We present measurements of the hyperfine structure splittings of $n{S}_{1/2}$ Rydberg states of ${}^{85}\mathrm{Rb}$ for $n=43$, 44, 45, and 46. From the splittings, the hyperfine coupling constant, $A_{\mathrm{HFS}}$, is determined to be 15.372(80) GHz. This result is an order-of-magnitude improvement from previous measurements. We study and account for systematic uncertainty sources, such as unwanted electric and magnetic fields, dipolar Rydberg-Rydberg interactions, and ac shifts. Initial evidence for hyperfine-mixed Rydberg pair states is found.

We present an analytical and numerical analysis of the particle creation in an optomechanical cavity in parametric resonance. We treat both the electromagnetic field and the mirror as quantum degrees of freedom and study the dynamical evolution as a closed quantum system. We consider different initial states and investigate the spontaneous emission of photons from phonons in the mirror. We find that, for initial phononic number states, the evolution of the photon number can be described as a nonharmonic quantum oscillator, providing a useful tool so as to estimate the maximum and mean number of photons produced for arbitrary high energies. The efficiency of this mechanism is further analyzed for a detuned cavity as well as the possibility of stimulating the photon production by adding some initial ones to the cavity. We also find relationships for the maximum and mean entanglement between the mirror and the wall in these states. Additionally, we study coherent states for the motion of the mirror to connect this model with previous results from quantum field theory with a classical mirror. Finally, we study thermal states of phonons in the wall and the equilibration process that leads to a stationary distribution.

The high-order harmonic generation process of ${\mathrm{H}}_2{}^{+}$ in a co-rotating two-color circularly polarized laser pulse was investigated by numerically solving the time-dependent Schrödinger equation. Compared with the target of the atom, the harmonic intensity of ${\mathrm{H}}_2{}^{+}$ is remarkably enhanced. Moreover, the harmonic intensity of ${\mathrm{H}}_2{}^{+}$ approaches its maximum when the electric field amplitude ratio of the fundamental frequency and the second one is approximately 1:2.3. By analyzing the evolution of the time-dependent wave packets, the enhancement of harmonic intensity may be attributed to an increase in the probability of the ionized electron recolliding with the parent ion. In addition, the dependence of harmonic intensity on the internuclear distance and the alignment angle of ${\mathrm{H}}_2{}^{+}$ is explored. We found that the ellipticity of the particular harmonic order changes with the molecular alignment angle, which provides a chance to generate an extreme ultraviolet coherent light pulse with controllable polarization.

We report the preparation of a heteronuclear two-atom system of ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ in the ground state in an optical tweezer. Dual-species Raman sideband cooling is applied to the two initially separated atoms to eliminate the crosstalk and three-dimensional ground-state probabilities of 0.91(5) for ${}^{87}\mathrm{Rb}$ and 0.91(10) for ${}^{85}\mathrm{Rb}$ are obtained. We then merge the two atoms into one trap with a species-dependent transport which is achieved by utilizing vector light shifts depending on the magnetic moments of specific atomic states and the trap polarizations. The measurable motional excitations due to merging are 0.013(1) and 0.006(3) axial vibrational quanta for the ${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$ atoms, respectively, while no obvious excitation is observed in the radial directions. This two-atom system offers a good starting point for building a single heteronuclear molecule and for investigating few-body physics. It can also be extended to other atomic species and molecules and thus can find application in ultracold chemistry.

We propose a model to study quantum population transfer via a structural continuum. The model is composed of two spins which are coupled to two bosonic modes separately by two control pulses, and the two bosonic modes are coupled to a common structural continuum. We show that efficient population transfer can be achieved between the two spins by using a multilevel stimulated Raman adiabatic passage (STIRAP) across the continuum, which we refer to as straddle STIRAP via continuum. We also consider the stability of this model against different control parameters and show that efficient population transfer can be achieved even in the presence of a moderate dissipation.

It is well known that a rotating Bose-Einstein condensate forms vortices to carry the angular momentum. For a first vortex to nucleate at the trap center, the rotational frequency must become larger than a certain critical value. The vortex nucleation process, however, is sensitive to the trap shape. It was shown earlier [Dagnino et al., Nat. Phys. 5, 431 (2009)] that, for a symmetry-breaking potential that preserves parity, at criticality the leading natural orbitals may become degenerate, giving rise to a “maximally entangled” quantum state, found from exact solutions for just a few bosons. Developing an effective two-state model, we show here that, in the limit of large particle numbers, the many-body ground state becomes either a so-called “twin”-like or a “Schrödinger cat”-like state. We corroborate this finding by a direct comparison to the exact numerical solution of the problem, feasible for moderate particle numbers $N\lesssim 50$ within the lowest Landau level approximation. We show that the nature of the quantum state at criticality can be controlled by both the quadrupolar deformation and the flatness of the confining potential.

For a practical quantum key distribution (QKD) system, parameter optimization, the choice of intensities and the probabilities of sending them, is a crucial step in gaining optimal performance, especially when one realistically considers a finite communication time. With the increasing interest in the field to implement QKD over free space on moving platforms, such as drones, handheld systems, and even satellites, one needs to perform parameter optimization with low latency and with very limited computing power. Moreover, with the advent of the internet of things, a highly attractive direction of QKD could be a quantum network with multiple devices and numerous connections, which provides a huge computational challenge for the controller that optimizes parameters for a large-scale network. Traditionally, such an optimization relies on brute-force search or local search algorithms, which are computationally intensive, and will be slow on low-power platforms (which increases latency in the system) or infeasible for even moderately large networks. In this work we present a method that uses a neural network to directly predict the optimal parameters for QKD systems. We test our machine learning algorithm on hardware devices including a Raspberry Pi 3 single-board computer (similar devices are commonly used on drones) and a mobile phone, both of which have a power consumption of less than 5 W, and we find a speedup of up to two to four orders of magnitude when compared to standard local search algorithms. The predicted parameters are highly accurate and can preserve, e.g., over 95%–99% of the optimal secure key rate for a given protocol. Moreover, our approach is highly general and can be applied effectively to various kinds of common QKD protocols.

Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is known about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario, even if only local projective measurements are accessible. This paper is an extended version of the companion paper Zhu and Hayashi, Phys. Rev. Lett. 123, 260504 (2019).

The sending-or-not-sending (SNS) protocol of the twin-field quantum key distribution can tolerate large misalignment error and its key rate can exceed the linear bound of repeaterless quantum key distribution. But the original SNS protocol requires the two users to use the same source parameters. Here we propose an SNS protocol with asymmetric source parameters and give the security proof of this protocol. Our asymmetric protocol has a much better performance than that of the original SNS protocol when the channel is asymmetric.

We derive a pseudopotential in two dimensions (2D) with a 2D Rashba spin-orbit coupling (SOC), following in the same spirit of the frame transformation by Guan and Blume [Q. Guan and D. Blume, Phys. Rev. A 95, 020702(R) (2017)]. The frame transformation correctly describes the nontrivial phase accumulation and partial-wave couplings due to the presence of SOC, which modifies the original Fermi pseudopotential in free space, even when the length scale of the SOC is significantly larger than the two-body potential range. As an application, we apply our pseudopotential within the Lippmann-Schwinger equation to obtain an analytical scattering matrix. To demonstrate the validity of our approach, we compare our results with a numerical scattering calculation of the finite-range potential that shows excellent agreement over a wide range of scattering energies and SOC strengths. Our pseudopotential is applicable in the cases of a strong energy-dependent $s$-wave scattering length and/or non-negligible $p$-wave interaction, where the original free-space pseudopotential fails. It sets an ideal starting point to explore many-body physics in the presence of synthetic SOC in cold atoms.

Localization of electromagnetic waves in disordered potentials is prevented by polarization terms, so only light-scattering systems of dimensions $d=1$ and 2 with scalar properties exhibit light localization. We discuss here the presence of surface modes in vectorial systems of dimensions $d=2$ and 3, which possess lower-dimensional scattering properties, and present features of Anderson localization. In particular, vectorial waves in three dimensions (two dimensions) presents surface localized modes with scaling consistent with localization in two dimensions (one dimension).

Almost a decade ago, physicists encountered a strange quantum phenomenon that predicts an unusual death of entanglement, under the influence of a local noisy environment, known as entanglement sudden death (ESD). This could be an immediate stumbling block in realizing all entanglement based quantum information and computation protocols. In this paper, we propose a scheme to tackle such shortcomings by exploiting the phenomenon of exceptional points. Starting with a binary mechanical $\mathcal{PT}$ symmetric system, realized over an optomechanical platform, we show that a substantial delay in ESD can be achieved via pushing the system towards an exceptional point. This finding has been further extended to a higher-order (third-order) exceptional point by taking a more complicated tripartite entanglement into account.

Exceptional points (EPs) correspond to degeneracies of open systems. These are attracting much interest in optics, optoelectronics, plasmonics, and condensed matter physics. In the classical and semiclassical approaches, Hamiltonian EPs (HEPs) are usually defined as degeneracies of non-Hermitian Hamiltonians such that at least two eigenfrequencies are identical and the corresponding eigenstates coalesce. HEPs result from continuous, mostly slow, nonunitary evolution without quantum jumps. Clearly, quantum jumps should be included in a fully quantum approach to make it equivalent to, e.g., the Lindblad master equation approach. Thus, we suggest to define EPs via degeneracies of a Liouvillian superoperator (including the full Lindbladian term, LEPs), and we clarify the relations between HEPs and LEPs. We prove two main theorems: Theorem 1 proves that, in the quantum limit, LEPs and HEPs must have essentially different properties. Theorem 2 dictates a condition under which, in the “semiclassical” limit, LEPs and HEPs recover the same properties. In particular, we show the validity of Theorem 1 studying systems which have (1) an LEP but no HEPs and (2) both LEPs and HEPs but for shifted parameters. As for Theorem 2, (3) we show that these two types of EPs become essentially equivalent in the semiclassical limit. We introduce a series of mathematical techniques to unveil analogies and differences between the HEPs and LEPs. We analytically compare LEPs and HEPs for some quantum and semiclassical prototype models with loss and gain.

We characterize the polygamy nature of quantum entanglement in multiparty systems in terms of $q$-expectation value for the full range of $q\ge 1$. By investigating some properties of generalized quantum correlations in terms of $q$-expectation value and Tsallis $q$-entropy, we establish a class of polygamy inequalities of multiparty quantum entanglement in arbitrary dimensions based on $q$-expected entanglement measure. As Tsallis $q$-entropy is reduced to von Neumann entropy, and $q$-expectation value becomes the ordinary expectation value when $q$ tends to 1, our results encapsulate previous results of polygamy inequalities based on von Neumann entropy as special cases.

Detectors in the laboratory are often unlike their ideal theoretical cousins. They have nonideal efficiencies, which may then lead to nontrivial implications. We show how it is possible to predict correct answers about whether a shared quantum state is entangled in spite of finite detector efficiencies, when the tool for entanglement detection is a nonlinear entanglement witness. We first consider the detection loophole for shared quantum states with nonpositive partial transpose. We subsequently find nonlinear witness operators for bound entangled states with positive partial transpose, and show how the detection loophole can be closed also in such instances.

Based on the recently developed interaction renormalization for the one-dimensional $p$-wave interaction, we study the problem of a single impurity immersed in a highly polarized Fermi sea. They interact through a narrow $p$-wave Feshbach resonance, so the effective range $r_0$ naturally appears in the system. We use the variational approach limited to single-particle–hole excitations on top of the unperturbed Fermi sea. The polaron exhibits two branches of solutions, namely, the attractive and repulsive branches, with varying scattering length across the resonance. We calculate the energy spectrum, residue, and effective mass for each of the branches. We compare the polaronic energy with the energy of the dressed molecule and find that the molecular state is energetically favored when increasing the interaction strength. The critical interaction strength for the polaron-to-molecule transition will shift to the BCS side of the $p$-wave resonance as the effective range increases.

A comprehensive study of three-photon electromagnetically induced transparency (EIT) and absorption (EIA) on the rubidium cascade $5S_{1/2}\to 5P_{3/2}$ (laser wavelength 780 nm), $5P_{3/2}\to 5D_{5/2}$ (776 nm), and $5D_{5/2}\to 28F_{7/2}$ (1260 nm) is performed. The 780-nm probe and 776-nm dressing beams are counteraligned through a Rb room-temperature vapor cell, and the 1260-nm coupler beam is co- or counteraligned with the probe beam. Several cases of EIT and EIA, measured over a range of detunings of the 776-nm beam, are studied. The observed phenomena are modeled by numerically solving the Lindblad equation, and the results are interpreted in terms of the probe-beam absorption behavior of velocity- and detuning-dependent dressed states. Interaction-time effects are discussed. To explore the utility of three-photon Rydberg EIA and EIT for microwave electric-field diagnostics, a sub-THz field generated by a signal source and a frequency quadrupler is applied to the Rb cell. The 100.633-GHz field resonantly drives the $28F_{7/2}\leftrightarrow 29D_{5/2}$ transition and causes Autler-Townes splittings in the Rydberg EIA and EIT spectra, which are measured and employed to characterize the performance of the microwave quadrupler.

We numerically investigate atomic interferometry based on spin-exchange collisions in $F=1$ spinor Bose-Einstein condensates in the regime of long evolution times $t\gg h/c$, where $c$ is the spin-dependent interaction energy. We show that the sensitivity of spin-mixing interferometry can be enhanced by using classically seeded initial states with a small population prepared in the $m_F=\pm 1$ states.

Coherent optical memory based on electromagnetically induced transparency (EIT) offers a convenient way to convert the frequency or polarization of an optical probe pulse by storing in one $\mathrm{\Lambda }$ system and retrieving in another $\mathrm{\Lambda }$ system. We present a theoretical study on the efficiency variation of such an EIT-memory-based optical converter in an atomic system with degenerate Zeeman states. Based on the Maxwell-Bloch equation, we obtain an approximate analytic solution for the converted light pulses which clarifies that two major factors affect the efficiency of the converted pulses. The first one is the finite bandwidth effect of the pulses and the difference in the delay-bandwidth product of the writing and reading channel due to the difference in the transition dipole moment. The second one is the mismatch between the stored ground-state coherence and the ratio of the Clebsch-Gordan coefficients for the probe and control transition in the reading channel, which results in a nonadiabatic energy loss. To correspond to real experimental conditions, we also perform a numerical calculation of the variation in conversion efficiency versus the Zeeman population distribution under the Zeeman-state optical pumping in storing a ${\sigma }^{+}$-polarized pulse and retrieving with ${\sigma }^{-}$ polarization in cesium atoms. Our work provides essential physical insights and quantitative knowledge for the development of a coherent optical converter based on EIT-memory.