This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting with a single mode of the radiation field. Our estimation strategy is based on the emerging state of the two-level system, whereas we determine both the minimum mean-square error and maximum likelihood estimators for uniform and Gaussian prior probability density functions. In the case of the maximum likelihood estimator, we develop a mathematical method which extends the already existing approaches to the variational problem of the average cost function. We demonstrate that long interaction times, large initial mean photon numbers, and nonzero detuning between two-level system transition and the frequency of the electromagnetic field mode have a deleterious effect on the optimality of the estimation scenario. We also present several cases where the estimation process is inconclusive, despite many ideal conditions being met.

Understanding how local potentials affect system eigenmodes is crucial for experimental studies of nontrivial bulk topology. Recent studies have discovered many exotic and highly nontrivial topological states in non-Hermitian systems. As such, it would be interesting to see how non-Hermitian systems respond to local perturbations. In this work we consider chiral and particle-hole-symmetric non-Hermitian systems on a bipartite lattice, including the Su-Schrieer-Heeger model and photonic graphene, and find that a disordered local potential could induce bound states evolving from the bulk. When the local potential on a single site becomes infinite, which renders a lattice vacancy, chiral-symmetry-protected zero-energy mode and particle-hole-symmetry-protected bound states with purely imaginary eigenvalues emerge near the vacancy. These modes are robust against any symmetry-preserved perturbations. Our work generalizes the symmetry-protected localized states to non-Hermitian systems.

When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally by a wider class of measures such as the quantum discord. In this paper, I introduce a simple thought experiment defining a measure of quantum correlations, which I call the accord, and write the result as a minimax optimization over unitary matrices. I find the exact result for pure states as a simple function of the Schmidt coefficients and provide a complete proof, and I likewise provide and prove the result for several classes of mixed states, notably including all states of two qubits and the experimentally relevant case of a pure state mixed with colorless noise. I demonstrate that for two qubit states the accord provides a tight lower bound on the discord; for Bell diagonal states it is also an upper bound on entanglement.

For a bipartite entangled state shared by two observers, Alice and Bob, Alice can affect the postmeasured states left to Bob by choosing different measurements on her half. Alice can convince Bob that she has such an ability if and only if the unnormalized postmeasured states cannot be described by a local-hidden-state (LHS) model. In this case, the state is termed steerable from Alice to Bob. By converting the problem to construct LHS models for two-qubit Bell diagonal states to the one for Werner states, we obtain the optimal models given by Jevtic et al. [J. Opt. Soc. Am. B 32, A40 (2015)], which are developed by using the steering ellipsoid formalism. Such conversion also enables us to derive a sufficient criterion for unsteerability of any two-qubit state.

In the mean-field theory, the stabilization of polar chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states as the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give the static nonlinear Schrödinger equations without free parameters to explore the achiral-chiral transitions of polar chiral molecules. We find that the polar chiral molecules of different species can be classified into two categories: At the critical point for the achiral-chiral transition, the mean-field ground state changes continuously in one category and changes discontinuously in the other category. We further give the mean-field phase diagram of the achiral-chiral transitions for both two categories.

We present a combined experimental and theoretical study of the transmission of single charged 1-keV Ar ions through a cylindrical glass capillary of macroscopic dimensions. From quantitative measurements of the incoming and transmitted ion currents, combined with a detailed analysis, the amount of beam entering the capillary was determined. This, combined with the measured transmitted currents, was used to determine the amount of charge deposited on the inner wall of the capillary which produces the guiding electric field. We show experimental results for fully, and partially, discharged conditions of the time evolution of the guided beam intensity following a wide range of times during which the capillary was allowed to discharge in order to provide information about the insulating surface charging and discharging rates. Combining our recent theoretical model describing the charge patch dynamics with these data, it is shown that the model is consistent with the experimental transmission curve data measured after the capillary was allowed to discharge for times ranging from 5 to 1000 s or longer and for injected currents that differed by a factor of 50. In contrast, models which do not include a dynamic rearrangement of charge along the surface prior to decay were found to be inconsistent with our experimental measurements. Additional data about the time dependences of the fraction of the injected beam which is transmitted as a function of injected beam current when transmission through the capillary is inhibited due to blocking are also presented. These data have a temporal dependence consistent with our model predictions that blocking occurs when the total capillary charge, i.e., the capillary potential, reaches a certain value.

We investigate the thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using self-consistent frameworks of strong-coupling diagrammatic approaches, both the ejection and the reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to the Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp transition near unitarity and to double-peak coexistence of attractive and repulsive branches in the strong-coupling regime. Our theory provides semiquantitative descriptions for a recent experiment on the ejection RF spectroscopy at unitarity [Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Phys. Rev. Lett. 122, 093401 (2019)] and suggests the importance of beyond-two-body correlations in the high-temperature regime due to the absence of Pauli-blocking effects.

We introduce a class of spiraling anomalous vortex beam (AVB) arrays in strongly nonlocal nonlinear media. The general analytical formula for the arrays is derived, and its propagation properties are analyzed. It is shown that the spiraling AVB arrays can present three different propagation states (shrink, expansion, and the dynamical bound state) depending on the absolute value of the transverse velocity parameter ($0<\left|\xi \right|<1,\left|\xi \right|>1$, and $\left|\xi \right|=1$). Accordingly, we propose the concept of array breathers and array solitons. The topological charge of the vortex and the number of the constituent AVB also play important roles in the evolution of the AVB arrays. It is found that the light intensity of the central region of the array's field under an in-phase incident condition is not zero during propagation if and only if the ratio between the two parameters is an integer. By using the derived analytical expression, a series of numerical examples is exhibited to graphically illustrate these typical propagation properties. In addition, we give a variety of array forms of multibeam interaction. Our results may provide insight into vortex beam arrays and may be applied in optical communication and particle control.

We describe and experimentally demonstrate a more practical three-party quantum secret sharing (QSS) protocol using polarization-entangled photon pairs. The source itself serves as an active participant and can switch between the required photon states by modulating the pump beam only, thereby making the protocol less susceptible to loss and amenable to fast switching. We derive a security proof based on quantum key distribution, demonstrating our QSS protocol to be secure against both eavesdropping and dishonest participants. Compared to three-photon protocols, the practical efficiency is dramatically improved as there is no need to generate, transmit, or detect a third photon.

We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qutrits. These states are extremal in the convex set of two-qutrit states with fixed marginals. Moreover, it is shown that they are always quasidistillable. As a by-product we prove that any maximally correlated state that is quasidistillable must be pure. Our observations for two qutrits are supported by numerical analysis.

The electric dipole moment of the electron ($e\mathrm{EDM}$) and the scalar-pseudoscalar (S-PS) interaction are probes of new physics beyond the standard model of elementary particles, but experiments to observe them using atoms and molecules are still in progress. Molecules that have a large effective electric field ($E_{\mathrm{eff}}$), S-PS coefficient ($W_s$), and permanent electric dipole moment (PDM) are in principle favorable candidates for such experiments, and hence, it is necessary to analyze these properties. In this work, we calculate $E_{\mathrm{eff}}$, $W_s$, and PDM for Ra systems: RaF, $\mathrm{Ra}X$ ($X=\mathrm{Cl}$, Br, I, and At), and $\mathrm{Ra}Z$ ($Z=\mathrm{Cu}$, Ag, and Au), using the Dirac-Fock and the relativistic coupled-cluster methods. The size of $E_{\mathrm{eff}}$ and $W_s$, and Ra of RaF, $\mathrm{Ra}X$, and $\mathrm{Ra}Z$ are overall similar, but the values of $\mathrm{Ra}X$ and $\mathrm{Ra}Z$ (except for RaAu) are larger than those of RaF, up to about $40\%$. We explain this finding by taking into consideration the large $s\text{−}p$ mixing for $\mathrm{Ra}X$ and $\mathrm{Ra}Z$, similar to what we had done in our previous work using hydrides and fluorides [Sunaga et al., Phys. Rev. A 95, 012502 (2017)]. We also discuss the suitability of $\mathrm{Ra}X$ and $\mathrm{Ra}Z$ molecules for $e\mathrm{EDM}$ experiments from the viewpoint of their large PDM and small polarizing electric field ($E_{\mathrm{pol}}$).

The photon-electron angular-momentum transfer is intrinsic and overwhelmingly important in light-molecule interaction. However, the photon-nuclei angular-momentum transfer is seldom observed because of the very large inertial moment and the very small dipole of nuclei as compared to those of the electron. Here, we report the theoretical and experimental observation of the transfer of the spin angular momentum of the photon into the nuclear orbital angular momentum of a molecule. This spin angular-momentum transfer is revealed by carefully examining the emission direction of the ejected proton from the breaking ${\mathrm{H}}_2$ molecule, which deviates from the initial orientation of the molecular axis. The deviation of the emission direction of the nuclear fragments from the molecular axis depends on its kinetic energy and the ellipticity of the driving laser field, which is confirmed in our numerical simulations.

We study quantum quench dynamics in the Fermi-Hubbard model, and its $\mathrm{SU}\left(N\right)$ generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized Néel order, namely, initial states in which there is a periodic $N$-spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) Néel domain walls. Those correlations resemble the ones in the ground state of the $\mathrm{SU}\left(N\right)$ model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting $\mathrm{SU}\left(N\right)$ gas into the rapidity distribution after long times. Finally, we study equilibration in $\mathrm{SU}\left(N\right)$ gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated $\mathrm{SU}\left(N\right)$ fermions at large $U$.

The vibronic dynamics of a trapped ion in the resolved-sideband regime can be described by the explicitly time-dependent nonlinear Jaynes-Cummings model. It is shown that the expectation value of the interaction Hamiltonian and its non-equal-time commutator can be determined by measuring the electronic-state evolution. This yields direct insight into the time-ordering contributions to the unitary time evolution. In order to prove extraction of the quantities of interest works for possibly real data, we demonstrate the procedure by means of generated data.

A recently proposed quantum protocol for counterfactual communication [Y. Aharonov and L. Vaidman, Phys. Rev. A 99, 010103(R) (2019)] relies on postselection to eliminate the weak trace in the transmission channel. We show that the postselection in this protocol additionally eliminates the flow of Fisher information from transmitter to receiver. However, we also show that a classical communication protocol with postselection can be counterfactual. Hence, we argue that postselection should not be allowed in genuine quantum counterfactual communication. In the proposed quantum protocol, the probability of discarding an event by postselection tends to zero with an increasing number of ideal optical components. But the counterfactual violation strength tends to infinity at a faster rate. Consequently, the quantum protocol is not counterfactual proper.

The working substance fueling a quantum heat engine may contain coherence in its energy basis, depending on the dynamics of the engine cycle. In some models of quantum Otto heat engines, energy coherence has been associated with entropy production and quantum friction. We considered a quantum Otto heat engine operating at finite time. Coherence is generated and the working substance does not reach thermal equilibrium after interacting with the hot heat reservoir, leaving the working substance in a state with residual energy coherence. We observe an interferencelike effect between the residual coherence (after the incomplete thermalization) and the coherence generated in the subsequent finite-time stroke. We introduce analytical expressions highlighting the role of coherence and examine how this dynamical interference effect influences the engine performance. Additionally, in this scenario in which coherence is present along the cycle, we argue that the careful tuning of the cycle parameters may exploit this interference effect and make coherence acts like a dynamical quantum lubricant. To illustrate this, we numerically consider an experimentally feasible example and compare the engine performance to the performance of a similar engine where the residual coherence is completely erased, ruling out the dynamical interference effect.

We consider the problem of characterizing states of a multipartite quantum system from restricted, quasi-local information, with emphasis on uniquely determined pure states. By leveraging tools from dissipative quantum control theory, we show how the search for states consistent with an assigned list of reduced density matrices may be restricted to a proper subspace, which is determined solely by their supports. The existence of a quasi-local observable which attains its unique minimum over such a subspace further provides a sufficient criterion for a pure state to be uniquely determined by its reduced states. While the condition that a pure state is uniquely determined is necessary for it to arise as a nondegenerate ground state of a quasi-local Hamiltonian, we prove the opposite implication to be false in general, by exhibiting an explicit analytic counterexample. We show how the problem of determining whether a quasi-local parent Hamiltonian admitting a given pure state as its unique ground state is dual, in the sense of semidefinite programming, to the one of determining whether such a state is uniquely determined by the quasi-local information. Failure of this dual program to attain its optimal value is what prevents these two classes of states from coinciding.

The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the measurement outcomes at the end of the system's evolution are random variables. Here, we provide the exact large-deviation form of their probability distribution, which is given by an exponentially decaying profile in the number of measurements. The most probable distribution of the measurement outcomes in a single realization of the system transformation is then derived, thus achieving predictions beyond the expectation value. The theoretical results are confirmed by numerical simulations of an experimentally reproducible two-level system with stochastic Hamiltonian.

Quantum annealing in a real device is necessarily susceptible to errors due to diabatic transitions and thermal noise. Nested quantum annealing correction is a method to suppress errors by using an all-to-all penalty coupling among a set of physical qubits representing a logical qubit. We show analytically that nested quantum annealing correction can suppress errors effectively in ferromagnetic and antiferromagnetic Ising models with infinite-range interactions. Our analysis reveals that the nesting structure can significantly weaken or even remove first-order phase transitions, in which the energy gap closes exponentially. The nesting structure also suppresses thermal fluctuations by reducing the effective temperature.

We show how the efficiency of a logical Bell measurement (BM) can be calculated for arbitrary Calderbank-Shor-Steane (CSS) codes with the experimentally important constraint of using only transversal static linear-optical BMs on the physical single-photon qubit level. For this purpose, we utilize the codes' description in terms of stabilizers in order to calculate general efficiencies for the loss-free case, but also for specific cases including photon loss. These efficiencies can be, for instance, used for obtaining transmission rates of all-optical quantum repeaters. In the loss-free case, we demonstrate that the important class of CSS codes with identical physical-qubit support for the two logical Pauli ($Z$ and $X$) operators can only achieve a logical BM efficiency of $\frac{1}{2}$ if one always employs the same ancilla-free static linear optical BMs on the physical level. We apply our methods to various CSS codes including two-dimensional planar color and planar surface codes. We then find that in many cases, the fixed use of the standard linear-optical BM for all physical BMs is suboptimal and performing linear-optical transformations before doing the standard linear-optical BM (still without any ancillary photons and without any feedforward) can increase the efficiency enormously. In fact, using this generalization in the no-loss (or sometimes also in the low-loss) case allows us, on the one hand, to improve the logical BM efficiency of quantum parity codes compared to previously known results and, on the other hand, it also enables us to enhance the efficiency of two-dimensional planar color codes, whose efficiency is otherwise subject to the above $\frac{1}{2}$ bound, to arbitrarily close to unity.