We offer a consistent dynamical formulation of stationary scattering in two and three dimensions (2D and 3D) that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional function space which we can represent as a $2\times 2$ matrix with operator entries. This operator encodes the information about the scattering properties of the potential and enjoys an analog of the composition property of its one-dimensional ancestor. Our results improve an earlier attempt in this direction [Phys. Rev. A 93, 042707 (2016)] by elucidating the role of the evanescent waves. We show that a proper formulation of this approach requires the introduction of a pair of intertwined transfer matrices, each related to the time-evolution operator for an effective nonunitary quantum system. We study the application of our findings in the treatment of the scattering problem for $\delta$-function potentials in 2D and 3D and clarify its implicit regularization property which circumvents the singular terms appearing in the standard treatments of these potentials. We also discuss the utility of our approach in characterizing invisible (scattering-free) potentials and potentials for which the first Born approximation provides the exact expression for the scattering amplitude.

We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability tradeoff via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM superconducting transmon processor. A detailed analysis of the results is provided. Despite finding good agreement with theory at a coarse level, we also identify small but persistent systematic deviations preventing the observation of full particlelike and wavelike statistics. We understand them by carefully modeling two-qubit gates, showing that even small coherent errors in their implementation preclude the observation of Bohr's strong formulation of complementarity.

Inspired by the definition of the non-Gaussian two-parametric continuous-variable analog of an isotropic state introduced by Mišta et al. [Phys. Rev. A 65, 062315 (2002)], we propose to take the Gaussian part of this state as an independent state by itself, which yields a simple, but with respect to the correlation structure interesting, example of a two-mode Gaussian analog of an isotropic state. Unlike conventional isotropic states which are defined as a convex combination of a thermal and an entangled density operator, the Gaussian version studied here is defined by a convex combination of the corresponding covariance matrices and can be understood as an entangled pure state with additional Gaussian noise controlled by a mixing probability. Using various entanglement criteria and measures, we study the nonclassical correlations contained in this state. Unlike the previously studied non-Gaussian two-parametric isotropic state, the Gaussian state considered here features a finite threshold in the parameter space where entanglement sets in. In particular, it turns out that it exhibits an analogous phenomenology as the finite-dimensional two-qubit isotropic state.

The optimal success probability of a communication game sets fundamental limitations on an operational theory. The quantum advantage of a parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [R. W. Spekkens et al., Phys. Rev. Lett. 102, 010401 (2009)]. The optimal quantum advantage in the $N$-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of the fine-grained uncertainty relation to the success probability of a PORAC game played with the quantum resource. Subsequently, we find the optimal success probability for a 2-dit PORAC game using mutually unbiased bases for the decoding strategy. Finally, we also derive an upper bound on the quantum advantage for the $N$-dit PORAC game.

Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement at a beam splitter as a notion of quantumness. A similar, yet distinct, notion of quantumness is the amount of entanglement generated by two-mode squeezers (i.e., four-wave mixers). We show that squeezed-vacuum states, paradoxically, both minimize and maximize these notions of quantumness, with the crucial resolution of the paradox hinging upon the relative phases between the input states and the devices. Our notion of quantumness is intrinsically related to eigenvalue equations involving creation and annihilation operators, governed by a set of inequalities that leads to generalized cat and squeezed-vacuum states.

Single- and double-electron-capture processes occurring in the system of hydrogen ions colliding with alkaline-earth atoms, ${\mathrm{H}}^{+}+\mathrm{Mg}$, are investigated in a broad energy domain ranging from 0.25 to 180 keV. Total and state-selective cross sections are calculated using a two-active-electron semiclassical asymptotic-state close-coupling approach. Our results show the best overall agreement with experimental data, and possible reasons for observed discrepancies are discussed. Comparison of our cross sections with previous theoretical results further demonstrates the importance of electronic correlations between the magnesium valence electrons and the strong couplings between various important channels. Furthermore, our investigations suggest that the oscillatory structures observed in the double-electron-capture cross sections stem from complex coherence effects between double-electron capture, electron transfer to excited states, and transfer-excitation processes.

We study the dynamics of a comagnetometer based on an alkali-metal—noble-gas hybrid tri-spin system by numerically solving coupled Bloch equations. A thorough analysis of the response dynamics is carried out in the standard experimental regime where the spin system can be mapped to a damped harmonic oscillator. The results show that a linear increasing response of the comagnetometer signal is found when the noble-gas nuclear spin magnetization and the alkali-metal spin lifetime parameters satisfy an overdamping condition. We find that an upper limit for the signal amplitude of the comagnetometer is imposed by the inherent dynamics of the hybrid tri-spin system. The results agree with currently available experimental data and provide useful guiding for future experiments.

We investigate the thermal instability of a Bose-Einstein condensate stirred by a rotating barrier in a ring-shaped trap. One would expect the critical angular speed to decrease with increasing temperature due to depletion of the condensate. However, we show that the critical velocity remains approximately constant within a considerable range of temperatures, contrary to expectation, and the thermal cloud has a stabilizing effect.

Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincaré invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference frames in Minkowski spacetime. It is a basic condition imposed on quantum theory in order to construct quantum field theories, hence, it plays a fundamental role in the standard model of particle physics too. As is well known, Minkowski spacetime follows from clear physical principles, like the relativity principle and the invariance of the speed of light. Here we reproduce such a derivation but leave the number of spatial dimensions $n$ as a free variable. Then, assuming that spacetime is Minkowski in $1+n$ dimensions and within the framework of general probabilistic theories, we reconstruct the qubit Bloch ball and finite dimensional quantum theory, and obtain that the number of spatial dimensions must be $n=3$, from Poincaré invariance and other physical postulates. Our results suggest a fundamental physical connection between spacetime and quantum theory.

The wave function is the cornerstone of quantum mechanics, although it is still open to different interpretations. It has been shown that the amplitude and the phase of a wave function are manifested in the imaginary and real parts of the momentum weak value, respectively. Based on this, we develop a weak measurement scheme to reconstruct the wave function through measuring the momentum weak value. A proof-of-principle experiment is made to confirm the feasibility of our measurement scheme, in which the polarization states and the momentum of light are coupled. We believe the experimental protocol has the potential to be applied in diverse fields such as wave-front sensing, edge detection, and optical communication, and measurement of the momentum weak value may offer valuable insight to better understand quantum mechanics.

We study the performance of quantum annealing for two sets of problems, namely, 2-satisfiability (2-SAT) problems represented by Ising-type Hamiltonians and nonstoquastic problems which are obtained by adding extra couplings to the 2-SAT problem Hamiltonians. In addition, we add to the transverse Ising-type Hamiltonian used for quantum annealing a third term, the trigger Hamiltonian with ferromagnetic or antiferromagnetic couplings, which vanishes at the beginning and end of the annealing process. We also analyze some problem instances using the energy spectrum, average energy or overlap of the state during the evolution with the instantaneous low-lying eigenstates of the Hamiltonian, and identify some nonadiabatic mechanisms which can enhance the performance of quantum annealing.

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. We introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

Implementing two-qubit gates via strong coupling between quantum-dot qubits and a superconducting microwave cavity requires achieving coupling rates that are much faster than decoherence rates. Typically, this involves tuning the qubit either to a sweet spot, where it is relatively insensitive to charge noise, or to a point where it is resonant with the microwave cavity. Unfortunately, such operating points seldom coincide. Here we theoretically investigate protocols, based on transverse or longitudinal sideband driving, for implementing two-qubit gates between quantum-dot hybrid qubits, mediated by a microwave cavity. The rich physics in these qubits gives rise to two types of sweet spots, which can occur at operating points with strong charge dipole moments. Such strong interactions provide new opportunities for off-resonant gating, thereby removing one of the main obstacles for long-distance two-qubit gates. We find that the transverse driving scheme yields faster gates, while longitudinal driving yields gates that are more resilient to photon decay. Our results suggest that the numerous tuning knobs of quantum-dot hybrid qubits make them good candidates for strong coupling. In particular, we show that off-resonant red-sideband-mediated two-qubit gates can exhibit fidelities greater than $95\%$ for realistic operating parameters, and we describe improvements that could potentially yield gate fidelities greater than $99\%$.

The frequencies of the analytic normal modes for $N$ identical particles are studied as a function of system parameters from the weakly interacting BCS regime to the strongly interacting unitary regime. The normal modes were obtained previously from a first-order $L=0$ group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction for confined identical particles. In a precursor to this study, the collective behavior of these normal modes was investigated as a function of $N$ from few-body systems to many-body systems analyzing the contribution of individual particles to the collective macroscopic motions. A specific case, the Hamiltonian for Fermi gases in the unitary regime, was studied in more detail. This regime is known to support collective behavior in the form of superfluidity and has previously been successfully described using normal modes. Two phenomena that could sustain the emergence and stability of superfluid behavior were revealed, including the behavior of the normal mode frequencies as $N$ increases. In this paper, I focus on a more detailed analysis of these analytic frequencies, extending my investigation to include Hamiltonians with a range of interparticle interaction strengths from the BCS regime to the unitary regime and analyzing the microscopic dynamics that lead to large gaps at unitarity. The results of the present study suggest that in regimes where higher-order effects are small, normal modes can be used to describe the physics of superfluidity from the weakly interacting BCS regime with the emergence of small excitation gaps to unitarity with its large gaps and can offer insight into a possible microscopic understanding of the behavior at unitarity. This approach could thus offer an alternative to the two-body pairing models commonly used to describe superfluidity along this transition.

A quantum resonance model is prepared by periodically kicking cold atoms exposed to an optical ratchet potential in the direction of the gravitational field. Within tailored parameters, intriguing phenomena emerge including absolute negative mobility, in which the atom surprisingly moves against the bias (gravity). In its upward motion, the particle current can be less or greater than or equal to the zero-gravity case, for which current reversal may prevail. Contrary to its associated zero-gravity case, the particle can be fully trapped or can slowly move downward. These phenomena occur when the classical counterpart is chaotic. With the present-day optical-lattice setup, it will be interesting to observe all these phenomena and, in particular, to see how the atom flies uphill.

Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction between lattice fermions, will suppress the phase separation instability. Taking the honeycomb lattice as an example, we use the unrestricted Hartree-Fock approximation to show that our proposal significantly enlarges the stable portion of the topological superfluid phase and increases the critical temperature by an order of magnitude. Our work opens a route to enhance the stability of topological superfluids by engineering interparticle interactions.

This work investigates the angular momentum induced by electromagnetic quantum fluctuations in a dielectric Mie sphere. The magneto-optical activity creates longitudinal electric modes with broken symmetry of magnetic quantum numbers. When excited by electromagnetic quantum fluctuations, angular momentum is created by a vortex of the Poynting vector that decays as $1/r$ from the center of the sphere. This longitudinal angular momentum, connected to the vector potential $\mathbf{A}(\mathbf{r},t)$, emerges as a QED modification of the traditional diamagnetic Einstein–de Haas effect, in which an applied external magnetic field, via its action on microscopic magnetism, enforces macroscopic rotation.

We introduce a stochastic optimization technique to obtain self-trapped beams in the generalized nonlinear Schrödinger equation. The method is based on combining a variational approach with a bio-inspired method: the cuckoo search algorithm that relies on Lévy flights. The proposed technique can be easily adapted to generate diverse self-trapped structures in a plethora of nonlinear media. Unlike the standard variational technique and some of the numerical algorithms previously reported, this algorithm allows for the optimization of different families of self-trapped beams concurrently.

Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e., simultaneous excitation of more than one Rydberg atom, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Rydberg atoms interacting via dipole-dipole exchange interactions. We study typical situations in current Rydberg atom experiments, where different types of dipole-dipole interactions can be achieved by varying Rydberg state couplings. An effective Hamiltonian governing underlying antiblockade dynamics is derived. We illustrate that geometric gates can be realized with the Rydberg antiblockade which is robust against the decay of Rydberg states. Our study may stimulate new experimental and theoretical exploration of quantum optics and strongly interacting many-body dynamics with Rydberg antiblockade driven by dipole-dipole interactions.

We predict that a photon condensate inside a dye-filled microcavity forms long-lived spatial structures that resemble vortices when incoherently excited by a focused pump orbiting around the cavity axis. The finely structured density of the condensates have a discrete rotational symmetry that is controlled by the orbital frequency of the pump spot and is phase coherent over its full spatial extent, despite the absence of any effective photon-photon interactions.