A set of cross sections for the formation of a pair of $2p$ atoms on an absolute scale is determined against the incident photon energy in the double photoexcitation of the isotopomers ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$, incorporating the same cross sections of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ obtained in our recent experiments [K. Hosaka et al., Phys. Rev. A 93, 063423 (2016)], and the oscillator strengths for the formation of a pair of $2p$ atoms from the precursor $Q_2{}^1{\mathrm{\Pi }}_u\left(1\right)$ state, $f_{2p2p}^{{\text{H}}_2/\text{HD}/{\text{D}}_2}(Q_2{}^1{\mathrm{\Pi }}_u\left(1\right))$, are determined from the cross sections. The oscillator strength of HD, $f_{2p2p}^{\text{HD}}(Q_2{}^1{\mathrm{\Pi }}_u\left(1\right))$, is found to be larger than the value expected from $f_{2p2p}^{{\text{H}}_2/{\text{D}}_2}(Q_2{}^1{\mathrm{\Pi }}_u\left(1\right))$, considering the same decay mechanism for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ molecules photoexcited to the $Q_2{}^1{\mathrm{\Pi }}_u\left(1\right)$ state, a mechanism which was revealed in our recent experiments for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ mentioned above. The origin of the enhancement in the oscillator strength for HD is discussed and we show that the enhancement is attributed to nonadiabatic transitions between a gerade electronic state and an ungerade one through a term neglected in the Born-Oppenheimer approximation that vanishes in the homonuclear isotopomers (${\mathrm{H}}_2$ and ${\mathrm{D}}_2$) but does not vanish in the heteronuclear isotopomer (HD). It turns out that approximately 10–20 % of $f_{2p2p}^{\text{HD}}(Q_2{}^1{\mathrm{\Pi }}_u\left(1\right))$ originates from such nonadiabatic transitions due to the breaking of the space-inversion symmetry for electrons.

Single-atomic impurities immersed in a dilute Bose gas in the spherically symmetric harmonic trap potentials are studied at zero temperature. In order to find the ground state of the polarons, we present a conditional variational method with fixed expectation values of the total angular momentum operators ${\widehat{J}}^2$ and ${\widehat{J}}_z$ of the system, using a cranking gauge transformation for bosons to move them in the frame co-rotating with the impurity. In the formulation, the expectation value $\langle {\widehat{J}}^2\rangle$ is shown to be shared in impurity and bosons, but the value $\langle {\widehat{J}}_z\rangle$ is carried by the impurity due to the rotational symmetry. We also analyze the ground-state properties numerically obtained in this variational method for the system of the attractive impurity-boson interaction, and find that excited boson distributions around the impurity overlap largely with impurity's wave function in their quantum-number spaces and also in the real space because of the attractive interaction employed.

We experimentally demonstrate a fundamental relationship between the weak value of an observable and the complex zero of the response function of a system by employing weak measurement on spin Hall shift of a Gaussian light beam. Using this relationship, we show that extremely large weak values far beyond its upper bound in the conventional linear-response regime can be experimentally obtained from the position of the minima of the pointer intensity profile corresponding to the real part of the complex zero of the response function. The imaginary part of the complex zero, on the other hand, is related to the spatial gradient of the geometric phase of light, which in this particular scenario evolves due to the weak interaction and the pre- and postselections of the polarization states. These relationships between the weak value and the complex zeros of the response function may provide new insights on weak measurements in a wide class of physical systems. Extraction of large weak values outside the usual domain of its validity and quantification of small interaction parameters using a physically meaningful and experimentally accessible system property such as the response function may open up a new paradigm of weak measurement.

We present a detailed study of interspecies Feshbach resonances of the bosonic ${}^{23}\mathrm{Na}+{}^{39}\mathrm{K}$ mixture for magnetic fields up to $750\mathrm{G}$ in various collision channels. A total of 14 Feshbach resonances are reported, as well as four zero crossings of the scattering length and three inelastic two-body loss features. We use the observed magnetic-field locations of the resonant features together with the known data on ${}^{23}\mathrm{Na}+{}^{40}\mathrm{K}$ to refine the singlet and triplet ground-state potentials of NaK and achieve a consistent description of Feshbach resonances for both the Bose-Bose mixture of ${}^{23}\mathrm{Na}+{}^{39}\mathrm{K}$ and the Bose-Fermi mixture of ${}^{23}\mathrm{Na}+{}^{40}\mathrm{K}$. We also discuss the influence of the interplay between inelastic two-body and three-body processes on the observation of a Feshbach resonance.

We investigate the orientation dependence of high-order harmonic generation (HHG) in nanowires by solving the time-dependent Schrödinger equation. It is found that the harmonic spectrum exhibits a two-plateau structure and the two plateaus have different orientation dependences. The harmonic yield of the first plateau reaches a maximum when the laser field is parallel to the nanowire and gets a strong suppression when the laser field is perpendicular to the nanowire. The harmonic yield of the second plateau increases first and reduces eventually with the change of the nanowire orientation. These phenomena can be explained by the time-dependent population imaging and the analysis of the transition probability between different energy bands. Our analysis shows a strong band-sensitive orientation dependence in low-dimensional material.

We demonstrate enhanced loading of strontium atoms into a magneto-optical trap using a repumping scheme from the metastable state via the doubly excited state $5s5p{}^3{P}_2\to 5p^2{}^3{P}_2$ at $481\mathrm{nm}$. The number of trapped atoms is increased by an order of magnitude. The frequency and intensity dependence of the atom number enhancement, with respect to the nonrepumping case, is well reproduced by a simple rate equation model, which also describes single-laser repumping schemes reported previously. The repumping scheme is limited by a weak additional loss channel into the long-lived $5s5p{}^3{P}_0$ state. For low repumping intensities, the signature of a halo formed by magnetically trapped atoms in the metastable state is found.

We study the many-body dynamics of stimulated Raman adiabatic passage in the presence of on-site interactions. In the classical mean-field limit, explored in A. Dey et al. [Phys. Rev. Lett. 121, 250405 (2018)], interaction-induced chaos leads to the breakdown of adiabaticity under the quasistatic variation of the parameters, thus producing low-sweep-rate boundaries on efficient population transfer. We show that for the corresponding many-body system, alternative quantum pathways from the initial to the target state open up at even slower sweep rates. These quantum detours avoid the chaotic classical path and hence allow a robust and efficient population transfer.

In the mass-polariton (MP) theory of light formulated by us recently [Phys. Rev. A 95, 063850 (2017)], light in a medium is described as a coupled state of the field and matter. The key result of the MP theory is that the optical force of light propagating in a transparent material drives forward an atomic mass density wave (MDW). In previous theories, it has been well understood that the medium carries part of the momentum of light. The MP theory is fundamentally different since it shows that this momentum is associated with the MDW that carries a substantial atomic mass density and the related rest energy with light. In this work, we prove the Lorentz covariance of the MP theory and show how the stress-energy-momentum (SEM) tensor of the MP transforms between arbitrary inertial frames. We also compare the MP SEM tensor with the conventional Minkowski SEM tensor and show how the well-known fundamental problems of the Minkowski SEM tensor become solved by the SEM tensor based on the MP theory. We have particularly written our work for nonexpert readers by pointing out how the Lorentz transformation and various conservation laws and symmetries of the special theory of relativity are fulfilled in the MP theory.

We compute the spontaneous relaxation rate of a two-level atom in a planar cavity with parity ($\mathcal{P}$) and parity-time ($\mathcal{PT}$) symmetry. We find that at the center of a $\mathcal{PT}$-symmetric cavity the evanescent contribution to the relaxation rate is greatly suppressed. As this is the dominant relaxation pathway for cavities smaller than the transition wavelength, $\mathcal{PT}$-symmetric microcavities are able to suppress the spontaneous relaxation rate dramatically and, in some cases, reduce it to below the free-space level. The ability to reduce the relaxation rate and lengthen the excited-state lifetime has many applications in quantum control and can, for example, be used to increase atomic trapping times, improve photonic storage, and help maintain the coherence of atomic qubits.

We report the results of two-photon quantum holography where spatial information stored in phase holograms is retrieved by measuring quantum spatial correlations between two images formed by spatially entangled twin photons with a Schmidt number of 450 in the two-dimensional transverse space. In our experiments, the entire flux of spontaneous down-converted photons illuminates the phase holograms and the photons of signal-idler pairs transmitted by the holograms are detected separately in the far field on two electron-multiplying charge coupled device cameras.

We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their general linear $\text{GL}(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic evolution of non-Hermitian quantum systems. We find that the adiabatic evolution is possible only when the eigenenergies are real. The accompanying geometric phase is found to be generally complex and associated with not only the phase of a wave function but also its amplitude. The condition for the real geometric phase is laid out. Our results are illustrated with two examples of non-Hermitian $\mathcal{PT}$-symmetric systems, the two-dimensional non-Hermitian Dirac fermion model and bosonic Bogoliubov quasiparticles.

We study the joint estimation of multiple Rabi frequencies in a multilevel system. By analytically identifying the optimal probe state and the optimal measurement, we obtain the highest precision limit for the joint estimation of multiple Rabi frequencies. We show that the joint estimation does not always outperform the separate estimation. In different regimes the joint estimation can either outperform or underperform the separate estimation. We further show that if additional adaptive quantum controls are allowed then the advantage of the joint estimation over the separate estimation can be reestablished.

We present a protocol to store a polynomial number of arbitrary bit strings, encoded as spin configurations, in the approximately degenerate low-energy manifold of an all-to-all connected Ising spin glass. The iterative protocol is inspired by machine learning techniques utilizing $k$-local Hopfield networks trained with $k$-local Hebbian learning and unlearning. The trained Hamiltonian is the basis of a quantum state-preparation scheme to create quantum many-body superpositions with tunable squared amplitudes using resources available in near term experiments. We find that the number of configurations that can be stored in the ground states and thus turned into superposition scales with the $k$-locality of the Ising interaction.

We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\alpha$ and $\beta$ such that for any quantum correlation measure $Q,Q^x$ is monogamous if $x\ge \alpha$ and polygamous if $0\le x\le \beta$ for a given multipartite state $\rho$. For $\beta <x<\alpha$, we show that the monogamy relation can be superactivated by finite $m$ copies ${\rho }^{\otimes m}$ of $\rho$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties. A tighter monogamy relation is presented at last.

We examine the performance of the single-mode Gottesman-Kitaev-Preskill (GKP) code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code. We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential. We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation. In the second part of this paper, we analyze and numerically assess the concatenation of the GKP code with the toric code. When toric code measurements and GKP error correction measurements are perfect, we find that by using GKP error information the toric code threshold improves from $10\%$ to $14\%$. When only the GKP error correction measurements are perfect we observe a threshold at $6\%$. In the more realistic setting when all error information is noisy, we show how to represent the maximum likelihood decoding problem for the toric-GKP code as a 3D compact QED model in the presence of a quenched random gauge field, an extension of the random-plaquette gauge model for the toric code. We present a decoder for this problem which shows the existence of a noise threshold at shift-error standard deviation ${\sigma }_0\approx 0.243$ for toric code measurements, data errors and GKP ancilla errors. If the errors only come from having imperfect GKP states, then this corresponds to states with just four photons or more. Our last result is a no-go result for linear oscillator codes, encoding oscillators into oscillators. For the Gaussian displacement error model, we prove that encoding corresponds to squeezing the shift errors. This shows that linear oscillator codes are useless for quantum information protection against Gaussian shift errors.

Recent experiments with ultracold lanthanide atoms which are characterized by a large magnetic moment have revealed the crucial importance of beyond-mean-field corrections in understanding the dynamics of the gas. We study how the presence of an external optical lattice modifies the structure of the corrections. We find that deep in the superfluid regime the equation of state is well described by introducing an anisotropic effective mass. However, for a deep lattice we find terms with anomalous density dependence which do not arise in free space. For a one-dimensional lattice, the relative orientation of the dipole axis with respect to the lattice plays a crucial role and the beyond-mean-field corrections can be either enhanced or suppressed.

One of the most effective methods for cooling micro and nanodevices to ultralow temperatures is the sideband method. Currently, this approach is being studied experimentally and theoretically. Theoretical results that relate to this method correspond to the case of the interaction of an electromagnetic field with a micro or nanoresonator through radiation pressure. Obviously, if you choose a charged micro or nanoresonator, the interaction will be different. In this paper, this case is considered and it is shown that cooling will be as effective as in the sideband method. The resulting final equation in the work, for the average value of the quantum number of the cooled resonator, has a surprisingly simple analytical form, which allows for the most complete analysis of the system under study.

We trace the $Q$ factor of the resonant modes which are limited to bound states in the continuum (BICs) for $N=\infty$ in the finite array of $N$ dielectric spheres and disks. For the symmetry-protected BICs we observe the quadratic dependence of the $Q$ factor on $N$ for high-refractive-index particles, while for low-refractive-index particles there is an interplay between the quadratic and cubic dependencies. The $Q$ factor of accidental BICs grows cubically with $N$. We show that a plane wave can excite these quasi-BICs for tuning of the angle of incidence.

Weak-value amplification has been used to enhance the sensitivity of a linear detector response to small interaction parameters. However, the generation of a large weak value gives rise to reduction in postselection probability, which restricts the feasibility of the weak-value amplification technique. Recently, theoretical works have shown that the use of entanglement can increase the efficiency of the weak-value amplification method. Specifically, it is proven that by entangling $n$ particles of a system, the maximum postselection probability scales quadratically with $n$ [Pang, Dressel, and Brun, Phys. Rev. Lett. 113, 030401 (2014)]. In this work, we demonstrate an experimental realization of entanglement-assisted weak-value amplification in a photonic system, which shows that importing quantum entanglement can indeed improve the efficiency of weak-value amplification.