We propose a method to detect the amplitude gradient of a microwave field by using a pair of entangled two-component Bose-Einstein condensates. We consider the two spatially separated condensates to be coupled to the two different magnetic fields. The magnetic-field gradient can be determined by measuring the variances of population differences and relative phases between the two-component condensates in two wells. The precision of measurement can reach the Heisenberg limit. We study the effects of one-body and two-body atom losses on the detection. We find that the entangled atoms can outperform the uncorrelated atoms in probing the magnetic fields in the presence of atom losses. The effect of atom-atom interactions is also discussed.

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi–von Weizsäcker (TF–vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity.

We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicality indicators could give further evidence of the quantum nature of the dynamical Casimir radiation in these circuits.

Modulational instability (MI) in a twin-core optical fiber with the combined effect of saturation of nonlinearity (SNL) and coupling coefficient dispersion (CCD) is presented. The CCD does not dramatically modify the spectrum of the symmetric or antisymmetric continuous wave (CW) case, but the SNL on the other hand behaves in a perceptible manner such that the gain and the unstable region inherently decrease. In the anomalous dispersion region, the gain of the instability spectrum increases (decreases) monotonously with power (coupling coefficient). The effective nonlinearity and the power threshold for the sustained CW solution becomes a function of power for the SNL case. The so-called nonlinear factor behaves in a unique way such that there exist two powers for the same value of nonlinear factor. The interplay between CCD and SNL is emphasized, where any nonzero value of CCD leads to new instability bands and the saturation on the other hand suppresses the gain of the instability band. We identified a pair of power corresponding to the constant value of the nonlinear factor, where the system becomes invariant, such that the number of instability bands, the gain, and the range of the unstable region are all preserved. In the case of the normal dispersion case, the MI is achieved purely by means of the coupling coefficient. In both cases, a critical CCD is predicted, where the system evolves dramatically in a different manner.

We introduce the term Majoranon to describe particles that obey the Majorana equation, which are different from the Majorana fermions widely studied in various physical systems. A general procedure to simulate the corresponding Majoranon dynamics, based on a decomposition of the Majorana equation into two Dirac equations, is described in detail. It allows the simulation of the two-component chiral spinors, the building blocks of modern gauge theories, in the laboratory with current technology. Specifically, a Majoranon in one spatial dimension can be simulated with a single qubit plus a continuous degree of freedom, for example, a single trapped ion. Interestingly, the dynamics of a Majoranon deviates most clearly from that of a Dirac particle in the rest frame, in which the continuous variable is redundant, making a possible laboratory implementation feasible with existing setups.

The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.

It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a massive relativistic particle in a superposition of two counterpropagating momentum states leads to a paradox. The paradox entails the instantaneous transmission of information between two spatially separated parties. A solution to the paradox is given when the physical construction of the corresponding state is taken into account, suggesting that we cannot in general linearly apply the Wigner rotations to a quantum state without considering the appropriate physical interpretation.

We study the ground-state entanglement in systems of spins forming the boundary of a quantum spin network in arbitrary geometries and dimensionality. We show that as long as they are weakly coupled to the bulk of the network, the surface spins are strongly entangled, even when distant and not directly interacting, thereby generalizing the phenomenon of long-distance entanglement occurring in quantum spin chains. Depending on the structure of the couplings between surface and bulk spins, we discuss in detail how the patterns of surface entanglement can range from multipair bipartite to fully multipartite. In the context of quantum information and communication, these results find immediate application to the implementation of quantum routers, that is, devices able to distribute quantum correlations on demand among multiple network nodes.

Two different theoretical methods have been used to complete a calculation of polarizability in the thallium $6p_{1/2}$, $7s$, and $7p_{1/2}$ states. The predictions of the two methods agree to within 1$\%$ for the $6p_{1/2}$ and $7s$ states and 2$\%$ for the $7p_{1/2}$ state. We find that the theoretical expression for the $6p_{1/2}$-$7s$ transition polarizability difference $\Delta {\alpha }_0$ is dominated (greater than 90$\%$ contribution) by mixing of the $7s$ state with the $7p_{1/2}$ and $7p_{3/2}$ states. By comparing the theoretical expression to an existing measurement of $\Delta {\alpha }_0$ [Doret et al., Phys. Rev. A 66, 052504 (2002)], highly accurate values for the thallium $7p$ excited-state lifetimes have been extracted. The scalar polarizability of the $7p_{1/2}$ state is also computed, anticipating an experimental determination of this quantity, which will then enable a high-precision determination of the $6d_j$-$7p_{j^{\prime }}$ transition rates and provide a benchmark test of the two theoretical approaches in the near future.

We study the creation of electron-positron pairs induced by two spatially separated electric fields that vary periodically in time. The results are based on large-scale computer simulations of the time-dependent Dirac equation in reduced spatial dimensions. When the separation of the fields is very large, the pair creation is caused by multiphoton transitions and mainly determined by the frequency of the fields. However, for small spatial separations a coherence effect can be observed that can enhance or reduce the particle yield compared to the case of two infinitely separated fields. If the travel time for a created electron or positron between both field locations becomes comparable to the period of the oscillating fields, we observe peaks in the energy spectrum which can be explained in terms of field-induced transient bound states.

We show by numerically solving the Bogoliubov–de Gennes equations and numerically integrating the Gross-Pitaevskii equation that the onset of the snake instability of ring dark solitons requires a broken symmetry. We elucidate explicitly the connection between imaginary Bogoliubov modes and the snake instability, predicting the number of vortex-antivortex pairs produced. In addition, we propose a simple model to give a physical motivation as to why the snake instability takes place and needs a broken symmetry. Finally, we show that tight confinement in a toroidal potential actually enhances soliton decay due to inhibition of soliton motion, but can lead to a periodic revival of the ring dark soliton after the first snake instability.

We study pattern formation in a passive nonlinear optical cavity on the basis of the classic Lugiato-Lefever model with a periodically modulated injection. When the injection amplitude sign alternates, e.g., following a sinusoidal modulation in time or in space, a phase-bistable response emerges, which is at the root of the spatial pattern formation in the system. An asymptotic description is given in terms of a damped nonlinear Schrödinger equation with parametric amplification, which allows gaining insight into the basic spatiotemporal dynamics of the system. One- and two-dimensional phase-bistable spatial patterns, such as bright and dark-ring cavity solitons and labyrinths, are demonstrated.

We experimentally generate arbitrary time-bin qubits using continuous-wave light. The advantage unique to our qubit is its compatibility with deterministic continuous-variable quantum information processing. This compatibility comes from its well-defined spatiotemporal mode and frequency spectrum within the operational bandwidth of the current continuous-variable technology. We also demonstrate an efficient scheme to characterize time-bin qubits via eight-port homodyne measurement. This enables the complete characterization of the qubits as two-mode states, as well as a flexible analysis equivalent to the conventional scheme based on a Mach-Zehnder interferometer and photon detection.

Topological quantum error-correction codes are extremely practical, typically requiring only a two-dimensional lattice of qubits with tunable nearest-neighbor interactions yet tolerating high physical error rates $p$. It is computationally expensive to simulate the performance of such codes at low $p$, yet this is a regime we wish to study as low physical error rates lead to low qubit overhead. We present a very general method of analytically estimating the low-$p$ performance of the most promising class of topological codes. Our method can handle arbitrary periodic quantum circuits implementing the error detection associated with this class of codes, and arbitrary Pauli error models for each type of quantum gate. Our analytic expressions take only seconds to obtain, versus hundreds of hours to perform equivalent low-$p$ simulations.

We show that far-field diffraction images of spontaneously scattered Raman photons can be used for detection of spin entanglement and for metrology of field gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in the spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. The gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precession, which suggests a possibility for precision measurements beyond the standard quantum limit without entanglement. Monitoring of the temporal decay of the diffraction peak can also realize a nondemolition probe of the temperature and collisional interactions in trapped cold atomic gases. The approach can be readily generalized to cold molecules, trapped ions, and solid-state spin ensembles.

We derive a Bohmian trajectory-based quantum dynamics approach for the calculation of adiabatic and nonadiabatic quantum effects in ab initio on-the-fly molecular dynamics simulations. The method is designed for calculations in the full, unconstrained, phase space of molecular systems described within density functional theory and time-dependent density functional theory. The problem of solving quantum hydrodynamic equations using trajectories in high dimensions is addressed using an expansion of the nuclear amplitude in atom centered Gaussians that are propagated along the quantum trajectories. In this work, we investigate the adiabatic limit of this theory, even though the full nonadiabatic case is derived. The method is first tested on the H${}_2$ molecule and then applied to the study of the proton transfer dynamics in the phase space of the molecular complex (H${}_3$N-H-NH${}_3$)${}^{+}$.

Saturation of vibrational Raman coherence and coherent anti-Stokes Raman scattering (CARS) using femtosecond (fs) excitation pulses is investigated theoretically. The pump in a typical fs-CARS configuration has a bandwidth of a few hundred cm${}^{-1}$ that can couple tens of rotational states of room-air nitrogen molecules simultaneously, unlike in CARS with longer pulse durations. It is demonstrated that the vibrational coherence and also the vibrational CARS with fs excitation display saturationlike behavior once the rotational coherence is saturated. The Raman saturation threshold for the fs pump is numerically estimated to be at a peak intensity of $\sim$${10}^{22}$ W/m${}^2$, which is six to seven orders of magnitude higher than that in the nanosecond regime. The results are compared with the known saturation thresholds in different pulse-duration regimes and placed in perspective with other nonlinear thresholds reported in fs excitation regimes.

We examine the feasibility of a parity nonconserving (PNC) optical rotation experiment for the ${}^2{P}_{3/2}\to$ ${}^2{P}_{1/2}$ transition of atomic iodine at 1315 nm. The calculated $E{1}_{\mathrm{PNC}}$ to $M1$ amplitude ratio is $R=0.80\left(16\right)\times {10}^{-8}$. We show that very large PNC rotations (greater than 10 $\mu$rad) are obtained for iodine-atom column densities of $\sim$${10}^{22}$ cm${}^{-2}$, which can be produced by increasing the effective interaction path length by a factor of $\sim$${10}^4$ with a high-finesse optical cavity. The simulated signals indicate that measurement of the nuclear anapole moment is feasible and that a 1$\%$ PNC precision measurement should resolve the inconsistency between previous measurements in Cs and Tl.

The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment state. We reexamine the connections between complete positivity and quantum discord within two different sets of assumptions about the relevant family of initial states. We present an example of a system-environment state with nonvanishing quantum discord that leads to a completely positive map. This invalidates an earlier claim about the necessity of vanishing quantum discord for completely positive maps. In our final remarks, we discuss the physical validity of each approach.