The evolution of high-dimensional entanglement in atmospheric turbulence is investigated. We study the effects of turbulence on photonic states generated by spontaneous parametric down-conversion, both theoretically and experimentally. One of the photons propagates through turbulence, while the other is left undisturbed. The atmospheric turbulence is simulated by a single phase screen based on the Kolmogorov theory of turbulence. The output after turbulence is projected into a three-dimensional (qutrit) basis composed of specific Laguerre-Gaussian modes. Full state tomography is performed to determine the density matrix for each output quantum state. These density matrices are used to determine the amount of entanglement, quantified in terms of the negativity, as a function of the scintillation strength. Theoretically, the entanglement is calculated using a single phase screen approximation. We obtain good agreement between theory and experiment.

We propose to realize a strongly interacting Fermi superfluid near a narrow Feshbach resonance using the recently discovered “orbital Feshbach resonance.” The orbital Feshbach resonance is a type of magnetic field tunable scattering resonance theoretically predicted and experimentally observed recently in the alkaline-earth-metal-like ${}^{173}\mathrm{Yb}$ atom. We first show that the orbital Feshbach resonance is a narrow resonance in energy, while it is hundreds Gauss wide in terms of magnetic field strength, taking the advantage that the magnetic moment difference between the open and closed channels is quite small. Therefore, this is an ideal platform for the experimental realization of a strongly interacting Fermi superfluid with narrow resonance. We further show that the transition temperature for the Fermi superfluid in this system, especially at the BCS side of the resonance, is even higher than that in a wide resonance, which is also due to the narrow character of this resonance. Our results will encourage experimental efforts to realize Fermi superfluid in the alikaline-earth-metal-like ${}^{173}\mathrm{Yb}$ system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali-metal ${}^{40}\mathrm{K}$ and ${}^6\mathrm{Li}$ systems.

Quantum systems in contact with an environment display a rich physics emerging from the interplay between dissipative and Hamiltonian terms. Here we focus on the role of the geometry of the coupling between the system and the baths. Specifically we consider a dissipative boundary driven ladder in the presence of a gauge field that can be implemented with ion microtrap arrays. We show that, depending on the geometry, the currents imposed by the baths can be strongly affected by the gauge field, resulting in nonequilibrium phase transitions. In different phases both the magnitude of the current and its spatial distribution are significantly different. These findings allow for strategies to manipulate and control transport properties in quantum systems.

We investigate universal properties of a $p$-wave Fermi gas with a resonant interaction in which the axisymmetry is broken spontaneously or externally. Here, we show that the short-range correlations can be completely characterized by the nine-component $p$-wave contact tensor, which can be measured through a generalized adiabatic sweep theorem. The distinctive features of the $p$-wave contact tensor emerge in a normal $p$-wave Fermi gas in an anisotropic trap and in a superfluid phase. An experimental scheme to measure the $p$-wave contact tensor and test the adiabatic sweep theorem is also discussed.

When spatially coherent radiation is diffracted by a crystalline object, the field is scattered in specific directions, giving rise to so-called von Laue patterns. We examine the role of spatial coherence in this process. Using the first-order Born approximation, a general analytic expression for the far-zone spectral density of the scattered field is obtained. This equation relates the coherence properties of the source to the angular distribution of the scattered intensity. We apply this result to two types of sources. Quasihomogeneous Gaussian Schell-model sources are found to produce von Laue spots whose size is governed by the effective source width. Delta-correlated ring sources produce von Laue rings and ellipses instead of point-like spots. In forward scattering, polychromatic ellipses are created, whereas in backscattering striking, overlapping ring patterns are formed. We show that both the directionality and the wavelength-selectivity of the scattering process can be controlled by the state of coherence of the illuminating source.

The large coupling rate between the acoustic and optical fields confined in GaAs/AlAs superlattice cavities makes them appealing systems for cavity optomechanics. We have developed a mathematical model based on the scattering matrix that allows the acoustic guided modes to be predicted in nano and micropillar superlattice cavities. We demonstrate here that the reflection at the surface boundary considerably modifies the acoustic quality factor and leads to significant confinement at the micropillar center. Our mathematical model also predicts unprecedented acoustic Fano resonances on nanopillars featuring small mode volumes and very high mechanical quality factors, making them attractive systems for optomechanical applications.

We consider the Wigner quasiprobability distribution function of a single mode of an electromagnetic or matter-wave field to address the question of whether a direct stochastic sampling and binning of the absolute square of the complex field amplitude can yield a distribution function ${\tilde{P}}_n$ that closely approximates the true particle number probability distribution $P_n$ of the underlying quantum state. By providing an operational definition of the binned distribution ${\tilde{P}}_n$ in terms of the Wigner function, we explicitly calculate the overlap between ${\tilde{P}}_n$ and $P_n$ and hence quantify the statistical distance between the two distributions. We find that there is indeed a close quantitative correspondence between ${\tilde{P}}_n$ and $P_n$ for a wide range of quantum states that have a smooth and broad Wigner function relative to the scale of oscillations of the Wigner function for the relevant Fock state. However, we also find counterexamples, including states with high mode occupation, for which ${\tilde{P}}_n$ does not closely approximate $P_n$.

We investigate the possibility of a Dicke-type superradiant phase transition of an atomic gas with an extended model which takes into account the short-range depolarizing interaction between atoms that approach each other as close as the atomic size scale, which interaction appears in a regularized electric-dipole picture of the QED of atoms. By using a mean-field model, we find that a critical density does indeed exist, though the atom-atom contact interaction shifts it to a higher value than that from the bare Dicke model.

Using the transfer matrix formalism, we study the transmission properties of a Bragg grating constructed from a layered axionic material. Such a material can be realized by a topological insulator subject to a time-symmetry-breaking perturbation, such as an external magnetic field or surface magnetic impurities. While the reflective properties of the structure are only negligibly changed by the presence of the axionic material, the grating induces a Faraday rotation and ellipticity in the transmitted light. We find that for transverse magnetic (TM)-polarized light incident on a 16-layer structure at ${76}^{\mathrm{o}}$ to the normal the Faraday rotation can approach $\sim 232\mathrm{mrad}(\sim {13}^{\mathrm{o}})$, while interference from the multilayered structure ensures high transmission. This is significantly higher than Faraday rotations for the TM polarization at normal incidences or the transverse electric (TE) polarization at any incident angle. Thus, Bragg gratings in this geometry show a strong optical signal of the magnetoelectric effect and, hence, provide an ideal system in which to observe this effect by optical means.

We study the role of quantum entanglement (particle entanglement and mode entanglement) in optical phase estimation by employing the mode description and the particle description of bosonic probe states. To determine the physical resources responsible for Heisenberg scaling (attainable only in the noiseless case), we restrict our analysis to noiseless quantum-limited optical phase estimation. The quantum Fisher information (QFI) is expressed as a function of the first- and second-order optical coherence functions. The resulting form of the QFI elucidates the deriving metrological resources for quantum phase estimation: field intensity and photon detection correlations. Our analysis confirms that mode entanglement is not required for quantum-enhanced interferometry, whereas particle entanglement is a necessary requirement. Furthermore, the derived forms of the QFI equations are summations of two terms: the classical (shot-noise-limit scaling) term and the quantum (Heisenberg scaling) term. This allows us to clearly identify the physical resources responsible for quantum enhancement in optical phase estimation.

We propose a nonperturbative approach to calculate bound-state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening.

Any tripartite state which saturates the strong subadditivity relation for the quantum entropy is defined as the Markov state. A tripartite pure state describing an open system, its environment, and their purifying system is a pure Markov state if and only if the bipartite marginal state of the purifying system and environment is a product state. It has been shown that as long as the purification of the input system-environment state is a pure Markov state, the reduced dynamics of the open system can be described, on the support of the initial system state, by a quantum channel for every joint unitary evolution of the system-environment composite even in the presence of initial correlations. Entanglement, discord, and classical correlations of the initial system-environment states implied by the pure Markov states are analyzed and it has been shown that all these correlations are entirely specified by the entropy of environment. Some implications concerning perfect quantum error correction procedure and quantum Markovian dynamics are presented.

We introduce chiral rotational spectroscopy, a technique that enables the determination of the orientated optical activity pseudotensor components $B_{XX}, B_{YY}$, and $B_{ZZ}$ of chiral molecules, in a manner that reveals the enantiomeric constitution of a sample and provides an incisive signal even for a racemate. Chiral rotational spectroscopy could find particular use in the analysis of molecules that are chiral solely by virtue of their isotopic constitution and molecules with multiple chiral centers. A basic design for a chiral rotational spectrometer together with a model of its functionality is given. Our proposed technique offers the more familiar polarizability components ${\alpha }_{XX}, {\alpha }_{YY}$, and ${\alpha }_{ZZ}$ as by-products, which could see it find use even for achiral molecules.

Energy levels of 30 low-lying states of ${\mathrm{Lu}}^{2+}$ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double, and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates, and lifetimes of the metastable $5d_{3/2}$ and $5d_{5/2}$ states are calculated. Recommended values are given for static polarizabilities of the $6s$, $5d$, and $6p$ states and tensor polarizabilities of the $5d$ and $6p_{3/2}$ states. Uncertainties of the polarizability values are estimated in all cases. The blackbody radiation shift of the $6s_{1/2}–5d_{5/2}$ transition frequency of the ${\mathrm{Lu}}^{2+}$ ion is calculated with the aid of the recommended scalar polarizabilities of the $6s_{1/2}$ and $5d_{5/2}$ states. Finally, $A$ and $B$ hyperfine constants are determined for states of ${}^{175}\mathrm{Lu}^{2+}$ with $n\le 9$. This work provides recommended values of transition matrix elements, polarizabilities, and hyperfine constants of ${\mathrm{Lu}}^{2+}$, critically evaluated for accuracy, for benchmark tests of high-precision theoretical methodology and planning of future experiments.

The two-photon-annihilation contribution to the true muonium hyperfine splitting arising from $e$ and $\tau$ loops is obtained analytically at order $m_{\mu }{\alpha }^6$. The contribution to the hyperfine splitting is $-2.031092873m_{\mu }{\alpha }^6/n^3{\pi }^2=-793.926988/n^3$ MHz. The contribution to the triplet true muonium decay rate has also been obtained and was found to be $9.825708266m_{\mu }{\alpha }^6/n^3{\pi }^2=3840.737698/n^3$ MHz. Additional results have been computed for other purely leptonic bound states.

We construct a simple model to calculate the trimer bound state energy $E_T^{\left(n\right)}$ and three-body recombination rate $K_3^0$ of three identical bosons with van der Waals interaction without using any two- or three-body fitting parameter. Using this simple model, we investigate the influence of the van der Waals finite-range effect on $E_T^{\left(n\right)}$ and $K_3^0$. Our calculation shows that the finite-range effect leads to the ground trimer state energy $E_T^{\left(0\right)}$ not crossing the atom-dimer threshold, and the scaled three-body recombination rate $K_3^0/a^4$ deviating from the universal three-body theory. The results of our simple model agree within a few percent with other theoretical works with van der Waals interaction and also the experimental data.

We use $D_1$ gray molasses to achieve Bose-Einstein condensation of a large number of ${}^{41}\mathrm{K}$ atoms in an optical dipole trap. By combining a specific configuration of a compressed magneto-optical trap with $D_1$ gray molasses, we obtain a cold sample of $2.4\times {10}^9$ atoms with a temperature as low as 42 $\mu \mathrm{K}$. After magnetically transferring the atoms into the final glass cell, we perform a two-stage evaporative cooling. A condensate with up to $1.2\times {10}^6$ atoms in the lowest Zeeman state $|F=1,m_F=1\rangle$ is achieved in the optical dipole trap. Furthermore, we observe two narrow Feshbach resonances in the lowest hyperfine channel, which are in good agreement with theoretical predictions.

We study the observability of the Higgs mode in BEC-BCS crossover. The observability of the Higgs mode is investigated by calculating the spectral weight functions of the amplitude fluctuation below the critical transition temperature. At zero temperature, we find that there are two sharp peaks on the spectral function of the amplitude fluctuation attributed to Goldstone and Higgs modes, respectively. As the system goes from the BCS to Bose-Einstein condensate (BEC) side, there is strong enhancement of spectral weight transfer from the Higgs to Goldstone mode. However, even at the unitary regime where the Lorentz invariance is lost, the sharp feature of the Higgs mode still exists. We specifically calculate the finite-temperature spectral function of the amplitude fluctuation at the unitary regime and show that the Higgs mode is observable at the temperature that present experiments can reach.

We study a system consisting of a superconducting flux qubit strongly coupled to a microwave cavity. The fundamental cavity mode is externally driven and the response is investigated in the weak nonlinear regime. We find that near the crossing point, at which the resonance frequencies of the cavity mode and qubit coincide, the sign of the Kerr coefficient changes, and consequently the type of nonlinear response changes from softening to hardening. Furthermore, the cavity response exhibits superharmonic resonances (SHR) when the ratio between the qubit frequency and the cavity fundamental mode frequency is tuned close to an integer value. The nonlinear response is characterized by the method of intermodulation and both signal and idler gains are measured. The experimental results are compared with theoretical predictions and good qualitative agreement is obtained. The SHRs have potential for applications in quantum amplification and generation of entangled states of light.