A disordered quantum system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer with no, or limited, error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spectral functions on a trapped-ion quantum computer for a one-dimensional Heisenberg model with disorder. Further, we design an error-mitigation technique which is effective at removing the noise from the measurement allowing clear signatures of localization to emerge as the disorder increases. Thus, we show that spectral functions can serve as a robust and scalable diagnostic of many-body localization on current and future generations of quantum computers.

Variational quantum algorithms dominate gate-based applications of modern quantum processors. The so-called layerwise trainability conjecture appears in various works throughout the variational quantum computing literature. The conjecture asserts that a quantum circuit can be trained piecewise, e.g., that a few layers can be trained in sequence to minimize an objective function. Here, we prove this conjecture false. Counterexamples are found by considering objective functions that are exponentially close (in the number of qubits) to the identity matrix. In the finite setting, we found abrupt transitions in the ability of quantum circuits to be trained to minimize these objective functions. Specifically, we found that below a critical (target-gate-dependent) threshold, circuit training terminates close to the identity and remains near to the identity for subsequently added blocks trained piecewise. A critical layer depth will abruptly train arbitrarily close to the target, thereby minimizing the objective function. These findings shed light on the divide-and-conquer trainability of variational quantum circuits and apply to a wide collection of contemporary literature.

In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding with two senders and a single receiver is performed and entanglement is measured in the senders:receiver bipartition. The normalized frequency distributions of DCC for randomly generated two-, three-, and four-qubit density matrices with global as well as local decodings at the receiver's end are reported. The estimation of mean DCC for two-qubit states is found to be in good agreement with the numerical simulations. Universally, we observe that the performance of random states for dense coding as well as teleportation decreases with the increase of the rank of states, which we have shown to be surmounted by the local preprocessing operations performed on the shared states before starting the protocols, irrespective of the rank of the states. The local preprocessing employed here is based on positive operator valued measurements along with classical communication and we show that unlike dense coding with two-qubit random states, the senders' operations are always helpful to probabilistically enhance the capabilities of implementing dense coding as well as teleportation.

Quantum manipulation based on geometric phases provides a promising way towards robust quantum gates. However, in the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions that induce geometric phases, thereby smearing their noise-resilient feature. In a recent experiment [Y. Xu et al., Phys. Rev. Lett. 124, 230503 (2020)], high-fidelity universal geometric quantum gates have been implemented in a superconducting circuit, which are robust to different types of errors under different configurations of the geometric evolution paths. Here, we apply the path-design strategy to explain in detail why both configurations can realize universal quantum gates in a single-loop way. Meanwhile, we purposefully induce our geometric manipulation by selecting the path configuration that is robust against the qubit-frequency-drift-induced error, which is the dominant error source on realistic superconducting circuits and has not been deliberately addressed. Moreover, our proposal can further integrate with the composite scheme to enhance the gate robustness, which is verified by numerical simulations. Therefore, our scheme provides a promising way towards practical realization of high-fidelity and robust nonadiabatic geometric quantum gates.

We measure and analyze the isotope shifts in the multiplet of transitions between the metastable $a^{5}F$ and excited $y^5{G}^o$ terms of neutral titanium by probing a titanium vapor in a hollow cathode lamp using saturated absorption spectroscopy. We resolve the five $J\to J+1$ and the four $J\to J$ transitions within the multiplet for each of the three $I=0$ stable isotopes (${}^{46}\mathrm{Ti}, {}^{48}\mathrm{Ti}$, and ${}^{50}\mathrm{Ti}$). The isotope shifts on these transitions allow us to determine the isotope-dependent variation in the fine-structure splitting of the $a^{5}F$ and $y^5{G}^o$ levels themselves. Combined with existing knowledge of the nuclear charge radii of titanium nuclei, we derive the specific mass and field shifts, which arise from correlated electronic motion and electronic density at the nucleus respectively, and further observe a strong $J$-dependent variation in each. Our results yield insight into the electronic and nuclear structure of transition metal atoms like titanium and also characterize optical transitions that may allow for optical manipulation of ultracold gases of transition-metal species.

Triatomic molecule RaOH combines the advantages of laser coolability and the spectrum with close opposite-parity doublets. This makes it a promising candidate for experimental study of the $\mathcal{P},\mathcal{T}$ violation. Previous studies concentrated on the calculations for different geometries without the averaging over the rovibrational wave function. The paper by V. Prasannaa et al. [Phys. Rev. A 99, 062502 (2019)] claimed that the dependence of the $\mathcal{P},\mathcal{T}$ parameters on the bond angle may significantly alter the observed value. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian. The potential surface is constructed based on the two-component relativistic coupled-cluster approximation with single, double, and perturbative triple excitation computations employing the generalized relativistic effective core potential for the radium atom. The averaged values of the parameters $E_{\mathrm{eff}}$ and $E_s$ describing the sensitivity of the system to the electron electric dipole moment and the scalar-pseudoscalar nucleon-electron interaction are calculated and the value of $l$ doubling is obtained.

The angular distributions of electrons ejected in laser photodetachment of the ${\mathrm{P}}^{-}$ ion have been studied in the photon energy range of 0.95–3.28 eV using a photoelectron spectrometer designed to accommodate a source consisting of collinearly overlapping photon and negative ion beams. We observe the value of the asymmetry parameter $\beta$ starting at zero near the threshold, falling to almost $-1$ about 0.5 eV above the threshold and eventually rising to a positive value. The experimental data has been fitted to a simplified model of the Cooper-Zare formula which yields a qualitative understanding of the quantum interference between the outgoing $s$ and $d$ waves representing the free electron. The present results are also compared with previous results for other elements involving $p$-electron photodetachment.

Molecular spectroscopy is a powerful tool for accelerating advances in materials science, chemistry, biology, and astronomy. Typically, molecular spectroscopy uses nanotips or nanoparticles to locally detect the molecule properties in a sample resulting from absorption of infrared and terahertz radiations. Here, we present an alternative that transient localized plasma can be applied to enhance the molecular spectroscopy. Our experiments show a significant enhancement of rotational transitions in carbon monoxide plasma under the illumination of terahertz waves. We proposed a semiclassical model for this enhancement, dominated by the energy exchange from electrons to molecules or ions via a collision process in the localized plasma. Our findings gain more insight into the nonequilibrium dynamics in laser-generated localized plasma. We also propose that the localized plasma can be used to improve the sensitivity of molecular spectroscopy.

A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_{\text{r}}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_{\text{r}}\to \infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $\mathrm{\Delta }S$ of a diffusive system at finite temperature in one or two dimensions is governed by hydrodynamic modes resulting in $\mathrm{\Delta }S\sim 1/\sqrt{t_{\text{r}}}$ in $d=1$ and $\mathrm{\Delta }S\sim ln\left(t_{\text{r}}\right)/t_{\text{r}}$ in $d=2$. In higher dimensions, entropy production is instead dominated by other high-energy modes with $\mathrm{\Delta }S\sim 1/t_{\text{r}}$. In order to verify the analytic prediction, we simulate the nonequilibrium dynamics of a classical two-component gas with pointlike particles in one spatial dimension and examine the total entropy production as a function of $t_{\text{r}}$.

We investigate theoretically the time- and frequency-domain two-particle correlations of a driven-dissipative Bose-Hubbard model at and near a dissipative phase transition (DPT). We compute the Hanbury Brown–Twiss (HBT)-type two-particle temporal correlation function $g^2\left(\tau \right)$ which, as a function of time delay $\tau$, exhibits oscillations with frequencies determined by the imaginary part of the Liouvillian gap. As the gap closes near a transition point, the oscillations at that point die down. For parameters slightly away from the transition point, the HBT correlations show oscillations from superbunching to antibunching regimes. We show that the Fourier transform of HBT correlations into the frequency domain provide information about DPT and Liouvillian dynamics. We numerically solve the many-body Lindblad master equation and calculate the Wigner distribution of the system in the steady state to ascertain the DPT. Below a certain drive strength, the Fourier transform shows a two-peak structure, while above that strength it exhibits either a Lorentzian-like single-peak structure or a structure with two dips. The width of the single-peak structure is minimal at the phase-transition point and the peak of this structure always lies at zero frequency. The positions of the two symmetrical peaks in case of a two-peak structure are given by the imaginary parts of the Liouvillian gap while their half width at half maximum is given by the real part of the gap. The positions and widths of the two dips are also related to low-lying eigenvalues of the Liouvillian operator. We discuss quantum statistical properties of the model in terms of the HBT correlation function and its Fourier transform.

We study the temporal expansion of an ultracold Bose gas in two-dimensional square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical [Bose-Einstein condensate (BEC)] part and quantum mechanical fluctuations. After a quench, i.e., after a sudden switch of the lattice nearest-neighbor hopping, the expanding bosonic cloud separates spatially into a fast ballistic forerunner and a slowly expanding central part controlled by self-trapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.

The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.

We determine the transmission of light through a planar atomic array beyond the limit of low light intensity that displays optical bistability in the mean-field regime. We develop a theory describing the intrinsic optical bistability, which is supported purely by resonant dipole-dipole interactions in free space, showing how bistable light amplitudes exhibit both strong cooperative and weak single-atom responses and how they depend on the underlying low light intensity collective excitation eigenmodes. Similarities of the theory with optical bistability in cavities are highlighted, while recurrent light scattering between atoms takes on the role of cavity mirrors. Our numerics and analytic estimates show a sharp variation in the extinction, reflectivity, and group delays of the array, with the incident light completely extinguished up to a critical intensity well beyond the low light intensity limit. Our analysis paves a way for collective nonlinear optics with cooperatively responding dense atomic ensembles.

One of the most elusive problems in quantum mechanics is the transition between classical and quantum physics. This problem can be traced back to Schrödinger's cat thought experiment. A key element that lies at the center of this problem is the lack of a clear understanding and characterization of macroscopic quantum states. Our understanding of macroscopic quantumness relies on states such as the Greenberger-Horne-Zeilinger (GHZ) or the NOON state. Here we take a first-principle approach to this problem. We start from coherence as the key quantity that captures the notion of quantumness and require the quantumness to be collective and macroscopic. To this end, we introduce macroscopic coherence which is the coherence between macroscopically distinct quantum states. We construct a measure that quantifies how global and collective the coherence of the state is. Our work also provides a first-principle way to derive well-established states like the GHZ and the NOON state as the states that maximize our measure. Our approach paves the way towards a better understanding of the quantum-to-classical transition.

We present a detailed study of quantum thermal machines employing quantum systems as working substances. In particular, we study two different types of two-stroke cycles where two collections of identical quantum systems with evenly spaced energy levels are initially prepared at thermal equilibrium by putting them in contact with a cold and a hot thermal bath, respectively. The two cycles differ in the absence or the presence of a mediator system, while, in both cases, nonresonant exchange Hamiltonians are exploited as particle interactions. We show that the efficiencies of these machines depend only on the energy gaps of the systems composing the collections and are equal to the efficiency of “equivalent” Otto cycles. Focusing on the cases of qubits or harmonic oscillators for both models, we maximize the engine power and analyze, in the model without the mediator, the role of the waiting time between subsequent interactions. It turns out that the case with the mediator can bring performance advantages when the interaction times are comparable with the waiting time of the correspondent cycle without the mediator. We find that in both cycles, the power peaks of qubit systems can surpass the Curzon-Ahlborn efficiency. Finally, we compare our cycle without the mediator with previous schemes of the quantum Otto cycle showing that high coupling is not required to achieve the same maximum power.

Point-to-point quantum privacy communication over a standard telecommunication fiber link can be implemented by continuous-variable quantum key distribution (CV QKD). However, as communication networks develop, the two-party CV QKD system may hardly meet the requirements of secret key sharing of multiple users (at least three users). In this paper, we consider a protocol called quantum secret sharing (QSS) which allows a legitimate user, a so-called dealer, to share a secret key with multiple remote users through an insecure quantum channel. These users can correctly recover the dealer's secret key only when they work cooperatively. We carry out QSS with discretely modulated coherent states (DMCSs) because they are easy to prepare and resilient to losses. An asymptotic security proof for the proposed DMCS-based QSS protocol against both eavesdroppers and dishonest users is presented. Numerical simulation based on a linear bosonic channel shows that the maximal transmission distance of the DMCS-based QSS protocol reaches more than 100 km, and it can be further lengthened by exploiting a higher-dimensional discrete modulation strategy. Moreover, the composable security of the DMCS-based QSS protocol is also presented.

We study the possibility of witnessing Gaussian entanglement between two continuous-variable systems with the help of two spatially separated qubits. Its key ingredient is a local lossy state transfer from the original systems onto local qubits. The qubits are initially in a pure product state, therefore by detecting entanglement between the qubits we witness entanglement between the two original systems.

The present paper reports on a merged-beam experiment on mutual neutralization between ${\mathrm{Na}}^{+}$ and ${\mathrm{D}}^{-}$. For this experiment, we have used the DESIREE ion-beams storage-ring facility. The reaction products are detected using a position- and time-sensitive detector, which ideally allows for determination of the population of each individual quantum state in the final atomic systems. Here, the $4s, 3d$, and $4p$ final states in Na are observed and in all cases the D atom is in its ground state $1s {}^{2}S$. The respective branching fractions of the states populated in Na are determined by fitting results from a Monte Carlo simulation of the experiment to the measured data. The center-of-mass collision energy is controlled using a set of biased drift tubes, and the branching fractions are measured for energies between 80 meV and 393 meV. The resulting branching fractions are found to agree qualitatively with the only available theoretical calculations for this particular system, which are based on a multichannel Landau-Zener approach using dynamic couplings determined with a linear combination of atomic orbitals model.

Electron magnetic circular dichroism (EMCD) can detect the magnetic properties of materials at the nanoscale, but its wide applications are limited by stringent specimen orientation and noisy signal outputs. To overcome these challenges, electron vortex beams (EVBs) were most recently proposed to develop chirality-dependent EMCD (CEMCD), yet convincing and reproducible CEMCD has not yet been demonstrated. In electron energy-loss spectroscopy (EELS) experiments of EMCD, electron-atom scattering has played a core role. Here, from a model research on the scattering of EVBs by a single atom in a magnetic field, we show a way of generating chirality-dependent scattering which is of potential application to CEMCD. The mechanism is to break the symmetry of the joint occupation probability amplitudes for two scattering channels with opposite magnetic quantum number differences ($\mathrm{\Delta }{m}_j$), respectively, for two EVBs with opposite topological charges ($l$). Particularly, the Zeeman effect and spin-orbit coupling jointly can lead to this chirality-dependent scattering, signaled as the chirality-dependent differential cross section (DCS) for the EVB. The DCS can be optimized by choosing the magnetic field strength and topological charge for getting the strongest EMCD. Due to angular momentum conservation, $l=\mathrm{\Delta }{m}_j$ is the optimum topological charge, which could be useful for the selective probe of an internal state. We show that using EVB with a narrow width can relax the requirement of precise controlling of the opening angle and improve the spatial resolution. Finally, we show that chirality-dependent scattering strength decreases with increasing of the impact parameter.