We conduct a detailed analysis of a phase estimation experiment with a Bose-Einstein condensate in a double potential well. Our goal is to confront the theoretical considerations with the conditions of a real experiment. We present a typical experimental procedure and the theoretical model. We simulate the estimation of phase between two modes in two cases: based on the full correlation function measurement for two atoms and on the center of mass position measurement for 20 atoms. We show that a lossless atom detection lets us exceed the shot noise (that is purely classical) limit of phase estimation precision with the currently available spatial resolution, while a few times higher resolution will make it possible to approach the highest precision allowed by quantum physics.

We study the directional properties of a radiation field emitted by a geometrically small system composed of two identical two-level emitters located at short distances and driven by an optical vortex beam, a Laguerre-Gaussian beam which possesses a structured phase and amplitude. We find that the system may operate as a nanoantenna for controlled and tunable directional emission. Polar diagrams of the radiation intensity are presented showing that a constant phase or amplitude difference at the positions of the emitters plays an essential role in the directivity of the emission. We find that the radiation patterns may differ dramatically for different phases and amplitude differences at the positions of the emitters. As a result the system may operate as a two- or one-sided nanoantenna. In particular, a two-sided highly focused directional emission can be achieved when the emitters experience the same amplitude and a constant phase difference of the driving field. We find the general directional property of the emitted field that when the phase differences at the positions of the emitters equal an even multiple of $\pi /4$, the system behaves as a two-sided antenna. When the phase difference equals an odd multiple of $\pi /4$, the system behaves as a one-sided antenna. The case when the emitters experience the same phase but different amplitudes of the driving field is also considered and it is found that the effect of different amplitudes is to cause the system to behave as a unidirectional antenna radiating along the interatomic axis.

Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by random matrix theory. Scattering resonances observed in ultracold atomic and molecular systems exhibit similar features as a consequence of their energy level structure. We study how the overlap between Feshbach resonances affects the distribution of resonance spacings. The spectrum of strongly overlapping resonances turns out to be non-Poisson even when the assumptions of random matrix theory are not fulfilled, but the spectrum is also not completely chaotic and tends towards being semi-Poisson.

Optomechanics is currently believed to provide a promising route towards the achievement of genuine quantum effects at the large, massive-system scale. By using a recently proposed figure of merit that is well suited to address continuous-variable systems, in this paper we analyze the requirements needed for the state of a mechanical mode (embodied by an end-cavity cantilever or a membrane placed within an optical cavity) to be qualified as macroscopic. We show that according to the phase-space-based criterion that we have chosen for our quantitative analysis, the state achieved through strong single-photon radiation-pressure coupling to a quantized field of light and conditioned by measurements operated on the latter might be interpreted as macroscopically quantum. In general, though, genuine macroscopic quantum superpositions appear to be possible only under quite demanding experimental conditions.

A universal deterministic noiseless quantum amplifier has been shown to be impossible. However, probabilistic noiseless amplification of a certain set of states is physically permissible. Regarding quantum state amplification as quantum state transformation, we show that deterministic noiseless amplification of coherent states chosen from a proper set is attainable. The relation between input coherent states and gain of amplification for deterministic noiseless amplification is thus derived. Furthermore, we extend our result to more general situation and show that deterministic noiseless amplification of Gaussian states is also possible. As an example of application, we find that our amplification model can obtain better performance in homodyne detection to measure the phase of state selected from a certain set. Besides, other possible applications are also discussed.

We analyze the momentum distribution function and its artificial-gauge-field dependence for the Mott insulator phases of the Hofstadter-Bose-Hubbard model. By benchmarking the results of the random-phase approximation approach against those of the strong-coupling expansion for the Landau and symmetric gauges, we find pronounced corrections to the former results, which is a clear manifestation of the critical role played by quantum fluctuations in two dimensions.

We study energy transport in a chain of quantum harmonic and anharmonic oscillators where the anharmonicity is induced by interaction between local vibrational states of the chain. Using adiabatic elimination and numerical simulations with matrix product states, we show how strong interactions significantly slow down the relaxation dynamics (with the emergence of a different time scale) and can alter the properties of the steady state. We also show that steady-state properties are completely different depending on the order in which the limits of infinite time and infinite interaction are taken.

Beliaev damping in a superfluid is the decay of a collective excitation into two lower-frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at $T=0$. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final-state momenta must be collinear to the initial state. We extend this treatment, showing that the inclusion of a gradient term in the Hamiltonian yields a realistic spectrum for the bosonic excitations; we then derive a formula for the decay rate of such excitations and show that even moderate nonlinearities in the spectrum can yield substantial deviations from the standard result. We apply our result to an attractive Fermi gas in the BCS–Bose-Einstein condensate crossover: Here the low-energy bosonic collective excitations are density oscillations driven by the phase of the pairing order field. These collective excitations, which are gapless modes as a consequence of the Goldstone mechanism, have a spectrum that is well established both theoretically and experimentally and whose linewidth, we show, is determined at low temperatures by the Beliaev decay mechanism.

Increasing the electron density of collisionally pumped plasma-based soft-x-ray lasers offers promising opportunities to deliver ultrashort pulses. However, strong nonlinear effects, such as overionization-induced refraction and self-focusing, hinder the propagation of the laser beam and thus the generation of elongated volume of lasing ions to be pumped. Using a particle-in-cell code and a ray-tracing model we demonstrate that optically preformed waveguides allow for addressing those issues through a self-regulation regime between self-focusing and overionization processes. As a result, guiding intense pulses over several millimeters leads to the implementation of saturated plasma amplifiers.

We study both theoretically and experimentally the effects of introducing deliberate disorder in a slow-light photonic crystal waveguide on the photon density of states. We introduce a theoretical model that includes both deliberate disorder through statistically moving the hole centers in the photonic crystal lattice and intrinsic disorder caused by fabrication imperfections. We demonstrate a disorder-induced mean blueshift and an overall broadening of the photonic density of states for deliberate disorder values ranging 0–12 nm. By comparing with measurements obtained from a GaAs photonic crystal waveguide, we find very good agreement between theory and experiment. These results highlight the importance of carefully including local field effects for modeling high-index contrast perturbations and demonstrate the efficiency of our perturbative approach for modeling disorder-induced changes in the density of states. Our work also demonstrates the importance of using asymmetric dielectric polarizabilities for positive and negative dielectric perturbations when modeling a perturbed dielectric interface in photonic crystal platforms. Finally, we also show examples of disorder-induced resonances that can appear for various instances of disorder.

We have measured the hyperfine structure and isotope shifts of the 402.0- and 399.6-nm resonance lines in ${}^{229}\mathrm{Th}^{+}$. These transitions could provide pathways towards the excitation of the ${}^{229}\mathrm{Th}$ low-energy isomeric nuclear state. An unexpected negative isotope shift relative to ${}^{232}\mathrm{Th}^{+}$ is observed for the 399.6-nm line, indicating a strong Coulomb coupling of the excited state to the nucleus. We have developed an all-order approach to the isotope shift calculations that is generally applicable to heavy atoms and ions with several valence electrons. The theoretical calculations provide an explanation for the negative isotope shift of the 399.6-nm transition and yield a corrected classification of the excited state. The calculated isotope shifts are in good agreement with experimental values.

Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such “mesoscopic quantum electrodynamics” is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to “doing quantum electrodynamics while thinking classically,” allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

Resonant charge transfer (RCT) between negative ions and a metallic nanosystem was investigated by means of a high-performance ab initio three-dimensional (3D) numerical solver. During RCT, an electron was shown to occupy succesively nanosystem eigenstates along the $z, \rho$, and $\phi$ coordinates. Electron tunneling into a nanosystem is a reversible process, because after some time the electron propagates back to the ion. RCT efficiency in a nanosystem was found to exhibit quantum-size effects as well as lateral ion position dependence. This means that during ion-surface interaction, the nanosystem's size and the ion trajectory strongly influence the final charge state of the ion. In the case of real 3D systems (without cylindrical symmetry), the electron density currents form quantum vortices; this result is rather nontrivial for static systems. In addition, the limits of the adiabatic approximation (rate equation) for the RCT calculation with nanosystems are defined.

A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and extends its capabilities. Specifically, the Schwinger variational approach gives results without the divergences that need to be regularized in other methods. Furthermore, it provides a framework to identify the origin of these singularities and possibly improve the local frame transformation. We have used the method to obtain the scattering parameters for different confining potentials symmetric in $x,y$. The method is also used to treat photodetachment processes in the presence of various confining potentials, thereby highlighting effects of the infinitely many closed channels. Two general features predicted are the vanishing of the total photoabsorption probability at every channel threshold and the occurrence of resonances below the channel thresholds for negative scattering lengths. In addition, the case of negative-ion photodetachment in the presence of uniform magnetic fields is also considered where unique features emerge at large scattering lengths.

We study theoretically many-body equilibrium magnetic phases and corresponding thermodynamic characteristics of ultracold three-component fermionic mixtures in optical lattices described by the SU(3)-symmetric single-band Hubbard model. Our analysis is based on the generalization of the exact diagonalization solver for multicomponent mixtures that is used in the framework of the dynamical mean-field theory. It allows us to obtain a finite-temperature phase diagram with the corresponding transition lines to magnetically ordered phases at filling one particle per site (1/3 band filling) in simple cubic lattice geometry. Based on the developed theoretical approach, we also attain the necessary accuracy to study the entropy dependence in the vicinity of magnetically ordered phases that allows us to make important predictions for ongoing and future experiments aiming to approach and study long-range-order phases in ultracold atomic mixtures.

We study a system of few fermions in a one-dimensional harmonic trap and focus on the case of dipolar majority particles in contact with a single impurity. The impurity is used both for quenching the system and for tracking the system evolution after the quench. Employing exact diagonalization, we investigate relaxation and thermalization properties. In the absence of dipolar interactions, the system dynamics remains oscillatory even on long time scales. On the other hand, repulsive as well as attractive dipolar interactions lead to quick relaxation to the diagonal ensemble average, which is significantly different from corresponding thermal averages. A Wigner-shaped level spacing distribution indicates level repulsion and thus chaotic dynamical behavior due to the presence of dipolar interactions.

Scaling in the dynamical properties of complex many-body systems has been of strong interest since turbulence phenomena became the subject of systematic mathematical studies. In this article, dynamical critical phenomena far from equilibrium are investigated with functional renormalization-group equations. The focus is set on scaling solutions of the stochastic driven-dissipative Burgers equation and their relation to solutions known in the literature for Burgers' and Kardar-Parisi-Zhang dynamics. We furthermore relate superfluid as well as acoustic turbulence described by the Gross-Pitaevskii model to known analytic and numerical results for scaling solutions. In this way, the canonical Kolmogorov exponent $\frac{5}{3}$ for the energy cascade in superfluid turbulence is obtained analytically. We also get results for anomalous exponents of acoustic and quantum turbulence. These are consistent with existing experimental data. Our results should be relevant for future experiments with, e.g., exciton-polariton condensates in solid-state systems as well as with ultracold atomic gases.