We report a joint experimental and theoretical study of a three-sideband (3-SB) modification of the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) setup. The 3-SB RABBIT scheme makes it possible to investigate phases resulting from interference between transitions of different orders in the continuum. Furthermore, the strength of this method is its ability to focus on the atomic phases only, independent of a chirp in the harmonics, by comparing the RABBIT phases extracted from specific SB groups formed by two adjacent harmonics. We verify earlier predictions that the phases and the corresponding time delays in the three SBs extracted from angle-integrated measurements become similar with increasing photoelectron energy. A variation in the angle dependence of the RABBIT phases in the three SBs results from the distinct Wigner and continuum-continuum coupling phases associated with the individual angular-momentum channels. A qualitative explanation of this dependence is attempted by invoking a propensity rule. Comparison between the experimental data and predictions from an $R$ matrix (close-coupling) with time dependence calculation shows qualitative agreement in most of the observed trends.

Rare-earth ions doped into low nuclear-spin density host crystals provide a promising platform for quantum information storage and processing. Calcium tungstate $\left({\mathrm{CaWO}}_4\right)$ is an attractive host crystal because it can be isotopically enriched to provide a nuclear spin free environment. Here, we report a spectroscopic investigation of the optical transitions and hyperfine transitions of praseodymium $\left({}^{141}\mathrm{Pr}^{3+}\right)$ doped in ${\mathrm{CaWO}}_4$ at liquid-helium temperatures. The hyperfine structures of the ${}^3{H}_4$(0) and ${}^1{D}_2$(0) states are determined by spectral hole burning. The results indicate that ${\mathrm{Pr}}^{3+}$:${\mathrm{CaWO}}_4$ is an appealing candidate for quantum memory in quantum information processing.

The inelastic squared form factors of the valence-shell excitations of ${\mathrm{D}}_2$ were measured by high-energy electron scattering and calculated by the multireference single- and double-excitation configuration interaction method in the present work. It is found that for the $B^1{\mathrm{\Sigma }}_u{}^{+}$ state of ${\mathrm{D}}_2$, the theoretical calculation cannot satisfactorily reproduce the inelastic squared form factors with a higher vibrational quantum number. For the vibronic states of $C^1{\mathrm{\Pi }}_u$ and $E{F}^1{\mathrm{\Sigma }}_g{}^{+}$ of ${\mathrm{D}}_2$, obvious discrepancies between our electron-scattering results and theoretical calculations are found. Similar phenomena observed for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ may be attributed to electronic-vibrational coupling and the failure of the first Born approximation at an incident electron energy of 1500 eV. Furthermore, the present inelastic squared form factors of ${\mathrm{D}}_2$ are in good agreement with the ones of ${\mathrm{H}}_2$ and HD, which indicates that there is no isotope effect for the electronic matrix elements of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ in the momentum space.

Ultrafast scattering using x-rays or electrons is an emerging method to obtain structure dynamics at the atomic lengthscales and timescales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector range and the probe energy. As a result, the time-resolved signal interpretation is mostly done in reciprocal space and relies on modeling and simulations of specific structures and processes. Here, we introduce a model-free approach to directly resolve scattering signals in real space, surpassing the diffraction limit, using scattering kernels and signal priors that naturally arise from the measurement constraints. We demonstrate the approach on simulated and experimental data, recover multiple atomic motions at sub-angstrom resolutions, and discuss the recovery accuracy and resolution limits versus signal fidelity. The approach offers a robust path to obtain high-resolution real-space information of atomic-scale structure dynamics using current time-resolved x-ray or electron scattering sources.

A judicious design of gain and loss leads to counterintuitive wave phenomena that are inaccessible by conservative systems. Notably, such designs can give rise to laser-absorber modes and anisotropic transmission resonances. Here, we analyze the emergence of these phenomena in an optical scatterer with sinusoid gain-loss modulation that is subjected to monochromatic oblique waves. We derive an analytical solution to the problem, with which we show how the scatterer parameters, and specifically the modulation phase and incident angle, constitute a real design space for these phenomena.

Photon-phonon interaction is a powerful mechanism for all-optical signal processing, slow (fast) light, microscopy, spectroscopy, microwave photonics, and sensing. Here, we demonstrate a photon-echo-like phenomenon induced by a phonon, whose mechanism is represented by a coherent photon-phonon chain interaction (PPCI) theory referring to the alternating evolution between Stokes scattering and anti-Stokes scattering. An analytical solution, including the impulse response of the coherent PPCI theory, is derived to quantitatively analyze the energy conversion between photon and phonon, showing a damped photoacoustic oscillation. All theoretical analysis, numerical simulation, and experiments confirm that the adjacent order echoes have a phase difference of π, i.e., phase flip, and the echoes generated by using photon and phonon as the initial excitation sources, respectively, are in inverse phase. As a result, the echoes up to the third-order are theoretically analyzed by the proposed coherent PPCI theory and verified by the experiment. This physical mechanism bodes well for a class of photonics applications in telecommunications, optical metrology, and optical computation.

We investigated optical localization and vibration in a synthetic photonic lattice (SPL) with two-phase modulators driven by different periodic voltages. By altering the periods of phase modulation, the induced phase circumfluences, band structure, and transmission behaviors of light in the SPL are studied. A transition from discrete diffraction to weak localization was observed in a small modulation period with equal modulation periodicities. For large modulation periods, the band structure exhibits a density distribution and the optical field delocalizes and vibrates. In contrast, strong localization occurs near the initial incident location with some moiré modulation periods of phases that correspond to a flat-band structure. This study reveals the effect of dual-periodic phase modulation on pulse propagation in discrete systems.

We propose a scheme to dissipatively produce steady-state entanglement in a two-qubit system, via an interaction with a bosonic mode. The system is driven into a stationary entangled state, while we compensate the mode dissipation by injecting energy via a coherent pump field. We also present a scheme which allows us to adiabatically transfer all the population to the desired entangled state. The dynamics leading to the entangled state in these schemes can be understood in analogy with electromagnetically induced transparency and stimulated Raman adiabatic passage, respectively.

We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems whose dynamics can be effectively described by a non-Hermitian Hamiltonian. We derive a timescale for the degree of mixedness for an input state undergoing non-Hermitian dynamics and specialize these results in the case of a driven-dissipative two-level system. Next, we derive a timescale for the growth of mixedness for bipartite quantum systems that depends on the effective non-Hermitian Hamiltonian. In the Hermitian limit, this result recovers the perturbative expansion for coherence loss in Hermitian systems, while it provides an entanglement timescale for initial pure and uncorrelated states. To illustrate these findings, we consider the many-body transverse-field XY Hamiltonian coupled to an imaginary all-to-all Ising model. We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states. Overall, each timescale depends on minimal ingredients such as the probe state and the non-Hermitian Hamiltonian of the system, and its evaluation requires low computational cost. Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and $\mathcal{PT}$-symmetric quantum field theory.

Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum states, and the Gram matrix is calculated from the overlap between these states. With the kernel at hand, a regular machine learning model is used for the learning process. In this paper we investigate the quantum support vector machine and quantum kernel ridge models to predict the degree of non-Markovianity of a quantum system. We perform digital quantum simulation of amplitude damping and phase damping channels to create our quantum data set. We elaborate on different kernel functions to map the data and kernel circuits to compute the overlap between quantum states. We show that our models deliver accurate predictions that are comparable with the fully classical models.

Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises to improve the metrology performance. Our scheme can automatically alter the parameter-encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. By comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in a nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments.

Nuclear-spin memories of divalent neutral atoms can allow spin-preserving resolved-sideband cooling in a strong magnetic field [I. Reichenbach and I. H. Deutsch, Phys. Rev. Lett. 99, 123001 (2007)]. We present a theory for cooling ${}^{87}\mathrm{Sr}$ nuclear-spin qubits in a weak magnetic field. The theory depends on laser excitation of $5s5p{}^{3}P_1$ to a nearby state which results in $m_J$-dependent AC Stark shifts large compared to the hyperfine interaction. This effectively suppresses the nuclear-spin mixing due to the hyperfine interaction. Sideband cooling via the clock state quenched by the AC Stark-shifted ${}^{3}P_1$ state leads to nuclear-spin-preserving spontaneous emission back to the ground state. More than being compatible with low magnetic fields, the theory is applicable when the nuclear-spin qubits are defined by the two lowest Zeeman substates.

In this work, we put forward an approach of constructing the optimal composite pulse sequence for robust population transfer in two-level systems. This approach is quite universal and applicable to a variety of systems, because the modulation parameters of composite pulses are obtained by minimizing the homemade cost function rather than nullifying the error coefficients of the transition probability. Specifically, we design different forms of the cost function for implementing optimal robustness with respect to the single or multiple errors. When slightly adjusting the constraints of the cost function, this approach can be easily extended to achieve arbitrary population transfer. The numerical results demonstrate that the optimized sequences are immune from various systematic errors, allowing us to produce a broadening excitation range of the transition probability. Therefore, this work offers an optimal robust design for controlling quantum states in error-prone environments.

We study the average density of $N$ spinless noninteracting fermions in a two-dimensional harmonic trap rotating with a constant frequency $\mathrm{\Omega }$ and in the presence of an additional repulsive central potential $\gamma /r^2$. The average density at zero temperature was recently studied in Phys. Rev. A 103, 033321 (2021), and an interesting multilayered “wedding-cake” structure with a “hole” at the center was found for the density in the large-$N$ limit. In this paper, we study the average density at finite temperature. We demonstrate how this “wedding-cake” structure is modified at finite temperature. We show that, while the bulk density profile gets smeared significantly at a temperature $T\sim O\left(1\right)$, the edge profile already acquires significant smearing at a much lower temperature $T\sim O(1/\sqrt{N})$. These large-$N$ results warrant going much beyond the standard local density approximation. We also generalize our results to a wide variety of trapping potentials, and we demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the “wedding cake.”

Ultracold atoms in a moving optical lattice with high controllability are a feasible platform to research the transport phenomenon. Here, we study the transport process of ultracold atoms at the $D$ band in a one-dimensional optical lattice and manipulate the transport of superposition states with different superposition weights of $S$-band and $D$-band atoms. In the experiment, we first load ultracold atoms into an optical lattice using the shortcut method and then accelerate the optical lattice by scanning the phase of lattice beams. The atomic transport at the $D$ band and $S$ band is demonstrated, respectively. The group velocity of atoms at the $D$ band is opposite to that at the $S$ band. By preparing superposition states with different superposition weights of the $D$-band and $S$-band atoms, we realize the manipulation of atomic group velocity from positive to negative, and observe the quantum interference between atoms at different bands. The influence of the lattice depth and acceleration on the transport process is also studied. Moreover, the multiorbital simulations are coincident with the experimental results. Our paper sheds light on the transport process of ultracold atoms at higher bands in optical lattices and provides a useful method to manipulate the transport of atomic superposition states.

We investigate the lifetimes of complexes formed in ultracold molecule collisions. Employing both transition-state theory and a non-Hermitian microscopic model, we examine processes that can extend the lifetime of complexes beyond that predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) theory. We focus on complexes that possess only one open channel, and find that the extreme distribution of widths for this case favors low decay rates. Thus, decay from a complex into a single energetically available channel can be anomalously slow, even orders of magnitude slower than the RRKM rate, and moreover the decay may be nonexponential in time.

We study a system of a few ultracold bosons loaded into states with orbital angular momentum $l=1$ of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers $+l$ and $-l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\varphi$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\pi$ flux through the plaquettes. We find nontrivial topological band structures and many-body Aharonov-Bohm caging in the $N$-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\varphi$ is introduced at an arbitrary lattice periodicity $\mathrm{\Gamma }$. For $\mathrm{\Gamma }>2$, the $\pi$ flux becomes nonuniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.

A quantum emitter placed in a nanophotonic structure can result in nonreciprocal phenomena like chiral light excitation. Here, we present a theoretical model to couple circularly polarized emitters described by the density-matrix formalism to the electromagnetic fields within a finite-difference time-domain simulation. In particular, we discuss how to implement complex electric fields in the simulation to make use of the rotating-wave approximation. By applying our model to a quantum emitter in a dielectric waveguide and an optical circulator, we show how the excitation of the quantum system depends on its position and polarization. In turn, the back-coupling can result in strongly asymmetric light excitation. Our framework and results will help better explain spatiotemporal dynamics of light fields in nanophotonic structures containing quantum emitters.

Giant atoms provide a promising platform for engineering decoherence-free interactions, which is a major task in modern quantum technologies. Here we study systematically how to implement complex decoherence-free interactions among giant atoms resorting to periodic coupling modulations and suitable arrangements of coupling points. We demonstrate that the phase of the modulation, which is tunable in experiments, can be encoded into the decoherence-free interactions and thus enables phase-dependent dynamics when the giant atoms constitute an effective closed loop. Moreover, we consider the influence of non-Markovian retardation effect arising from large separations of the coupling points and study its dependence on the modulation parameters.