We analyze multi-longitudinal-mode semiconductor lasers experimentally. We show that the intensity of each mode displays large amplitude oscillations but obeys a highly organized antiphase dynamics leading to an almost constant total intensity output. For each mode, regular switching is observed in the megahertz range, while the optical frequency as a function of time follows a well defined sequence from blue to red. Using a multimode theoretical model, we identify that four-wave mixing is the dominant mechanism at the origin of the observed dynamics. The asymmetry of the susceptibility function of semiconductor materials allows us to explain the optical frequency sequence.

We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation (Kraus representation) regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples.

A method for obtaining a single $\mathrm{sub}\text{−}50\text{−}\text{attosecond}$ pulse using harmonic radiation is proposed. For the generation of broad harmonic radiation during a single half-optical cycle, atoms are driven by a femtosecond laser pulse with intensity above the saturation intensity for optical field ionization and hence experience a large nonadiabatic increase of the laser electric field between optical cycles. Although the chirped structure of the harmonic radiation imposes a limit on the minimum achievable pulse duration, we demonstrate that its positive chirp can be compensated by the negative group delay dispersion of an appropriately selected x-ray filter material, used also for the spectral selection, resulting in a single attosecond pulse with a duration less than $50\mathrm{as}$.

We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system—in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an $n$-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applies only to a limited class of superselection rules, those in which the superselection sectors are labeled by unitary irreducible representations of a compact symmetry group. The second method uses the concept of the format of a message sent between parties—by verifying the format, the recipient of a message can check whether the message could have been sent by a party who performed charge-conserving operations. By this method, we prove that protocols subject to general superselection rules (including those pertaining to non-Abelian anyons in two dimensions) are no more secure than protocols in the unrestricted world. However, the proof applies only to two-party protocols. Our results show in particular that, if no assumptions are made about the computational power of the cheater, then secure quantum bit commitment and strong quantum coin flipping with arbitrarily small bias are impossible in a world subject to superselection rules.

An approach has been proposed and developed to study the positronium (Ps) formation cross sections in the ground and excited $n=2$ levels for the exothermic reaction in a positron-negative hydrogen-ion $\left({\mathrm{H}}^{-}\right)$ collision in the framework of Coulomb distorted eikonal approximation. Both the differential cross sections (DCS) as well as integrated cross sections [partial total cross sections (TCS)] have been investigated for the $1s$, $2s$, and $2p$ states in a broad energy range, e.g., $1–200\text{eV}$. For lower incident energy, the Ps formation in the $2p$ state is found to dominate over the $1s$ and $2s$ states while for the higher incident energy, the formation to ground state $\left(1s\right)$ dominates the other two states. Present results have been compared with other existing theoretical results where available in the absence of any experimental data. Both the DCS and the partial TCS results are found to agree quite satisfactorily with the coupled pseudostate results of McAlinden et al. [Phys. Rev. A 65, 032715 (2002)] in the low-energy range $1–10\text{eV}$. At higher incident energies, the present results are always lower than the Coulomb Born and orthogonalized Coulomb Born results of Basu Choudhury et al. [Phys. Rev. A 33, 2358 (1986)] and Straton et al. [Phys. Rev. A 44, 7335 (1991)], respectively. The present DCS $\left(1s,2s\right)$ exhibits double peak structure at high incident energy that could be attributed to higher-order effects. The signature of the present double peak structure which is totally absent in the Coulomb Born approximation or in the orthogonalized Coulomb Born approximation becomes more prominent with increasing incident energy.

We study the dynamics of a straight vortex line in a partially Bose-Einstein condensed atomic gas. Using a variational approach to the stochastic field equation that describes the dynamics of the condensate at nonzero temperature, we derive the stochastic equations of motion for the position of the vortex core. Using these results, we calculate the time it takes the vortex to spiral out of the condensate. Due to the fact that we include thermal fluctuations in our description, this lifetime of the vortex is finite even if its initial position is in the center of the condensate.

We study entanglement of electron spins in many-body systems based on the Green’s function approach. As an application we obtain the two-particle density matrix of a noninteracting electron gas and identify its two-spin density matrix as a Werner state. We calculate entanglement measures, a classical correlation, mutual information, and a pair-distribution function of two electrons at zero and finite temperatures. We find that changes of entanglement measures are proportional to $T^2$ at low temperatures.

We illuminate the importance of a self-consistent many-body treatment in calculations of vacuum polarization corrections to the energies of atomic orbitals in many-electron atoms. Including vacuum polarization in the atomic Hamiltonian causes a readjustment (relaxation) of the electrostatic self-consistent field. The induced change in the electrostatic energies is substantial for states with the orbital angular momentum $l>0$. For such orbitals, the relaxation mechanism determines the sign and even the order of magnitude of the total vacuum polarization correction. This relaxation mechanism is illustrated with numerical results for the Cs atom.

We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.

The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup and by a general uncertainty relation valid for the optimal estimates of the same two observables when the state of the system prior to measurement is known. A formula is given for the optimal estimate of any given observable, based on arbitrary measurement data and prior information about the state of the system, which generalizes and provides a more robust interpretation of previous formulas for “local expectations” and “weak values” of quantum observables. As an example, the canonical joint measurement of position $X$ and momentum $P$ corresponds to measuring the commuting operators $X_J=X+X^{\prime }$ and $P_J=P-P^{\prime }$, where the primed variables refer to an auxiliary system in a minimum-uncertainty state. It is well known that $\Delta X_J\Delta P_J⩾\hslash$. Here it is shown that given the same physical experimental setup and knowledge of the system density operator prior to measurement, one can make improved joint estimates $X_{opt}$ and $P_{opt}$ of $X$ and $P$. These improved estimates are not only statistically closer to $X$ and $P$ but further satisfy $\Delta X_{opt}\Delta P_{opt}⩾\hslash ∕4$, where equality can be achieved in certain cases. Thus one can do up to four times better than the standard lower bound (where the latter corresponds to the limit of no prior information). Other applications include the heterodyne detection of orthogonal quadratures of a single-mode optical field and joint measurements based on Einstein-Podolsky-Rosen correlations.

We critically study the possibility of the quantum Zeno effect for indirect measurements. If the detector is prepared to detect the emitted signal from the core system, and does not reflect this signal back to the core system, then we can prove that the decay probability of the system is not changed by the continuous measurement of the signal and the quantum Zeno effect would never take place. This argument also applies to the quantum Zeno effect for accelerated two-level systems and unstable particle decays.

Local approximations, formulated in the context of a relativistic extension of the self-consistent $\alpha$ method, are advanced for the case of the relativistic exact Coulomb exchange functional—defined as the Dirac-Fock exchange—and for the Breit expression for the transverse photon exchange, given in terms of the expectation value of the Breit operator. The resulting potentials are local (multiplicative) operators, in both cases. Using these new functionals, fully relativistic calculations have been performed for selected atoms with $Z$ between 10 and 94, within the framework of relativistic density functional theory (RDFT). The total and exchange energies and ionization potentials obtained from these functionals are quite close to those of the relativistic optimized potential method (ROPM). The computational effort involved in the application of this new method is, however, significantly lower.

Absolute total single- and double-electron-capture cross sections for ${\mathrm{C}}^{q+}\left(q=3,4\right)$ with $\text{CO}$ have been measured at $\sim 0.5\text{keV}∕\text{amu}$ using a reflection-time-of-flight mass spectrometer with a laser ablation ion source. The single- and double-electron-capture cross sections for ${\mathrm{C}}^{3+}$ with $\text{CO}$ at $423\pm 48\text{eV}∕\text{amu}$ are found to be $\left(0.96\pm 0.12\right)\times {10}^{-15}{\text{cm}}^2$ and $\left(0.99\pm 0.13\right)\times {10}^{-15}{\text{cm}}^2$, respectively. The single- and double-electron-capture cross sections for ${\mathrm{C}}^{4+}$ with $\text{CO}$ at $565\pm 65\text{eV}∕\text{amu}$ are measured to be $\left(3.16\pm 0.42\right)\times {10}^{-15}{\text{cm}}^2$ and $\left(1.05\pm 0.21\right)\times {10}^{-15}{\text{cm}}^2$, respectively. This suggests that double capture should not be ignored in modeling the emission from cascading processes in comet atmosphere.

Experimental data are presented for the scattering of cold electrons by ${\text{SF}}_6$ and ${\mathrm{C}}_6{\mathrm{F}}_6$, down to energies of a few meV, with an energy resolution varying between 0.95 and $1.5\text{meV}$ (full width at half maximum) in the electron beam. The measured scattering cross sections rise rapidly at low energy and represent effects of bound-state attachment and scattering in the case of ${\text{SF}}_6$ and virtual state scattering in the case of ${\mathrm{C}}_6{\mathrm{F}}_6$. Data are combined with known attachment cross sections for ${\text{SF}}_6$ to yield elastic-scattering cross sections, from which phase shifts for elastic scattering are derived. The $s$-wave phase shift rises as energy falls as theory requires for a potential supporting a nonadiabatic bound state and possessing a large positive $s$-wave scattering length. The behavior at very low energy of the $s$-wave phase shift is, however, anomalous, the phase shift remaining far from an odd multiple of $\pi$ at $5\text{meV}$ collision energy; a similar anomaly was found in electron scattering by ${\text{CCl}}_4$. These results should stimulate further theoretical development. By contrast with ${\text{SF}}_6$, ${\mathrm{C}}_6{\mathrm{F}}_6$ offers an example of a system with a large negative scattering length. Data are analyzed to reveal a strong virtual state effect at low collision energy, similar to ${\text{CO}}_2$ but with a considerably greater cross section. The $s$-wave phase shift falls as energy drops and both this and the $p$-wave phase shift follow the precepts of effective range theory. It is proposed that the strong virtual state effect may act as a gateway to attachment through collisional or radiative stabilization of long-lived anions, with implications for both man-made and natural plasmas.

We observe destructive interference in the ground-state Rb two-photon ionization cross section when the single photon energy is tuned between the $5S\to 5P$ and $5S\to 6P$ transition energies. The minimum cross section is $5.9\left(1.5\right)\times {10}^{-52}{\text{cm}}^4\mathrm{s}$ and it occurs at a wavelength of $441.0\left(3\right)\text{nm}$ (in vacuo). Relative measurements of these cross sections are made at various wavelengths by counting ions produced when magneto-optically trapped Rb atoms are exposed to light from a tunable pulsed laser. This relative curve is calibrated to an absolute cross-section measurement at $532\text{nm}$ using the trap loss method. A simple calculation agrees reasonably with our results.

The relative phase between two uncoupled Bose-Einstein condensates tends to attain a specific value when the phase is measured. This can be done by observing their decay products in interference. We discuss exactly solvable models for this process in cases where competing observation channels drive the phases to different sets of values. We treat the case of two modes which both emit into the input ports of two beam splitters and of a linear or circular chain of modes. In these latter cases, the transitivity of the relative phase becomes an issue.

The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov–de Gennes theory. Various thermodynamic properties are calculated, and the shift in the critical temperature due to the presence of the vortex is analyzed. The gapless excitations inside the vortex core are studied, and a scheme to detect these states and thus the presence of the vortex is examined. The numerical results are compared with various analytical expressions when appropriate.

We report on recent experimental results of the spontaneous antiphase dynamics that occurs in a laser-diode-pumped multimode passively $Q$-switched microchip $\mathrm{Yb}:\mathrm{YAG}$ (where YAG is yttrium aluminum garnet) lasers with a saturable absorber $\mathrm{GaAs}$. We observe that the pulse sequence of the first mode characterized by one, two, and three pulses as a group and all the modes display an antiphase state as the pumping ratio rises. We modify the multimode rate equations to account for nonlinear absorption due to $\mathrm{GaAs}$ in the presence of spatial hole burning. We perform numerical simulations based on the proposed rate equations and reproduce the observed antiphase state of two and three active modes.

We report an efficient quantum algorithm for estimating the local density of states (LDOS) on a quantum computer. The LDOS describes the redistribution of energy levels of a quantum system under the influence of a perturbation. Sometimes known as the “strength function” from nuclear spectroscopy experiments, the shape of the LDOS is directly related to the survivial probability of unperturbed eigenstates, and has recently been related to the fidelity decay (or “Loschmidt echo”) under imperfect motion reversal. For quantum systems that can be simulated efficiently on a quantum computer, the LDOS estimation algorithm enables an exponential speedup over direct classical computation.

We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable.