By considering a solvable driven-dissipative quantum model, we demonstrate that continuous phase transitions in dissipative systems may occur without an accompanying symmetry breaking. As such, the underlying mechanism for this type of transition is qualitatively different from that of continuous equilibrium phase transitions. In our model, the transition is solely a result of the interplay between Hamiltonian and dissipative dynamics and manifests as a nonanalyticity in the steady state ${\widehat{\rho }}_{\mathrm{ss}}$ in the thermodynamic limit. Based on knowledge from critical classical models we suggest that this behavior derives from a rounding of a first-order phase transition into a continuous one due to large environment-induced fluctuations. Despite being conceptually different from the traditional continuous transitions, we show that expectations of local observables can still be characterized by a set of critical exponents.

The generic nature of band touching points in three-dimensional band structures is at the heart of the rich phenomenology, topological stability, and novel Fermi arc surface states associated with Weyl semimetals. Here we report on the corresponding scenario emerging in systems effectively described by non-Hermitian Hamiltonians. Remarkably, three-dimensional non-Hermitian systems have generic band touching along one-dimensional closed contours, forming exceptional rings and links in reciprocal space. The associated Seifert surfaces support open “Fermi ribbons” where the real part of the energy gap vanishes, providing a novel class of higher-dimensional bulk generalizations of Fermi arcs which are characterized by an integer twist number. These results have possible applications to a plethora of physical settings, ranging from mechanical systems and optical metamaterials with loss and gain to heavy fermion materials with finite-lifetime quasiparticles. In particular, photonic crystals provide fertile ground for simulating the exuberant phenomenology of exceptional links and their concomitant Fermi ribbons.

Quantum steering is a kind of quantum correlations stronger than entanglement but weaker than Bell nonlocality. In an optomechanical system pumped by squeezed light and driven in the red sideband, we study—under thermal effects—stationary Gaussian steering and its asymmetry of two mechanical modes. In the resolved sideband regime using experimentally feasible parameters, we show that Gaussian steering can be created by quantum fluctuations transfer from the squeezed light to the two mechanical modes. Moreover, one-way steering can be observed by controlling the squeezing degree or the environmental temperature. A comparative study between Gaussian steering and Gaussian Rényi-2 entanglement of the two considered modes shows on one hand that both steering and entanglement suffer from a sudden death-like phenomenon with early vanishing of steering in various circumstances. On the other hand, steering is found stronger than entanglement, however, remains constantly upper bounded by Gaussian Rényi-2 entanglement, and decays rapidly to zero under thermal noise.

We have developed a method to calculate a secret key rate of a continuous-variable quantum-key-distribution scheme using four coherent states and postselection for a general model of Gaussian attacks. We assume that the transmission line and detection process are described by a pair of Gaussian channels. In our analysis, while the loss and noise on the transmission line are induced by an eavesdropper, Eve, who can replace the transmission line with a lossless and noiseless optical fiber, she is assumed inaccessible to the detection process. By separating the transmission noise and detection noise, we can always extract a larger key compared with the case that all loss and noises are induced by an eavesdropper's interference. An asymptotic key rate against collective Gaussian attacks can be determined numerically for the given channels' parameters. The improvement of the key rates turns out to be more significant for the reverse-reconciliation scheme.

We define the deconstruction cost of a tripartite quantum state on systems $ABE$ as the minimum rate of noise needed to apply to the $AE$ systems, such that there is negligible disturbance to the marginal state on the $BE$ systems, while the system $A$ of the resulting state is locally recoverable from the $E$ system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems $ABE$ is equal to its conditional quantum mutual information (CQMI) $I(A;B|E)$, thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems $AE$ in order to decouple system $A$ from systems $BE$, while causing negligible disturbance to the marginal state of systems $BE$. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI $I(A;B|E)$. State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction and/or conditional erasure if Alice has available the best possible system $E$ to help in the deconstruction and/or conditional erasure task.

Continuous-variable quantum cryptographic systems, including random number generation and key distribution, are often based on coherent detection. The essence of the security analysis lies in the randomness quantification. Previous analyses employ a semiquantum picture, where the strong local oscillator limit is assumed. Here we investigate the randomness of homodyne detection in a full quantum scenario by accounting for the shot noise in the local oscillator, which requires us to develop randomness measures in the infinite-dimensional scenario. Similar to the finite-dimensional case, our introduced measure of randomness corresponds to the relative entropy of coherence defined for an infinite-dimensional system. Our results are applicable to general coherent detection systems, in which the local oscillator is inevitably of finite power. As an application example, we employ the analysis method to a practical vacuum-fluctuation quantum random number generator and explore the limits of generation rate given a continuous-wave laser.

A tripartite quantum network is said to be bilocal if two independent sources produce a pair of bipartite entangled states. Quantum nonbilocal correlation emerges when the central party which possesses two particles from two different sources performs Bell-state measurement on them and nonlocality is generated between the other two uncorrelated systems in this entanglement-swapping protocol. The interaction of such systems with the environment reduces quantum nonbilocal correlations. Here we show that the diminishing effect modeled by the amplitude damping channel can be slowed down by employing the technique of weak measurements and reversals. It is demonstrated that for a large range of parameters, the quantum nonbilocal correlations are preserved against decoherence by taking into account the average success rate of the postselection governing weak measurements.

We consider the time-dependent resonance interaction energy between two identical atoms, one in the ground state and the other in an excited state, and interacting with the vacuum electromagnetic field, during a nonequilibrium situation such as the dynamical atomic self-dressing process. We suppose the two atoms prepared in a correlated, symmetric or antisymmetric, state. Since the atoms start from a nonequilibrium conditions, their interaction energy is time dependent. We obtain, at second order in the atom-field coupling, an analytic expression for the time-dependent resonance interaction energy between the atoms. We show that this interaction vanishes when the two atoms are outside the light cone of each other, in agreement with relativistic causality, while it instantaneously settles to its stationary value after time $t=R/c$ ($R$ being the interatomic distance), as obtained in a time-independent approach. We also investigate the time-dependent electric energy density in the space around the two correlated atoms, in both cases of antisymmetric (subradiant) and symmetric (super-radiant) states, during the dressing process of our two-atom system. We show that the field energy density vanishes in points outside the light cone of both atoms, thus preserving relativistic causality. On the other hand, inside the light cone of both atoms, the energy density instantaneously settles to its stationary value. Specifically, for points at equal distance from the two atoms, we find that it vanishes if the two atoms are prepared in the antisymmetric (subradiant) state, while it is enhanced, with respect to the case of atoms in a factorized state, in the symmetric (super-radiant) state. The physical meaning of these results is discussed in detail in terms of interference effects of the field emitted by the two atoms.

The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green's function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_2$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1\le Z\le 68$ are provided in a tabular form. A simple formula for the polarizability of a nonrelativistic two-dimensional hydrogenic atom, reported previously by several other authors, is recovered from our result in the nonrelativistic limit.

We investigate dissociative single and double ionization of ${\mathrm{HeH}}^{+}$ induced by intense femtosecond laser pulses. By employing a semiclassical model with nuclear trajectories moving on field-dressed surfaces and ionization events treated as stochastical jumps, we identify a strong-field mechanism wherein the molecules dynamically align along the laser polarization axis and stretch towards a critical internuclear distance before dissociative ionization. As the tunnel-ionization rate is larger for larger internuclear distances and for aligned samples, ionization is enhanced. The strong dynamical rotation originates from the anisotropy of the internuclear distance-dependent polarizability tensor, which features a maximum at certain internuclear distances. Good qualitative agreement with our experimental observations is found. Finally, we investigate under which experimental conditions isotope effects of different isotopologues of ${\text{HeH}}^{+}$ can be observed.

We present an analysis of the appearance of the Cooper minimum in singly ionized argon in both the photoionization cross-section (PICS) and high-harmonic generation (HHG) spectrum. We employ two computational approaches based on the same $R$-matrix technique to provide a coherent description of the atomic structure of the ${\mathrm{Ar}}^{+}$ system, finding that the PICS and HHG spectrum are affected differently by the inclusion of additional residual ion states and the improved description of correlation effects. Both the PICS and HHG spectrum possess a clear minimum for all atomic structure models used, with the center of the minimum at 55 eV in the PICS and 60 eV in the HHG spectrum for the most complete description employed. The HHG minimum is systematically shifted to higher energies with respect to the PICS minimum. We also find that the initial magnetic alignment (magnetic quantum number) of the ${\mathrm{Ar}}^{+}$ system does not affect substantially the position and shape of the HHG minimum (given a sufficiently detailed atomic structure description), but the harmonic yield is enhanced by two orders of magnitude for $M_L=1$ over $M_L=0$. We also perform similar calculations for neutral argon, finding that this system is more sensitive to enhancements in the atomic structure description.

We investigate theoretically the photoassociation (PA) of two $\mathrm{Cs}$ atoms using a slowly-turned-on and rapidly-turned-off (STRT) laser pulse at the temperature of $54\mu \mathrm{K}$ by taking the thermal average of the initial continuum states into account. For comparison, the PA probabilities under the action of the STRT and typical Gauss-type pulses are calculated, respectively. The rising and falling times of the STRT pulse are set to be ${\tau }_r=10$ ps and ${\tau }_f=0.2$ ps, and the two Gauss-type pulses are set to be ${\tau }_r={\tau }_f=10$ ps and ${\tau }_r={\tau }_f=5.1$ ps, respectively. Compared to the calculation considering a single initial continuum state (non-thermal-average calculations), the PA probabilities with the consideration of the thermal average are reduced to different extents according to different laser pulses. The PA process induced by the STRT pulse is more robust than that by the two Gauss-type pulses. For the STRT pulse, the PA probability is reduced by roughly 30%, while for the two Gauss-type pulses, it is reduced by roughly 97% and 64%, respectively. Because of the larger bandwidth and the asymmetric time profile of the STRT pulse, the PA probability induced by this pulse is related to both the off-resonant and the near-resonant transitions in a much broader phase space formed by the initial continuum states and the final vibrational states. Consequently, the thermal average of the initial continuum states has relatively smaller influence on the PA probability induced by the STRT pulse. By changing the pulse shape of the standard Gaussian to the ${\sin }^2$ and the Lorentz ones, the STRT pulse still results in the highest PA probability and is the most robust to the thermal average.

A scheme is presented to perform an entangling gate between two atomic ensembles or Bose-Einstein condensates in a optical cavity with a common optical mode. The method involves using a generalized stimulated Raman adiabatic passage (STIRAP) to adiabatically evolve the ground state. We show that dark states exist for any atom number within the cavities and find that the operation produces an unusual type of evolution where the minimum of the number of atoms between two level transitions to another state. This produces an unconventional type of entangling Hamiltonian which creates a phase depending on the minimum operation. We analyze its reliability under a variety of conditions ranging from the ideal decoherence-free case to that including photon loss and spontaneous emission. Ways of combating decoherence are analyzed, and the amount of entanglement that is generated is calculated.

The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of end states. We provide an intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological end states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.

The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the resulting patterns depend on a quasitime $\tau$ given by a function of the coordinate along the propagation axis in a classical combination $z_0-t^{2}F/m$, while the diffraction effects along transverse axes are due solely to $m/\hslash$. The consequences on the precision at which the equivalence principle can be tested are discussed. Realizations with ultracold neutrons, Bose-Einstein condensates, and molecular beams are proposed.

We theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that, by suitably driving $\mathrm{\Lambda }$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Thereby, we can manipulate heating and cooling effects. Particularly, we develop an optomechanical cooling strategy that can mutually cancel the heating effect of the outgoing and incoming radiation, rendering the motional ground state attainable by net cooling. Our proposal complements other efforts in quantum cooling of macroscopic objects since it requires neither a cavity nor perfect alignment.

Frequency-resolved correlation (FRC) is investigated in fluorescent emission radiated from a $\mathrm{\Lambda }$-type atomic system by employing weak coupling regime between quantum emitter and cavities, in which each cavity substituting a Lorentzian filter is assumed to pass through only one fluorescent photon at a time so that the analytical discussions for time orderings can be carried out in a truncated Hilbert space with single-excitation state for each cavity mode. In the limit of bad cavity (large passband width of filter) and short delay, the conditional time ordering amplitudes are introduced with the help of conditioned dressed atom-photon states prepared by preselection to probe into the effect of preferential screening for time orderings of filter-detector systems. Meanwhile, the past quantum state formalism is also applied in FRC to further excavate their collective monitoring effect. Based on the obtained two-mode correlation signals, it is found that, in nonresonant two-photon cascaded processes, bunching and antibunching can appear in two opposite detection orderings, respectively, and can be switched. The physical origin is explored that the two different transition amplitudes of emitted photons from a common spectral band of resonance fluorescence are responsible for opposite time orderings, thus, the imbalance between two complementary time orderings can be enhanced, which is impossible to achieve in resonance fluorescence of two-level atoms. This mechanism is embodied in the conditional time ordering amplitudes produced by this detection theory of cavity modes.

We investigate the manipulation of the quantum interference (QI) in an electromagnetically induced transparency (EIT) system via phase fluctuations and their correlation of interacting fields. We show that the field fluctuation correlation and atomic dephasing rate have a similar effect to atomic coherence, and furthermore that QI is dependent on the fluctuation and correlation. Using the theoretical model in a dressed-state representation, the contribution of QI and Autler-Townes splitting (ATS) to probe absorption can be expressed in separate terms, such that the obvious enhancement of QI is found with highly correlated fields while ATS remains unchanged. In particular, when the relative large Rabi frequency of coupling field is applied, in which case the ATS plays a more prominent role than QI, we can still modulate the QI to be higher than ATS with correlated fields. This result could allow the strict EIT condition to be relaxed and be easily realized, or it may be a method to get a narrow EIT window for applications in efficient light storage and quantum interface.

We introduce the one-dimensional $\mathcal{PT}$-symmetric Schrödinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatorylike potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of $\mathcal{PT}$-symmetry-breaking transitions, controlled by the parameters of the superoscillatory function. One scenario of the transitions proceeds smoothly via a set of threshold values, while another one exhibits a sudden jump to the broken $\mathcal{PT}$ symmetry. Another noteworthy finding is the possibility of restoration of the $\mathcal{PT}$ symmetry, following its original loss, in the course of the variation of the parameters.

We propose here a scheme based on the measurement of quadrature phase coherence that is aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate Einstein-Podolsky-Rosen–like correlations between the quadratures of the output fields of the two cavities and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality.