The Josephson junction model is applied to the experimental implementation of classical bifurcation in a quadrupolar nuclear magnetic resonance system. There are two regimes, one linear and one nonlinear, which are implemented by the radio-frequency and the quadrupolar terms of the Hamiltonian of a spin system, respectively. These terms provide an explanation of the symmetry breaking due to bifurcation. Bifurcation depends on the coexistence of both regimes at the same time in different proportions. The experiment is performed on a lyotropic liquid crystal sample of an ordered ensemble of ${}^{133}$Cs nuclei with spin $I=7/2$ at room temperature. Our experimental results confirm that bifurcation happens independently of the spin value and of the physical system. With this experimental spin scenario, we confirm that a quadrupolar nuclei system could be described analogously to a symmetric two-mode Bose-Einstein condensate.

We propose a scheme to produce ultraslow ($3+1$)-dimensional helical optical solitons, also called helical optical bullets, in a resonant three-level $\Lambda$-type atomic system via quantum coherence. We show that, due to the effect of electromagnetically induced transparency, the helical optical bullets can propagate with an ultraslow velocity up to ${10}^{-5}$ $c$ ($c$ is the light speed in vacuum) in the longitudinal direction and a slow rotational motion (with velocity ${10}^{-7}$ $c$) in transverse directions. The generation power of such optical bullets can be lowered to microwatts, and their stability can be achieved by using a Bessel optical lattice potential formed by a far-detuned laser field. We also show that the transverse rotational motion of the optical bullets can be accelerated by applying a time-dependent Stern-Gerlach magnetic field. Because of the ultraslow velocity in the longitudinal direction, a significant acceleration of the rotational motion of optical bullets may be observed for a very short medium length.

Pulsed parametric down-conversion (PDC) processes generate photon pairs with a rich spectral-temporal structure, which offer an attractive potential for quantum information and communication applications. We investigate the four-dimensional chronocyclic Wigner function $W_{\mathrm{PDC}}({\omega }_{\mathrm{s}},{\omega }_{\mathrm{i}},{\tau }_{\mathrm{s}},{\tau }_{\mathrm{i}})$ of the PDC state, which naturally lends itself to the pulsed characteristics of these states. From this function we derive the conditioned time-bandwidth product of one of the pair photons, a quantity which not only is a valid measure of entanglement between the PDC photons but also allows us to highlight a remarkable link between the discrete- and continuous-variable descriptions of PDC. We numerically analyze PDC processes with different conditions to demonstrate the versatility of our approach, which is applicable to a large number of current PDC sources.

We review recent experimental investigation on spatial shock waves formed by the self-defocusing action of a laser beam propagating in disordered thermal nonlinear media.

A $\mathcal{PT}$-symmetric Bose-Einstein condensate can be theoretically described using a complex optical potential; however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a $\mathcal{PT}$-symmetric system, where the $\mathcal{PT}$-symmetric currents of a two-well system are implemented by coupling two additional wells to the system, which act as particle reservoirs. In terms of a simple four-mode model we derive conditions under which the two middle wells of the Hermitian four-well system behave exactly as the two wells of the $\mathcal{PT}$-symmetric system. We apply these conditions to calculate stationary solutions and oscillatory dynamics. By means of frozen Gaussian wave packets we relate the Gross-Pitaevskii equation to the four-mode model and give parameters required for the external potential, which provides approximate conditions for a realistic experimental setup.

We explore a model of the world based on real-vector-space quantum theory. In our model the familiar complex phase appearing in quantum states is replaced with a single binary object that we call the ubit, which is not localized and which can interact with any object in the world. Ordinary complex-vector-space quantum theory can be recovered from this model if we simply impose a certain restriction on the sets of allowed measurements and transformations (Stueckelberg's rule), but in this paper we try to obtain the standard theory, or a close approximation to it, without invoking such a restriction. We look particularly at the effective theory that applies to a subsystem when the ubit is interacting with a much larger environment. In a certain limit it turns out that the ubit-environment interaction has the effect of enforcing Stueckelberg's rule automatically, and we obtain a one-parameter family of effective theories—modifications of standard quantum theory—that all satisfy this rule. The one parameter is the ratio $s/\omega$, where $s$ quantifies the strength of the ubit's interaction with the rest of the world and $\omega$ is the ubit's rotation rate. We find that when this parameter is small but not zero, the effective theory is similar to standard quantum theory but is characterized by spontaneous decoherence of isolated systems.

The relativistic quantum dynamics of an electron in an intense single-mode quantized electromagnetic field is investigated with special emphasis on the spin degree of freedom. In addition to fast spin oscillations at the laser frequency, a second time scale is identified due to the intensity-dependent emissions and absorptions of field quanta. In analogy to the well-known phenomenon in atoms at a moderate laser intensity, we put forward the conditions of collapses and revivals for the spin evolution in laser-driven electrons starting at the feasible intensity of ${10}^{18}$ W/cm${}^2$.

The testability of the Kochen-Specker theorem is a subject of ongoing controversy. A central issue is that experimental implementations relying on sequential measurements cannot achieve perfect compatibility between the measurements and that therefore the notion of noncontextuality does not apply. We demonstrate by an explicit model that such compatibility violations may yield a violation of noncontextuality inequalities, even if we assume that the incompatibilities merely originate from context-independent noise. We show, however, that this problem can be circumvented by combining the ideas behind Leggett-Garg inequalities with those of the Kochen-Specker theorem.

In the framework of dilatation transformation based on complex scaling, we show that the dilated non-Hermitian Hamiltonian may be decoupled into two separated Hermitian operators, namely, the resonance energy operator and the decay rate operator, i.e., the FWHM. We present an intrinsic relationship between these operators. Specifically, we show that the effective potential for resonance decay rate is a virial function of the effective potential for resonance energy. As examples of their application, we invoke the decoupled Hamiltonian operators for resonance states of a single particle in a central force field and to problems in potential scattering to identify the resonance states and determine resonance energy and decay rate.

We present a mechanism that permits the parallel execution of multiple quantum gate operations within a single long linear ion chain. Our approach is based on large coherent forces that occur when ions are electronically excited to long-lived Rydberg states. The presence of Rydberg ions drastically affects the vibrational mode structure of the ion crystal, giving rise to modes that are spatially localized on isolated subcrystals which can be individually and independently manipulated. We theoretically discuss this Rydberg mode shaping in an experimentally realistic setup and illustrate its power by analyzing the fidelity of two conditional phase flip gates executed in parallel. The ability to dynamically shape vibrational modes on the single-ion level might find applications in quantum simulators and quantum computation architectures.

We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the “standard” five-qubit and CSS codes, on solid-state qubits with Ising or $XY$-type interactions. Using pulse sequences, we show how to dynamically generate the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and errors caused by local sources.

We analyze the accuracy of quantum phase gates acting on “0-$\pi$ qubits” in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an $LC$ oscillator and a qubit or pair of qubits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance $\sqrt{L/C}$ is large compared to $\hslash /4e^2\approx 1\mathrm{k}\Omega$. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.

A non-Hermitian shortcut to adiabaticity is introduced. By adding an imaginary term in the diagonal elements of the Hamiltonian of a two-state quantum system, we show how one can cancel the nonadiabatic losses and perform an arbitrarily fast population transfer, without the need to increase the coupling. We apply this technique to two popular level-crossing models: the Landau-Zener model and the Allen-Eberly model.

The hyperspherical adiabatic curves (adiabatic eigenenergies as functions of the hyperradius $R$) of helium for zero total angular momentum are analyzed by studying the underlying classical dynamics which in the adiabatic treatment reduces to constrained two-electron motion on a hypersphere. This dynamics supports five characteristic classical configurations which can be represented by five types of short periodic orbits: the frozen planet (FP), the inverted frozen planet (IFP), the asymmetric stretch (AS), the asynchronous (ASC), and the Langmuir periodic orbit (PO). These POs are considered as fundamental modes of the two-electron motion on a hypersphere which, after quantization, give five families of so-called adiabatic lines (adiabatic energies related to these POs as functions of $R$). It is found that multiplets, each of them consisting of adiabatic curves which converge to the same ionization threshold, are at large values of $R$ delimited from the bottom and from the top by the adiabatic lines which are related to the IFP and stable AS POs and to the FP PO, respectively. At smaller values of $R$, where the AS PO becomes unstable, the curves move to the area between the ASC (bottom) and AS (top) lines by crossing the latter. Therefore, at different values of $R$ the lower limiting line of the multiplet is related to the three types of PO (IFP, AS, and ASC), which are all stable in the negative-energy part of this line. As a consequence, the quantum states of helium in principle are not related individually to a single classical configuration on the hypersphere. In addition, it is demonstrated that “unstable parts” of adiabatic lines (the so-called diabatic curves) determine the positions and type of avoided and hidden crossings between hyperspherical adiabatic curves. Two clearly visible classes of avoided crossings are related to the AS and ASC POs. In addition, a number of avoided crossings of the adiabatic curves is observed at the positions where the adiabatic lines that are related to different types of PO cross mutually. Finally, a class of hidden crossings which is located near the saddle point of the potential is related to the Langmuir orbit. The large spacing between adiabatic curves at the positions of these hidden crossings is explained by high instability of the Langmuir PO compared to the AS and ASC POs.

We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values and uncertainties are provided for the relevant electric-dipole matrix elements. Polarizabilities of the $4s$, $4p_j$, $5s$, $5p_j$, and $3d_j$ states are compared with other theoretical and experimental values when possible. We identify magic wavelengths for the $4s-np$ transitions for $n=4,5$, i.e., those wavelengths for which the two levels have the same ac Stark shifts. The magic wavelengths for the $4s-5p$ transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interesting region of $1050–1130$ nm.

In a recent publication [D. Assafrão et al., Phys. Rev. A 84, 022713 (2011)] a model-potential approach was proposed to positron-atom scattering based on an adiabatic method that treats the positron as a light nucleus. In this paper the formalism is further improved by the introduction of semiempirical energy terms which appropriately account for the positron-target interaction at long and short ranges. Our method allows us to describe the main observed features of the elastic cross sections for positron scattering from He, Ne, Ar, Kr, and Xe. Valuable insights into the cross-section behavior below the positronium formation threshold, the scattering lengths, and other aspects of the low-energy positron-noble gases scattering are presented.

Optical laser pulses play important roles in various fields, and the phononlike analog, i.e., phonon laser pulses, should also be very useful. We show the possibility of pulsed phonon lasing in trapped ions based on our observation that coherent phonon pulses are generated and then transferred between transverse dimensions due to nonlinear resonance once the oscillation amplitude of the trapped ions is larger than a threshold. We study the pulsed phonon output with the multiple-scale method using the first-order nonlinear differential equations which govern time evolution of the amplitudes and phases of the interacting modes. We also discuss the feasibility of $Q$-switched pulsed phonon lasing and the potential application.

The molecular high-order-harmonic generation (molecular HHG) of HeH${}^{2+}$ is investigated by numerical integration of the non-Born-Oppenheimer time-dependent Schrödinger equation. The results show that multichannel interference plays a very important role in the process of asymmetric molecular high-order-harmonic generation. By means of the classical returning kinetic energy map and the time-frequency distribution, the mechanism of molecular HHG for HeH${}^{2+}$ is discussed in detail. Further studies show that asymmetric molecular harmonic emission is very sensitive to the nuclear signatures, i.e., the initial vibrational state and the isotopic effect. Besides, the electron-nuclear probability density distributions are calculated to better understand the process of the asymmetric molecular HHG, from which the electron-nuclear dynamics can be revealed.

We study analytically and numerically the binding properties, in particular the ground state, of the so-called $(2+1)$-fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system.

We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of both hopping and population imbalance by means of dynamical mean-field theory (DMFT). It is shown that these mixtures can have easy-axis antiferromagnetic, ferrimagnetic, charge-density wave, and canted-antiferromagnetic order or be unordered depending on parameters of the system. We study the resulting phase diagram in detail and investigate the stability of the different phases with respect to thermal fluctuations. We also perform a quantitative analysis for a gas confined in a harmonic trap, both within the local density approximation and using a full real-space generalization of DMFT.