading nonuniversal corrections from the two-body effective range to bound-state and scattering observables. In particular, we compute the three-body binding energies, the boson-dimer scattering properties, and the three-body recombination rate for finite energies. We find significant effective range effects for three-body observables in the vicinity of the unitary limit. The implications of this result for future experiments are briefly discussed.

Using momentum-resolved electron-ion multicoincidence spectroscopy, we have investigated interatomic Coulombic decay (ICD) in the heteronuclear NeAr dimer following Ne $1s$ Auger decay. The measured intensity ratio for the three ICD transitions Ne${}^{2+}$($2s^{-1}2p^{-1}\hspace{0.5em}{}^{1}P$)Ar to Ne${}^{2+}$($2p^{-2}\hspace{0.5em}{}^{1}S$)–Ar${}^{+}$($3p^{-1}$), Ne${}^{2+}$($2s^{-1}2p^{-1}\hspace{0.5em}{}^{1}P$)Ar to Ne${}^{2+}$($2p^{-2}\hspace{0.5em}{}^{1}D$)-Ar${}^{+}$($3p^{-1}$), and Ne${}^{2+}$($2s^{-1}2p^{-1}\hspace{0.5em}{}^{3}P$)Ar to Ne${}^{2+}$($2p^{-2}\hspace{0.5em}{}^{3}P$)-Ar${}^{+}$($3p^{-1}$) reasonably agree with predictions. The kinetic energy release distribution for the fragmentation to Ne${}^{2+}$($2p^{-2}\hspace{0.5em}{}^{1}D$)-Ar${}^{+}$($3p^{-1}$) after the ICD transition from singlet Ne${}^{2+}$($2s^{-1}2p^{-1}\hspace{0.5em}{}^{1}P$)Ar state, which is a mirror image of the kinetic energy distribution of the emitted ICD electrons, suggests that the corresponding ICD rate is roughly two times lower than predicted by ab initio calculations.

Photoelectron ionization spectra of a system interacting with a neighbor two-level atom are investigated using the Laplace-transform method. These spectra are typically composed of several peaks. Photoelectron ionization spectra conditioned by the measurement on the two-level atom show oscillations at the Rabi frequency. The presence of spectral zeros occurring periodically with the Rabi period is predicted. This phenomenon is analyzed in detail.

We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multiparticle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the latter phase. The effective physics of the trimer gas is studied as well. Last, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.