We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. These structured discrimination problems allow for a scheme that provides a certified level of error; that is, answers that never deviate from the true value by more than a specified distance and hence control the desired quality of the results. We obtain an efficient semidefinite program and also find a general lower bound valid for any error distance that only requires the knowledge of an optimal minimum-error scheme. We apply our results to the cases of quantum change point and quantum state anomaly detection.

A structure with local minima is found in the low-energy part of the above-threshold-ionization electron spectrum for several one-electron atomic and molecular targets initially in excited electronic states. The ionization regime is neither tunneling nor pure multiphoton with the Keldysh parameter slightly larger than unity. The effect is nonperturbative and depends on the frequency and intensity of the driving field. Although the ionization process is generally nonresonant, our analysis reveals an important role of intermediate bound states in formation of the structure.

We study the nonequilibrium dynamics of relaxation and dressing of a mobile impurity with velocity $v$, suddenly immersed, or quenched, into a zero-temperature homogeneous Bose-Einstein condensate. A many-body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depends crucially on the Mach number $\beta =v/c$, with $c$ the speed of sound of superfluid phonons, and features many different timescales. Quantum Zeno behavior at early time is followed by nonequilibrium dynamics determined by Cerenkov emission of long-wavelength phonons for $\beta >1$ with a relaxation rate ${\mathrm{\Gamma }}_p\propto {(\beta -1)}^3$. The polaron dressing dynamics slows down as $\beta \to 1$ and is characterized by power laws $t^{-\alpha }$ with exponents $\alpha =3/2,1/2,2$ for $\beta >1,=1,<1,$ respectively. The asymptotic entanglement entropy features a sharp discontinuity, and the residue features a cusp at $\beta =1$. These nonequilibrium features suggest universal dynamical critical phenomena near $\beta \simeq 1$ and are a direct consequence of the linear dispersion relation of long-wavelength superfluid phonons. We conjecture on the emergence of an asymptotic dynamical attractor with $\beta \le 1$.

We investigate theoretically the application of attosecond transient-absorption spectroscopy to a one-dimensional periodic crystal in a regime where the dynamical Franz-Keldysh effect is presented around the energy gap. It is found that in the presence of a few-cycle dressing pulse the delay-dependent absorption spectrogram from the numerically exactly solvable model exhibits a general feature of the V-shaped fringes of subcycle oscillations. This structure represents femtosecond-resolved transient modulation of the conductivity, which is similar to recent experimental observation. We identify a regime where the higher-order even oscillation frequency becomes remarkable in the absorption spectrum for using the midinfrared pump laser. An analytical formula is also developed with the two-band approximation in order to facilitate analysis of the absorption spectrum. Our result shows that the full information on the momentum-dependent band gap across the entire Brillouin zone is encoded into the absorption spectrogram, thus suggesting an all-optical method to reconstruct the one-dimensional gap structure. The reconstruction feasibility is successfully demonstrated by a two-step algorithm even if considering the effect of noise. Moreover, we derive an analytical expression of the delay- and frequency-dependent conductivity with some additional assumptions. Some important features are successfully interpreted in terms of this analytical approach.

Inspired by complete graph theory, we demonstrate that a metallic claw “meta-atom” structure can carry a high number of nearly degenerate resonant modes. A photonic metacrystal composed of a lattice of such meta-atoms exhibits a large number of flat bands that are squeezed into a narrow frequency window, and these flat bands can be designed to locate in a wide complete three-dimensional band gap. The degeneracy dimension ($N_f$) of the flat bands is determined by the number of branches ($N_b$) of the metallic claw with $N_f=N_b\text{–}3$, which is geometrically related to the complete graph theory. Different from those flat bands emerging from special lattice arrangements (e.g., kagome lattice), the isolated flat bands here are insensitive to lattice perturbations. The proposed mechanism offers a platform for realizing various dispersionless phenomena and a paradigm to realize high density of states and spectra compressing.

The nonequilibrium statistics and kinetics of a simple bistable system (resonantly driven nonlinear oscillator coupled to reservoir) have been investigated by means of master equation for the density matrix and quasiclassical Fokker–Planck equation in quasienergy space. We found that the system's statistical and kinetic properties drastically change when the quasienergy states become nearly degenerate and the occupation of the most excited state is strongly enhanced. It has been revealed that, in nearly degenerate case, a critical quasienergy parameter emerges. Below the critical quasienergy value the eigenstates are superpositions of the quasiclassical states from different phase-space regions, while above this value the eigenstates correspond to only one particular region of the phase space. We have also generalized Keldysh theory for ionization of atoms in the electromagnetic field for bistable systems. It has been demonstrated that Keldysh parameter in the bistability region is large when pumping intensity is smaller than the critical value. It has been shown by direct calculations that multiphoton transition amplitude coincides with the tunneling amplitude. So, multiphoton transitions and tunneling between the regions of the phase space are just the same effects. We also demonstrated that, for bistable systems, the Keldysh parameter logarithmically depends on the external field amplitude.

In this paper we propose a practical quantum key distribution protocol based on geometrically uniform states and a standard decoy state technique. The protocol extends the ideas used in SARG04 to the limit where the core quantum communication is secure against unambiguous state discrimination and provides some level of inherent resistance to photon number splitting attacks. An additional decoy state overlay ensures its conformity to the conventional security requirements. The protocol security is analyzed by an explicit construction of the most optimal unitary attack, which is known to reach the tight security bound in the case of BB84.

We in theory proposed a hybrid system consisting of a mechanical resonator, an optical Fabry-Pérot cavity, and two superconducting microwave circuits to generate stationary continuous-variable quantum entanglement between two microwave modes. We show that the hybrid system can also achieve quantum entanglement of other bipartite subsystems in experimentally accessible parameter regimes, which has the potential to be useful in quantum information processing and quantum illumination radar.

Doubly polar molecules, possessing an electric dipole moment and a magnetic dipole moment, can strongly couple to both an external electric field and a magnetic field, providing unique opportunities to exert full control of the system quantum state at ultracold temperatures. We propose a method for creating a purely long-range doubly polar homonuclear molecule from a pair of strongly magnetic lanthanide atoms, one atom being in its ground level and the other in a superposition of quasidegenerate opposite-parity excited levels [Phys. Rev. Lett. 121, 063201 (2018)]. The electric dipole moment is induced by coupling the excited levels with an external electric field. We derive the general expression of the long-range, Stark, and Zeeman interaction energies in the properly symmetrized and fully-coupled basis describing the diatomic complex. Taking the example of holmium, our calculations predict a few shallow long-range wells in the potential energy curves that support vibrational levels accessible by direct photoassociation from pairs of ground-level atoms.

We investigate the tunneling dynamics of an ultracold bosonic impurity species which interacts repulsively with a second, larger Bose gas. Both species are held in a finite-sized quasi-one-dimensional box potential. In addition, the impurity bosons experience a periodic potential generated by an optical lattice. We initially prepare our binary mixture in its ground state, such that the impurities and Bose gas are phase separated and the impurities localize pairwise in adjacent sites of the periodic potential, by tuning the interaction strengths and the lattice depth correspondingly. The dynamics is initiated by suddenly lowering the repulsive interspecies interaction strength, thereby entering a different regime in the crossover diagram. For specific postquench interspecies interaction strengths we find that a single impurity tunnels first to the neighboring empty site and depending on the quench strength can further tunnel to the next-neighboring site. Interestingly, this effect is highly sensitive to the presence of the Bose gas and does not occur when the Bose gas does not interact with the impurity species throughout the dynamics. Moreover, we find that the tunneling process is accompanied by strong entanglement between the Bose gas and the impurity species as well as correlations among the impurities.

We develop the theory of pure dephasing in a solid exposed to an ultrashort laser pulse beyond the commonly used Markov approximation. This approach takes into account the finite cutoff energy of the bath and can be applied to both many-particle and phonon environments. With numerical simulations performed with the time-dependent Hartree-Fock equations, we investigate how the excitation probability and high-harmonic generation are described by different models of decoherence. It is shown that the time-dependent rates allow for temporally high dephasing to successfully reproduce the main features of high-harmonics spectrum and avoid an overestimation of the charge carrier population after the pulse, which is a common problem of the Markov approximation.

Consider the set $\mathcal{S}=\left\{{\rho }_{SE}\right\}$ of possible initial states of the system-environment, steered from a tripartite reference state ${\omega }_{RSE}$. Buscemi [F. Buscemi, Phys. Rev. Lett. 113, 140502 (2014)] showed that the reduced dynamics of the system, for each ${\rho }_S\in {\mathrm{Tr}}_E\mathcal{S}$, is always completely positive if and only if ${\omega }_{RSE}$ is a Markov state. There, during the proof, it has been assumed that the dimensions of the system and the environment can vary through the evolution. Here, we show that this assumption is necessary: we give an example for which, though ${\omega }_{RSE}$ is not a Markov state, the reduced dynamics of the system is completely positive, for any evolution of the system-environment during which the dimensions of the system and the environment remain unchanged. As our next result, we show that the result of Muller-Hermes and Reeb [A. Muller-Hermes and D. Reeb, Ann. Henri Poincare 18, 1777 (2017)], of monotonicity of the quantum relative entropy under positive maps, cannot be generalized to the Hermitian maps, even within their physical domains.

We theoretically analyze the observations reported in a four-path quantum interference experiment via multiple-beam Ramsey interference [Phys. Rev. Lett. 86, 559 (2001)]. In this experiment, a selective scattering of photons from just one interfering path causes decoherence. However, contrary to expectations, there is an increase in the contrast of the interference pattern, demonstrating that path selective decoherence can not only lead to a decrease but, under certain conditions, lead to an increase of the fringe contrast. Here we explain this seemingly counterintuitive effect based on a model for a multipath interference, with four to six slits, in the presence of decoherence. The effect of the environment is modeled via a coupling to a bath of harmonic oscillators. When decoherence is introduced in one of the multiple paths, an enhancement in fringe contrast is seen under certain conditions. A similar effect is shown to appear if instead of path-selective decoherence, a selective path detector is introduced. Our analysis points to the fact that while traditional fringe visibility captures the wave nature in the two-path case, it can fail in multipath situations. We explain the enhancement of fringe visibility and also show that quantum coherence based on the $l_1$ norm of coherence, in contrast to traditional visibility, remains a good quantifier of wave nature, even in such situations. The enhancement of fringe contrast in the presence of environmental decoherence underscores the limitations of traditional visibility as a good measure for wave nature in quantifying complementarity and also makes it an unlikely candidate for quantifying decoherence. Our analysis could lead to better insight in ways to quantify decoherence in multipath interference and in studies that seek to exploit quantum superpositions and quantum coherence for quantum information applications.

Entanglement is considered as a purely quantum effect. The present paper, however, joins many other works that pursue the idea of describing it using classical quantities. In particular, we are interested in the entanglement dynamics of a pure state composed of two parts, initially prepared in a product of coherent states and governed by a generic Hamiltonian. In this scenario, the linear entropy of the reduced state, our entanglement quantifier, was shown to be written, in the short-time regime, in terms of a real trajectory of the underlying classical dynamics. We extend this semiclassical result by demonstrating that it is possible to include complex trajectories in the calculation. This strategy contributes to improving the previous approximation, extending its accuracy for longer values of time. We also show, for a particular Hamiltonian, a first application of the achieved formula, attesting to its efficiency.

For a given Hamiltonian $H$ on a multipartite quantum system, one is interested in finding the energy $E_0$ of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one looks for the minimal expectation value ${\lambda }_{\min }^{\otimes }$ of $H$ among all product states. For several concrete model Hamiltonians, we investigate the difference ${\lambda }_{\min }^{\otimes }-E_0$, called the separability gap, which vanishes if the ground state has a product structure. In the generic case of a random Hermitian matrix of the Gaussian orthogonal ensemble, we find explicit bounds for the size of the gap which depend on the number of subsystems and hold with probability one. This implies an effective entanglement criterion applicable for any multipartite quantum system: If an expectation value of a typical observable of a given state is sufficiently distant from the average value, the state is almost surely entangled.

The possibility of discriminating the statistics of a thermal bath using indirect measurements performed on quantum probes is presented. The scheme relies on the fact that, when weakly coupled with the environment of interest, the transient evolution of the probe toward its final thermal configuration is strongly affected by the fermionic or bosonic nature of the bath excitations. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we discuss how to achieve the greatest precision in this statistics tagging procedure, analyzing different models of probes and different initial preparations and by optimizing over the time of exposure of the probe.

An atomic frequency comb (AFC) made of an ensemble of atoms with a periodic optical resonance was originally proposed as a viable approach for quantum memory for photons. In this paper we examine the quantum cloning capacity of an AFC in terms of the spectral distribution of the atomic populations in the energy levels associated with the optical transition. Expressions are derived for the memory readout efficiency, signal to noise ratio, and fidelity for an input at the single photon level. When applied to a square-toothed AFC, our analysis shows that there is a region where amplification from the excited state population results in greater than unit readout efficiency at a cost of fidelity being less than perfect, but still greater than the classical limit. The theory is developed under the assumption that both AFC and photon wave packets are spatially uniform. This can be regarded as a single spatial location inside an AFC and can be further expanded to study optically thick AFC with atomic population in both levels, which may find applications for quantum memory and quantum cloning machine.

The progress in optical clocks with uncertainty at a level of ${10}^{-18}$ requires unprecedented precision in estimating the contributions of multipolar and higher-order effects of atom-field interactions. Current theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the magic wavelength for the Sr clock differ substantially. We combine the Dirac-Fock plus core polarization and relativistic configuration interaction methods to calculate dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr atom. Our differential dynamic hyperpolarizability at the magic wavelength is $-2.09\left(43\right)\times {10}^7$ a.u., which is consistent with existing theoretical and experimental results. Our differential multipolar polarizability is $2.68\left(94\right)\times {10}^{-5}$ a.u., which validates independently the theoretical work of Porsev et al. [Phys. Rev. Lett. 120, 063204 (2018)], but is different from recent measurements of Ushijima et al. [Phys. Rev. Lett. 121, 263202 (2018)].

We revisit the basic properties of Fano-Feshbach resonances in two-body systems with van der Waals tail interactions, such as ultracold neutral atoms. Using a two-channel model and two different methods, we investigate the relationship between the width and shift of the resonances and their dependence on the low-energy parameters of the system. Unlike what was previously believed [C. Chin et al., Rev. Mod. Phys. 82, 1225 (2010)] for magnetic resonances, we find that the ratio between the width and the shift of a resonance does not depend only on the background scattering length, but also on a closed-channel scattering length. We obtain different limits corresponding to different cases of optical and magnetic resonances. Although the generalization of the theory to the multichannel case remains to be done, we found that our two-channel predictions are verified for a specific resonance of lithium-6.