In the present paper, we consider a suitable definition of a noninformative prior on the quantum statistical model of pure states. While the full pure-states model is invariant under unitary rotation and admits the Haar measure, restricted models, which we often see in quantum channel estimation and quantum process tomography, have less symmetry and no compelling rationale for any choice. We adopt a game-theoretic approach that is applicable to classical Bayesian statistics and yields a noninformative prior for a general class of probability distributions. We define the quantum detection game and show that there exist noninformative priors for a general class of a pure-states model. Theoretically, it gives one of the ways that we represent ignorance on the given quantum system with partial information. Practically, our method proposes a default distribution on the model in order to use the Bayesian technique in the quantum-state tomography with a small sample.

Scaling of quantum capacitances is explored for lanthanide and actinide atoms. For lighter atoms, quantum capacitances have been seen to scale linearly with mean radii of the atoms’ outermost occupied orbitals. This scaling law is used to analyze two recent, differing sets of theoretical calculations for lanthanide electron affinities $A$. Consistent with the scaling law, $A$ values predicted by O’Malley and Beck for lanthanides [Phys. Rev. A 78, 012510 (2008)], using a relativistic configuration interaction (RCI) method, produce capacitances that scale with the atoms’ mean radii along a single line to a high degree of confidence. Similar linear scaling behavior also results for the actinides from O’Malley and Beck's RCI calculations of their $A$ values. However, lanthanide $A$ values predicted by Felfli et al. [Phys. Rev. A 81, 042707 (2010)], using a Regge-pole approach, unexpectedly produce capacitance scaling along two different lines for atoms with similar neutral electron configurations. Both types of linear capacitance scaling are internally consistent, though, and do not serve to determine definitively which set of electron affinity predictions for the lanthanides is likely to be more accurate. Still, evidence from this and prior capacitance scaling investigations tends to favor the O'Malley and Beck results. In addition, linear capacitance scaling for the actinides is applied to estimate the previously unknown $A$ values for Fm and Md as 0.007 eV and $-0.006$ eV, respectively.

A recent theoretical paper [Colgan et al., J. Phys. B 44, 175205 (2011)] has reopened the problem of C${}^{6+}$ ionization of He at 100 MeV/amu. The issue concerns ionization in the plane perpendicular to the momentum transfer $\mathbf{q}$ for the case where the ejected electron has an energy of 6.5 eV and $q=0.75$ a.u. Here, even after deconvolution, experiment finds two peaks near 90${}^{\circ }$ and 270${}^{\circ }$, contrary to earlier theoretical works that had predicted dips. Now, Colgan et al. also find peaks. We have reinvestigated the problem using the second Born approximation whose results are supported by a nonperturbative impact-parameter coupled-pseudostate approximation. Dips are again predicted. By comparing C${}^{6+}$ impact with that of its antiparticle ${\overline{\mathrm{C}}}^{6-}$ a “mirror-image” situation is observed in which the dips are converted into peaks, i.e., positively (negatively) charged projectiles give dips (peaks) near 90${}^{\circ }$ and 270${}^{\circ }$. A physical interpretation of this result is suggested. Applying exactly the same second Born approximation to $e^{\pm }$ impact ionization of He at 1 keV under similar dynamical conditions to C${}^{6+}$, we see exactly the same patterns, but now the results for $e^{-}$, showing peaks near 90${}^{\circ }$ and 270${}^{\circ }$ in the plane perpendicular to $\mathbf{q}$, are in quite good agreement with experiment in this and other geometries. This is strong support for the predictions of the second Born approximation for C${}^{6+}$. A paper by Egodapitiya et al. [Phys. Rev. Lett. 106, 153202 (2011)] warns of coherence problems with heavy-particle beams. It is suggested that this, together with experimental resolutions, may explain the experimental data for C${}^{6+}$.

Here we consider three possible biased electrostatic guides of polar molecules. The design of these guides is motivated by their possible uses in a precision measurement of the electron's electric dipole moment. These guides may also have applications in the alignment-preserving transportation of ultracold molecules.

We have studied the process of direct (nonsequential) two-photon double ionization of molecular hydrogen (H${}_2$). Solving the time-dependent Schrödinger equation by an ab initio method, total (generalized) and single-differential cross sections are obtained at photon energies from 26 to 33 eV. Both parallel and perpendicular orientation of the molecule with respect to the laser polarization direction are considered, and the results are compared with previously calculated cross sections at 30 eV, as well as the predictions of a simple model.

Light transmission or diffraction from different quantum phases of cold atoms in an optical lattice has recently come up as a useful tool to probe such ultracold atomic systems. The periodic nature of the optical lattice potential closely resembles the structure of a diffraction grating in real space but is loaded with a strongly correlated quantum many-body state which interacts with the incident electromagnetic wave, a feature that controls the nature of light transmission or dispersion through such quantum media. In this paper we show that, as one varies the relative angle between the cavity mode and the optical lattice, the peak of the transmission spectrum through such cavities also changes, which reflects the statistical distribution of the atoms in the illuminated sites. Consequently, the angle-resolved transmission spectrum of such quantum diffraction gratings can provide a plethora of information about the Fock-space structure of the many-body quantum state of ultracold atoms in such an optical cavity that can be explored in current state-of-the-art experiments.

Using renormalization-group arguments we show that the low-temperature thermodynamics of a three- or two-dimensional dilute Bose gas is fully determined by a universal scaling function ${\mathcal{F}}_d(\mu /k_{B}T,\tilde{g}\left(T\right))$ once the mass $m$ and the $s$-wave scattering length $a_d$ of the bosons are known ($d$ is the space dimension). Here $\mu$ and $T$ denote the chemical potential and temperature of the gas, and the temperature-dependent dimensionless interaction constant $\tilde{g}\left(T\right)$ is a function of $m{a}_d^2{k}_{B}T/{\hslash }^2$. We compute the scaling function ${\mathcal{F}}_2$ using a nonperturbative renormalization-group approach and find that both the $\mu /k_{B}T$ and $\tilde{g}\left(T\right)$ dependencies are in very good agreement with recent experimental data obtained for a quasi-two-dimensional Bose gas with or without optical lattice. We also show that the nonperturbative renormalization-group estimate of the Berezinskii-Kosterlitz-Thouless transition temperature compares well with the result obtained from a quantum Monte Carlo simulation of an effective classical field theory.

We report the observation of enhanced magneto-optic rotation as the coherent superposition of different hyperfine states is established in an atomic sample. The polarization rotation near the two-photon Raman resonance condition appears to have an analogous characteristic to the well established Faraday rotation observed in the vicinity of a single-photon resonance; however, it contains sharp features arising from coherent population trapping states. The profile of the two-photon rotation signal exhibits interesting features for a slightly imbalanced circular polarization component of the laser field as well as for on and away from the single-photon resonance. The investigation can be used to explore the effect of superposition states generated by coherent population trapping on optical activity. A complete density matrix based numerical simulation that consistently captures all the relevant features of the experiment is presented. The experimental and theoretical investigation can be useful for magnetometry using polarization rotation near two-photon Raman resonance.

The spectra of Compton radiation emitted during electron scattering off an intense laser beam are calculated using the framework of strong-field quantum electrodynamics. We model these intense laser beams as finite length plane-wave-fronted pulses, similar to Neville and Rohrlich [Phys. Rev. D 3, 1692 (1971)], or as trains of such pulses. Expressions for energy and angular distributions of Compton photons are derived such that a comparison of both situations becomes meaningful. Comparing frequency distributions for both an isolated laser pulse and a laser pulse train, we find a very good agreement between the results for long pulse durations which breaks down, however, for ultrashort laser pulses. The dependence of angular distributions of emitted radiation on a pulse duration is also investigated. Pronounced asymmetries of angular distributions are found for very short laser pulses, which gradually disappear with increasing the number of laser field oscillations. Those asymmetries are attributed to asymmetries of the vector potential describing an incident laser beam.

We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with all the modes of the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms. When the atoms have the same coupling with the laser field, it is shown that their steady-state density operator is approximately an $X$ state and this is used to obtain simple approximate analytic expressions for steady-state quantum and classical correlations which are characterized as functions of the laser field intensity and the distance between the two atoms. Moreover, the values of both the laser field intensity and the distance between the two atoms that maximize correlations are identified.

We propose a scalable scheme for engineering multipartite entangled $W$ states in a Heisenberg spin chain. The rather simple scheme is mainly built on the accumulative angular squeezing technique first proposed in the context of quantum kicked rotor for focusing a rotor to a delta-like angular distribution [I. Sh. Averbukh and R. Arvieu, Phys. Rev. Lett. 87, 163601 (2001)]. We show how the efficient generation of various $W$ states may be achieved by engineering the interaction between a spin chain (short or long) and a time-dependent parabolic magnetic field. Our results may further motivate the use of spin chains as a test bed to investigate complex properties of multipartite entangled states. We further numerically demonstrate that our scheme can be extended to engineer arbitrary spin chain quasimomentum states as well as their superposition states.

We study the zero-temperature phase diagram of bosons interacting via screened Coulomb (Yukawa) potential by means of the diffusion Monte Carlo method. The Yukawa potential is used as a model interaction in the neutron matter, dusty plasmas, and charged colloids. As shown by Petrov et al. [Phys. Rev. Lett. 99, 130407 (2007)], interactions between weakly bound molecules of heavy and light fermionic atoms are described by an effective Yukawa potential with a strength related to the heavy-light mass ratio $M/m$, which might lead to crystallization in a two-dimensional geometry if the mass ratio of heavy-light fermions exceeds a certain critical value. In the present work we do a thorough study of the quantum three-dimensional Yukawa system. For strong interactions (equivalently, large mass ratios) the system experiences several phase transitions as the density is increased, passing from gas to solid and to gas phase again. Weakly interacting Yukawa particles do not crystallize at any density. We find the minimal interaction strength at which the crystallization happens. In terms of the two-component fermionic system, this strength corresponds to a heavy-light mass ratio of $M/m\sim 180$, so that it is impossible to realize the gas-crystal transition in a conventional bulk system. For the Yukawa model of fermionic mixtures we also analyze the possibility of building molecular systems with very large effective mass ratios by confining the heavy component to a sufficiently deep optical lattice. We show how the effective mass of the heavy component can be made arbitrarily large by increasing the lattice depth, thus leading to a tunable effective mass ratio that can be used to realize a molecular superlattice.

We study the best attainable measurement precision when a double-well trap with bosons inside acts as an interferometer to measure the energy difference of the atoms on the two sides of the trap. We introduce time-independent perturbation theory as the main tool in both analytical arguments and numerical computations. Nonlinearity from atom-atom interactions will not indirectly allow the interferometer to beat the Heisenberg limit, but in many regimes of the operation the Heisenberg limit scaling of measurement precision is preserved in spite of added tunneling of the atoms and atom-atom interactions, often even with the optimal prefactor.

We develop an efficient method to derive a class of surface states in photonic superlattices. In a kind of infinite bichromatic superlattice satisfying some specific conditions, we obtain a finite portion of their in-gap states, which are superpositions of finite numbers of their unstable Bloch waves. By using these unstable in-gap states, we construct exactly several stable surface states near various interfaces in photonic superlattices. We analytically explore the parametric dependence of these exact surface states. Our analysis provides an exact demonstration for the existence of surface states and would be also helpful to understand surface states in other lattice systems.

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schrödinger models. We show by means of both numerical simulations and analytical estimates that the stability of bright solitons in the presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on the evolution of the Hamiltonian of the soliton and its power. The first criterion allows us to estimate a time (or distance) over which the soliton preserves its form. The second criterion gives the lifetime of the solitary wave packet in terms of its radiative power losses. We derive a simplified mean field approach which allows us to calculate the power loss analytically in the physically relevant case of weakly correlated noise, which in turn serves as a lower estimate of the lifetime for correlated noise in the general case.

We consider the scenario in which a damped three-level atom in a ladder or $\mathsf{V}$ configuration is coupled to a single cavity mode whose vacuum state is amplified by dint of the dynamical Casimir effect. We obtain approximate analytical expressions and exact numerical results for the time-dependent probabilities, demonstrating that the presence of the third level modifies the photon statistics and its population can serve as witness of photon generation from a vacuum.

Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation, conditions for classical behavior are imposed on one of its subsystems and the corresponding hybrid dynamical equations are derived. The presented formalism suggests that the hybrid systems have properties that are not exhausted by those of quantum and classical systems.

We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a postselection of the particles' momenta, representing a major difference in relation to nonrelativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles' spin. We also show that the amount of violation of the CHSH inequality depends on the reference frame and that in some frames the inequality may not be violated.

We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without revealing complete information about the states? We find that the claim “the same” can never be concluded without any doubts unless the information is complete. Moreover, we prove that a universal comparison (that perfectly distinguishes all states) also requires complete information about the states. Nevertheless, for some measurements, the probability distribution of outcomes still allows one to make an unambiguous conclusion regarding the difference between the states even in the case of incomplete information. We analyze an efficiency of such a comparison of qudit states when it is based on the swap measurement. For qubit states, we consider in detail the performance of special families of two-valued measurements, enabling us to successfully compare at most half of the pairs of states. Finally, we introduce almost-universal comparison measurements which can distinguish almost all nonidentical states (up to a set of measure zero). The explicit form of such measurements with two and more outcomes is found in any dimension.

Using entanglement of assistance, we establish a general polygamy inequality of multiparty entanglement in arbitrary-dimensional quantum systems. For multiparty closed quantum systems, we relate our result with the monogamy of entanglement, and clarify that the entropy of entanglement bounds both monogamy and polygamy of multiparty quantum entanglement.