Rydberg-state excitation of atoms in strong infrared laser fields provides a new complementary aspect of the perspective of atom–strong field interactions. In this article, we perform an experimental and theoretical study on the corresponding process of diatomic molecules, ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$. We show that neutral molecules can also survive strong 800-nm laser fields in high Rydberg states, while their behavior is remarkably different in comparison with their companion atoms, Ar and Xe. The Rydberg excitation of ${\mathrm{N}}_2$ generally behaves similarly to Ar, while that of ${\mathrm{O}}_2$ is more significantly suppressed than the ionization compared to Xe in a high intensity region, which can be understood in the frame of a semiclassical picture, together with their different structures of molecular orbitals. However, distinct quantum features in the Rydberg excitation processes that are apparently beyond the semiclassical picture have been identified, i.e., the less suppressed probability of ${\mathrm{O}}_2$ at low intensity and the oscillation behavior of the ratio between ${\mathrm{N}}_2$ and Ar, indicating that our understanding of the relevant physics is still far from complete.

We report on an implementation of the multiconfigurational time-dependent Hartree method (MCTDH) for spin-polarized fermions (MCTDHF). Our approach is based on a mapping for operators in Fock space that allows a compact and efficient application of the Hamiltonian and solution of the MCTDHF equations of motion. Our implementation extends, builds on, and exploits the recursive implementation of MCTDH for bosons (r-mctdhb) package. Together with r-mctdhb, the present implementation of MCTDHF forms the mctdh-x package. We benchmark the accuracy of the algorithm with the harmonic interaction model and a time-dependent generalization thereof. These models consider parabolically trapped particles that interact through a harmonic interaction potential. We demonstrate that MCTDHF is capable of solving the time-dependent many-fermion Schrödinger equation to an arbitrary degree of precision and can hence yield numerically exact results even in the case of Hamiltonians with time-dependent one-body and two-body potentials. We study the problem of two initially parabolically confined and charged fermions tunneling through a barrier to open space. We demonstrate the validity of a model proposed previously for the many-body tunneling to open space of bosonic particles with contact interactions [Proc. Natl. Acad. Sci. USA 109, 13521 (2012)]. The many-fermion tunneling can be built up from sequentially happening single-fermion tunneling processes. The characteristic momenta of these processes are determined by the chemical potentials of trapped subsystems of smaller particle numbers: The escaped fermions convert the different chemical potentials into kinetic energy. Using the two-body correlation function, we present a detailed picture of the sequentiality of the process and are able to tell tunneling from over-the-barrier escape.

We study one-dimensional strongly interacting quantum gas mixtures, including both the Bose-Fermi and spin-$1/2$ Fermi-Fermi mixtures, with weak $p$-wave interaction between intracomponent fermions, and demonstrate that the weak $p$-wave interaction cannot be omitted in the strong interaction region where the strength of $p$-wave interaction is comparable with the inverse of the strength of strongly repulsive $s$-wave interaction. While the total density distribution is not sensitive to the weak $p$-wave interaction, we find that the $p$-wave interaction plays an important role in determining the species-dependent (or spin-dependent) density distributions and produces significant physical effects on the low-energy spin dynamics. We also derive effective spin-exchange models for strongly interacting quantum gas mixtures with weak $p$-wave interaction, which indicate that a quantum phase transition from an antiferromagnetic state to a ferromagnetic state can be induced by tuning the relative strengths of intracomponent and intercomponent interactions.

Ultracold atoms provide clues to an important many-body problem regarding the dependence of the Bose-Einstein condensation transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and theoretical evaluations of the $T_c$ shift of trapped interacting Bose gases are challenging. While previous predictions of the leading-order shift have been confirmed, more recent experiments exhibit higher-order corrections beyond available mean-field theories. By implementing two large-$\mathcal{N}$-based theories with the local density approximation (LDA), we extract next-order corrections of the $T_c$ shift. The leading-order large-$\mathcal{N}$ theory produces results quantitatively different from the latest experimental data. The leading-order auxiliary-field (LOAF) theory, containing both normal and anomalous density fields, captures the $T_c$ shift accurately in the weak-interaction regime. However, the LOAF theory shows incompatible behavior with the LDA, and forcing the LDA leads to density discontinuities in the trap profiles. We present a phenomenological model based on the LOAF theory, which repairs the incompatibility and provides a prediction of the $T_c$ shift in the stronger-interaction regime.

We study numerically the detailed structure and decay dynamics of isolated monopoles in conditions similar to those of their recent experimental discovery. We find that the core of a monopole in the polar phase of a spin-1 Bose-Einstein condensate contains a small half-quantum vortex ring. Well after the creation of the monopole, we observe a dynamical quantum phase transition that destroys the polar phase. Strikingly, the resulting ferromagnetic order parameter exhibits a Dirac monopole in its synthetic magnetic field. We observe quantitatively matching decay dynamics for both ferromagnetic and antiferromagnetic spin-spin interactions.

We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of $N=4,8,\cdots ,40$ particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower $N$ due to the dominance of the two-body sector. At large momenta $k$, the momentum distribution displays the expected $k^{-4}$ behavior, but its onset shifts from $k\simeq 1.8k_F^{}$ at weak coupling towards higher $k$ at strong coupling.

Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such a scenario is very interesting from a fundamental point of view, because it allows exploration of the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze this problem from two approximate but valuable perspectives: the classical limit and the limit of small quantum fluctuations. We show that, in the presence of optomechanical coupling, the well-known classical phase diagram of the optical problem is modified by the appearance of additional dynamical instabilities. As for the quantum-mechanical description, we prove the ability of the squeezed down-converted field to cool down the mechanical motion not only to thermal but also to squeezed thermal mechanical states, and in a way that can be much less sensitive to the parameters (e.g., detuning of the driving laser) than standard sideband cooling.

We develop a theoretical framework for the analysis of the quantum coherence of light emitted by two independent single-photon sources in an arbitrary environment. The theory provides design rules for the control of the degree of quantum coherence in terms of classical quantities widely used in nanophotonics. As an important example, we derive generalized conditions to generate superradiant and subradiant states of the emitters and demonstrate the ability of a structured environment to induce long-range quantum coherence. These results should have broad applications in quantum nanophotonics and for the sensing of fluorescent sources in complex environments.

It is assumed that in a measurement the system under study interacts with a macroscopic measuring apparatus, in such a way that the density matrix of the measured system evolves according to the Lindblad equation. Under an assumption of nondecreasing von Neumann entropy, conditions on the operators appearing in this equation are given that are necessary and sufficient for the late-time limit of the density matrix to take the form appropriate for a measurement. Where these conditions are satisfied, the Lindblad equation can be solved explicitly. The probabilities appearing in the late-time limit of this general solution are found to agree with the Born rule, and are independent of the details of the operators in the Lindblad equation.

We investigate maximally coherent states to provide a refinement in quantifying coherence and give a measure-independent definition of the coherence-preserving operations. A maximally coherent state can be considered a resource to create arbitrary quantum states of the same dimension by merely incoherent operations. We propose that only maximally coherent states should achieve the maximal value for a coherence measure and use this condition as an additional criterion for coherence measures to obtain a refinement in quantifying coherence that excludes invalid and inefficient coherence measures. Under this criterion, we then give a measure-independent definition of the coherence-preserving operations, which play a role in quantifying coherence similar to that played by the local unitary operations in the scenario of studying entanglement.

We demonstrate how conservation of longitudinal magnetization can have pronounced effects on both stability and structure of vortices in the atomic spin-1 Bose-Einstein condensate by providing a systematic characterization of nonsingular and singular vortex states. Constructing spinor wave functions for vortex states that continuously connect ferromagnetic and polar phases, we systematically derive analytic models for nonrotating cores of different singular vortices and for composite defect states with distinct small- and large-distance topology. We explain how the conservation law provides a stabilizing mechanism when the coreless vortex imprinted on the condensate relaxes in the polar regime of interatomic interactions. The resulting structure forms a composite defect: The inner ferromagnetic coreless vortex deforms toward an outer singly quantized polar vortex. We also numerically show how other even more complex hierarchies of vortex-core topologies may be stabilized. Moreover, we analyze the structure of the coreless vortex also in a ferromagnetic condensate and show how reducing magnetization leads to a displacement of the vortex from the trap center and eventually to the deformation and splitting of its core where a singular vortex becomes a lower-energy state. For the case of singular vortices, we find that the stability and the core structure are notably less influenced by the conservation of magnetization.

We theoretically investigate a weakly interacting degenerate Bose gas coupled to an empty Markovian bath. We show that in the universal phononic limit the system evolves towards an asymptotic state where an emergent temperature is set by the quantum noise of the outcoupling process. For situations typically encountered in experiments, this mechanism leads to significant cooling. Such dissipative cooling supplements conventional evaporative cooling and dominates in settings where thermalization is highly suppressed, such as in a one-dimensional quasicondensate.

In this paper we propose a scheme for the generation of a nonclassical non-Gaussian motional state of a mechanical resonator (MR) in the three-mode optomechanical system in which two linearly coupled single-mode cavities interact dispersively with the mechanical oscillator simultaneously. With one cavity driven by a weak laser field and by properly tuning the driving frequency, a desirable phononic Liouvillian superoperator can be obtained by engineering the selective interaction Hamiltonian confined to Fock subspaces. It is shown that the MR can be driven dissipatively into a steady non-Gaussian nonclassical state, which possesses sub-Poisson statistics, although its Wigner function is positive. The present scheme can be useful for obtaining single phonons.

We discuss the properties of atom-photon bound states in waveguide QED systems consisting of single or multiple atoms coupled strongly to a finite-bandwidth photonic channel. Such bound states are formed by an atom and a localized photonic excitation and represent the continuum analog of the familiar dressed states in single-mode cavity QED. Here we present a detailed analysis of the linear and nonlinear spectral features associated with single- and multiphoton dressed states and show how the formation of bound states affects the waveguide-mediated dipole-dipole interactions between separated atoms. Our results provide both a qualitative and quantitative description of the essential strong-coupling processes in waveguide QED systems, which are currently being developed in the optical and microwave regimes.

We theoretically and experimentally explore the redistribution of polarization states and orbital angular momentum (OAM) in the output plane, induced by the symmetry breaking in the spatial frequency domain. When the vector fields are obstructed by sector-shaped filters in the spatial frequency domain, the local polarization states in the output plane undergo an abrupt transition from linear to circular polarization. The results reveal the polarization-dependent splitting and the appearance of a series of opposite OAMs in the output plane. We also find the self-healing effect of the vector fields broken in the spatial frequency domain and further explore its potential application. If the vector optical fields are used for information transferring or for imaging, even if the optical field carrying the information or image is partially blocked, the complete information or image can still be obtained, implying that which may increase the robustness of the information transferring and the imaging.

In a recent paper [Phys. Rev. A 92, 022309 (2015)], the authors proposed a quantum oblivious set-member decision protocol, which is designed to allow a server to check whether a private secret of a user is a member of his private set in an oblivious manner. Such protocols should protect the privacies of both the server and the user. However, we find that the user in their protocol can steal $l-1$ bits of information about the server's private set by sending the false decoy states.

Measurements of the high-order-harmonic generation yield of the argon (Ar) atom driven by a strong elliptically polarized laser field are shown to completely determine the field-free differential photoionization cross section of Ar, i.e., the energy dependence of both the angle-integrated photoionization cross section and the angular distribution asymmetry parameter.

Sensing in the presence of environmental noise is a problem of increasing practical interest. In a master equation description, where the state of the environment is unobserved, the effect of the signal and noise is described by system operators only. In this context it is well known that noise that is orthogonal in an external signal can be corrected for without perturbing the signal, while similarly efficient strategies for nonorthogonal signal and noise operators are not known. Here we make use of the fact that system-environment interaction typically arises via local two-body interactions describing the exchange of quanta between system and environment, which are observable in principle. That two-body-interactions are usually orthogonal on system operators allows us to develop error-corrected sensing supported by the observation of the quanta that are emitted into the environment. We describe such schemes and outline possible proof-of-principle experiments in an ion trap setup and with color centers in diamond.

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretizes the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution to a boundary value problem and compare the quantum algorithm's theoretical performance with that of a standard classical algorithm—the conjugate gradient method. Prior work claimed that the quantum algorithm could be exponentially faster but did not determine the overall classical and quantum run times required to achieve a predetermined solution accuracy. Taking this into account, we find that the quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation. In addition, we give evidence that no improvement of the quantum algorithm can lead to a superpolynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.