We propose to demonstrate nonreciprocal conversion between microwave and optical photons in an electro-optomechanical system where a microwave mode and an optical mode are coupled indirectly via two nondegenerate mechanical modes. The nonreciprocal conversion is obtained in the broken time-reversal symmetry regime, where the conversion of photons from one frequency to the other is enhanced for constructive quantum interference while the conversion in the reversal direction is suppressed due to destructive quantum interference. It is interesting that the nonreciprocal response between the microwave and optical modes in the electro-optomechanical system appears at two different frequencies with opposite directions. The proposal can be used to realize nonreciprocal conversion between photons of any two distinctive modes with different frequencies. Moreover, the electro-optomechanical system can also be used to construct a three-port circulator for three optical modes with distinctively different frequencies by adding an auxiliary optical mode coupled to one of the mechanical modes.

Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $\text{SU}\left(2\right)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $\text{SU}\left(3\right)$ symmetry. Using a combination of homotopy analysis and analytic field theory we identify a family of solitonic wave functions characterized by integer charge $\mathbf{Q}=(Q_A,Q_B,Q_C)$, with $Q_A+Q_B+Q_C=0$. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that solitons with charge $\mathbf{Q}=(1,1,-2)$ spontaneously decay into a pair of solitons with elementary topological charge, and emergent interactions. This result suggests that it could be possible to realize a class of interacting soliton, with no classical analog, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge group $\text{U}\left(1\right)\times \text{U}\left(1\right)$.

In the theory of Bethe-ansatz integrable quantum systems, rapidities play an important role as they are used to specify many-body states, apart from phases. The physical interpretation of rapidities going back to Sutherland is that they are the asymptotic momenta after letting a quantum gas expand into a larger volume making it dilute and noninteracting. We exploit this picture to make a direct connection to quantities that are accessible in sudden-expansion experiments with ultracold quantum gases. By a direct comparison of Bethe-ansatz and time-dependent density matrix renormalization group results, we demonstrate that the expansion velocity of a one-dimensional Fermi-Hubbard model can be predicted from knowing the distribution of occupied rapidities defined by the initial state. Curiously, an approximate Bethe-ansatz solution works well also for the Bose-Hubbard model.

We explore quantum beats in the photoelectron signal produced when a bound electron wave packet created by an isolated attosecond pulse is ionized by a delayed, few-cycle infrared pulse. Our calculations for helium atoms show that the broad bandwidth of the few-cycle pulse creates spectrally overlapping photoelectron peaks that result from one-, two-, or three-photon ionization processes. The beat signals can, in principle, be interferometrically resolved with high resolution, giving access to the relative phase between different multiphoton ionization pathways. For few-cycle near-infrared fields the relative spectral phases can be extracted over a large energy region, and dynamical information becomes available. We find that multiphoton ionization is temporally shifted with respect to one-photon ionization by several hundred attoseconds. Our results also reveal the impact of depletion and resonant pathways on the phase of the quantum beats.

We report on the realization of sub-Doppler laser cooling of sodium atoms in gray molasses using the $D_1$ optical transition $\left(3s{}^{2}S_{1/2}\to 3p{}^{2}P_{1/2}\right)$ at 589.8 nm. The technique is applied to samples containing $3\times {10}^9$ atoms, previously cooled to $350\mu \mathrm{K}$ in a magneto-optical trap, and it leads to temperatures as low as $9\mu \mathrm{K}$ and phase-space densities in the range of ${10}^{-4}$. The capture efficiency of the gray molasses is larger than 2/3, and we observe no density-dependent heating for densities up to ${10}^{11}{\mathrm{cm}}^{-3}$.

We study the sensitivity of coupled condensate formation dynamics on the history of initial stochastic domain formation in the context of instantaneously quenched elongated harmonically trapped immiscible two-component atomic Bose gases. The spontaneous generation of defects in the fastest condensing component, and subsequent coarse-graining dynamics, can lead to a deep oscillating microtrap into which the other component condenses, thereby establishing a long-lived composite defect in the form of a dark-bright solitary wave. We numerically map out diverse key aspects of these competing growth dynamics, focusing on the role of shot-to-shot fluctuations and global parameter changes (initial state choices, quench parameters, and condensate growth rates), with our findings also qualitatively confirmed by realistic finite-duration quenches. We conclude that phase-separated structures observable on experimental time scales are likely to be metastable states whose form is influenced by the stability and dynamics of the spontaneously emerging dark-bright solitary wave.

Three identical bosons or fermions are considered in the limit of zero-range interactions and finite effective range. By using a two-channel model, we show that these systems are not integrable and that the wave function verifies specific continuity conditions at the contact of three particles. This last feature permits us to solve a contradiction brought by the contact model which can lead to an opposite result concerning the integrability issue. For fermions, the vicinity of integrability is characterized by large deviations with respect to the predictions of the Bethe ansatz.

Negative refraction of a probe field is studied in a dense gas consisting of cascade-type four-level atoms. By coupling the magnetic component of the probe field to a $\mathrm{\Lambda }$ scheme with initially prepared coherence in the two lower levels, strong negative permeability with minimal absorption can be obtained. The permittivity of the gas to the electric component of the probe field can be made negative by taking into account the local field effect of the dense atoms. Strong negative refraction with zero absorption can be achieved in a wide range of parameters in our scheme. A possible experimental realization is also discussed.

We propose a scheme for continuous detection of itinerant microwave photons in circuit quantum electrodynamics. In the proposed device, a superconducting qubit is coupled dispersively to two resonators: one is used to form an impedance-matched $\mathrm{\Lambda }$ system that deterministically captures incoming photons, and the other is used for continuous monitoring of the event. The present scheme enables efficient photon detection: for realistic system parameters, the detection efficiency reaches 0.9 with a bandwidth of about 10 MHz.

We present and analyze a technique to drive high-order harmonics by laser pulses with an angular spatial chirp. Results of our numerical simulations show that each harmonic is emitted with an angular chirp which scales inversely with the harmonic order and leads to additional control of the spatial and temporal resolution of the spectrum. In particular, the use of angular chirp leads to separation of the harmonics in two dimensions where (i) high spectral resolution can be achieved and (ii) the temporal periodicity of the harmonic pulse trains can be controlled. We show that this technique does not require carrier-envelope-phase stabilization when using few-cycle laser pulses.

Reciprocity is a universal principle that has a profound impact on many areas of physics. A fundamental phenomenon in condensed-matter physics, optical physics, and acoustics, arising from reciprocity, is the constructive interference of quantum or classical waves which propagate along time-reversed paths in disordered media, leading to, for example, weak localization and metal-insulator transition. Previous studies have shown that such coherent effects are suppressed when reciprocity is broken. Here we experimentally show that by tuning a nonreciprocal phase we can coherently control complex coherent phenomena, rather than simply suppress them. In particular, we manipulate coherent backscattering of light, also known as weak localization. By utilizing a magneto-optical effect, we control the interference between time-reversed paths inside a multimode fiber with strong mode mixing, observe the optical analog of weak antilocalization, and realize a continuous transition from weak localization to weak antilocalization. Our results may open new possibilities for coherent control of waves in complex systems.

Due to the low cross section of $p$-wave threshold photodetachment and the complicated electronic structures, the uncertainty of electron affinities for many transition elements still remains around 10 meV, which has not been improved for three decades. In this study, the electron affinity of Nb is measured as 917.40(6) meV or $7399.35\left(50\right)\mathrm{c}{\mathrm{m}}^{-1}$ using the slow electron velocity imaging method. The accuracy was improved by a factor of more than 400 with respect to the previous measurement. Furthermore, the fine structures of $\mathrm{N}{\mathrm{b}}^{-}$ were successfully resolved: 16.87(12) meV $\left({}^5{D}_1\right)$, 46.75(12) meV (${}^5{D}_2$), 86.85(12) meV (${}^5{D}_3$), and 156.00(37) meV (${}^5{D}_4$) above the ground ${}^5{D}_0$, respectively.

We determine quantitatively the laser pulse duration dependence of the low-energy structure (LES) in strong-field atomic ionization and establish its universal character. The electron energy measurement is performed on krypton and argon by varying the duration of a 1.8 $\mu \mathrm{m}$ midinfrared pulse from two to ten cycles. Comparing the experiment with analytical and numerical results, the soft-recollision mechanism leading to electron momentum bunching is confirmed as the origin of the LES. The universal behavior of the LES peak energy on pulse duration emerges from an analytical description as a product of two factors: one contains the influence of the laser parameters and the target, while the other one describes the pulse duration dependence in terms of optical cycles.

We propose an approach for the collective enhancement of precision for remote optical lattice clocks and a way of generating the Einstein-Podolsky-Rosen (EPR) state of remote clocks. In the first scenario, a distributed spin-squeezed state (SSS) of $M$ clocks is generated by a collective optical quantum nondemolition measurement on clocks with parallel Bloch vectors. Surprisingly, optical losses, which usually present the main limitation to SSS, can be overcome by an optimal network design which provides close to Heisenberg scaling of the time precision with the number of clocks $M$. We provide an optimal network solution for distant clocks as well as for clocks positioned within close proximity of each other. In the second scenario, we employ collective dissipation to drive two clocks with oppositely oriented Bloch vectors into a steady-state entanglement. The corresponding EPR state provides secret time sharing beyond the projection noise limit between the two quantum synchronized clocks protected from eavesdropping. An important application of the EPR-entangled clock pair is the remote sensing of, for example, gravitational effects and other disturbances to which clock synchronization is sensitive.

We study the creation of nonlocal states with ultracold atoms trapped in an optical lattice. We show that these states violate Bell inequality by measuring one- and two-body correlations. Our scheme only requires beam-splitting operations and global phase shifts, and can be realized within the current technology, employing single-site addressing. This proposal paves the way to study multipartite nonlocality and entanglement in ultracold-atomic systems.

We introduce a class of three-dimensional color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows for the transversal implementation of a non-Clifford $\pi /8$ logical gate, which when combined with the logical Clifford gates that are transversal in the 2D color code give a gate set that is both fault-tolerant and universal without requiring nonstabilizer magic states. We then show that the layers forming the stacked code can be unfolded and arranged in a 2D layout. As only Clifford gates can be implemented transversally for 2D topological stabilizer codes, a nonlocal operation must be incorporated in order to allow for this transversal application of a non-Clifford gate. Our code achieves this operation through the transformation from a 2D color code to the unfolded stacked code induced by measuring only geometrically local stabilizers and gauge operators within the bulk of 2D color codes together with a nonlocal operator that has support on a one-dimensional boundary between such 2D codes. We believe that this proposed method to implement the nonlocal operation is a realistic one for 2D stabilizer layouts and would be beneficial in avoiding the large overheads caused by magic state distillation.

We study the entanglement Rényi $\alpha$ entropy $\left(\mathrm{ER}\alpha \mathrm{E}\right)$ as the measure of entanglement. Instead of a single quantity in standard entanglement quantification for a quantum state by using the von Neumann entropy for the well-accepted entanglement of formation (EoF), the $\mathrm{ER}\alpha \mathrm{E}$ gives a continuous spectrum parametrized by variable $\alpha$ as the entanglement measure, and it reduces to the standard EoF in the special case $\alpha \to 1$. The $\mathrm{ER}\alpha \mathrm{E}$ provides more information in entanglement quantification and can be used, for example, to determine the convertibility of entangled states by local operations and classical communication. A series of results is obtained: (i) we show that the $\mathrm{ER}\alpha \mathrm{E}$ of two states, which can be mixed or pure, may be incomparable, in contrast to the fact that there always exists an order for the EoF of two states; (ii) similar to the case of EoF, we study in a fully analytical way the $\mathrm{ER}\alpha \mathrm{E}$ for arbitrary two-qubit states, the Werner states, and isotropic states in the general $d$ dimension; and (iii) we provide a proof of the previous conjecture for the analytical functional form of the EoF of isotropic states in the arbitrary $d$ dimension.

We analyze the contribution of the quiver kinetic energy acquired by an electron in an oscillating electric field of a short laser pulse to the energy balance in atomic ionization processes. Due to the time dependence of this additional kinetic energy, a temporal average is assumed to preserve a stationary energy conservation rule, which is used to predict the position of the energy peaks observed in the photoelectron (PE) spectra. For a plane wave and a flattop pulse, the mean value of the quiver energy over the whole pulse leads to the concept of ponderomotive energy $U_p$. However, for a short pulse with a fast changing intensity, the stationary approximation loses its validity. We check these concepts by studying first the PE spectrum within the semiclassical model (SCM) for multiple-step pulses. The SCM offers the possibility to establish a connection between emission times and the PE spectrum in the energy domain. We show that PE substructures stem from ionization at different times mapping the pulse envelope. We also analyze the PE spectrum for a realistic sine-squared envelope within the Coulomb-Volkov and ab initio calculations solving the time-dependent Schrödinger equation. We found that the electron emission amplitudes produced at different times interfere with each other producing, in this way, a new additional pattern that modulates the above-threshold ionization (ATI) peaks.