According to the Schiff theorem the nuclear electric dipole moment (EDM) is screened in neutral atoms. In ions this screening is incomplete. We extend a derivation of the Schiff theorem to ions and molecules. The finite nuclear size effects are considered including $Z^2{\alpha }^2$ corrections to the nuclear Schiff moment, which are significant in all atoms and molecules of experimental interest. We show that in a majority of ionized atoms the nuclear EDM contribution to the atomic EDM dominates, while in molecules the contribution of the Schiff moment dominates. We also consider the screening of electron EDM in ions.

In a single free two-valence-electron atom, the motion of the electron spin is a consequence of quantum statistics and the Pauli exclusion principle. Subsequently, during an electron impact exchange excitation from a ${}^1{S}_0{M}_S=0$ to a ${}^3{S}_1{M}_S=0$ state, the electron spin is “parallel transported” around a closed path with a geometrical Berry phase of π radians creating an aligned exchange spin angular momentum. This alignment is observed via the Stokes parameter $P_2$ of the photon decay into a ${}^{3}P$ state. The geometric phase is in addition to the dynamic phase. Measurements from zinc and mercury atoms in different laboratories show the effect close to the excitation threshold where there are no competing excitation processes. Similar effects are expected in other atomic and molecular quantum scattering processes where comparable geometrical or topological paths exist. Electron quantum scattering theories use antisymmetrized wave functions but none include this geometrical exchange angular momentum.

We present a method for phase and number squeezing in two-mode Bose systems using dissipation. The effectiveness of this method is demonstrated by considering cold Bose gases trapped in a double-well potential. The extension of our formalism to an optical lattice gives control of the phase boundaries of the steady-state phase diagram, and we discover a phase characterized by a nonzero condensate fraction and thermal-like particle-number statistics. We also show how to perform amplitude squeezing in a single-mode system using dissipation.

We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains by using a many-body generalization recently reported Chen et al. [Nature Phys. 7, 61 (2011)], within the decoupling approximation and the one-level band scheme. The energy spectrum shows evidence of the structure of the avoided level crossings as a function of the onsite interparticle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle Landau-Zener predictions. In the strong-coupling regime, we find that there is a critical value of the onsite interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.

We theoretically investigate the condensate state and collective excitations of a two-component Bose gas in a two-dimensional harmonic trap subject to isotropic Rashba spin-orbit coupling. In the weakly interacting regime when the interspecies interaction is larger than the intraspecies interaction ($g_{\uparrow \downarrow }>g$), we find that the condensate ground state has a half-quantum angular momentum vortex configuration with spatial rotational symmetry and skyrmion-type spin texture. Upon increasing the interatomic interaction beyond a threshold $g_c$, the ground state starts to involve higher-order angular momentum components and thus breaks rotational symmetry. In the case of $g_{\uparrow \downarrow }<g$, the condensate becomes unstable toward the superposition of two degenerate half-quantum vortex states. Both instabilities (at $g>g_c$ and $g_{\uparrow \downarrow }<g$) can be determined by solving the Bogoliubov equations for collective density oscillations of the half-quantum vortex state and by analyzing the softening of mode frequencies. We obtain the phase diagram as a function of the interatomic interactions and the spin-orbit coupling. In addition, we directly simulate the time-dependent Gross-Pitaevskii equation to examine the dynamical properties of the system. Finally, we investigate the stability of the half-quantum vortex state against both trap anisotropy and anisotropy in the spin-orbit coupling.

Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal model, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party preforms measurements along three perpendicular directions on the Bloch sphere, then the parties will always violate a Bell inequality. Furthermore, we prove that this probability is highly robust against local depolarizing noise, in that small levels of noise only decrease the probability of violating a Bell inequality by a small amount. We also show that generalizing to $N$ parties can increase the robustness against noise. These results improve on previous ones that only allowed a high probability of violating a Bell inequality for large numbers of parties.

The $S$(3) electric-quadrupole transition of the (3-0) overtone of molecular hydrogen has been recorded with a continuous-wave cavity ring-down spectrometer and calibrated with sub-megahertz accuracy using a temperature-stabilized Fabry-Pérot interferometer. The collision-induced frequency shift and the frequency at zero pressure limit are derived from a fit of the spectral profiles. The absolute transition frequency of the $S$(3) line is determined to be 376 531 818.1 MHz with a 1.6-MHz accuracy ($\delta \nu /\nu =4\times {10}^{-9}$) by measuring the shift to a Rb line at 795 nm. As the best determined transition frequency of neutral H${}_2$ in the ground electronic state, this value agrees well with recent high-level quantum chemistry calculations including relativistic and quantum electrodynamics corrections.

Selective production of the doubly excited state in 464 MeV/u He-like Ar${}^{16+}$ ions was accomplished using three-dimensional resonant coherent excitation in a thin foil of silicon crystal. Through a coherent interaction with the periodic crystal field, the Ar${}^{16+}$ ions were resonantly excited sequentially from the ground state to the $1s2p$ (${}^{1}P$) state and then $2p^2$ (${}^{1}D$) state in a way analogous to two-color x-ray laser excitation. The periodic crystal fields of 10${}^{11}$ V/m in the projectile's frame are equivalent to the fields generated by x-ray lasers with photon energies of 3139.55 and 3286.95 eV and an energy flux of 10${}^{16}$ W/cm${}^2$. We confirmed the doubly excited state formation through observation of the subsequent collisional ionization, Auger ionization, and radiative deexcitation.

We study phase transitions and hysteresis in a system of dipolar bosons loaded into triangular optical lattices at zero temperature. We find that the quantum melting transition from supersolid to superfluid phase is first order, in contrast with the previous report. We also find that due to strong quantum fluctuations the supersolid (or solid)-superfluid transition can exhibit an anomalous hysteretic behavior, in which the curve of density versus chemical potential does not form a standard loop structure. Furthermore, we show that the transition occurs unidirectionally along the anomalous hysteresis curve.

Optomechanical cooling of levitated dielectric particles represents a promising new approach in the quest to cool small mechanical resonators toward their quantum ground state. We investigate two-mode cooling of levitated nanospheres in a self-trapping regime. We identify a structure of overlapping, multiple cooling resonances and strong cooling even when one mode is blue-detuned. We show that the best regimes occur when both optical fields cooperatively cool and trap the nanosphere, where cooling rates are over an order of magnitude faster compared to corresponding single-resonance cooling rates.

This paper provides some necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment engineering problem for pure-Gaussian-state preparation can be straightforwardly dealt with in the linear algebraic framework. In fact, based on one of those conditions, for an arbitrary given pure Gaussian state, we obtain a complete parametrization of the Gaussian master equation having that state as a unique steady state; this leads to a systematic procedure for engineering a desired dissipative system. We demonstrate some examples including Gaussian cluster states.

It is shown that, under certain boundary conditions, the virial theorem has to be modified. We analyze the origin of the extra term and compute it for particular examples. The Coulomb and harmonic oscillator with the point interaction have been studied in light of this generalization of the virial theorem.

In this work we study the effects of collapse and revival, as well as the zitterbewegung (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some Landau level $n_0$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and their evolution is visualized. Our computations demonstrate that due to the dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time $t=T_R/2$ its reshaping takes place first. It is shown that the behavior of the wave packet containing the states of both energy bands (with $E_n>0$ and $E_n<0$) is more complicated. At short times of a few classical periods such a packet splits into two parts, which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have a significant overlap that leads to ZB, and at the time of fractional revival each of two subpackets is decomposed into few packet fractions. However, at $t=T_R$ each of the two subpackets (with positive or negative energy) restores at various points of the cyclotron orbit, which makes reshaping of the initial wave packet impossible, entirely unlike the wave packet which consists of states with energies $E_n>0$ only. The obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where superhigh magnetic field has a value of the order ${10}^8–{10}^9$T, as well as for interpretation of experiments with trapped ions.

We show that a positive homogeneous function that is invariant under determinant-1 stochastic local operations and classical communication (SLOCC) transformations defines an $N$-qubit entanglement monotone if and only if the homogeneous degree is not larger than 4. We then describe a common basis and formalism for the $N$-tangle and other known invariant polynomials of degree 4. This allows us to elucidate the relation of the four-qubit invariants defined by Luque and Thibon [Phys. Rev. A 67, 042303 (2003)] and the reduced two-qubit density matrices of the states under consideration, thus giving a physical interpretation for those invariants. We demonstrate that this is a special case of a completely general law that holds for any multipartite system with bipartitions of equal dimension, e.g., for an even number of qudits.

We study the ability to control $d$-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semianalytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semianalytic protocol is compared to a brute-force, full numerical search. For small inhomogeneities, $<$$1\%$, both approaches achieve average fidelities greater than 0.99, but the brute-force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.

Transferring a quantum state of a light field to a memory is of particular importance. However, this transfer is usually hampered because the memory system is subjected to some noise and this can limit the performance of the state transfer greatly. In this paper, we consider the transfer of a Gaussian state of light to a linear medium memory such as an optomechanical oscillator and propose a dynamical feedback controller that suppresses the noise in the memory system. To protect an unknown state, the feedback scheme employs the specific configuration of the quantum error correction; that is, a three-mode Gaussian state having appropriate syndromes is taken as the input. Correspondingly, the memory consists of three independent linear systems. The syndrome errors are estimated continuously in time through the measurement of the output field, and the results are then fed back to control the system. Because the input is Gaussian and the systems are all linear, it is possible to formulate the problem using the framework of the celebrated classical Kalman filtering and linear quadratic Gaussian control. A numerical simulation demonstrates the effectiveness of the control scheme.

An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (nonuniversal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) has been studied in quantum information theory, and it is known that no quantum-computational advantage can be obtained without the help of an additional nonstabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons can not exhibit nonlocality (in the sense of violating a Bell inequality) when only topologically protected stabilizer operations are performed. To produce correlations that can not be described by a local hidden variable model again requires the use of a nonstabilizer operation. Using geometric techniques, we relate the sets of operations that enable universal quantum computing (UQC) with those that enable violation of a Bell inequality. Motivated by the fact that nonstabilizer operations are expected to be highly imperfect, our aim is to provide a benchmark for identifying UQC-enabling operations that is both experimentally practical and conceptually simple. We show that any (noisy) single-qubit nonstabilizer operation that, together with perfect stabilizer operations, enables violation of the simplest two-qubit Bell inequality, can also be used to enable UQC. This benchmarking requires finding the expectation values of two distinct Pauli measurements on each qubit of a bipartite system.

We study the backaction of a driven nonlinear resonator on a multilevel superconducting qubit. Using unitary transformations on the multilevel Jaynes-Cummings Hamiltonian and quantum optics master equation, we derive an analytical model that goes beyond linear response theory. Within the limits of validity of the model, we obtain quantitative agreement with experimental and numerical data, both in the bifurcation and in the parametric amplification regimes of the nonlinear resonator. We show in particular that the measurement-induced dephasing rate of the qubit can be rather small at high drive power. This is in contrast to measurement with a linear resonator where this rate increases with the drive power. Finally, we show that, for typical parameters of circuit quantum electrodynamics, correctly describing measurement-induced dephasing requires a model going beyond linear response theory, such as the one presented here.

We develop the mean-field theory for Bose-Einstein condensates in a one-dimensional ring with two types of nonlinear double-well potentials, based on a pair of $\delta$ functions or Gaussian of a finite width, placed at diametrically opposite points. By analyzing the ground states (GSs) in these cases, we find a qualitative difference between them. With the Gaussian profile, the GS always undergoes the phase transition from the symmetric shape to an asymmetric one at a critical value of the norm. In contrast, the symmetry-breaking transition does not happen with the $\delta$-functional profile of the nonlinearity, and the GS always remains symmetric. In addition, the numerical analysis for the Gaussian profile demonstrates that the type of symmetry-breaking transition depends on the width of the nonlinear-potential well.