We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population of the cavity photons. Even though the dynamics of each ensemble are chaotic, their motions repeat one another. In our system, chaos first emerges via quasiperiodicity and then synchronizes. We identify the signatures of synchronized chaos, chaos, and quasiperiodicity in the experimentally observable power spectra of the light emitted by the cavity.

The near-field polarization structure of a high-refractive-index dielectric nanosphere in a nonmagnetic and nonabsorbing medium is studied numerically in free space and in the vicinity of a flat dielectric substrate. Polarization patterns of the near field are obtained for linear and circular polarizations of the incident light and visualized using the polarization degree and three-dimensional Stokes parameters. Calculations are performed using the finite-element method and verified analytically using the Mie solution for scattering by a sphere with an extension of Weyl's method allowing description of reflection by a flat substrate. It is shown that the nanosphere drastically affects the polarization leading to a complex butterflylike structure. For instance, the near-field polarization is found to be qualitatively modified near the Mie electric and magnetic dipole and quadrupole resonances: linear polarization of the incident field results in circular polarization in some areas around the particle and vice versa. The areas of strong polarization change are found to be spatially localized in certain places around the particle making it possible to perform an experimental mapping. It is shown how a dielectric substrate affects the polarization distribution of the near-field of the particle. Also, several schemes of potential experiments to map the near-field intensity and polarization have been discussed.

We derive conditions in the form of inequalities to detect the genuine $N$-partite entanglement of $N$ systems. The inequalities are expressed in terms of variances of spin operators and can be tested by local spin measurements performed on the individual systems. Violation of the inequalities is sufficient (but not necessary) to certify the multipartite entanglement and occurs when a type of spin squeezing is created. The inequalities are similar to those derived for continuous-variable systems, but instead are based on the Heisenberg spin-uncertainty relation $\mathrm{\Delta }{J}_x\mathrm{\Delta }{J}_y\ge \left|\langle J_z\rangle \right|/2$. We also extend previous work to derive spin-variance inequalities that certify the full tripartite inseparability or genuine multipartite entanglement among systems with fixed spin $J$, as in Greenberger–Horne–Zeilinger (GHZ) states and W states where $J=1/2$. These inequalities are derived from the planar spin-uncertainty relation ${\left(\mathrm{\Delta }{J}_x\right)}^2+{\left(\mathrm{\Delta }{J}_y\right)}^2\ge C_J$ where $C_J$ is a constant for each $J$. Finally, it is shown how the inequalities detect multipartite entanglement based on Stokes operators. We illustrate with experiments that create entanglement shared among separated atomic ensembles, polarization-entangled optical modes, and the clouds of atoms of an expanding spin-squeezed Bose-Einstein condensate. For each example, we give a criterion to certify the mutual entanglement.

Electron-positron pair production in an oscillating Sauter potential is investigated in the framework of the computational quantum field theory. For a Sauter potential well that oscillates both in its depth and width, the number of created pairs depends on the phase difference between the two oscillations. The optimal phase differences for different oscillation frequencies are obtained. For slow-varying fields, the phase difference has a great effect on the number of pairs, which can be explained by the instantaneous bound states and the effective interaction time. For the higher-frequency case, the phase difference effect is weakened, which is related to the enhancement of the multiphoton effect and Pauli blocking effect. Compared with a Sauter potential well with only the depth in oscillations, this model can generate more pairs at the same frequency. These results can provide a theoretical reference for the experimental creation of the electron-positron pairs.

We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control, associated with sensing the parameter, by reducing the noise in operations under our control, associated with preparing and measuring probes and ancillae. To that end, we introduce noise thresholds to quantify the noise resilience of parameter estimation schemes. We demonstrate improved noise thresholds over the non-fault-tolerant schemes. We use quantum Reed-Muller codes to retrieve more information about a single phase parameter being estimated in the presence of full-rank Pauli noise. Using only error detection, as opposed to error correction, allows us to retrieve higher thresholds. We show that better devices, which can be engineered, can enable us to counter larger noise in the field beyond our control. Further improvements in fault-tolerant quantum metrology could be achieved by optimizing in tandem parameter-specific estimation schemes and transversal quantum error correcting codes.

Under the unitary evolutions it is always possible to distinguish different Hamiltonians with zero-error probability within a finite time. At the presence of noises, however, the error probability does not always go to zero within a finite time. In this article, we give a necessary and sufficient condition for Markovian dynamics to achieve zero-error quantum hypothesis testing in a finite time. We show that when the condition fails, the maximal fidelity of the output states under two different Hamiltonians, aided with arbitrary control operations, is always lower bounded by an exponential function, which remains positive at any finite time; zero-error quantum hypothesis testing thus cannot be achieved within any finite time. However, when the condition holds, quantum error corrections can be used to correct the noises and partially maintain the coherent evolutions, zero-error quantum hypothesis testing can then be achieved within a finite time.

The random-phase approximation (RPA) is exact for the exchange energy of a many-electron ground state, but RPA makes the correlation energy too negative by about 0.5 eV/electron. That large short-range error, which tends to cancel out of isoelectronic energy differences, is largely corrected by an exchange-correlation kernel, or (as in RPA+) by an additive local or semilocal correction. RPA+ is by construction exact for the homogeneous electron gas, and it is also accurate for the jellium surface. RPA+ often gives realistic total energies for atoms or solids in which spin-polarization corrections are absent or small. RPA and RPA+ also yield realistic singlet binding energy curves for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$, and thus RPA+ yields correct total energies even for spin-unpolarized atoms with fractional spins and strong correlation, as in stretched ${\mathrm{H}}_2$ or ${\mathrm{N}}_2$. However, RPA and RPA+ can be very wrong for spin-polarized one-electron systems (especially for stretched ${{\mathrm{H}}_2}^{+}$), and also for the spin-polarization energies of atoms. The spin-polarization energy is often a small part of the total energy of an atom, but important for ionization energies, electron affinities, and the atomization energies of molecules. Here we propose a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities, in the same simple semilocal way that the correlation energy densities of many metageneralized gradient approximations are made self-correlation free. By construction, gRPA+ does not degrade the exact RPA+ description of jellium. gRPA+ is found to greatly improve upon RPA and RPA+ for the ionization energies and electron affinities of light atoms. Many versions of RPA with an approximate exchange-correlation kernel fail to be exact for all one-electron densities, and they can also be self-interaction corrected in this way.

The fine and hyperfine interactions in $X{}^2{\mathrm{\Sigma }}^{+}\left(v=0\right)$ and $A^2{\mathrm{\Pi }}_{1/2}\left(v=0\right)$ states of ${}^{173}\mathrm{YbF}$ have been characterized using a combination of high-resolution laser-induced fluorescence spectroscopy of the $A{}^2{\mathrm{\Pi }}_{1/2}$−$X{}^2{\mathrm{\Sigma }}^{+}$ (0,0) electronic transition and ground-state microwave spectroscopy. Fourteen microwave transition frequencies associated with the $N=3\to N=4$ and $N=4\to N=5$ pure rotational spectra were recorded using a separated field pump-probe microwave optical double-resonance (PPMODR) scheme. Five transition frequencies associated with the $N=0\to N=1$ rotational spectrum were recorded using Fourier transform microwave spectroscopy. A combined analysis of the $A^2{\mathrm{\Pi }}_{1/2}$−$X^2{\mathrm{\Sigma }}^{+}$ (0,0) electronic transition and the pure rotational spectrum of the $X^2{\mathrm{\Sigma }}^{+}$ state has been performed to derive the molecular fine, magnetic hyperfine, and nuclear electric quadrupole moment parameters, $e^{2}Q{q}_0$, for ${}^{173}\mathrm{Yb}\left(I=5/2\right)$. The determined $e^{2}Q{q}_0$ parameters are in agreement with a recent theoretical prediction [Mol. Phys. 114, 1110 (2016)]. The determined ${}^{173}\mathrm{Yb}$ hyperfine parameters will be useful for the spectroscopic analysis of the ${}^{173}\mathrm{YbOH}$ molecule, which has been suggested [Phys. Rev. Lett. 119, 133002 (2017)] for use in the magnetic quadrupole moment search.

The usual treatment of a Bose-Fermi mixture relies on weak-coupling Gross-Pitaevskii (GP) and density-functional (DF) Lagrangians, often including the more realistic perturbative Lee-Huang-Yang (LHY) corrections. We suggest analytic non-perturbative beyond-mean-field Bose and Fermi Lagrangians valid along the crossover from weak- to strong-coupling limits of intraspecies interactions consistent with the LHY corrections and the strong-coupling (unitarity) limit for small and large scattering lengths $\left|a\right|$, respectively, and use these to study the Bose-Fermi mixture. We study numerically mixing-demixing and spontaneous symmetry breaking in Bose-Fermi mixtures in spherically symmetric and quasi-one-dimensional traps, while the intraspecies Bose and Fermi interactions are varied from weak-coupling to strong-coupling limits. The LHY correction is appropriate for medium to weak atomic interactions and diverges for stronger interactions (large scattering length $\left|a\right|$), whereas the present beyond-mean-field Lagrangian is finite in the unitarity limit ($\left|a\right|\to \infty$). We illustrate our results using the Bose-Fermi ${}^7\mathrm{Li}{\text{−}}^6\mathrm{Li}$ mixture under a spherically-symmetric and a quasi-one-dimensional trap. The results obtained with the present model for density distribution of the Bose-Fermi mixture along the crossover could be qualitatively different from the usual GP-DF Lagrangian with or without LHY corrections. Specifically, we identified spontaneous symmetry breaking and demixing in the present model not found in the usual model with the same values of the parameters.

We study the nonequilibrium dynamics of a one-dimensional Bose-Hubbard model in a gradient potential and a superlattice, beginning from a deep Mott insulator regime with an average filling of one particle per site. Studying a quench that is near resonance to tunneling of the particles over two lattice sites, we show how a spin model emerges consisting of two coupled Ising chains that are coupled by interaction terms in a staggered geometry. We compare and contrast the behavior in this case with that in a previously studied case where the resonant tunneling was over a single site. Using optimized tensor network techniques to calculate finite-temperature behavior of the model, as well as finite-size scaling for the ground state, we conclude that the universality class of the phase transition for the coupled chains is that of a tricritical Ising point. We also investigate the out-of-equilibrium dynamics after the quench in the vicinity of the resonance and compare dynamics with recent experiments realized without the superlattice geometry. This model is directly realizable in current experiments and reflects a general way to realize spin models with ultracold atoms in optical lattices.

Dark solitons in superfluid Bose gases decay through the snake instability mechanism, unless they are strongly confined. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, we show using both an effective field numerical simulation and a perturbative analysis that there is a qualitative difference between soliton decay in the BEC and BCS regimes. On the BEC side of the interaction domain, the characteristic snaking deformations are induced by fluctuations of the amplitude of the order parameter, while on the BCS side, fluctuations of the phase destroy the soliton core through the formation of local Josephson currents without the presence of snaking deformations. The latter mechanism is qualitatively different from the snaking instability and this difference should be experimentally detectable.

We theoretically investigate the dynamics of polar bright soliton under the influence of spin-orbit coupling (SOC) in spin-1 three component Bose-Einstein condensate (BEC). Periodically oscillating dark-bright-dark solitons are found to be induced by the SOC with their multifrequency oscillations jointly determined by the interparticle nonlinear interaction and the SOC strength. Explicit formulas are provided to identify these frequencies, which are in good agreement with the numerical simulation results. A linear Zeeman interaction is further introduced to break the time-reversal symmetry and change the polarity of the spinor BECs, which results in the periodic transition of the system from polar state to ferromagnetic state.

In this paper, we first consider the generation of mechanical squeezing in a dispersively or dissipatively coupled optomechanical system by continuously homodyning the output field of the optomechanical cavity. It is found that strong steady-state mechanical squeezing beyond the 3 dB limit can be achieved in both of the optomechanical systems. The properties of the squeezing are quite different for the two types of systems and the reasons for the differences are analyzed. We next consider the achievement of optomechanical steering in the dispersive or dissipative optomechanical system via continuously monitoring the position of the mechanical oscillator. It is revealed that the monitoring can lead the steady-state optomechanical entanglement to be enhanced considerably such that strong steerable correlations can be achieved between the mechanical oscillator and the cavity field. The effects of thermal phonons are studied and it is shown that the generated squeezing and steering are quite robust against the thermal fluctuations.

We report a theoretical study of the propagation of electromagnetic waves (EWs) through an array of superconducting qubits, i.e., coherent two-level systems, embedded in a low-dissipation transmission line. We focus on the near-resonant case as the frequency of EWs $\omega \simeq {\omega }_q$, where ${\omega }_q$ is the qubit frequency. In this limit we derive the effective dynamic nonlinear wave equation allowing one to obtain the frequency-dependent transmission coefficient of EWs, $D\left(\omega \right)$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D\left(\omega \right)$ in both cases of a single qubit and chains composed of a large number of densely arranged qubits. However, in narrow frequency regions a chain of qubits allows the resonant transmission of EWs with greatly enhanced $D\left(\omega \right)$. In the nonlinear regime realized for a moderate power of applied microwave radiation, we predict and analyze various transitions between states characterized by high and low values of $D\left(\omega \right)$. These transitions are manifestations of nonequilibrium steady states of an array of qubits achieved in this regime.

We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We show that the generated macroscopic entangled states are non-Gaussian and their lifetime is limited by coherence time of the qubit. The entanglement is attainable in a wide range of parameters with appropriate control of the qubit. We confirm the performance of our scheme by numerically solving the quantum-optical master equation including sources of noise. The effect of imperfections, such as asymmetries in the coupling rates as well as mechanical thermal noise, is studied and it is shown how they affect the amount and lifetime of the entangled state. Due to the nonlinear nature of the qubit, the initial Gaussian state of mechanical resonators evolves into a quasistationary non-Gaussian state, which is essential for universal quantum information processing in continuous-variable systems. This work, therefore, provides the first step towards a universal continuous-variable quantum network.

We report on the controllable response of the lasing frequency to the cavity round-trip path change. This is achieved by modifying the dispersion of the intracavity medium in the four-wave mixing regime in Rb. We can either increase the response by at least a factor of 2.7 or drastically reduce it. The former regime is useful for sensitive measurements tracking the cavity round-trip length and the latter regime is useful for precision metrology.

We propose a method for learning a quantum probabilistic model of a perceptron. By considering a cross entropy between two density matrices we can learn a model that takes noisy output labels into account while learning. Although some work has been done that aims to utilize the curious properties of quantum systems to build a quantum perceptron, these proposals rely on the ad hoc introduction of a classical cost function for the optimization procedure. We demonstrate the usage of a quantum probabilistic model by considering a quantum equivalent of the classical log-likelihood, which allows for both a quantum model and training procedure. We show that this allows us to better capture noisiness in data compared to a classical perceptron. By considering entangled qubits we can learn nonlinear separation boundaries, such as xor.

Selected states of the $EF{}^1\mathrm{\Sigma }_{\mathrm{g}}^{+}$ electronic manifold of the hydrogen molecule are computed as resonances of the four-body problem. Systematic improvement of the basis representation for the variational treatment is achieved through an energy-tracking optimization procedure. The resulting nonrelativistic energy is converged within a few nano-Hartree, while the predissociative width is found to be negligible at this level of accuracy. The four-particle nonrelativistic energies are appended with relativistic and quantum electrodynamics corrections which close the gap between the experimental observations and earlier theoretical work.

The interaction between atomic transition dipoles and photons leads to the formation of many-body states with collective dissipation and long-ranged interactions. Here, we put forward and explore a scenario in which a dense atomic gas—where the separation of the atoms is comparable to the transition wavelength—is weakly excited by an off-resonant laser field. We develop the theory for describing such a dressed many-body ensemble and show that collective excitations are responsible for the emergence of many-body interactions, i.e., effective potentials that cannot be represented as a sum of binary terms. We illustrate how collective effects may be probed experimentally through microwave spectroscopy. We analyze time-dependent line shifts, which are sensitive to the phase pattern of the dressing laser, and show that the strong interactions lead to a dramatic slowdown of the relaxation dynamics. Our study provides a so far little explored perspective on dense atomic ensembles interacting with light and promotes this platform as a setting for the exploration of dissipative nonequilibrium many-body physics.

We propose an approach to obtain lasing without inversion, which does not require preparation of the quantum superposition of states in the active medium. We demonstrate that with periodically variable pumping, lasing is achievable even in the case when the population inversion of the active medium is always negative. This is possible due to the fact that laser in strong-coupling regime is a non-Hermitian system with an exceptional point existing at negative value of population inversion. We show that due to nonorthogonality of eigenstates near the exceptional point, the time variation of pump power can result in parametric instability in the laser and excitation of the electromagnetic field self-oscillations. These oscillations take place even when the population inversion of the active medium is always negative. Our results help to pave the way for the creation of a new class of lasers operating at negative value of population inversion.