The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions in which a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in the laser, and we observe their effects on the collapse and revival of the initially encoded information. Our work demonstrates that the ion trap is a powerful platform for simulating open quantum dynamics with complicated reservoir structures.

Quantum teleportation is an essential application of quantum entanglement. The examination of teleportation fidelity in two-party standard teleportation schemes reveals a critical threshold distinguishing separable and entangled states. For separable states, their teleportation fidelities cannot exceed the threshold, emphasizing the significance of entanglement. We extend this analysis to multiparty scenarios known as controlled teleportation. Our study provides thresholds that $N$-qudit $k$-separable states cannot exceed in a controlled teleportation scheme, where $N\ge 3$ and $2\le k\le N$. This not only establishes a standard for utilizing a given quantum state as a resource in controlled teleportation but also enhances our understanding of the influence of the entanglement structure on controlled teleportation performance. In addition, we show that genuine multipartite entanglement is not a prerequisite for achieving a high controlled teleportation capability.

The experimental evaluation of many quantum mechanical quantities requires the estimation of several directly measurable observables, such as local observables. Due to the necessity to repeat experiments on individual quantum systems in order to estimate expectation values of observables, the question of how many repetitions to allocate to a given directly measurable observable arises. We show that an active learning scheme can help to improve such allocations, and the resultant decrease in experimental repetitions required to evaluate a quantity with the desired accuracy increases with the size of the underlying quantum mechanical system.

Kirkwood-Dirac (KD) quasiprobability is a quantum analog of classical phase space probability. It offers an informationally complete representation of quantum state wherein the quantumness associated with quantum noncommutativity manifests in its nonclassical values, i.e., the nonreal and/or negative values of the real part. This naturally raises a question: how does such form of quantumness comply with the uncertainty principle which also arises from quantum noncommutativity? Here, first, we obtain sufficient conditions for the KD quasiprobability defined relative to a pair of projection-valued measure (PVM) bases to have nonclassical values. Using these nonclassical values, we then introduce two quantities which capture the amount of KD quantumness in a quantum state relative to a single PVM basis. They are defined, respectively, as the nonreality and the classicality—which captures both the nonreality and negativity—of the associated KD quasiprobability over the PVM basis of interest, and another PVM basis, and maximized over all possible choices of the latter. We obtain their lower bounds, and derive trade-off relations respectively reminiscent of the Robertson and Robertson-Schrödinger uncertainty relations but with lower bounds maximized over the convex sets of Hermitian operators whose complete sets of eigenprojectors are given by the PVM bases. We discuss their measurement using weak value measurement and classical optimization. We then suggest an information theoretical interpretation of the KD nonreality relative to a PVM basis as a lower bound to the maximum total root-mean-squared error in an optimal estimation of the PVM basis, and thereby obtain a lower bound and a trade-off relation for the root-mean-squared error. Finally, we suggest an interpretation of the KD nonclassicality relative to a PVM basis as a lower bound to the total state disturbance caused by a nonselective projective binary measurement associated with the PVM basis, and derive a lower bound and a trade-off relation for the disturbance.

Classical shadow tomography, harnessing randomized informationally complete (IC) measurements, provides an effective avenue for predicting many properties of unknown quantum states. In $n$-qubit systems, projections onto $2^n+1$ mutually unbiased bases (MUBs) are widely recognized as minimal and optimal IC measurements for full-state tomography. Mutually unbiased base circuits, structured as $\text{−}\mathrm{CZ}\text{−}S\text{−}H\text{−}$, form the minimal subset of the whole $2^{n^2+2n}{\prod }_{j=1}^n(4^j-1)$ Clifford circuit ensemble. Each of them can be generated by $n$ special MUB circuits. We study how to use MUB circuits as the ensemble in classical shadow tomography. For general observables, the variance to predict their expectation value is shown to be exponential to the number of qubits $n$. However, for a special class referred to as appropriate MUB-average (AMA) observables, the variance decreases to $\text{poly}\left(n\right)$. Additionally, we find that through biased sampling of MUB circuits, the variance for non-AMA observables can again be reduced to $\text{poly}\left(n\right)$ with the MUB-sparse condition. The performance and complexity of using the MUB and Clifford circuits as the ensemble in the classical shadow tomography are compared.

Lee-Yang (LY) zeros, points on the complex plane of physical parameters where the partition function goes to zero, have found diverse applications across multiple disciplines like statistical physics, protein folding, percolation, and complex networks. However, experimental extraction of the complete set of LY zeros for general asymmetrical classical systems remains a crucial challenge to put those applications into practice. Here, we propose a qubit-based method to simulate an asymmetrical classical Ising system, enabling the exploration of LY zeros at arbitrary values of physical parameters like temperature and internal couplings. Without assuming system symmetry, the full set of LY zeros forms an algebraic variety in a higher-dimensional complex plane. To determine this variety, we project it into sets representing magnitudes (amoeba) and phases (coamoeba) of LY zeros. Our approach uses a probe qubit to initialize the system and to extract LY zeros without assuming any control over the system qubits. This is particularly important as controlling system qubits can get intractable with the increasing complexity of the system. Initializing the system at an amoeba point, coamoeba points are sampled by measuring probe qubit dynamics. Iterative sampling yields the entire algebraic variety. Experimental demonstration of the protocol is achieved through a three-qubit NMR register. This paper expands the horizon of quantum simulation to domains where identifying LY zeros in general classical systems is pivotal. Moreover, by extracting abstract mathematical objects like amoeba and coamoeba for a given polynomial, our paper integrates pure mathematical concepts into the realm of quantum simulations.

Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary noisy intermediate-scale quantum (NISQ) era. The quantum approximate optimization algorithm (QAOA) is one such algorithm, used in solving the maximum cut (Max-Cut) problem for a given graph by successive implementation of $L$ quantum circuit layers within a corresponding Trotterized ansatz. The challenge of exploring the cost function of VQAs arising from an exponential proliferation of local minima with increasing circuit depth has been well documented. However, fewer studies have investigated the impact of circuit depth on QAOA performance in finding the correct Max-Cut solution. Here we employ basin-hopping global optimization methods to navigate the energy landscapes for QAOA ansätze for various graphs, and analyze QAOA performance in finding the correct Max-Cut solution. The structure of the solution space is also investigated using discrete path sampling to build databases of local minima and the transition states that connect them, providing insightful visualizations using disconnectivity graphs. We find that the corresponding landscapes generally have a single funnel organization, which makes it relatively straightforward to locate low-lying minima with good Max-Cut solution probabilities. In some cases below the adiabatic limit the second lowest local minimum may even yield a higher solution probability than the global minimum. This important observation has motivated us to develop broader metrics in evaluating QAOA performance, based on collections of minima obtained from basin-hopping global optimization. Hence we establish expectation thresholds in elucidating useful solution probabilities from local minima, an approach that may provide significant gains in elucidating reasonable solution probabilities from local minima.

We theoretically study the buildup of Rabi oscillations in the two-photon ionization process in atomic Hydrogen, where both resonant and nonresonant ionization paths play a significant role. Using spectrally and angularly resolved electron interferometry, we reconstruct the temporal profiles of electron wave packets (EWPs) and the time evolution of photoelectron energy spectra (PESs) for the $s$ and $d$ partial waves from the numerical results of time-dependent Schrödinger equation. Our results reveal the differences between the $s$ and $d$ waves in terms of the minimum of the temporal EWPs and the asymmetry of the time-evolving PESs. Based on a three-level model, we attribute these phenomena to the different contributions of the nonresonant path in these two partial waves. Further, with this model we highlight the opposite effects of the AC-Stark effect on resonant and nonresonant paths. Our work directly reveals the time-varying influence of the oscillating populations on the dynamics of resonant and nonresonant paths, and provides a feasible method for assessing the partial-wave resolved contribution of the nonresonant path in the time domain.

The spectra produced by high-order harmonic generation (HHG) typically exhibit well-defined peaks at odd integers times the laser frequency. However, in recent investigations of HHG from correlated materials, spectra exhibit signals at noninteger harmonics which do not conform to the well-known symmetry-based selection rules for HHG spectra. Here, we use the Fermi-Hubbard model to study HHG from a linear chain of atoms. This model allows us to study both the correlated and uncorrelated phases through a specification of the amount of onsite electron-electron repulsion. The presence of signal at noninteger harmonics can be interpreted as originating from the population of multiple Floquet states. We show how this coupling to different Floquet states depends on the characteristics of the driving pulse and the strength of the electron-electron interaction in the system.

Physical systems in reduced dimensions exhibit intriguing properties. For instance, the dependences of two-body and many-body physics on scattering lengths are distinct from their counterparts in three dimensions. Whereas many studies of ultracold atoms and molecules in reduced dimensions have been focusing on closed systems, two-body losses may occur in such systems. Here, we show that the two-body inelastic loss rate in reduced dimensions can be expressed in universal relations that are governed by contacts. These universal relations correlate the two-body decay rate with other physical observables at zero and finite temperatures and generic interaction strengths. Our results will provide experimentalists with a new protocol to study inelastic scatterings in both few- and many-body systems in reduced dimensions.

We use a two-channel model to investigate an interacting Bose gas across a narrow Feshbach resonance within a field path integral approach. The ground-state properties show strong deviation from that of a broad Feshbach resonance or a single-channel interaction. The deviation can be interpreted by the strong energy dependence of two-body scattering length near a narrow Feshbach resonance. As the density increases, the chemical potential and energy per particle are found to saturate while the inverse compressibility and the phonon velocity undergo a significant reduction. We also take Gaussian fluctuations into account and calculate the ground-state energy correction as well as the quantum depletion.

The equation of state (EOS) for a pure two-dimensional (2D) Bose gas exhibits a logarithmic dependence on the $s$-wave scattering length [L. Salasnich, Phys. Rev. Lett. 118, 130402 (2017)]. The pronounced disparity between the EOS of a 2D Bose gas and its three-dimensional (3D) counterpart underscores the significance of exploring the dimensional crossover between these two distinct dimensions. In this paper, we are motivated to deduce nonuniversal corrections to the EOS for an optically trapped Bose gas along the dimensional crossover from 3D to 2D, incorporating the finite-range effects of the interatomic potential. Employing the framework of effective field theory, we derive the analytical expressions for both the ground-state energy and quantum depletion. The introduction of the lattice induces a transition from a 3D to a quasi-2D regime. In particular, we systematically analyze the asymptotic behaviors of both the 2D and 3D aspects of the model system, with a specific focus on the nonuniversal effects on the EOS arising from finite-range interactions. The nonuniversal effects proposed in this paper along the dimensional crossover represent a significant stride toward unraveling the intricate interplay between dimensionality and quantum fluctuations.

The non-Hermitian interaction in many-body systems may lead to novel phenomena. We study an impurity immersed in three-dimensional ideal Fermi gases, with a complex-valued contact interaction between the fermions and impurity that arise from two-body dissipation. Generalizing the unified variational approach to the non-Hermitian case, we study the effects of the dissipative attraction on the polaronic and molecular states of the impurity for different mass ratios. We find that the dissipation attraction can induce polaron-molecule transition despite the transition being absent in the Hermitian case, which is demonstrated to be a first-order phase transition between different total momenta. In addition, we show that the non-Hermitian attraction leads to significant decay of the polaronic and molecular states; however, increasing the mass ratio between the impurity and majority fermions will help suppress the decay. Our results illustrate the applicability of the unified variational approach in non-Hermitian Fermi polaron systems and the method may be extended to include higher-order particle-hole excitations and to study other types of bound states.

The two-body loss associated with inelastic interactions between fermions plays a significant role in realistic many-body systems. Here we study a two-component non-Hermitian Bardeen-Cooper-Schrieffer superfluidity with spin imbalance and two-body loss characterized by a complex-valued $s$-wave interaction in a square lattice. At the mean-field level, we map out the zero-temperature phase diagram and observe a dissipation-induced transition from superfluid to normal phase as well as a distinctive revival of the superfluid state in the weakly interacting regime applicable to both spin-balanced and spin-imbalanced systems. In the spin-imbalanced case, we find that the effective density of states involving weight functions reduces the regions in $\mathbf{k}$ space contributing to pairing, hence leading to a pronounced expansion of the normal phase on the phase diagram. Additionally, we analyze the order parameter, condensate energy, quasiparticle spectra, momentum distribution, and compressibility to characterize the presenting phases and phase transitions.

In this paper we utilize the half Pearcey function as a means to describe a surface plasmon, the half Pearcey plasmon. The abrupt autofocusing and self-healing properties from the superposition of the half Pearcey plasmon are observed and discussed. The tunable focal intensity covers three orders of magnitude and the autofocusing property can be maintained with the potential well. Additionally, with the $\pi$ phase offset, we construct multiple plasmonic bottles with the chirp factor; both the bottle structure and propagating direction are adjustable. The focusing properties of the plasmon under the chirp depend on the spatial spectrum separation, resulting in the construction of plasmonic bottles with different positions and sizes. The validity of our results is confirmed by finite-difference time-domain numerical simulations. Our findings may provide potential for spectral enhancement, nanoscale plasmonic devices, and plasmonic trapping.

We study chiroptical scattering properties of magneto-optical structures possessing rotation symmetries, with both rotation axis and externally applied static magnetic field parallel to the incident direction. For no less than threefold rotation symmetries (with or without magnetizations), cross sections of scattering and extinction are invariant as long as the incident polarizations locate on the same latitude line of the Poincaré sphere (polarization ellipses of the same ellipticity but different orientations), while for general incident polarizations, cross sections of scattering and extinction are ellipticity-weighted arithmetic average of those for circularly polarized incident waves. We further characterize the chiroptical responses through relative distinctions between cross sections for incident waves of left-handed and right-handed circular polarizations, and reveal that the external magnetic field can both suppress and enhance the chiroptical responses, depending on its direction and strength. When the chiroptical response is fully eliminated by the magnetization, the cross sections get decoupled to the polarization ellipticities as well, becoming fully independent of arbitrary incident polarizations. Our arguments are based on global structural symmetries only, and thus all conclusions drawn are irrelevant to local geometric parameters or specific material parameters of the scatterers, as long as the rotation symmetry is preserved. The principles we have revealed can be applied in many magnetism-induced nonreciprocal structures, and are robust against any rotation-symmetry-preserving structural defects and perturbations.

Nonlinear optical effects in vacuum have been investigated as a means to verify quantum electrodynamics in a region of low photon energy. By considering nonlinear electromagnetic waves in a three-dimensional cylindrical cavity, we report that the orbital angular momentum of light strongly affects self-modulations in a long timescale. The variation in optical phase is shown to enhance the vacuum nonlinearity. Moreover, we demonstrate the time evolution of the phase shift and of the energy transfer between cavity modes, which may pave the way for verification experiments.

We propose the direction-tunable chiral photonic propagation of spontaneous emission based on magnetic helicity and finite-size effect in a topological honeycomb photonic crystal slab. The chiral edge state channels are excited by emitters with magnetic polarization due to the $C_6$ symmetry, where their propagation directions are tuned by the emitter's position on the magnetic helicity pattern. Meanwhile, the finite size of the honeycomb photonic crystal brings chirality oscillation, which also decides the chirality of photonic propagation. This method of controlling chiral transport in two-dimensional designs can be extended to a three-dimensional silicon-based photonic crystal slab containing a silver split ring resonator as the emitter providing spontaneous emission, which is convenient to fabricate via existing nanotechnology. Moreover, we show the magnetic Purcell effect with chiral transport in the three-dimensional topological PC slab structure. Our research reduces the threshold of on-chip photonic transmission under topological protection, which is helpful for single-photon sources, photonic integrated chip manufacturing, and quantum information processing.