We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry. In particular, we use this result to completely characterize the dynamics of the two oscillators interacting in the ultrastrong-coupling regime with additional single-mode squeezing on both oscillators, as well as higher-order terms. Furthermore, we compute quantities of interest, such as the average number of excitations and the correlations that are established between the two subsystems due to the evolution. We find that this model predicts a second-order phase transition and we compute the critical exponents and the critical value. We also provide an exact decoupling of the time evolution in terms of simple quantum optical operations, which can be used for practical implementations and studies. Finally, we show how our techniques can be extended to include more oscillators and higher-order interactions.

In the recent years important experimental advances in resonant electro-optic modulators as high-efficiency sources for coherent frequency combs and as devices for quantum information transfer have been realized, where strong optical and microwave mode coupling were achieved. These features suggest electro-optic-based devices as candidates for entangled optical frequency comb sources. In the present work, I study the generation of entangled optical frequency combs in millimeter-sized resonant electro-optic modulators. These devices profit from the experimentally proven advantages such as nearly constant optical free spectral ranges over several gigahertz, and high optical and microwave quality factors. The generation of frequency multiplexed quantum channels with spectral bandwidth in the MHz range for conservative parameter values paves the way towards novel uses in long-distance hybrid quantum networks, quantum key distribution, enhanced optical metrology, and quantum computing.

The ability that one system immediately affects another one by using local measurements is regarded as quantum steering, which can be detected by various steering criteria. Recently, Mondal et al. [Phys. Rev. A 98, 052330 (2018)] derived the complementarity relations of coherence steering criteria, and revealed that the quantum steering of a system can be observed through the average coherence of a subsystem. Here, we experimentally verify the complementarity relations between quantum steering criteria by employing two-photon Bell-like states and three Pauli operators. The results demonstrate that if prepared quantum states can violate two setting coherence steering criteria and turn out to be steerable states, then they cannot violate the complementary settings criteria. Three measurement settings inequalities, which establish a set of complementarity relations between these two coherence steering criteria, are always obeyed by all prepared quantum states in experiment. In addition, we experimentally certify that the strengths of coherence steering criteria depend on the choice of coherence measure. In comparison with two setting coherence steering criteria based on $l_1$ norm of coherence and relative entropy of coherence, our experimental results show that the steering criterion based on skew information of coherence is the strongest in detecting the steerability of two-photon Bell-like states. Thus, our experimental demonstration can deepen the understanding of the relation between the quantum steering and quantum coherence.

We propose an all-optical setup to produce a wide class of $X$ states with an intense laser beam using spin-orbit modes. In order to characterize such simulated states, we reconstructed the density matrix by simulating spin-orbit tomography and studied the discord and concurrence for different states. The results show very good agreement with theoretical predictions. We also propose two different optical circuits to prepare the single-photon spin-orbit $X$ state.

In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces of local observables. The open system dynamics is described by a general Markovian master equation based on which the Hamiltonian identification problem can be formulated as minimizing the distance between the real time traces of the observables and those predicted by the master equation. The unknown parameters can then be learned with a gradient descent algorithm from the measurement data. We verify the effectiveness of our algorithm in a circuit QED system described by a Jaynes-Cummings model whose Hamiltonian identification has been rarely considered. We also show that our gradient algorithm can learn the spectrum of a non-Markovian environment based on an augmented system model.

We analyze the convex combinations of noninvertible generalized Pauli dynamical maps. By manipulating the mixing parameters, one can produce a channel with shifted singularities, additional singularities, or even no singularities whatsoever. In particular, we show how to use noninvertible dynamical maps to produce the Markovian semigroup. Interestingly, the maps whose mixing results in a semigroup are generated by the time-local generators and time-homogeneous memory kernels that are not regular; that is, their formulas contain infinities. Finally, we show how the generators and memory kernels change after mixing the corresponding dynamical maps.

We carry out infrared-infrared double-resonance spectroscopy of the $2{\nu }_3{A}_1\text{−}{\nu }_3$ band of methane. Ten transitions of Q(1) to Q(4) are observed with an 88.5-THz difference-frequency-generation (DFG) source, while the lower levels are pumped through the ${\nu }_3$ band transition by another 90.5-THz DFG source phase-locked to an optical frequency comb (OFC). The transition frequencies are determined using the OFC with an uncertainty of 10 kHz, which is an improvement of 4 orders of magnitude compared with the previous studies.

We investigate theoretically and experimentally fluctuations of high spin ($F>\frac{1}{2}$) beyond the linear response regime and demonstrate dramatic modifications of the spin noise spectra in the high power density probe field. Several effects related to an interplay of high spin and perturbation are predicted theoretically and revealed experimentally, including strong sensitivity of the spin noise spectra to the mutual orientation of the probe polarization plane and magnetic field direction, appearance of high harmonics of the Larmor frequency in the spin noise, and the fine structure of the Larmor peaks. We demonstrate the ability of spin noise spectroscopy to access the nonlinear effects related to the renormalization of the spin states by strong electromagnetic fields.

We investigate the transverse mode effects on the frequency combs generated by a type-I optical parametric oscillator (OPO) below threshold. We take the diffraction effects fully into account, considering usual OPO architectures instead of the self-imaging design. Further, we show that an OPO pumped with structured light produces multiple frequency combs simultaneously, corresponding to different combinations of spatial modes in the downconverted fields. This result may apply to the production of hybrid multipartite entanglement in the spatiotemporal modes of a single OPO.

We study the nonequilibrium dynamics of a quantum system under the influence of two noncommuting fluctuation sources, i.e., purely dephasing fluctuations and relaxational fluctuations. We find that increasing purely dephasing fluctuations suppress increasing relaxation in the quantum system. This effect is further enhanced when both fluctuation sources are fully correlated. These effects arise for medium to strong primary fluctuations already when the secondary fluctuations are weak due to their noncommuting coupling to the quantum system. Dephasing, in contrast, is increased by increasing any of the two fluctuations. Fully correlated fluctuations result in overdamping at much lower system-bath coupling than uncorrelated noncommuting fluctuations. In total, we observe that treating subdominant secondary environmental fluctuations perturbatively leads, as neglecting them, to erroneous conclusions.

We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity triality relation of Jakob and Bergou [arXiv:quant-ph/0302075; Opt. Commun. 283, 827 (2010)]. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.

While the Rydberg-blockade regime provides the natural setting for creating $W$-type entanglement with cold neutral atoms, it is demonstrated here that a scalable entanglement resource of this type can even be obtained under completely different physical circumstances. To be more precise, a special instance of twisted $W$ states—namely, $\pi$-twisted ones—can be engineered in one-dimensional arrays of cold neutral atoms with Rydberg-dressed resonant dipole-dipole interaction. In particular, it is shown here that this is possible even when a (dressed) Rydberg excitation is coupled to the motional degrees of freedom of atoms in their respective, nearly harmonic optical-dipole microtraps, which are quantized into dispersionless (zero-dimensional) bosons. For a specially chosen (“sweet-spot”) detuning of the off-resonant dressing lasers from the relevant internal atomic transitions, the desired $\pi$-twisted $W$ state of Rydberg-dressed qubits is the ground state of the effective excitation—boson Hamiltonian of the system in a broad window of the relevant parameters. Being at the same time separated from the other eigenstates by a gap equal to the single-boson energy, this $W$ state can be prepared using a Rabi-type driving protocol. The corresponding preparation times are independent of the system size and several orders of magnitude shorter than the effective lifetimes of the relevant atomic states.

We study isolated core excitation of ultracold ytterbium Rydberg atoms of high orbital angular momentum quantum number $\ell$. Measurements were performed on the $6s_{1/2}40\ell \to 6p_{1/2}40\ell$ transition with $\ell =5–9$. The extracted energy shifts and autoionization rates are in good agreement with a model based on independent electrons, taking interactions into account in a perturbative approach. We reveal a slow decrease in the autoionization rates with $\ell$, explained by the strong coupling of the $6p_{1/2}n\ell$ autoionizing state with the $5d_{3/2}\epsilon {\ell }^{\prime }$ continua compared to previously studied divalent atoms.

The problem of photoionization of atomic hydrogen in a white-dwarf-strength magnetic field is revisited to understand the existing discrepancies in the positive-energy spectra obtained by a variety of theoretical approaches reported in the literature. Oscillator strengths for photoionization are calculated with the adiabatic-basis-expansion method developed by Mota-Furtado and O'Mahony [Phys. Rev. A 76, 053405 (2007)]. A comparative study is performed between the adiabatic-basis-expansion method and our previously developed coupled-channel theory [L. B. Zhao, O. Zatsarinny, and K. Bartschat, Phys. Rev. A 94, 033422 (2016)]. A detailed analysis of the positive-energy spectra obtained here and those from other theoretical approaches shows that the adiabatic-basis-expansion method can produce more accurate positive-energy spectra than other reported approaches for low field strengths.

To provide spectroscopic data for lowly charged tungsten ions relevant to fusion research, this work focuses on the ${\mathrm{W}}^{8+}$ ion. Six visible spectra lines from ${\mathrm{W}}^{8+}$ in the range of 420–660 nm are observed with a compact electron-beam ion trap in Shanghai. Furthermore, transition energies are calculated for the 30 lowest levels of the $4f^{14}5s^{2}5p^4, 4f^{13}5s^{2}5p^5$, and $4f^{12}5s^{2}5p^6$ configurations of ${\mathrm{W}}^{8+}$ by using the flexible atomic code (fac) and grasp package. Reasonably good agreement is found between our two independent atomic-structure calculations. The resulting atomic parameters are adopted to simulate the spectra based on the collisional-radiative model implemented in the fac code. This assists us with identification of six strong magnetic-dipole transitions in the $4f^{13}5s^{2}5p^5$ and $4f^{12}5s^{2}5p^6$ configurations from our experiments.

We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\downarrow$ impurities attractively interacting with a sea of $\uparrow$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\uparrow$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperature due to the thermal occupation of excited states in the impurity spectral function. However, remnants of the single-impurity transition are apparent in the momentum-resolved spectral function, which can in principle be probed with Raman spectroscopy. We furthermore show that the Tan contact exhibits a characteristic nonmonotonic dependence on temperature that provides a signature of the zero-temperature polaron-molecule transition. For a finite impurity density, we argue that descriptions purely based on the behavior of the Fermi polaron are invalid near the polaron-molecule transition, since correlations between impurities cannot be ignored. In particular, we show that the spin-imbalanced system undergoes phase separation at low temperatures due to the strong attraction between $\uparrow \downarrow$ molecules induced by the Fermi sea. Thus, we find that the impurity spectrum and the induced impurity-impurity interactions are key to understanding the phase diagram of the spin-imbalanced Fermi gas.

We study the correlated dynamics of few interacting bosonic impurities immersed in a one-dimensional harmonically trapped bosonic environment. The mixture is exposed to a time-dependent impurity-medium interaction pulse moving it across the relevant phase-separation boundary. For modulation frequencies smaller than the trapping one, the system successively transits through the miscible and immiscible phases according to the driving of the impurity-medium interactions. For strong modulations, and driving from the miscible to the immiscible regime, a significant fraction of the impurities is expelled to the edges of the bath. They exhibit a strong localization behavior and tend to equilibrate. Following the reverse driving protocol, the impurities perform a breathing motion while featuring a two-body clustering and the bath is split into two incoherent parts. Interestingly, in both driving scenarios, dark-bright solitons are nucleated in the absence of correlations. A localization of the impurities around the trap center for weak impurity-impurity repulsions is revealed, which subsequently disperse into the bath for increasing interactions.

We consider a wide family of optical coherent feedback loops acting on an optomechanical system operating in the linearized regime. We assess the efficacy of such loops in improving key operations, such as cooling, steady-state squeezing and entanglement, as well as optical-to-mechanical state transfer. We find that mechanical sideband cooling can be enhanced through passive, interferometric coherent feedback, achieving lower steady-state occupancies and considerably speeding up the cooling process; we also quantify the detrimental effect of nonzero delay times on the cooling performance. Steady-state entanglement generation in the blue sideband can also be assisted by passive interferometric feedback, which allows one to stabilize otherwise unstable systems, though active feedback (including squeezing elements) does not help to this aim. We show that active feedback loops only allow for the generation of optical, but not mechanical, squeezing. Finally, we prove that passive feedback can assist state transfer at transient times for red-sideband-driven systems in the strong-coupling regime.

We present analytic threshold formulas applicable to both dispersive (time-domain) and diffractive (pattern-forming) instabilities in Fabry-Perot Kerr cavities of arbitrary finesse. We do so by extending the gain-circle technique, recently developed for counterpropagating fields in single-mirror-feedback systems, to allow for an input mirror. In time-domain counterpropagating systems, walk-off effects are known to suppress cross-phase modulation contributions to dispersive instabilities. Applying the gain-circle approach with appropriately adjusted cross-phase couplings extends previous results to arbitrary finesse, beyond mean-field approximations, and describes Ikeda instabilities.