Using the slowly varying envelope approximation in space and time and the expression for the cooperative Lamb shift, I obtain an approximate analytic expression for the spectral distribution of the radiation from a slab of two atoms that was initially weakly excited by an ultrashort resonant pulse. The closed-form expression obtained reproduces very accurately the numerical exact results computed from the eigenmode analysis for the emission from the front face of the slab.

A formulation of quantum-classical hybrid dynamics is presented which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and may be relevant for the foundations of quantum mechanics, in particular, when it comes to experiments exploring the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto but shares with it the fulfillment of all consistency requirements discussed in the literature, while earlier attempts have failed in this respect. Our work is based on the representation of quantum mechanics in the framework of classical analytical mechanics by A. Heslot, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics. This is suitably generalized for quantum-classical hybrids here.

The weak measurement proposed by Aharonov and his colleagues extracts information about a physical quantity of the system by the postselection as shifts of the argument of the probe wave function. The more the postselected state is orthogonal to the preselected state, the larger the shift determined by the weak value becomes. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wave function and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound, in contrast to the Gaussian probe wave function, and that the amplified signal is sharp.

We present a proof-of-principle way to generate nondegenerate multipartite continuous-variable entanglement via atomic spin wave induced by the strong coupling and probe fields in the Λ-type electromagnetically induced transparency configuration in an atomic ensemble. Quantum correlated or anticorrelated and entangled Stokes and anti-Stokes fields, simultaneously produced through scattering the applied laser fields off the atomic spin wave, can be achieved. This method can, in principle, be extended to flexibly and conveniently create multicolor multipartite entangled narrow-band fields to any desired order with long correlation time, which may find promising applications in quantum information processing and quantum networks.

We study random-number-expansion protocols based on the $n\to 1$ quantum random access codes (QRACs). We consider them in the semi-device-independent scenario where the inner workings of the devices are unknown to us but we can certify the dimensions of the systems being communicated. This approach does not require the use of entanglement and makes the physical realization of these protocols much easier than in the standard device-independent scenario. In our work, we propose a protocol for randomness expansion, compute min-entropy for the semi-device-independent protocol, and investigate $n\to 1$ QRACs with a view to their use in randomness-expansion protocols. We also calculate the dependence of the effectiveness of the randomness generation on $n$ and find it optimal for $n=3$, and provide the explanation for this fact.

In this paper, we report a measurement of a single photoionization cross section of atomic Cr as a function of photon energy between 10 and 35 eV. The result is compared to a semiempirical model employing orbital-based ionization cross-section calculations from the literature. While the wide energy splitting of the singly ionized valence states explains the behavior of the ionization cross section in the lower-energy end, reasons for the mismatch between the calculations and the experiment in the higher-energy end are discussed.

We study the behavior of the expectation value of the acceleration of a particle in a one-dimensional periodic potential when an external homogeneous force is suddenly applied. The theory is formulated in terms of modified Bloch states that include the interband mixing induced by the force. This approach allows us to understand the behavior of the wave packet, which responds with a mass that is initially the bare mass, and subsequently oscillates around the value predicted by the effective mass. If Zener tunneling can be neglected, the expression obtained for the acceleration of the particle is valid over time scales of the order of a Bloch oscillation, which are of interest for experiments with cold atoms in optical lattices. We discuss how these oscillations can be tuned in an optical lattice for experimental detection.

We present a method based on time-dependent perturbation theory and complex rotation to treat the interaction of a short light pulse with a correlated atomic system. The pulse is built from two short and weak pulses with Gaussian envelopes that are centered at two different frequencies. The method is applied to the negative hydrogen ion in the vicinity of a doubly excited resonance and it is shown that the two light pulses can be used to alter the Fano profile of a resonance.

The modulation of an optical lattice potential that breaks time-reversal symmetry enables the realization of complex tunneling amplitudes in the corresponding tight-binding model. For a superfluid Fermi gas in a triangular lattice potential with complex tunnelings, the pairing function acquires a complex phase, so the frustrated magnetism of fermions can be realized. Bose-Fermi mixtures of bosonic molecules and unbound fermions in the lattice also show interesting behavior. Due to boson-fermion coupling, the fermions become enslaved by the bosons and the corresponding pairing function takes the complex phase determined by the bosons. In the presence of bosons the Fermi system can reveal both gapped and gapless superfluidity.

By direct application of the fluctuation-dissipation theorem, we numerically calculate the fundamental thermal fluctuations of the dimensions of crystalline CaF${}_2$ whispering-gallery resonators in the case of structural damping, and the limit that this noise imposes on the frequency stability of such resonators at both room and cryogenic temperatures. We analyze elasto-optic noise—the effect of Brownian dimensional fluctuation on frequency via the strain-dependence of the refractive index—a noise term that has so far not been considered for whispering-gallery resonators. We find that dimensional fluctuation sets a lower limit of ${10}^{-16}$ to the Allan deviation for a 10-mm-radius sphere at 5 K, predominantly via induced fluctuation of the refractive index.

I present a feasible scheme to investigate the geometric phase for an atom trapped in an optical cavity induced by the effective decay process due to cavity-photon loss. The cavity mode, together with the external driving fields, acts as the engineered environment of the atom. When the parameters of the reservoir are adiabatically and cyclically changed, the system initially in the nontrivial dark state of the effective Lindblad operator undergoes a cyclic evolution and acquires a geometric phase. The geometric phase can be observed with the atomic-Ramsey-interference oscillation in the decoherence-free subspace.

We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance–optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A optimization is a nonlinear minimization problem; however, we find an analytic solution for 1-qubit state estimation using projective measurements, reducing computational effort. We compare numerically the performances of two adaptive and two nonadaptive schemes for finite data sets and show that the A-optimality criterion gives more precise estimates than standard quantum tomography.

The problem of recognizing (non-)Markovianity of a quantum dynamics is revisited through analyzing quantum correlations. We argue that instantaneouslyvanishing quantum discord provides a necessary and sufficient condition for Markovianity of a quantum map. This is used to introduce a measure of non-Markovianity. This measure, however, requires demanding knowledge about the system and the environment. By using a quantum correlation monogamy property and an ancillary system, we propose a simplified measure with fewer requirements. Non-Markovianity is thereby decided by quantum state tomography of the system and the ancilla.

Charge-state correlated cross sections for single- and multiple-electron removal processes (capture and ionization) in proton-H${}_2$O collisions are calculated by using the nonperturbative basis generator method adapted for ion-molecule collisions [Phys. Rev. A 80, 060702(R) (2009)]. The results are compared with experimental data for a wide range of impact energies spanning from 20 keV to several MeV. Single-electron removal probabilities in each molecular orbital are evaluated using the inclusive-probability formalism to predict the yields of charged fragments (H${}_2$O${}^{+}$, OH${}^{+}$, H${}^{+}$, O${}^{+}$) according to branching ratios that are valid at high impact energies. At intermediate and low energies, we calculate improved fragmentation cross sections that include the effects of multiple-electron removal processes. The resulting fragmentation yields agree with experiments at the 20$\%$–30$\%$ level even below 100 keV impact energy.

Adiabatic approximations are a powerful tool for simplifying nonlinear quantum dynamics, and are applicable whenever a system exhibits a hierarchy of time scales. Current interest in small nonlinear quantum systems, such as few-mode Bose-Hubbard models, warrants further development of adiabatic methods in the particular context of these models. Here we extend our recent work on a simple four-mode Bose-Hubbard model with two distinct dynamical time scales, in which we showed that among the perturbations around excited stationary states of the system is a slow collective excitation that is not present in the Bogoliubov spectrum. We characterized this mode as a resonant energy exchange with its frequency shifted by nonlinear effects, and referred to it as a second Josephson oscillation, in analogy with the second sound mode of liquid helium II. We now generalize our previous theory beyond the mean-field regime, and construct a general Bogoliubov free quasiparticle theory that explicitly respects the system's adiabatic invariant as well the exact conservation of particles. We compare this theory to the numerically exact quantum energy spectrum with up to 40 particles, and find good agreement over a significant range of parameter space.

We formulate a self-consistent Hartree-Fock theory for a spin-1 Bose gas at finite temperature and apply it to characterization of the phase diagram. We find that spin coherence between thermal atoms in different magnetic sublevels develops via coherent collisions with the condensed atoms, and is a crucial factor in determining the phase diagram. We develop analytical expressions to characterize the interaction- and temperature-dependent shifts of the phase boundaries.

We study the problem of a single impurity of mass $M$ immersed in a Fermi sea of particles of mass $m$. The impurity and the fermions interact through an $s$-wave narrow Feshbach resonance, so that the Feshbach length $R_{*}$ naturally appears in the system. We use simple variational ansätze, limited to at most one pair of particle-hole excitations of the Fermi sea, and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed-channel population which is experimentally accessible. Finally, we identify a nontrivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.

We report on the observation of periodic modulations in the second-order photon correlation of single-mode vertical-cavity surface-emitting lasers (VCSELs) in steady-state operations. We realized the fast photon correlation measurement of VCSELs by using a streak camera operated in a photon-counting mode. Fast modulation signals were observed in second-order photon correlations at and around the threshold. The calculations using photon rate equations that include a gain medium dynamics shows that the oscillating signals originate from relaxation oscillations.

We investigate the spatial and spectral properties of broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback by a volume Bragg grating. We demonstrate wavelength locking similar to the case of edge emitters but the spatial mode selection is different from the latter. On-axis spatial solitons obtained at threshold give way to off-axis extended lasing states beyond threshold. The investigations focus on a self-imaging external cavity. We analyze how deviations from the self-imaging condition affect the pattern formation and a certain robustness of the phenomena is demonstrated.