We revisit a continuous-variable version of the Clauser-Horne-Shimony-Holt inequality with sign binning, first proposed by Bell [J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 1st ed. (Cambridge University, New York, 1987); Ann. N.Y. Acad. Sci. 480, 263 (1986)]. To explore Bell nonlocality, we use a biphoton effective wave function resulting from a type-I spontaneous parametric down-conversion process. After reviewing the approximations involved in the production and time evolution of such biphotons, we judiciously choose a series expansion for the sinc function part of the biphoton wave function in order to integrate the Wigner function. We conclude that we can qualitatively achieve Bell nonlocality within a regime in which the twin photons are described.

Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a mapping of a quantum circuit to an adiabatic evolution, and then showing that the minimum spectral gap of the adiabatic Hamiltonian is at least inverse polynomial in the number of computational steps $L$. In this paper we provide two simplified proofs that the gap is inverse polynomial. Both proofs result in the same lower bound for the minimum gap, which for $L\gg 1$ is ${min}_s{\mathrm{\Delta }}_0\gtrsim {\pi }^2/\left[8{(L+1)}^2\right]$, an improvement over previous bounds. Our first method is a direct approach based on an eigenstate ansatz, while the second uses Weyl's theorem to leverage known exact results into a bound for the gap. Our results suggest that it may be possible to use these methods to find bounds for spectral gaps of Hamiltonians in other scenarios.

Secret sharing allows three or more parties to share secret information which can only be decrypted through collaboration. It complements quantum key distribution as a valuable resource for securely distributing information. Here we take advantage of hybrid spin and orbital angular momentum states to access a high-dimensional encoding space, demonstrating a protocol that is easily scalable in both dimension and participants. To illustrate the versatility of our approach, we first demonstrate the protocol in two dimensions, extending the number of participants to ten, and then demonstrate the protocol in three dimensions with three participants. We reconstruct secrets depicted as images with a fidelity of up to 0.979. Moreover, our scheme exploits the use of conventional linear optics to emulate the quantum gates needed for transitions between basis modes on a high-dimensional Hilbert space, allowing us to exceed the 1 bit per photon limit of two-dimensional protocols. Our work offers a practical approach for sharing information across multiple parties, a crucial element of any quantum network.

We present an algorithm to design networks that feature pretty good state transfer (PGST), which is of interest for high-fidelity transfer of information in quantum computing. Realizations of PGST networks have so far mostly relied either on very special network geometries or imposed conditions such as transcendental on-site potentials. However, it was recently shown that PGST generally arises when a network's eigenvectors and the factors $P_{\pm }$ of its characteristic polynomial $P$ fulfill certain conditions, where $P_{\pm }$ correspond to eigenvectors which have $\pm 1$ parity on the input and target sites. We combine this result with the so-called isospectral reduction of a network to obtain $P_{\pm }$ from a dimensionally reduced form of the Hamiltonian. Equipped with the knowledge of the factors $P_{\pm }$, we show how a variety of setups can be equipped with PGST by proper tuning of $P_{\pm }$. Having demonstrated a method of designing networks featuring pretty good state transfer of single site excitations, we further show how the obtained networks can be manipulated such that they allow for robust storage of qubits. We hereby rely on the concept of compact localized states, which are eigenstates of a Hamiltonian localized on a small subdomain, and whose amplitudes completely vanish outside of this domain. Such states are natural candidates for the storage of quantum information, and we show how certain Hamiltonians featuring pretty good state transfer of single site excitation can be equipped with compact localized states such that their transfer is made possible.

We show that existing calculations of the interaction between nuclear Schiff moments and electrons in molecules use an inaccurate operator which gives rise to significant errors. By comparing the matrix elements of the accurate and imprecise Schiff moment operators, we calculated the correction factor as a function of the nuclear charge $Z$ and presented corrected results for the time- and parity-violating interaction of the nuclear spin with the symmetry axis in the TlF, RaO, PbO, TlCN, ThO, and AcF molecules and in the ferroelectric solid ${\mathrm{PbTiO}}_3$. We also provide an updated limit on the Schiff moment of the ${}^{205}\mathrm{Tl}$ nucleus, $S\left({}^{205}\mathrm{Tl}\right)=\left(3.6\pm 6.1\right)\times {10}^{-11}e{\mathrm{fm}}^3$, and limits on the the CP-violating $\pi$-meson-nucleon interaction constants, $0.13g{\overline{g}}_0-0.004g{\overline{g}}_1-0.27g{\overline{g}}_2=\left(3.6\pm 6.1\right)\times {10}^{-11}$; the QCD parameter, $\overline{\theta }=\left(1.3\pm 2.3\right)\times {10}^{-9}$; the quark chromoelectric dipole moments (EDMs), $12{\overline{d}}_d+9{\overline{d}}_u=\left(4.2\pm 7.1\right)\times {10}^{-23}\mathrm{cm}$; and proton EDM $d_p=\left(0.9\pm 1.5\right)\times {10}^{-23}e\mathrm{cm}$.

We present results on the effect of short-range, attractive interactions on the properties of balanced tw-dimensional Fermi gases in the nonsuperfluid (normal) phase. Our approach combines the renormalization group (RG) with perturbation theory, yielding observables such as the equation of state and compressibility. We find good agreement with recent experiments that measured the equation of state in trapped gases in the balanced regime, showing that these results are consistent with logarithmic corrections in the equation of state.

A Bose gas under the effect of Raman spin-orbit coupling (SOC) is analyzed using the discrete spin T-moves diffusion Monte Carlo method. Upon computing the energy as well as the static structure factor and the superfluid fraction of the system, the emergence of an energetically favorable supersolid stripe state is observed, which is in agreement with recent observations. A significant enhancement of the stability of the stripe phase with respect to the mean-field prediction is observed when the strength of the interatomic correlations is increased. We also quantify and characterize the degree of superfluidity of the stripes and show that this quantity is mostly determined by the ratio between the Raman coupling and the square of the momentum difference between the pair of SOC-inducing laser beams.

By exploiting the nonlinear nature of the Jaynes Cumming interaction, one can get photon population trapping in cavity-QED arrays. However, the unavoidable dissipative effects in a realistic system would destroy the self-trapped state by continuous photon leakage, and the self-trapping remains only as a temporary effect. To circumvent this issue, we aim to achieve an indefinitely long-lived self-trapped steady state rather than a localization with limited lifetime. We show that a careful engineering of drive, dissipation, and Hamiltonian results in achieving indefinitely sustained self-trapping. We show that the intricate interplay between drive, dissipation, and light-matter interaction results in requiring an optimal window of drive strengths in order to achieve such nontrivial steady states. We treat the two-cavity and four-cavity cases by using exact open quantum many-body calculations. Additionally, in the semiclassical limit we scale up the system to a long one-dimensional chain and demonstrate localized and delocalized steady-states in a driven-dissipative cavity-QED lattice. Although our analysis is performed by keeping cavity-QED systems in mind, our work is applicable to other driven-dissipative systems where nonlinearity plays a pivotal role.

We demonstrate coherent control of optomechanically induced transparency and Fano resonances in a four-mirror macroscopic optomechanical cavity, with two movable mirrors, each driven by an external mechanical pump. The variable control of the amplitude and phase of the coherent mechanical pumps provides a means of tuning the shape and nature of the Fano profiles. Further, our scheme shows the occurrence of tunable optomechanical features, even at very low mechanical driving field amplitudes, in macroscopic optomechanical cavities.

We predict and theoretically study in detail the ratchet effect for the spectral magnetization of periodic discrete-time quantum walks (DTQWs)—a repetition of a sequence of $m$ different DTQWs. These generalized DTQWs are achieved by varying the corresponding coin operator parameters periodically with discrete time. We consider periods $m=1$, 2, and 3. The dynamics of $m$-periodic DTQWs is characterized by a two-band dispersion relation ${\omega }_{\pm }^{\left(m\right)}\left(k\right)$, where $k$ is the wave vector. We identify a generalized parity symmetry of $m$-periodic DTQWs. The symmetry can be broken for $m=2$ and 3 by proper choices of the coin operator parameters. The obtained symmetry breaking results in a ratchet effect, i.e., the appearance of a nonzero spectral magnetization $M_s\left(\omega \right)$. This ratchet effect can be observed in the framework of continuous quantum measurements of a time-dependent correlation function of periodic DTQWs.

We investigate in detail the properties of the stationary quantum steering of two mechanical modes, where the two mechanical modes interact with two coupling cavity modes, and two four-tone driving lasers are used to pump the two cavity modes. By controlling the pumping lasers, the two cavity modes can act as two engineered reservoirs to cool the two mechanical modes to a squeezed state. When the damping rates of the two mechanical modes are different, numerical simulation results show that there are parameter regions where the state of the two mechanical modes only has one-way quantum steering, which is the most prominent feature of quantum steering from quantum entanglement.

We demonstrate the emergence of selective $k$-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between the rotating and counterrotating terms produces multiphoton interactions whose resonance frequencies depend, due to the Stark term, on the state of the bosonic mode. We develop an analytical framework to explain these $k$-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with a Stark term by using the internal and vibrational degrees of freedom of a trapped ion, and demonstrate its performance with numerical simulations considering realistic physical parameters.

By applying recently introduced, phase-of-the-phase spectroscopy [S. Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015)], we analyze the phase-dependent photoelectron signal from Xe ionized in intense, parallel, two-color (1800 nm and 900 nm) laser fields. With such a field configuration, tuning of the relative phase between the ionizing, $\omega$, and the perturbative, $2\omega$, field results in a modulation of the ionization rate, as well as modifications of the trajectories of electrons propagating in the laser-dressed continuum. Based on a semiclassical model, we confirm that phase dependencies, due to the perturbation of the ionization rate, encode the ionization times of the electrons. Here, using the fork structure, a well-known feature originating from well-defined dynamics allows us to distinguish between electrons ionized within distinct time windows. However, due to the simultaneous perturbation of the electron trajectories, the assignment of the ionization times can be distorted by up to 80 as, i.e., a ${10}^{\circ }$ phase shift, which is independent of the degree of the perturbation.

We demonstrate the emission of correlated atom jets from a matter-wave soliton in a quasi-one-dimensional optical trap. We characterize the dependence of jet properties on the frequency, amplitude, and length of the modulation, and qualitatively reproduce the trends in the mean-field picture with a one-dimensional time-dependent Gross-Pitaevskii equation simulation. High-order jets are observed for sufficiently long pulses. A double-pulse modulation sequence produces consecutive jets, and a multipulse sequence may lead to irregular three-dimensional jets at a finite angle to the direction of the channel. In the limit of vanishing high-order jets beyond-mean-field number correlations of jet pairs are demonstrated, implying possible number squeezing.

We demonstrate a previously unknown two-photon effect in a discrete-time quantum walk. Two identical bosons with no mutual interactions nonetheless can remain clustered together as they walk on a lattice of directionally reversible optical four-ports acting as Grover coins; both photons move in the same direction at each step due to a two-photon quantum interference phenomenon reminiscent of the Hong-Ou-Mandel effect. The clustered two-photon amplitude splits into two localized parts, one oscillating near the initial point and the other moving ballistically without spatial spread, in solitonlike fashion. But the two photons are always clustered in the same part of the superposition, leading to potential applications for transport of entanglement and opportunities for novel two-photon interferometry experiments.

Current metrological bounds typically assume full control over all particles that are involved in the protocol. Relaxing this assumption, we study metrological performance when only limited control is available. As an example, we measure a static magnetic field when a fully controlled quantum sensor is supplemented by particles over which only global control is possible. We show that even for a noisy quantum sensor, a protocol that maps the magnetic field to a precession frequency can achieve transient super-Heisenberg scaling in measurement time and Heisenberg scaling in the particle number. This leads to an estimation uncertainty that approaches that achievable under full control to within a factor independent of the particle number for a given total time. Applications to hybrid sensing devices and the crucial role of the quantum character of the sensor are discussed.

We demonstrate the transition from local to global noise in a two-qubit all-optical quantum simulator subject to classical random fluctuations. Qubits are encoded in the polarization degree of freedom of two entangled photons generated by parametric down-conversion (PDC) while the environment is implemented by using their spatial degrees of freedom. The ability to manipulate with high accuracy the number of correlated pixels of a spatial-light-modulator and the PDC spectral width allows us to control the transition from a scenario where the qubits are embedded in local environments to the situation where they are subject to the same global noise. We witness the transition by monitoring the decoherence of the two-qubit state.

We study analytically and numerically the properties of phonon modes in an ion quantum computer. The ion chain is placed in a harmonic trap with an additional periodic potential of which dimensionless amplitude $K$ determines three main phases available for quantum computations: at zero $K$ we have the case of Cirac-Zoller quantum computer, below a certain critical amplitude $K<K_c$ the ions are in the Kolmogorov-Arnold-Moser (KAM) phase, with delocalized phonon modes and free chain sliding, and above the critical amplitude $K>K_c$ ions are in the pinned Aubry phase with a finite frequency gap protecting quantum gates from temperature and other external fluctuations. For the Aubry phase, in contrast to the Cirac-Zoller and KAM phases, the phonon gap remains independent of the number of ions placed in the trap keeping a fixed ion density around the trap center. We show that in the Aubry phase the phonon modes are much better localized compared to the Cirac-Zoller and KAM cases. Thus in the Aubry phase the recoil pulses lead to local oscillations of ions, while in the other two phases they spread rapidly over the whole ion chains, making them rather sensible to external fluctuations. We argue that the properties of localized phonon modes and phonon gap in the Aubry phase provide advantages for the ion quantum computations in this phase with a large number of ions.

We assess whether a confined Wigner molecule constituted by $2N$ fermions behaves as $N$ bosons or $2N$ fermions. Following the work by Law [Phys. Rev. A 71, 034306 (2005)] and Chudzicki et al. [Phys. Rev. Lett. 104, 070402 (2010)] we discuss the physical meaning and the reason why a large amount of entanglement is needed in order to ensure a bosonic composite behavior. By applying a composite boson ansatz, we found that a Wigner molecule confined in a two-dimensional trap presents a bosonic behavior induced by symmetry. The two-particle Wigner molecule ground state required by the composite boson ansatz was obtained within the harmonic approximation in the strong interacting regime. Our approach allows us to address few-particle states (widely studied within a variety of theoretical and numerical techniques) as well as a large number of particles (difficult to address due to computational costs). For a large number of particles, we found strong fermionic correlations exposed by the suppression of particle fluctuations. For a small number of particles, we show that the wave function calculated within the composite boson ansatz captures the Friedel-Wigner transition. The latter is shown in a regime in which strong correlations due to the Pauli exclusion principle arise; therefore, we conclude that the coboson ansatz reproduces the many-particle physics of a confined Wigner molecule, even in the presence of strong deviations of the ideal bosonic behavior due to fermionic correlations.