Interference between two waves is a well-known concept in physics, and its generalization to more than two waves is straightforward. The order of interference is defined as the number of paths that interfere in a manner that cannot be reduced to patterns of a lower order. In practice, second-order interference means that in, say, a triple-slit experiment, the interference pattern when all three slits are open can be predicted from the interference patterns between all possible pairs of slits. Quantum mechanics is often said to only exhibit second-order interference. However, this is only true under specific assumptions, typically single particles undergoing linear evolution. Here we experimentally show that nonlinear evolution can in fact lead to higher-order interference. The higher-order interference in our experiment can be understood using a simple classical or quantum description, namely optical coherent states interacting in a nonlinear medium. Our work shows that nonlinear evolution could open a loophole for experiments attempting to verify Born's rule by ruling out higher-order interference.

This paper is aimed at investigating the feasibility of generating quantum conditional entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We consider the squeezing of the states of the mechanical common and the differential motions of the mirrors by the action of measuring the common and the differential output light beams in the Fabry-Pérot-Michelson interferometer. We carefully derive a covariance matrix for the mechanical mirrors in a steady state, employing the Kalman filtering problem with dissipative cavities. We demonstrate that Gaussian entanglement between the mechanical mirrors is generated when the states of the mechanical common and differential modes of the mirrors are squeezed with high purity in an asymmetric manner. Our results also show that quantum entanglement between 7-mg mirrors is achievable in the short term.

We develop finite-dimensional versions of the quantum error-correcting codes proposed by Albert, Covey, and Preskill (ACP) for continuous-variable quantum computation on configuration spaces with non-Abelian symmetry groups. Our codes can be realized by a charged particle in a Landau level on a spherical geometry, in contrast to the planar Landau level realization of the qudit codes of Gottesman, Kitaev, and Preskill (GKP), or more generally by spin coherent states. Our quantum error-correction scheme is inherently approximate, and the encoded states may be easier to prepare than those of GKP or ACP.

Optical switches and rerouting networks are considered essential in optical quantum computers where they are used for injection and dejection of the necessary quantum states into an optical quantum computer. Practical optical switches and rerouting networks are, however, experimentally challenging as they must have extremely low loss, small switching time, high repetition rate, and minimum optical nonlinearity, requirements that are difficult to achieve simultaneously. In this paper, we present an optical quantum computation platform that does not require such optical switches. Our method is based on continuous-variable measurement-based quantum computation where, instead of the typical cluster states, we modify the structure of the quantum entanglement, so that the quantum teleportation protocol can be employed instead of optical switching and rerouting. The quantum entanglement structure in our architecture has additional modes that allow quantum states to be teleported in or out of the computation along the cluster state, a task that normally requires optical switches. We also outline how to combine our platform with Gottesman-Kitaev-Preskill encoding, the currently most promising encoding for a continuous-variable system.

Backflow, or retropropagation, is a counterintuitive phenomenon in which for a forward-propagating wave the energy locally propagates backward. In this study the energy backflow is examined in connection with relatively simple causal unidirectional finite-energy solutions of the wave equation which are derived from a factorization of the so-called basic splash mode. Specific results are given for the energy backflow arising in known azimuthally symmetric unidirectional wave packets, as well as in some azimuthally asymmetric extensions. Using the Bateman-Whittaker technique, a finite-energy unidirectional null localized wave has been constructed that is devoid of energy backflow and has some of the topological properties of the basic hopfion.

Quantum steering is an asymmetric correlation which occupies a place between entanglement and Bell nonlocality. In the paradigmatic scenario involving the protagonists Alice and Bob, the entangled state shared between them is said to be steerable from Alice to Bob if the steering assemblage on Bob's side does not admit a local hidden state (LHS) description. Quantum conditional entropies, on the other hand, provide for another characterization of quantum correlations. Contrary to our common intuition, conditional entropies for some entangled states can be negative, marking a significant departure from the classical realm. Quantum steering and quantum nonlocality, in general, share an intricate relation with quantum conditional entropies. In the present contribution, we investigate this relationship. For a significant class, namely the two-qubit Weyl states, we show that negativity of conditional Rényi 2-entropy and conditional Tsallis 2-entropy is a necessary and sufficient condition for the violation of a suitably chosen three settings steering inequality. With respect to the same inequality we find an upper bound for the conditional Rényi 2-entropy, such that the general two-qubit state is steerable. Moving from a particular steering inequality to local hidden-state descriptions, we show that some two-qubit Weyl states which admit a LHS model possess nonnegative conditional Rényi 2-entropy. However, the same does not hold true for some non-Weyl states. Our study further investigates the relation between nonnegativity of conditional entropy and LHS models in two-qudits for the isotropic and Werner states. There we find that, whenever these states admit a LHS model, they possess a nonnegative conditional Rényi 2-entropy. We then observe that the same holds true for a noisy variant of the two-qudit Werner state.

The problem of the availability of trajectories for the Feynman path integral is considered. Forbidden trajectories for single-particle integrals are featured in the case of quantum tunneling across barriers. In the case of multiparticle systems of indistinguishable identical particles, some limits for the availability of cyclotron braid trajectories are demonstrated, which leads to the explanation of statistics and correlation in quantum Hall systems of interacting 2D electrons. The homotopy-type restrictions for trajectories close to general-relativity singularities are discussed with indication of quantum properties of black holes manifesting themselves at quasar luminosity or at neutron star merger collapses. The related supplementation to conventional models of accretion disk luminosity in the close vicinity of the event horizon of a supermassive black hole is proposed and compared with observations.

We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between the instantaneous eigenstates of the Lewis-Riesenfeld invariant. Therefore, different driving protocols associated with corresponding Lewis-Riesenfeld invariants result in different open system dynamics and symmetries. In particular, we show that since the instantaneous steady state of the driven double two-level system is one of eigenstates of the Lewis-Riesenfeld invariant at ultralow reservoir temperature, the inverse engineering method based on the Lewis-Riesenfeld invariants has a good performance in rapidly preparing the quantum state of open quantum systems. As an example, a perfect entangled state is generated by means of the inverse engineering method.

Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize the explicit counting of even- and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction.

State-of-the-art experiments using Rydberg atoms can now operate with large numbers of trapped particles with tunable geometry and long coherence time. We propose a way to utilize this in a hybrid setup involving neutral ground-state atoms to efficiently simulate condensed-matter models featuring electron-phonon coupling. Such implementation should allow for controlling the coupling strength and range as well as the band structure of both the phonons and atoms, paving the way towards studying both static and dynamic properties of extended Hubbard-Holstein models.

The polyatomic molecules YbOH and ${\mathrm{YbOCH}}_3$ have been recognized as being of potential value for spectroscopic experiments that explore charge-parity and time-reversal symmetry violation effects. These measurements require very high precision, which, in turn, will necessitate that the molecules be manipulated at ultracold temperatures. Both YbOH and ${\mathrm{YbOCH}}_3$ have electronic transitions that appear suitable for laser cooling ($\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\text{−}\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$ and $\tilde{A}{}^2{E}_{1/2}\text{−}\tilde{X}{}^2{A}_1$, respectively) but the currently available spectroscopic data are not sufficient to determine the extent to which population leaks may compromise the optical cooling processes. A further complication is that the quantum states of interest for these measurements will need to be selectively populated. The $\tilde{A}\text{–}\tilde{X}$ band systems of both YbOH and ${\mathrm{YbOCH}}_3$ show evidence of vibronic perturbations, such that there are unassigned vibronic features at energies that are just above the origin bands. In the present study we have recorded spectra for the $\tilde{A}$ ${}^2{\mathrm{\Pi }}_{1/2}\text{−}\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$ transition of jet-cooled YbOD to facilitate the vibronic assignments. In addition, spectra for the $\tilde{B}{}^2{\mathrm{\Sigma }}^{+}\text{−}\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$ transition of YbOH were recorded, establishing the origin band at 20 473.8 $\mathrm{c}{\mathrm{m}}^{-1}$. Previously, the reaction of Yb with ${\mathrm{CH}}_3\mathrm{OH}$ has been used to generate gas-phase ${\mathrm{YbOCH}}_3$. As this reaction also yields YbOH, there have been complications in spectroscopic studies of ${\mathrm{YbOCH}}_3$ due to overlap of the $\tilde{A}\text{–}\tilde{X}$ band systems. To identify specific regions of overlap, resonantly enhanced two-photon ionization spectra were recorded using mass-resolved detection of the $\mathrm{YbO}{\mathrm{H}}^{+}$ and ${\mathrm{YbOCH}}_3^{+}$ ions. These data confirmed the overlap of vibronic bands near 17 640 and 17 680 $\mathrm{c}{\mathrm{m}}^{-1}$. Two-photon ionization spectroscopy also provided accurate ionization energies (IE), $\mathrm{IE}\left(\mathrm{YbOH}\right)=45788\left(10\right)$ and $\mathrm{IE}\left({\mathrm{YbOCH}}_3\right)=45283\left(10\right)\mathrm{c}{\mathrm{m}}^{-1}$. The IE for YbOH is relevant to problems encountered in previous attempts to determine the bond-dissociation energy of $\mathrm{YbO}{\mathrm{H}}^{+}$.

A full density-matrix simulation is performed for optical deflection of a barium monofluoride (BaF) beam. Pairs of counterpropagating laser pulses are used for absorption followed by stimulated emission. The scheme produces a force which is nearly an order of magnitude larger than that obtainable using continuous-wave laser deflection, and yields a force-to-spontaneous-decay ratio which is more than an order of magnitude larger. The large reduction in spontaneous decay is key to optical deflection of molecules, where branching ratios to other vibrational states do not allow for cycling transitions. This paper is part of an effort by the ${\mathrm{EDM}}^3$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Deflection of BaF molecules will separate them from the other ablation products coming from a buffer-gas-cooled ablation source, before embedding them into the argon solid. Our simulations show that sufficiently large deflections for this separation are feasible.

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from $s$-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\pi$ Dirac points into a single quadratic touching point with flux $2\pi$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard $s$-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.

In the present work we consider models of quantum droplets within a weakly interacting mass-balanced binary Bose-Bose mixture in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations, and dynamics in one-, two-, and three-dimensional settings. In the absence of an explicit solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed systematically and the unstable states, as well as the dynamics past the existence of stable states, are monitored. The connection of the resulting states with dark solitonic patterns in one dimension, vortical states in two dimensions, and vortex rings in three dimensions is accordingly elucidated.

We investigate the relation between indistinguishability and quantum entanglement in Hong-Ou-Mandel interference experiments theoretically and relate these quantum mechanical principles to the theorem of entanglement monogamy. Employing Glauber's theory of quantum coherence we compute the detection statistics in HOM interference of frequency-entangled photons and find an additional term in the coincidence detection probability, which is related to the spectral indistinguishability of the considered photons that arises from finite-bandwidth effects and therefore is relevant in the limit of low-frequency separations or large single-photon bandwidths. Compared to previous work in that context we treat all photonic degrees of freedom on equal footing.

We propose a scheme for individual addressing of trapped ion qubits, selecting them via their motional frequency. We show that geometric phase gates can perform single-qubit rotations using the coherent interference of spin-independent and (global) spin-dependent forces. The spin-independent forces, which can be generated via localized electric fields, increase the gate speed while reducing its sensitivity to motional decoherence, which we show analytically and numerically. While the scheme applies to most trapped ion experimental setups, we numerically simulate a specific laser-free implementation, showing cross-talk errors below ${10}^{-6}$ for reasonable parameters.

High-order harmonic spectroscopy (HHS), as an emerging technique, provides a way to detect molecular structures with ångström spatial resolution and ultrafast electron dynamics in molecules on an attosecond timescale. However, the implementation of HHS still encounters great difficulties due to the coherent average of single-molecule emissions from different alignment angles. Here, we provide a machine learning algorithm based on the iterative projection method to fully retrieve the complex single-molecule dipole of a linear molecule from the harmonic spectra measured at different delays and polarization angles between the alignment and driving pulses. We demonstrated our algorithm both theoretically and experimentally using the ${\mathrm{N}}_2$ molecule. The results show that our algorithm can accurately retrieve the complex single-molecule dipole from the harmonic spectra with good noise stability and robustness. From the retrieved single-molecule dipole, the contributions of multiple orbitals in high harmonic generation are identified even with a low degree of alignment.