The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet-state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various “relaxed” Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen “free will” theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows that existence of an outcome-independent model is equivalent to existence of a deterministic model.

Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale.

We show that in wave packet tunneling, localization of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wave packet plays the role of the initial pointer state. Under tunneling conditions such “self-measurement” is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as postselection in the final state becomes improbable. We also demonstrate that it is a good precision, or a ‘not really weak’ quantum measurement: no matter how wide the barrier $d$, it is possible to transmit a wave packet with a width $\sigma$ small compared to the observed advancement. As is the case with all weak measurements, the probability of transmission rapidly decreases with the ratio $\sigma /d$.

Quantum Fisher information of a parameter characterizes the sensitivity of the state with respect to changes of the parameter. In this article, we study the quantum Fisher information of a state with respect to $\mathrm{SU}\left(2\right)$ rotations under three decoherence channels: the amplitude-damping, phase-damping, and depolarizing channels. The initial state is chosen to be a Greenberger-Horne-Zeilinger state of which the phase sensitivity can achieve the Heisenberg limit. By using the Kraus operator representation, the quantum Fisher information is obtained analytically. We observe the decay and sudden change of the quantum Fisher information in all three channels.

We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or three-fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible number of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (for both bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: The bosonic bunching results in a low number of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.

We study a Hamiltonian system describing a three-spin-$1/2$ clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

We discuss the equilibrium properties of dilute Bose gases using a nonperturbative formalism based on auxiliary fields related to the normal and anomalous densities. We show analytically that for a dilute Bose gas of weakly interacting particles at zero temperature, the leading-order auxiliary field (LOAF) approximation leads to well-known analytical results. Close to the critical point the LOAF predictions are the same as those obtained using an effective field theory in the large-$N$ approximation. We also report analytical approximations for the LOAF results in the unitarity limit, which compare favorably with our numerical results. LOAF predicts that the equation of state for the Bose gas in the unitarity limit is $E/\left(pV\right)=1$, unlike the case of the Fermi gas when $E/\left(pV\right)=3/2$.

In the mean-field theory of atom-molecule systems, where bosonic atoms combine to form molecules, there is no usual $\text{U}\left(1\right)$ symmetry, presenting an apparent hurdle for defining the Berry phase and Berry curvature for these systems. We define a Berry connection for this system, with which the Berry phase and Berry curvature can be naturally computed. We use a three-level atom-molecule system to illustrate our results. In particular, we have computed the mean-field Berry curvature of this system analytically, and compared it to the Berry curvature computed with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our definition.

We present results for cross sections summed over partial waves $L=0$–2 for electron-impact excitation of the $2s$ and $2p$ states of He${}^{+}$ in the energy range of 40.84 to 45.66 eV. We find that these cross sections exhibit cusps at the excitation threshold of 40.81 eV.

Polarization-entangled photon pairs have been widely used as a light source of quantum communication. The polarization-entangled photon pairs are generally obtained at the crossing points of the light cones that are generated from a type-II nonlinear crystal. However, it is hard to pick up the photon pairs coming out from the crossing points because of their invisible wavelength and low intensity. In our previous work, we succeeded in generating polarization-entangled photon pairs by overlapping two light paths for the photon-pair generation. The photon pairs could be entangled in all of the generated photon pairs without clipping the crossing points, even with some difficulty in its alignment to overlap the two light paths. In this paper, we have developed an optical system which generates polarization-entangled photon pairs using a beamlike photon pair, without the difficulty in alignment. The measured results show that the photon pairs generated in the system are entangled in their polarizations.

The ground-state energy of heavy one-electron ions in an inhomogeneous locally bounded magnetic field is estimated by the variational principle. The ions are described by means of the pseudorelativistic Herbst-Chandrasekhar operator. Two classes of magnetic fields are considered which model a field-free region around the central charge. It is shown that for a certain size of this region the ground-state energy becomes positive and increases strongly with the magnetic field strength. This behavior is in contrast to the two-dimensional case where electrons can be bound by such a field-free region.

Large-scale $R$-matrix calculations are carried out for the electron-impact excitation of Ne${}^{3+}$ and Ne${}^{6+}$. For Ne${}^{3+}$, a 581-$LSJ$-level $R$-matrix intermediate coupling frame transformation calculation is made for excitations up to the $n=4$ shell. For some transitions, large effective collision strength differences are found with current 23-$jKJ$-level Breit-Pauli $R$-matrix and earlier 22-$LSJ$-level $R$-matrix $jj$ omega (JAJOM) calculations. For Ne${}^{6+}$, a 171-$jKJ$-level Breit-Pauli $R$-matrix calculation is made for excitations up to the $n=5$ shell. For some transitions, large effective collision strength differences are found with current 46-$jKJ$-level Breit-Pauli $R$-matrix and earlier 46-$LSJ$-level $R$-matrix JAJOM calculations. Together with existing $R$-matrix calculations for other ion stages, high-quality excitation data are now available for astrophysical and laboratory plasma modeling along the entire Ne isonuclear sequence.

We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on spin-1 Bose-Einstein condensates (BECs). By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respectively, which can be imaged by using the polarization-dependent phase-contrast method.

We examine the generation of bright matter-wave solitons in the Gross-Pitaevskii equation describing Bose-Einstein condensates with a time-dependent complex potential, which is composed of a repulsive parabolic background potential and a gravitational field. By performing a modified lens-type transformation, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effects of the gravitational field, as well as of the parameter related to the feeding or loss of atoms in the condensate, on the instability growth rate. It is evident from numerical simulations that the feeding with atoms and the magnetic trap have opposite effects on the dynamics of the system. It is shown that the feeding or loss parameter can be well used to control the instability domain. Our study shows that the gravitational field changes the condensate trail of the soliton trains during the propagation. We also perform a numerical analysis to solve the Gross-Pitaevskii equation with a time-dependent complicated potential. The numerical results on the effect of both the gravitational field and the parameter of feeding or loss of atoms in the condensate agree well with predictions of the linear stability analysis. Another result of the present work is the modification of the background wave function in the Thomas-Fermi approximation during the numerical simulations.

Electromagnetically induced transparency in a multilevel system is investigated in ${}^{173}$Yb. The level structure investigated is “open” in that the light that gives rise to the transparency also resonantly couples the atoms to excited states which do not exhibit electromagnetically induced transparency. The resulting reduction of transparency is investigated experimentally and theoretically. It is found that, while the transparency is poor in certain regimes, it can be made to perform arbitrarily well in the limit of a large intensity imbalance between the optical fields.

We investigate the cutoff law for high-order above-threshold ionization (HATI) within a semiclassical framework. By explicitly adopting the tunneling effect and considering the initial position shift of the tunneled electron from the origin in the model, the cutoff energy position in HATI spectrum exhibits a well-defined upshift from the simple-man model prediction. The comparison between numerical results from our improved semiclassical model and the quantum-orbit theory shows a good agreement for small values of the Keldysh parameter $\gamma$, implying the important role of the inherent quantum tunneling effect in HATI dynamics.

We propose a method for the determination of the interaction potential of Rydberg atoms. Specifically, we consider a laser-driven Rydberg gas confined in a one-dimensional lattice and demonstrate that the Rydberg atom number after a laser excitation cycle as a function of the laser detuning provides a measure for the Rydberg interaction coefficient. With the lattice spacing precisely known, the proposed scheme only relies on the measurement of the number of Rydberg atoms and thus circumvents the necessity to map the interaction potential by varying the interparticle separation.

We propose an experimentally feasible setup with ultracold alkaline-earth-metal atoms to simulate the dynamics of U(1) lattice gauge theories in 2 $+$ 1 dimensions with a Chern-Simons term. To this end we consider the ground-state properties of spin-5/2 alkaline-earth-metal fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin-liquid state with $2\pi /3$ flux per plaquette, which violates time-reversal invariance. We demonstrate that due to the breaking of time-reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge-field dynamics. We discuss also properties of the lowest energy competing orders.

We demonstrate that the mechanical action of light manifests itself in the perceived topography measured with a scanning probe microscope. This modality of sensing optically induced forces opens up possibilities to quantify properties of electromagnetic fields.

In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study the universal comparison of mixed quantum states, and prove that this task is generally impossible to accomplish. Then, we focus on the unambiguous comparison of $n$ mixed quantum states arbitrarily chosen from a set of $k$ mixed quantum states. The condition for the existence of an unambiguous measurement operator which can produce a conclusive result when the unknown states are actually the same and the condition for the existence of an unambiguous measurement operator when the unknown states are actually different are studied independently. We derive a necessary and sufficient condition for the existence of the first measurement operator, and a necessary condition and two sufficient conditions for the second. Furthermore, we find that the sufficiency of the necessary condition for the second measurement operator has a simple and interesting dependence on $n$ and $k$. At the end, a unified condition is obtained for the simultaneous existence of these two unambiguous measurement operators.