The paper presents a theoretical study of synchronization between two coupled lasers. A theory valid for arbitrary coupling between lasers is used. Its key feature is that the laser field is decomposed in terms of the composite-cavity modes reflecting the spatial field dependence over the entire coupled-laser system. The ensuing multimode equations are reduced to class-$B,$ and further to class-$A$ equations which resemble competing species equations. Bifurcation analysis, supported by insight provided by analytical solutions, is used to investigate influences of pump, carrier decay rate, polarization decay rate, and coupling mirror losses on synchronization between lasers. Population pulsation is found to be an essential mode competition mechanism responsible for bistability in the synchronized solutions. Finally, we discovered that the mechanism leading to laser synchronization changes from strong composite-cavity mode competition in class-$A$ regime to frequency locking of composite-cavity modes in class-$B$ regime.

We consider storage and retrieval of light based on electromagnetically induced transparency in an atomic medium using nonadiabatic switching of a control field. We derive various conditions for writing (and reading) the light information to (and from) the atomic coherence. We obtain an analytical solution for the retrieval of the stored pulse that is in excellent agreement with the full numerical results. We identify the origin of distortion at the output and derive a condition to correct the distortions by manipulating the retrieval process.

We present an integrated wire-based magneto-optical trap for the simplified trapping and cooling of large numbers of neutral atoms near material surfaces. With a modified $\mathrm{U}$-shaped current-carrying $\text{Cu}$ structure we collect more than $3\times {10}^8$ ${}^{87}\mathrm{Rb}$ atoms in a mirror magneto-optical trap without using quadrupole coils. These atoms are subsequently loaded to a $\mathrm{Z}$-wire trap where they are evaporatively cooled to a Bose-Einstein condensate close to the surface.

High-order harmonic generation has been explored theoretically and experimentally in ${\text{CO}}_2$, a linear molecule characterized by doubly antisymmetric highest-occupied molecular orbitals. For the first time to our knowledge, the high-harmonic yield is studied as a function of the angle between the molecular axis and the polarization direction. A minimum yield is found at $0°$ for all harmonics, which constitutes evidence for destructively interfering terms in the ionization probability amplitude playing an important role in strong-field phenomena in molecules. The maximum yield is always found at intermediate angles, but the detailed behavior is harmonic specific. Numerical simulations reproduce the main features observed in the experiment.

We derive the stochastic Schrödinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We require only unbiasedness of the detector states and an integrability condition sufficient to ensure a central limit effect. Despite taking a weak interaction as opposed to a weak measurement limit, the resulting stochastic wave equation is of the same form as that derived in a recent paper by Scott and Milburn for the specific case of joint Gaussian states.

We analyze decoherence of an electron in a double dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.

Calculations of absolute triple-differential and single-differential cross sections for helium double photoionization are performed using an implementation of exterior complex scaling in $B$-splines. Results for cross sections, well converged in partial waves, are presented and compared with both experiment and earlier theoretical calculations. These calculations establish the practicality and effectiveness of the complex $B$-spline approach to calculations of double ionization of atomic and molecular systems.

The double structure potential predicted in the atomic cloud of a magneto-optical trap by one- (Doppler part) and two-photon process (sub-Doppler part) is experimentally observed and studied through the parametric excitation with the modulation of cooling laser intensities. Modulating the intensity of the cooling laser at around twice its resonant frequency of Doppler part, the atoms in Doppler part are divided and they oscillate reciprocally with finite amplitude due to the nonlinearity of the trap, and the others in sub-Doppler part are not influenced. By the modulation, we can investigate the sub-Doppler part spatially without Doppler part and also measure the temperature of sub-Doppler part independently.

Slowly rotating spin-1 Bose-Einstein condensates are studied through a variational approach based upon lowest Landau level calculus. The author finds that in a gas with ferromagnetic interactions, such as ${}^{87}\mathrm{Rb}$, angular momentum is predominantly carried by clusters of two different types of skyrmion textures in the spin-vector order parameter. Conversely, in a gas with antiferromagnetic interactions, such as ${}^{23}\mathrm{Na}$, angular momentum is carried by $\pi$ disclinations in the nematic order parameter which arises from spin fluctuations. For experimentally relevant parameters, the cores of these $\pi$ disclinations are ferromagnetic, and can be imaged with polarized light.

In an electron-spin two-level system a bichromatic radiation field, consisting of a transverse microwave field and a radio frequency field oriented parallel to the static magnetic field, can induce multiple photon transitions of the type ${\sigma }_{\text{mw}}^{+}+k{\pi }_{\text{rf}}$, with the photons ${\sigma }_{\text{mw}}^{+}$ and ${\pi }_{\text{rf}}$ absorbed from the microwave and radio frequency fields, and $k$ being an integer. The two-level spin system may become transparent under such a bichromatic radiation field. This phenomenon directly depends on the presence of the $\pi$ photons of the longitudinal radio frequency field. An analytical description of the multiple photon processes and the resulting transparency effects, based on a toggling-frame approach, is given. The effective field amplitudes of the multiple photon transitions are found to have a Bessel-function-like dependence on the radio frequency amplitude. The behavior of the magnetization vector during a bichromatic pulse is illustrated by using classical equations of motion. The theoretically predicted effects are verified experimentally. As an example for an application of the investigated type of electromagnetically induced transparency, a one-pulse echo experiment is described, where the free evolution period is created artificially.

We study the elliptically polarized states in the spin-flip model for vertical-cavity-surface-emitting lasers. The stability analysis reveals some unexpected features. In correspondence with particular values of the birefringence parameter, which are shown to scale very simply with the ratio of the spin-flip rate to the linewidth enhancement factor, the stability domain can be quite large. Moreover, in some cases two different dynamical regimes can arise from the destabilization of the elliptically polarized states, and they can coexist in a finite interval of the pump parameter. Finally, we show that the bifurcation from the lower frequency linearly polarized state to the elliptically polarized states can be subcritical when the linewidth enhancement factor is roughly smaller than 1.

We studied the modes of the highest-quality factor $Q_m$ in disordered photonic crystals. By varying the strength of disorder, we identified five different scaling regimes of the ensemble averaged $⟨Q_m⟩$ with the system size. For sufficiently large systems, $⟨Q_m⟩$ reaches the maximum at some finite degree of disorder, where its value is comparable to the quality factor of an intentionally introduced single defect at the center of a photonic band gap. Near this optimal degree of disorder, we predict a superexponential increase of $⟨Q_m⟩$ with the system size, due to migration of the frequencies of the highest-quality modes toward the photonic band-gap center. Our result may lead to the design and fabrication of ultralow-threshold random laser.

The survival amplitude $G\left(t\right)$ of a nonstationary state decaying into a purely continuous spectrum is treated in terms of an integral transform of an energy distribution with $\infty >E⩾0$. We examine three such distributions. Two are real functions, the Lorentzian $g^L\left(E\right)$ and a modified Lorentzian $G\left(E\right)=g^L\left(E\right)E^{1∕2}$, and one is the complex version of $g^L\left(E\right),g_c^L\left(E\right)$. Real distributions are associated with Hermitian treatments while complex ones result from non-Hermitian treatments. The difference between the two has repercussions on the $G\left(t\right)$ for nonexponential decay (NED) and on the understanding of irreversible decay at the quantum level. For all three distributions, we derive analytically amplitudes (propagators) for NED and then show that these satisfy differential equations, from which additional insight into the decay process for very long and very short times can be obtained. By making analogy with the classical Langevin equation, the terms of the differential equation that are derived when the simpler $g^L\left(E\right)$ and $g_c^L\left(E\right)$ are employed, are interpreted using concepts such as friction and fluctuation. On the other hand, when $g^L\left(E\right)$ is multiplied by an energy-dependent factor, as in $G\left(E\right)$, the results are, as expected, more complicated and the interpretability of the differential equation satisfied by the NED propagator loses clarity.

By formally generalizing the classical Hellinger distance and affinity on the space of probability densities, we introduce their quantum analog on the quantum state space consisting of all density operators. We show that the infinitesimal form of the quantum Hellinger distance is the skew information introduced by Wigner and Yanase in 1963. We compare the Hellinger distance and affinity with the Bures distance and fidelity, and establish a variety of their fundamental properties. We further apply them to characterizing entanglement and to establishing some unusual uncertainty relations relating nonsimultaneous measurements of a single observable in two different quantum states.

The need to maximize the number of operations of a quantum bit within its decoherence time may require the ratio of Rabi frequency to transition frequency to be large enough to invalidate the rotating-wave approximation. The state of the quantum bit under any initial condition then depends explicitly on the phase of the driving field, resulting in driver-phase-correlated fluctuations and a violation of the rule that the degree of excitation depends only on the pulse area. This is due to the interference of the excitations caused by the corotating and counterrotating fields, and is a significant source of error, correctable only by controlling the driver phase. We present a scheme for observing this effect under currently realizable parameters.

We propose two feasible experimental implementations of an optimal asymmetric $1\to 2$ quantum cloning of a polarization state of photon. Both implementations are based on a partial and optimal reverse of recent conditional symmetrical quantum cloning experiments. The reversion procedure is performed only by a local measurement of one from the clones and ancilla followed by a local operation on the other clone. The local measurement consists only of a single unbalanced beam splitter followed in one output by a single-photon detector and the asymmetry of fidelities in the cloning is controlled by a reflectivity of the beam splitter.

This paper proposes a protocol for quantum dense key distribution. This protocol embeds the benefits of a quantum dense coding and a quantum key distribution and is able to generate shared secret keys four times more efficiently than the Bennet-Brassard 1984 protocol. We hereinafter prove the security of this scheme against individual eavesdropping attacks, and we present preliminary experimental results, showing its feasibility.

We present a measurement of the lifetime of the metastable $3d{}^{2}D_{5∕2}$ state in the ${}^{40}\mathrm{Ca}^{+}$ ion, using the so-called shelving technique on a string of five Doppler laser-cooled ions in a linear Paul trap. A detailed account of the data analysis is given, and systematic effects due to unwanted excitation processes and collisions with background gas atoms are discussed and estimated. From a total of 6805 shelving events, we obtain a lifetime $\tau =1149\pm 14(\text{stat}.)\pm 4(\text{sys}.)\text{ms}$, a result which is in agreement with the most recent measurements.

When a gaseous sample of ${}^{13}\mathrm{CH}_3\mathrm{F}$ is prepared with a spin-isomer population ratio (ortho and para forms) far from the equilibrium given by nuclear spin statistics, it relaxes towards this equilibrium with an exponential decay rate. This phenomenon, called nuclear spin conversion, is mainly governed by intramolecular spin-spin and spin-rotation interactions which couple two pairs of quasidegenerate ortho-para levels ($J=9,K=3;$ $J^{\prime }=11,K^{\prime }=1$) and ($J=20,K=3;$ $J^{\prime }=21,K^{\prime }=1$). The presence of a static electric field can induce the degeneracy for Stark sublevels and yields an increase of the conversion rate. Such a “conversion spectrum” has been recorded experimentally. The intensities of the peaks are directly related to the intramolecular magnetic interaction strengths, and their widths depend on how the collisions break the coherence between ortho and para levels which is created by the interactions. Such collision-induced rates are directly determined and compared to the rate of rotationally inelastic molecular collisions.

We report on the observation of a mixed-spin-channel Feshbach resonance at the low magnetic field value of $9.09\pm 0.01\mathrm{G}$ for a mixture of $\mid 2,-1⟩$ and $\mid 1,+1⟩$ states in ${}^{87}\mathrm{Rb}$. This mixture is important for applications of multicomponent Bose-Einstein condensates of ${}^{87}\mathrm{Rb}$, e.g., in spin mixture physics and for quantum entanglement. Values for position, height, and width of the resonance are reported and compared to a recent theoretical calculation of this resonance.