We explore the dependence of the double ionization of the He atom on the frequency of a strong laser field while keeping the ponderomotive energy constant. As we increase the frequency we find that the remarkable “fingerlike” structure for high momenta recently found for $\omega =0.055\mathrm{a.u.}$ persists for higher frequencies. At the same time, at $\omega =0.187\mathrm{a.u.}$, a new X-shaped structure emerges for small momenta that prevails in the correlated momenta distribution. The role of this structure as a signature of the frequency dependence of nonsequential double ionization is discussed.

We study the breathing mode frequencies of a rotating Fermi gas trapped in a harmonic plus radial quartic potential. We find that as the radial anharmonicity increases, the lowest order radial mode frequency increases while the next lowest order radial mode frequency decreases. Then at a critical anharmonicity, these two modes merge and beyond this merge the cloud is unstable against the oscillations. The critical anharmonicity depends on both rotational frequency and the chemical potential. As a result of the large chemical potential in the BCS regime, even with a weak anharmonicity the lowest order mode frequency increases with decreasing the attractive interaction. For large enough anharmonicities in the weak-coupling BCS limit, we find that the excitation of the breathing mode frequencies make the atomic cloud unstable.

We present the theory of “normal mode splitting” (sometimes also called, in the low-intensity limit, “vacuum Rabi splitting”) for a Doppler-broadened two-level medium in an optical cavity, and illustrate it with experimental results. We note that, in the extreme Doppler limit, the absorptive and dispersive properties of the medium are due to almost completely different groups of atoms, and hence it is possible, in principle, to partially saturate the absorbing atoms without changing the dispersion very much; as a result of this, for a sufficiently high probe intensity, transmission peaks well within the Doppler absorption profile are visible, even though the medium is optically dense. Some interesting features exhibited by this system in various regimes are transmission peaks that are unrelated to the “zero-phase” condition, and three-peaked transmission spectra for high atomic density and high cavity input power.

We report a detailed analytical, numerical, and experimental study of microdisk resonators doped with nanometer sized silicon quantum dots (nanocrystals). An intuitive analytical ray-optics-based model is developed and used to capture the behavior of the quality factor $\left(Q\right)$ as a function of the disk size and the attenuation coefficient. Two regimes in the behavior of $Q$ with the disk size establish a simple design rule for optimizing the performance of these cavities. The validity of our analytical model is verified by full-vectorial finite element method calculations of the microcavity modes. Based on the predictions of the analytical and numerical calculations, we have fabricated microdisk resonators with diameters ranging between 2 and $8\mu \mathrm{m}$. $Q>{10}^3$ are obtained for disk radii as small as $4\mu \mathrm{m}$—highest observed for Si-nanocrystal-doped microdisk resonators. The fundamental limit on $Q$ is estimated by quantifying all of the potential optical loss processes through a careful analysis which includes the effects of nanocrystal size distribution. Our theoretical calculations match well with experiments and reveal that the line-edge roughness scattering and radiation loss can be minimized sufficiently to enable study and quantification of more fundamental optical loss processes of this material due to band-to-band absorption, Mie scattering, and free-carrier absorption in the Si nanocrystals. Using the experimental $Q$’s and the mode volumes, we predict the maximum low-temperature Purcell enhancement factor in our structures on the order of 6 and with some design improvements enhancements up to 50 can be realized.

We have found a dissipative soliton resonance which applies to nonlinear dynamical systems governed by the complex cubic-quintic Ginzburg-Landau equation. Specifically, for particular values of the equation parameters, the soliton energy increases indefinitely. These equation parameters can easily be found using approximate methods, and the results agree very well with numerical ones. The phenomenon can be very useful in the design of high-power passively mode-locked lasers.

We investigate polarization squeezing of ultrashort pulses in optical fiber, over a wide range of input energies and fiber lengths. Comparisons are made between experimental data and quantum dynamical simulations to find good quantitative agreement. The numerical calculations, performed using both truncated Wigner and exact $+P$ phase-space methods, include nonlinear and stochastic Raman effects, through coupling to phonon variables. The simulations reveal that excess phase noise, such as from depolarizing guided acoustic wave Brillouin scattering, affects squeezing at low input energies, while Raman effects cause a marked deterioration of squeezing at higher energies and longer fiber lengths. We also calculate the optimum fiber length for maximum squeezing.

Laser cooling and amplification of mechanical modes in an optical cavity are now possible with several device geometries. Quantum back action sets the fundamental limit to cooling. It has, however, not been considered in the regenerative oscillator, wherein mechanical amplification overcomes loss, leading to self-sustained, coherent oscillations at rf and microwave rates. In these devices, the spectral purity, as measured by the phase noise, has a back-action contribution that is herein derived and evaluated in recently characterized systems. Beyond its importance as a fundamental stability limit, it can provide a way to observe quantum back action within the context of cavity optomechanics. The analysis is also applied to the case of cooling, and a pump contribution to the cooling limit is derived.

We study nonclassical and spectral properties of a strongly driven single-atom laser engineered within a photonic crystal that facilitates a frequency-dependent reservoir. In these studies, we apply a dressed atom model approach to derive the master equation of the system and study the properties of the dressed laser under the frequency-dependent transition rates. By going beyond the secular approximation in the dressed-atom cavity-field interaction, we find that if, in addition, the nonsecular terms are included into the dynamics of the system, then nonlinear processes can occur that lead to interesting aspects of cavity field behavior. We calculate variances of the quadrature phase amplitudes and the incoherent part of the spectrum of the cavity field and show that they differ qualitatively from those observed under the secular approximation. In particular, it is found that the nonlinear processes lead to squeezing of the fluctuations of the cavity field below the quantum shot noise limit. The squeezing depends on the relative population of the dressed states of the system and is found only if there is no population inversion between the dressed states. Furthermore, we find a linewidth narrowing below the quantum limit in the spectrum of the cavity field that is achieved only when the secular approximation is not made. An interpretation of the linewidth narrowing is provided in terms of two phase-dependent noise (squeezing) spectra that make up the incoherent spectrum. We establish that the linewidth narrowing is due to squeezing of the fluctuations in one quadrature phase components of the cavity field.

The spatial fragmentation patterns of clusters have been investigated around the Rayleigh instability barrier with a momentum-resolving reaction microscope akin to cold target recoil ion momentum spectroscopy (COLTRIMS). Liquidlike Ne and solid Xe clusters are studied in order to alter the short-range interaction. In the fission regime the neon clusters show spatially anisotropic fragmentation from an expanded geometry as predicted by the liquid drop model, whereas the xenon data suggest a charge separation from neighboring atom positions. For cluster explosion, both systems exhibit an isotropic fragment distribution in agreement with theoretical predictions. The results show how the atom mobility influences the fragmentation dynamics.

We investigate scattering in a one-dimensional two-channel system using a model that is analytically tractable. We find anomalously large time advance over a small energy range of the transmission in the incident channel. This time advance for transmission occurs at energies above threshold of the second channel. Since this feature is related to the phase shifts of the interaction it is not peculiar to the form of the interaction. The anomalous times advance can be related to the pole structure of the $S$ matrix, in particular resonant and shadow poles of the $S$ matrix.

We investigate the most general conditions under which a finite ferromagnetic long-range interacting spin chain achieves unitary fidelity and the shortest transfer time in transmitting an unknown input qubit. A deeper insight into system dynamics, allows us to identify an ideal system involving sender and receiver only. However, this two-spin ideal chain is unpractical due to the rapid decrease of the coupling strength with the distance. Therefore, we propose an optimization scheme for approaching the ideal behavior, while keeping the interaction strength still reasonably high. The procedure is scalable with the size of the system and straightforward to implement.

We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a nonstandard choice of the cost, which is not quadratic in the field. These algorithms can be constructed for pure- and mixed-state quantum systems. The efficiency of the method is shown numerically for molecular orientation with a nonlinearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.

Single-photon core-valence double ionization of molecular oxygen has been studied using a magnetic bottle time-of-flight electron coincidence spectrometer. The $K^{-1}{V}^{-1}$ double ionization electron spectrum of ${\mathrm{O}}_2$ is reported and is assigned with the aid of ab initio calculations. A direct comparison of the core-valence double ionization electron spectra with the conventional valence band photoelectron spectrum is made. The lowest core-valence double ionization energy is found to be $571.6\mathrm{eV}$ and is associated with a ${}^3\Pi$ dicationic state.

The speed of sound of a Bose-Einstein condensate in an optical lattice is studied both analytically and numerically in all spatial three dimensions. Our investigation shows that the sound speed depends strongly on the strength of the lattice. In the one-dimensional case, the speed of sound falls monotonically with increasing lattice strength. The dependence on lattice strength becomes much richer in two and three dimensions. In the two-dimensional case, when the interaction is weak, the sound speed first increases and then decreases as the lattice strength increases. For the three-dimensional lattice, the sound speed can even oscillate with the lattice strength. These rich behaviors can be understood in terms of compressibility and effective mass. Our analytical results in the limit of weak lattices also offer an interesting perspective to help with our understanding: they show that the lattice component perpendicular to the sound propagation increases the sound speed while the lattice component parallel to the propagation decreases the sound speed. The various dependences of the sound speed on the lattice strength are the result of this competition.

A balanced eight-port photon-number-resolving detector is developed. The employed scheme is based on an optical-fiber time-multiplexed device with the unique total optical transmittance reaching 93% and a pair of avalanche photodiodes. The balanced operation is achieved even for imperfect unbalanced fiber splitters used in the time-multiplexed device. The complete characterization of the detector for both classical and single-photon signals is presented. High-speed photon counting at the rates of $100\mathrm{kHz}$ with the total detection efficiency exceeding 50% is verified.

We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From this definition we derive an explicit formula for the hitting time, and explore its dependence on the measurement rate. As the measurement rate goes to either 0 or infinity the hitting time diverges; the first divergence reflects the weakness of the measurement, while the second limit results from the quantum zeno effect. Continuous-time quantum walks, like discrete-time quantum walks but unlike classical random walks, can have infinite hitting times. We present several conditions for existence of infinite hitting times, and discuss the connection between infinite hitting times and graph symmetry.

Linear ${\mathrm{H}}_{2n}$ chains of ${\mathrm{H}}_2$ units are experimentally unrealizable but simple and widely studied exemplars of the response coefficients (polarizabilities and hyperpolarizabilities) of polymer chains in uniform longitudinal electric fields. They show two surprising features: (1) Their response coefficients, unlike those of bulk solids, show a strong nonlinear dependence upon length or $n$. (2) Their response coefficients are seriously too large when computed with standard local or semilocal density functionals, but are much more correct when computed with self-interaction-free approaches (including Hartree-Fock). We propose a simple charge-transfer model which explains both of these effects in analytic terms. In this model, charge is transferred between ${\mathrm{H}}_2$ units paired up at equal distances from but on opposite sides of the chain center. All symmetric pairs of ${\mathrm{H}}_2$ units, not just the one for the chain ends, are included. This transfer is driven by the external electric field, and opposed by the chemical hardness of each ${\mathrm{H}}_2$ unit. Unlike the situation in a bulk solid, this charge transfer is not suppressed (or even much affected) by electrostatic interactions among the transferred charges for $n⩽7$. Self-interaction-free approaches increase the chemical hardness of an ${\mathrm{H}}_2$ unit in comparison with semilocal density functionals, and so reduce the charge transfer. The physical picture behind the model is validated and its limitations are revealed by an analysis of the charge density from self-consistent electronic structure calculations. An appendix presents an accurate method to extract the hyperpolarizability from self-consistent calculations, and its results.