The time-dependent theory of an atomic cascade decay process is discussed. We show that it is useful to measure the spectra of the emitted particles (electrons or photons) as a function of time and introduce time-dependent spectra and time-dependent coincidence spectra. The analysis reveals that there are several timescales involved in the atomic cascades and in the respective spectra. The work prepares the ground for the discussion of molecules, clusters, and solids, where the nuclear dynamics strongly participate in the cascade decay process making it much more complex.

Experiments have shown that the microwave ionization probability of a highly excited, almost monodimensional, hydrogen atom subjected to a microwave pulse sometimes grows in steps when the peak electric field of the pulse is increased. Classical pulsed simulations display the same steps, which have been traced to phase-space metamorphoses. Quantum numerical calculations again exhibit the same ionization steps. I show that the time sequence of two-level interactions, responsible for the observed steps in the quantum picture, is strictly related to the classical phase-space structures generated by the above-mentioned metamorphoses.

A number of recent experiments with nearly pure atomic Bose-Einstein condensates have confirmed the predicted dark soliton oscillations when under harmonic trapping. However, a dark soliton propagating in an inhomogeneous condensate has also been predicted to be unstable to the emission of sound waves. Although harmonic trapping supports an equilibrium between the coexisting soliton and sound, we show that the ensuing dynamics are sensitive to trap anharmonicities. Such anharmonicities can break the soliton-sound equilibrium and lead to the net decay of the soliton on a considerably shorter time scale than other dissipation mechanisms. Thus, we propose that small realistic modifications to existing experimental setups could enable the experimental observation of this decay channel.

The impurity-induced self-trapping and stable moving soliton and breather of two-component Bose-Einstein condensates (BEC’s) in deep $D$-dimensional optical lattices are discussed both analytically and numerically. Under the tight-binding approximation and within a time-dependent variational approach, analytical criteria for occurrences of a self-trapping, moving soliton and breather in the system are obtained. The analytical results are confirmed by direct numerical simulation. It is shown that the dynamics of the condensates can be modified significantly by a minor admixture of an impurity (the second component). The diffusion state of the single-component BEC will transit to the self-trapped state due to the minor admixture of an impurity, even if the two condensates are only with marginal spatial overlap. Furthermore, we find that, in certain conditions, a stable moving soliton can exist in high-dimensional lattices for the two-component BEC’s, which is very different from the single-component BEC (where a moving soliton cannot be stabilized in high-dimensional lattices). On the other hand, the impurity can play a crucial role in causing important coherence-decoherence and localization-delocalization phase transitions.

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.

Using the spin-wave approximation, we study the geometric phase (GP) of a central spin (signal qubit) coupled to an antiferromagnetic (AF) environment under the application of an external global magnetic field. The external magnetic field affects the GP of the qubit directly and also indirectly through its effect on the AF environment. We find that when the applied magnetic field is increased to the critical magnetic field point, the AF environment undergoes a spin-flop transition, a first-order phase transition, and at the same time the GP of the qubit changes abruptly to zero. This sensitive change of the GP of a signal qubit to the parameter change of a many-body environment near its critical point may serve as another efficient tool or witness to study the many-body phase transition. The influences of the AF environment temperature and crystal anisotropy field on the GP are also investigated.

Continuous measurements on correlated quantum systems, in addition to providing information on the state vector of the system in question, induce evolution in the unmeasured degrees of freedom conditioned on the measurement outcome. However, experimentally accessing these nontrivial regimes requires high-efficiency measurements over time scales much longer than the temporal resolution of the measurement apparatus. We report the observation of such a continuous conditioned evolution in the state of a light-collective atomic excitation system undergoing photoelectric measurement.

A sudden change in the Hamiltonian parameter drives a quantum system out of equilibrium. For a finite-size system, expectations of observables start fluctuating in time without converging to a precise limit. A new equilibrium state emerges only in the probabilistic sense, when the probability distribution for the observable expectations over long times concentrates around their mean value. In this paper we study the full statistic of generic observables after a small quench. When the quench is performed around a regular (i.e., noncritical) point of the phase diagram, generic observables are expected to be characterized by Gaussian distribution functions (“good equilibration”). Instead, when quenching around a critical point a new, universal, double-peaked distribution function emerges for relevant perturbations. Our analytic predictions are numerically checked for a nonintegrable extension of the quantum Ising model.

We study how to protect quantum information in quantum systems subjected to local dissipation. We show that combining the use of three-level systems, environment monitoring, and local feedback can fully and deterministically protect any available quantum information, including entanglement initially shared by different parties. These results can represent a gain in resources and/or distances in quantum communication protocols such as quantum repeaters and teleportation as well as time for quantum memories. Finally, we show that monitoring local environments physically implements the optimum singlet conversion protocol, which is essential for classical entanglement percolation.

The entanglement between noncomplementary blocks of a many-body system, where a part of the system forms an ignored environment, is a largely untouched problem without analytic results. We rectify this gap by studying the logarithmic negativity between two macroscopic sets of spins in an arbitrary tripartition of a collection of mutually interacting spins described by the Lipkin-Meshkov-Glick Hamiltonian. This entanglement measure is found to be finite and universal at the critical point for any tripartition whereas it diverges for a bipartition. In this limiting case, we show that it behaves as the entanglement entropy, suggesting a deep relation between the scaling exponents of these two independently defined quantities which may be valid for other systems.

We demonstrate how near-perfect entanglement (in fact arbitrarily close to maximal entanglement) can be generated between the end spins of an antiferromagnetic isotropic Heisenberg chain of length $N$, starting from the ground state in the $N/2$ excitation subspace, by applying a magnetic field along a given direction, acting on a single spin only. Temporally optimal magnetic fields to generate a singlet pair between the two end spins of the chain are calculated for chains up to length $20$ using optimal control theory. The optimal fields are shown to remain effective in various nonideal situations including thermal fluctuations, magnetic field leakage, random system couplings, and decoherence. Furthermore, the quality of the entanglement generated can be substantially improved by taking these imperfections into account in the optimization. In particular, the optimal pulse of a given thermal initial state is also optimal for any other initial thermal state with lower temperature.

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled. We find that on short time scales the relative phase shows “light cone”-like dynamics and creates a metastable superfluid state, which can be supercritical. We also demonstrate similar light cone dynamics for the transverse field Ising model. On longer time scales the supercritical state relaxes to a disordered state due to dynamical vortex unbinding. This scenario of dynamically suppressed vortex proliferation constitutes a reverse-Kibble-Zurek effect. We study this effect both numerically using truncated Wigner approximation and analytically within a newly suggested time dependent renormalization group approach (RG). In particular, within RG we show that there are two possible fixed points for the real-time evolution corresponding to the superfluid and normal steady states. So depending on the initial conditions and the microscopic parameters of the Hamiltonian the system undergoes a nonequilibrium phase transition of the Kosterlitz-Thouless type. The time scales for the vortex unbinding near the critical point are exponentially divergent, similar to the equilibrium case.

Two-path interferometry with coherent states and a squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent light. Here, we investigate the phase sensitivity of such states in the presence of photon losses. It is shown that the Cramer-Rao bound of phase sensitivity can be achieved experimentally by using a weak local oscillator and photon counting in the output. The phase sensitivity is then given by the Fisher information $F$ of the state. In the limit of high squeezing, the ratio $(F–N)/N^2$ of Fisher information above shot noise to the square of the average photon number $N$ depends only on the average number of photons lost, $n_{\mathrm{loss}}$, and the fraction of squeezed vacuum photons $\mu$. For $\mu =1/2$, the effect of losses is given by $(F–N)/N^2=1/(1+2n_{\mathrm{loss}})$. The possibility of increasing the robustness against losses by lowering the squeezing fraction $\mu$ is considered, and an optimized result is derived. However, the improvements are rather small, with a maximal improvement by a factor of 2 at high losses.

Time-delayed systems often exhibit multistability of coexisting attractors, which can result in long chaotic transients on the way to one of the coexisting states. Strong enough noise can transform this transient chaos into noise-sustained dynamics. Here we study the interplay between delay-induced multistability, chaotic transients, and noise, in the case of a semiconductor laser with optical feedback from an external reflector. The time-delayed feedback renders the laser multistable, with a set of coexisting fixed points, and induces dynamical events called low-frequency fluctuations (LFFs), consisting of sudden intensity dropouts at irregular times. The deterministic Lang-Kobayashi model shows that, for a large range of realistic laser parameters, the LFFs are just a transient dynamics toward a stable fixed point. Here we analyze the statistical properties of the transient LFF dynamics and investigate the influence of various parameters. We find that realistic values of the noise strength do not affect the average transient time or its distribution, provided the model includes an explicit delay. On the other hand, nonlinear gain saturation has a strong effect: it increases both the duration of the LFF transients and the probability of noise-induced escapes from the stable fixed point. Our results suggest that the LFFs observed experimentally can be, at least in part, sustained by the interplay of noise and various nonlinear effects, which are phenomenologically represented by a gain saturation coefficient.

Tunable far-infrared laser pulses were generated efficiently during two-color filamentation in air. Understanding the creation of few-cycle far-infrared laser pulses is important since it is at the frontier between two possible generation mechanisms. The first one is the four-wave mixing generation, associated to the generation of wavelengths from ultraviolet up to mid-infrared laser pulses. The second process is the formation of transient photocurrent, which was recently used to describe the generation of submillimetric (terahertz) waves. Comparison between experiments and simulations revealed that the four-wave mixing mechanism is dominant for the far-infrared generation during two-color filamentation.

We develop a general scheme for studying the optical response of ultracold atoms driven into a regime of standing-wave electromagnetically induced transparency. We rely on full numerical solutions of the Maxwell-Liouville equations without invoking secular and adiabatic approximations and arbitrary initial state assumptions. These approximations and assumptions can conceal, e.g., significant loss and diffusion responsible for the decay of stationary light pulses in cold atomic samples. The complex decay dynamics of a stationary light pulse is here analyzed in terms of higher-order spin and optical coherences that arise from nonlinear interactions of the stationary light pulse with the two counterpropagating components of a standing-wave driving field. Specific results for stationary light pulses in cold ${}^{87}\mathrm{Rb}$ atoms have been discussed for temperature regimes where the residual Doppler broadening is negligible.

The feasibility of Bell tests depends to a large extent on the tradeoff of difficulty between the preparation and the measurement of entangled systems. Polarization-entangled systems, though easy to measure, pose a relative challenge in their preparation. The opposite holds with entangled energy eigenstates for which the preparation is relatively straightforward. A way to perform measurements using a photodetector along the $x$, $y$, and $z$ axes (in a Bloch sphere picture) on such Fock-state qubits shall be worked out, taking the $W$ state as our entangled system. This will, by the same token, allow us to determine the minimum quantum efficiency required to perform a conclusive Bell test with the $W$ energy eigenstate.

We present a spectrally decorrelated photon pair source bridging the visible and telecom wavelength regions. Tailored design and fabrication of a solid-core photonic crystal fiber (PCF) lead to the emission of signal and idler photons into only a single spectral and spatial mode. Thus no narrowband filtering is necessary and the heralded generation of pure photon number states in ultrafast wave packets at telecom wavelengths becomes possible.

We calculate the polarization correlation function in the Einstein-Podolsky-Rosen–type experiments with relativistic spin-$1/2$ particles. This function depends monotonically on the particle momenta. Moreover, we also show that the polarization correlation function violates the Clauser-Horn-Shimony-Holt inequality and the degree of this violation can depend on the particle momenta and the motion of observers.