Imperfections in matter-wave beams have been recently characterized experimentally through the measurement of a parameter presented as a beam quality factor. While this parameter is adequate to propagate the transverse width of a cylindrical atomic beam in the paraxial regime, it is not well suited for the description of matter waves in general atom-optical systems. A different quality factor, consistent with the general propagation of matter waves, is proposed.

Systems of solitary waves in the one-dimensional Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyze the soliton nature of these solitary waves, a particle analogy for the solitary waves is formulated. Exact soliton solutions exist in the absence of an external trapping potential, which behave in a particlelike manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present up to a gradual shift in the trajectories when the harmonic trap period is short compared with the collision time of the solitons. We find that the collision time of the solitons is dependent on the relative phase of the solitons as they collide. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. This phase preservation can be used to find regimes where there is agreement between the wave and particle models. This also implies that soliton regimes may be found in three-dimensional geometries where solitary waves can be made to repeatedly collide out of phase, stabilizing the condensate against collapse. The extension to three particles supports both regular and chaotic regimes. The trajectory shift observed for two solitons carries over to the case of three solitons. This shift aside, the agreement between the particle model and the wave dynamics remains good, even in chaotic regimes.

Two different formulas relating the index of refraction $n$ of gases for atom waves to the scattering amplitude have been published. We show here that these two formulas are not consistent with the definition of the total scattering cross section while the formula developed by one of us [C. Champenois, Ph.D. thesis, Université P. Sabatier, 1999 (unpublished)] is in agreement with this standard knowledge. We discuss this result, in particular in the neutron case for which such an index was first introduced. We finally evaluate the index of refraction as a function of well-known quantities and we discuss the order of magnitude of the ratio of $\left(n-1\right)/n_t$, where $n_t$ is the gas density.

We present a full quantum mechanical three-dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum interfaces, where the quantum fluctuations of light are mapped onto the atoms and back onto light. We show that the interaction of the light with the atoms may be separated into a mean effect of the ensemble and a deviation from the mean. The mean effect of the interaction effectively gives rise to an index of refraction of the gas. We formally change to a dressed state picture, where the light modes are solutions to the diffraction problem, and develop a perturbative expansion in the fluctuations. The fluctuations are due to quantum fluctuations as well as the random positions of the atoms. In this perturbative expansion we show how the quantum fluctuations are mapped between atoms and light while the random positioning of the atoms give rise to decay due to spontaneous emission. Furthermore we identify limits, where the full three-dimensional theory reduces to the one-dimensional theory typically used to describe the interaction.

It has previously been shown theoretically that the exchange of linear momentum between the light field in an optical cavity and a vibrating end mirror can entangle the electromagnetic field with the vibrational motion of that mirror. In this paper we consider the rotational analog of this situation and show that radiation torque can similarly entangle a Laguerre-Gaussian cavity mode with a rotating end mirror. We examine the mirror-field entanglement as a function of ambient temperature, radiation detuning, and orbital angular momentum carried by the cavity mode.

We employ high-order degenerate laser cavities to analogously investigate the morphology of macroscopic superposition states of three-dimensional coherent waves. The spatial features of macroscopic superposition states are found to exhibit dashed and dotted wave patterns. We evaluate the mode volume to explore the domination of macroscopic superposition states. A large-aperture laser resonator is experimentally implemented to confirm the theoretical results.

We experimentally demonstrate temporal shaping of a heralded single-photon wave packet, prepared by conditional measurement of the idler photon of the entangled photon pair in the process of spontaneous parametric down-conversion. The heralded single-photon wave packet for the signal photon, after being tailored with the help of chirp broadening and interference effects, was observed directly by measuring the time-correlated single-photon-counting histogram. We also demonstrate remote control of the temporal shaping effect by spectral filtering of the idler photon.

In this paper we show how weak measurement and local feedback can be used to control entanglement generation between two qubits. To do this, we make use of a decoherence free subspace. Weak measurement and feedback can be used to drive the system into this subspace rapidly. Once within the subspace, feedback can generate entanglement rapidly, or turn off entanglement generation dynamically. We also consider, in the context of weak measurement, some of the differences between purification and generating entanglement.

What are the orbital angular momentum correlations between spatially entangled photon pairs generated in spontaneous parametric down-conversion? We show that the answer to this question can be given in two alternative, although complementary, ways. The answer posed in this Brief Report explains satisfactorily the seemingly contradictory results obtained in different experiments, and theoretical approaches.

We produce a heteronuclear quantum degenerate mixture of two bosonic species, ${}^{87}\mathrm{Rb}$ and ${}^{41}\mathrm{K}$, in a three-dimensional optical lattice. On raising the lattice barriers, we observe the disappearance of the inference pattern of the heavier ${}^{87}\mathrm{Rb}$, shifting toward shallower lattice depths in the presence of a minor fraction of ${}^{41}\mathrm{K}$. This effect is sizable and requires only a marginal overlap between the two species. We compare our results with similar findings reported for Fermi-Bose mixtures and discuss the interpretation scenarios proposed to date, arguing that the explanation may be linked to the increased effective mass due to the interspecies interactions.

Based on macroscopic quantum electrodynamics in linear media, we develop a general theory of the resonant Casimir-Polder force on an excited two-level atom in the presence of arbitrary linear bodies, with special emphasis on the strong-coupling regime where reabsorption of an emitted photon can give rise to (vacuum) Rabi oscillations. We first derive a simple time-independent expression for the force by using a dressed-state approximation. For initially single-quantum excited atom-field systems we then study the dynamics of the force by starting from the Lorentz force and evaluating its average as a function of time. For strong atom-field coupling, we find that the force may undergo damped Rabi oscillations. The damping is due to the decay of both the atomic excitation and the field excitation, and both amplitude and mean value of the oscillations depend on the chosen initial state.

Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a single “soft” $\pi$ pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be made zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters and use the results to analyze the structure of error operators for a controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly suppressed oscillator heating.

The effect of static and dynamic electron correlation on the nature of excited states and state-to-state transition dipole moments is studied with a multideterminant wave function approach on the example of all-trans linear polyenes (${\text{C}}_4{\text{H}}_6$, ${\text{C}}_6{\text{H}}_8$, and ${\text{C}}_8{\text{H}}_{10}$). Symmetry-forbidden singlet $n{A}_g$ states were found to separate into three groups: purely single, mostly single, and mostly double excitations. The excited-state absorption spectrum is dominated by two bright transitions: $1B_u\text{−}2A_g$ and $1B_u\text{−}m{A}_g$, where $m{A}_g$ is the state, corresponding to two-electron excitation from the highest occupied to lowest unoccupied molecular orbital. The richness of the excited-state absorption spectra and strong mixing of the doubly excited determinants into lower-$n{A}_g$ states, reported previously at the complete active space self-consistent field level of theory, were found to be an artifact of the smaller active space, limited to $\pi$ orbitals. When dynamic $\sigma \text{−}\pi$ correlation is taken into account, single- and double-excited states become relatively well separated at least at the equilibrium geometry of the ground state. This electronic structure is closely reproduced within time-dependent density-functional theory (TD DFT), where double excitations appear in a second-order coupled electronic oscillator formalism and do not mix with the single excitations obtained within the linear response. An extension of TD DFT is proposed, where the Tamm-Dancoff approximation (TDA) is invoked after the linear response equations are solved (a posteriori TDA). The numerical performance of this extension is validated against multideterminant-wave-function and quadratic-response TD DFT results. It is recommended for use with a sum-over-states approach to predict the nonlinear optical properties of conjugated molecules.

This paper discusses the possibility of measuring the variance in the electron-to-proton mass ratio $\beta$ using the $\mid X{}^2\Sigma$, $n_v=0$, $N=0$, $J=1∕2$, $F=1$, $M_F=1⟩\to \mid X{}^2\Sigma$, $n_v=1$ or 2, $N=0$, $J=1∕2$, $F=1,M_F=1⟩$ transition frequencies of magnetically trapped cold ${}^{24}\mathrm{MgH}$ or ${}^{40}\mathrm{CaH}$ molecules. The uncertainty in this transition frequency can potentially be lower than ${10}^{-15}$, which makes it possible to measure the variance in $\beta$. The ${}^{24}\mathrm{MgH}$ transition is more advantageous for measurement than the ${}^{40}\mathrm{CaH}$ transition, because of the lower collision-loss rate, light shift, and collision shift.

This work presents accurate ab initio determination of the hyperfine splitting for the ground state and a few low-lying excited states of ${{}^{113}\text{C}\text{d}}^{+}$, an important candidate for the frequency standard in the microwave region, using the coupled-cluster theory in the relativistic framework. The hyperfine energy splittings, which are estimated here theoretically in the literature, are in good agreement with the recent experimental results. We have also carried out the lifetime calculations of the $5{{}^{2}P}_{1/2}$ and $5{{}^{2}P}_{3/2}$ states, which are in good agreement with the available experimental results. The role of different electron correlation effects in the determination of these quantities are discussed and their contributions are presented.

By applying the standard adiabatic approximation and using the accurate analytical expression for the corresponding local chemical potential obtained in our previous work [Phys. Rev. A 75, 063610 (2007)] we derive an effective 1D equation that governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. This equation, which is more simple than previous proposals, is also more accurate. Moreover, it allows treating condensates containing an axisymmetric vortex with no additional cost. Our effective equation also has the correct limit in both the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to derive fully analytical expressions for ground-state properties such as the chemical potential, axial length, axial density profile, and local sound velocity. These analytical expressions remain valid and accurate in between the above two extreme regimes. Following the same procedure we also derive an effective 2D equation that governs the transverse dynamics of mean-field disk-shaped condensates. This equation, which also has the correct limit in both the quasi-2D and the Thomas-Fermi regime, is again more simple and accurate than previous proposals. We have checked the validity of our equations by numerically solving the full 3D Gross-Pitaevskii equation.

Using coordinate transformation stated earlier by Pendry et al. [Science 312, 1780 (2006)], we deduced the material parameter equation for elliptic cylinder cloaks and reported the numerical simulations as well. The theoretical and numerical results indicate that, an elliptic cylinder cloak, which is constructed with metamaterials possessing the permittivity and permeability ruled by our equation, can exclude the electromagnetic fields from the interior region without perturbing the exterior fields and therefore the objects in it can be effectively invisible to the outer region.

The conventional probabilistic point of view implies that if a particle has a probability $p$ to make a transition from one site to another site, then the average transport should be $⟨Q⟩=p$ with a variance $\mathrm{var}\left(Q\right)=(1-p)p$. In the quantum mechanical context this observation becomes a nontrivial manifestation of restricted quantum-classical correspondence. We demonstrate this observation by considering the full counting statistics which is associated with a two level coherent transition in the context of a continuous quantum measurement process. In particular we test the possibility of getting a valid result for $\mathrm{var}\left(Q\right)$ within the framework of the adiabatic picture, analyzing the simplest nontrivial example of a Landau-Zener crossing.

We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins 1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this qubit-parity meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multiparticle CNOT gate are further discussed: electron spins in double quantum dots in the singlet-triplet encoding, and $\nu =5/2$ Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.

We derive a general lower bound on the minimum-error probability for ambiguous discrimination between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom limit. Also, we give a general lower bound on the minimum-error probability for discriminating quantum operations. Then we further analyze how this lower bound is attainable for ambiguous discrimination of mixed quantum states by presenting necessary and sufficient conditions related to it. Furthermore, with a restricted condition, we work out an upper bound on the minimum-error probability for ambiguous discrimination of mixed quantum states. Therefore, some sufficient conditions are obtained for the minimum-error probability attaining this bound. Finally, under the condition of the minimum-error probability attaining this bound, we compare the minimum-error probability for ambiguously discriminating arbitrary $m$ mixed quantum states with the optimal failure probability for unambiguously discriminating the same states.