We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called “sparse” mean-field spin glasses that have been studied widely on random networks of finite (average or regular) degree, the networks studied here are randomly bond diluted to an overall density $p$, such that the average degree diverges as $\sim pN$ with the system size $N$. Ground state energies are obtained with high accuracy for random instances over a wide range of fixed $p$. Since this is an NP-hard combinatorial problem, we employ the extremal optimization heuristic to that end. We find that the exponent describing the finite-size corrections $\omega$ varies continuously with $p$, a somewhat surprising result, as one would not expect that gradual bond dilution would change the $T=0$ universality class of a statistical model. For $p\to 1$, the familiar result of $\omega (p=1)\approx \frac{2}{3}$ for the SK model is obtained.

We report results on solving a long outstanding problem—whether the two-dimensional spin-$3/2$ antiferromagnetic valence-bond model of Affleck, Kennedy, Lieb, and Tasaki (AKLT) possesses a nonzero gap above its ground state. We exploit a relation between the anticommutator and sum of two projectors and apply it to ground-space projectors on regions of the honeycomb lattice. After analytically reducing the complexity of the resultant problem, we are able to use a standard Lanczos method to establish the existence of a nonzero gap. This approach is also successfully applied to spin-$3/2$ AKLT models on other degree-3 semiregular tilings, namely, the square-octagon, star, and cross lattices, where the complexity is low enough that exact diagonalization can be used instead. In addition, we close the previously open cases of hybrid AKLT models on the singly decorated honeycomb and singly decorated square lattices.

The $S=1$ Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the $S=3/2$ AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental problem of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound $\mathrm{\Delta }>0.006$ on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives an analytical, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion numerically by performing state-of-the-art DMRG calculations on the subsystem.

Population leakage outside the qubit subspace presents a particularly harmful source of error that cannot be handled by standard error correction methods. Using a trapped ${}^{171}{\mathrm{Yb}}^{+}$ ion, we demonstrate an optical pumping scheme to suppress leakage errors in atomic hyperfine qubits. The selection rules and narrow linewidth of a quadrupole transition are used to selectively pump population out of leakage states and back into the qubit subspace. Each pumping cycle reduces the leakage population by a factor of $\sim 3$, allowing for an exponential suppression in the number of cycles. We use interleaved randomized benchmarking on the qubit subspace to show that this pumping procedure has negligible side effects on the qubit subspace, bounding the induced qubit memory error by $\le 2.0(8)\times {10}^{-5}\mathrm{per}$ cycle, and qubit population decay to $\le 1.4(3)\times {10}^{-7}\mathrm{per}$ cycle. These results clear a major obstacle for implementations of quantum error correction and error mitigation protocols.

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian $|e⟩⟨e|({\widehat{a}}^{†}\widehat{b}+\widehat{a}{\widehat{b}}^{†})$ that swaps the quantum states of two motional modes, depending on the ion’s internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

We demonstrate that gravitational waves generated by efficient gauge preheating after axion inflation generically contribute significantly to the effective number of relativistic degrees of freedom $N_{\mathrm{eff}}$. We show that, with existing Planck limits, gravitational waves from preheating already place the strongest constraints on the inflaton’s possible axial coupling to Abelian gauge fields. We demonstrate that gauge preheating can completely reheat the Universe regardless of the inflationary potential. Further, we quantify the variation of the efficiency of gravitational wave production from model to model and show that it is correlated with the tensor-to-scalar ratio. In particular, when combined with constraints on models whose tensor-to-scalar ratios would be detected by next-generation cosmic microwave background experiments, $r\gtrsim {10}^{-3}$, constraints from $N_{\mathrm{eff}}$ will probe or rule out the entire coupling regime for which gauge preheating is efficient.

In an ongoing effort to explore quantum effects on the interior geometry of black holes, we explicitly compute the semiclassical flux components ${⟨T_{uu}⟩}_{\mathrm{ren}}$ and ${⟨T_{vv}⟩}_{\mathrm{ren}}$ ($u$ and $v$ being the standard Eddington coordinates) of the renormalized stress-energy tensor for a minimally coupled massless quantum scalar field, in the vicinity of the inner horizon (IH) of a Reissner-Nordström black hole. These two flux components seem to dominate the effect of backreaction in the IH vicinity, and furthermore, their regularization procedure reveals remarkable simplicity. We consider the Hartle-Hawking and Unruh quantum states, the latter corresponding to an evaporating black hole. In both quantum states, we compute ${⟨T_{uu}⟩}_{\mathrm{ren}}$ and ${⟨T_{vv}⟩}_{\mathrm{ren}}$ in the IH vicinity for a wide range of $Q/M$ values. We find that both ${⟨T_{uu}⟩}_{\mathrm{ren}}$ and ${⟨T_{vv}⟩}_{\mathrm{ren}}$ attain finite asymptotic values at the IH. Depending on $Q/M$, these asymptotic values are found to be either positive or negative (or vanishing in between). Note that having a nonvanishing ${⟨T_{vv}⟩}_{\mathrm{ren}}$ at the IH implies the formation of a curvature singularity on its ingoing section, the Cauchy horizon. Motivated by these findings, we also take initial steps in the exploration of the backreaction effect of these semiclassical fluxes on the near-IH geometry.

We report the first experimental evidence of spontaneous electron emission from a homonuclear dimer anion through direct measurements of ${\text{Ag}}_2^{-}\to {\text{Ag}}_2+e^{-}$ decays on milliseconds and seconds timescales. This observation is very surprising as there is no avoided crossing between adiabatic energy curves to mediate such a process. The process is weak, yet dominates the decay signal after 100 ms when ensembles of internally hot ${\mathrm{Ag}}_2^{-}$ ions are stored in the cryogenic ion-beam storage ring, DESIREE, for 10 s. The electron emission process is associated with an instantaneous, very large reduction of the vibrational energy of the dimer system. This represents a dramatic deviation from a Born-Oppenheimer description of dimer dynamics.

Strong (${10}^{10}\mathrm{V}/\mathrm{m}$) electric fields capable of inducing atomic bond breaking represent a powerful tool for surface chemistry. However, their exact effects are difficult to predict due to a lack of suitable tools to probe their associated atomic-scale mechanisms. Here we introduce a generalized dipole correction for charged repeated-slab models that controls the electric field on both sides of the slab, thereby enabling direct theoretical treatment of field-induced bond-breaking events. As a prototype application, we consider field evaporation from a kinked W surface. We reveal two qualitatively different desorption mechanisms that can be selected by the magnitude of the applied field.

Graphene can develop large magnetic moments in custom-crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nanosystems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulenelike graphene systems and demonstrate that they possess a spin $S=1$ ground state. Scanning tunneling spectroscopy identifies the fingerprint of an underscreened $S=1$ Kondo state on these flakes at low temperatures, signaling the dominant ferromagnetic interactions between two spins. Combined with simulations based on the meanfield Hubbard model, we show that this $S=1$ $\pi$ paramagnetism is robust and can be turned into an $S=1/2$ state by additional H atoms attached to the radical sites. Our results demonstrate that $\pi$ paramagnetism of high-spin graphene flakes can survive on surfaces, opening the door to study the quantum behavior of interacting $\pi$ spins in graphene systems.

Entanglement witness is of great importance in characterizing quantum systems. The imperfections in conventional entanglement witness schemes could lead to the misidentification of a separated state as an entangled state. Measurement-device-independent entanglement witness (MDIEW) has been proposed and demonstrated to resolve the imperfect measurement devices. So far, however, the MDIEW has been restricted to a two-party qubit entangled state. Here, for the first time, we demonstrate MDIEW for multipartite entangled states. We experimentally detect the genuine entanglement and the entanglement structure of a tripartite entangled state based on an eight-photon interferometry. Furthermore, with the verified multipartite entangled state, we demonstrate quantum randomness generation and open-destination quantum key distribution in an measurement-device-independent manner. Our research presents an important step toward building a robust and secure quantum network.

We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator—a recently suggested measure of information scrambling in quantum chaotic systems—and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.

The concept of quantum many-body scars has recently been put forward as a route to describe weak ergodicity breaking and violation of the eigenstate thermalization hypothesis. We propose a simple setup to generate quantum many-body scars in a doubly modulated Bose-Hubbard system which can be readily implemented in cold atomic gases. The dynamics are shown to be governed by kinetic constraints which appear via density-assisted tunneling in a high-frequency expansion. We find the optimal driving parameters for the kinetically constrained hopping which leads to small isolated subspaces of scared eigenstates. The experimental signatures and the transition to fully thermalizing behavior as a function of driving frequency are analyzed.

Ultracompact dark matter (DM) minihalos at masses at and below ${10}^{-12}{M}_{\odot }$ arise in axion DM models where the Peccei-Quinn (PQ) symmetry is broken after inflation. The minihalos arise from density perturbations that are generated from the nontrivial axion self-interactions during and shortly after the collapse of the axion-string and domain-wall network. We perform high-resolution simulations of this scenario starting at the epoch before the PQ phase transition and ending at matter-radiation equality. We characterize the spectrum of primordial perturbations that are generated and comment on implications for efforts to detect axion DM. We also measure the DM density at different simulated masses and argue that the correct DM density is obtained for $m_a=25.2\pm 11.0\mu \mathrm{eV}$.

We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous dimensions. Our approach is to Laurent expand four-loop quark and gluon form factors in the parameter of dimensional regularization. We employ finite field and syzygy techniques to reduce the relevant Feynman integrals to a basis of finite integrals, and subsequently evaluate the basis integrals directly from their standard parametric representations.

The polarizations of promptly produced ${\chi }_{c1}$ and ${\chi }_{c2}$ mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at $\sqrt{s}=8\mathrm{TeV}$. The ${\chi }_c$ states are reconstructed via their radiative decays ${\chi }_c\to J/\psi \gamma$, with the photons being measured through conversions to $e^{+}{e}^{-}$, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the ${\chi }_{c2}$ to ${\chi }_{c1}$ yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the $J/\psi \to {\mu }^{+}{\mu }^{-}$ decay, in three bins of $J/\psi$ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum.

We develop a broadly applicable approach that drastically increases the ability to predict the properties of complex atoms accurately. We apply it to the case of ${\mathrm{Ir}}^{17+}$, which is of particular interest for the development of novel atomic clocks with a high sensitivity to the variation of the fine-structure constant and to dark matter searches. In general, clock transitions are weak and very difficult to identify without accurate theoretical predictions. In the case of ${\mathrm{Ir}}^{17+}$, even stronger electric-dipole ($E1$) transitions have eluded observation despite years of effort, raising the possibility that the theoretical predictions are grossly wrong. In this work, we provide accurate predictions of the transition wavelengths and $E1$ transition rates for ${\mathrm{Ir}}^{17+}$. Our results explain the lack of observations of the $E1$ transitions and provide a pathway toward the detection of clock transitions. The computational advances we demonstrate in this work are widely applicable to most elements in the periodic table and will allow us to solve numerous problems in atomic physics, astrophysics, and plasma physics.

A large ensemble of $\sim {10}^9$ ${\mathrm{H}}_2$ ($v=7$, $j=0$) molecules is prepared in the collision-free environment of a supersonic beam by transferring nearly the entire ${\mathrm{H}}_2$ ($v=0$, $j=0$) ground-state population, where $v$ and $j$ are the vibrational and rotational quantum numbers, respectively. This is accomplished by controlling the crossing of the optically dressed adiabatic states using a pair of phase coherent laser pulses. The preparation of highly vibrationally excited ${\mathrm{H}}_2$ molecules opens new opportunities to test fundamental physical principles using two loosely bound yet entangled H atoms.