We demonstrate optomechanical interference in a multimode system, in which an optical mode couples to two mechanical modes. A phase-dependent excitation-coupling approach is developed, which enables the observation of destructive interference in dynamical backactions. The destructive interference prevents the coupling of the mechanical system to the optical mode, suppressing optically induced mechanical damping. These studies establish optomechanical interference as an essential tool for controlling the interactions between light and mechanical oscillators.

Quantum networks require flying qubits that transfer information between the nodes. This may be implemented by means of single atoms (the nodes) that emit and absorb single photons (the flying qubits) and requires full control of photon absorption and emission by the individual emitters. In this paper, we theoretically characterize the wave packet of a photon emitted by a single atom undergoing a spontaneous Raman transition in a three-level scheme. We investigate several excitation schemes that are experimentally relevant and discuss control parameters that allow one to tailor the spectrum of the emitted photon wave packet.

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of $N$ oscillators and $M(<N)$ two-level systems.

Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time $t$. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a different perspective on causality relations and time evolution in quantum mechanics.

Inspired by the idea of mimicking the measurement on a quantum system through a decoherence process to target specific eigenstates based on Born's law, i.e., the hierarchy of probabilities instead of the hierarchy of eigenvalues, we transform a Lindblad equation for the reduced density operator into a nonlinear Schrödinger equation to obtain a computationally feasible simulation of the decoherent dynamics in the open quantum system. This gives the opportunity to target the eigenstates which have the largest $L^2$ overlap with an initial superposition state and hence more flexibility in the selection criteria. One can use this feature, for instance, to approximate eigenstates with certain localization or symmetry properties. As an application of the theory we discuss eigenstate towing, which relies on the perturbation theory to follow the progression of an arbitrary subset of eigenstates along a sum of perturbation operators with the intention to explore, for example, the effect of interactions on these eigenstates. The easily parallelizable numerical method shows an exponential convergence and its computational costs scale linearly for sparse matrix representations of the involved Hermitian operators.

We analyze the propagation of quantum states in the presence of weak disorder. In particular, we investigate the reliable transmittance of quantum states, as potential carriers of quantum information, through disorder-perturbed waveguides. We quantify wave-packet distortion, backscattering, and disorder-induced dephasing, which all act detrimentally on transport, and identify conditions for reliable transmission. Our analysis relies on the treatment of the nonequilibrium dynamics of ensemble-averaged quantum states in terms of quantum master equations.

Quantifications of coherence are intensively studied in the context of completely decoherent operations (i.e., von Neuamnn measurements, or equivalently, orthonormal bases) in recent years. Here we investigate partial coherence (i.e., coherence in the context of partially decoherent operations such as Lüders measurements). A bona fide measure of partial coherence is introduced. As an application, we address the monotonicity problem of $K$-coherence (a quantifier for coherence in terms of Wigner-Yanase skew information) [Girolami, Phys. Rev. Lett. 113, 170401 (2014)], which is introduced to realize a measure of coherence as axiomatized by Baumgratz, Cramer, and Plenio [Phys. Rev. Lett. 113, 140401 (2014)]. Since $K$-coherence fails to meet the necessary requirement of monotonicity under incoherent operations, it is desirable to remedy this monotonicity problem. We show that if we modify the original measure by taking skew information with respect to the spectral decomposition of an observable, rather than the observable itself, as a measure of coherence, then the problem disappears, and the resultant coherence measure satisfies the monotonicity. Some concrete examples are discussed and related open issues are indicated.

Over the past few years, Heisenberg's error-disturbance uncertainty relation has experienced increased attention since several experimental publications verified the theoretical findings of Ozawa predicting the violation and thus necessary reformulation of Heisenberg's relation. However, soon after their appearance, an alternative theory was presented by Busch and co-workers, which proclaimed the validity of Heisenberg's relation and thus gave rise to heated debates. Here, we present an experimental comparison of the competing approaches by applying them to the same neutron optical measurement apparatus. Empirical results for the different definitions of error and disturbance are presented for special input states and configurations of the apparatus to illustrate the opposing approaches. The inequalities restricting errors and disturbances are particularly emphasized. Despite the strong controversy, in the case of projectively measured qubit observables, both approaches lead to equal outcomes.

Topological error-correcting codes, such as surface codes and color codes, are promising because quantum operations are realized by two-dimensionally (2D) arrayed quantum bits (qubits). However, physical wiring of electrodes to qubits is complicated, and 3D integration for the wiring requires further development of fabrication technologies. Here, we propose a method to reduce the congestion of wiring to qubits by just adding a swap gate after each controlled-not (cnot) gate. swap gates exchange roles of qubits. Then, the roles of qubits are shared between different qubits. We found that our method transforms the qubit layout and reduces the number of qubits that cannot be two-dimensionally accessed. We show that fully 2D layouts including both qubits and control electrodes can be achieved for surface and color codes of minimum sizes. This method will be beneficial to simplifications of the fabrication process of quantum circuits in addition to improvements in the reliability of qubit systems.

An “ultrafine” splitting in positronium between the $L=1$ spin-singlet state and the spin average of the spin-triplet states is shown to arise only at order ${\alpha }^6$. The QED prediction for $n=2$ states is ${\mathrm{\Delta }}_{2,P}=(683/172800)m{\alpha }^6=73.7\left(2.6\right)$ kHz. This represents the smallest leading-order QED splitting known. Current experimental efforts could observe this splitting, and its observation can constrain new ultralight interactions, such as axions or $Z^{\prime }$.

We provide a unified theoretical framework for recently emerging experiments that retrieve fixed-in-space molecular information through time-domain rotational coherence spectroscopy. Unlike a previous approach by Makhija et al. (V. Makhija et al., arXiv:1611.06476), our method can be applied to the retrieval of both real-valued (e.g., ionization yield) and complex-valued (e.g., induced dipole moment) molecular response information. It is also a direct retrieval method without using iterations. We also demonstrate that experimental parameters, such as the fluence of the aligning laser pulse and the rotational temperature of the molecular ensemble, can be quite accurately determined using a statistical method.

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We consider two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the Zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K. Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S. M. Barnett, Phys. Rev. Lett. 118, 114802 (2017)].

Majorana zero modes, quasiparticles with non-Abelian statistics, have gained increasing interest for their fundamental role as building blocks in topological quantum computation. Previous studies have mainly focused on two well-separated Majorana zero modes, which could form two degenerate states serving as one nonlocal qubit for fault-tolerant quantum memory. However, creating and manipulating multiple Majorana zero modes, which could encode more qubits, remain an ongoing research topic. Here we report that multiple Majorana zero modes can exist in atomic Fermi double wires with spin-orbit coupling and perpendicular Zeeman field. This system belongs to the topological BDI class, thus all the topological superfluids are classified by integer numbers. Especially, diverse topological superfluids can be formed in a trap, where the zero energy modes can be found at the interfaces between different topological superfluids. The structure of these zero energy modes in the trap can be engineered by the trapping potential as well as other system parameters. This system would be a significant step towards utilization of Majorana zero modes in quantum computation.

We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.

Bose-Einstein condensates with balanced gain and loss can support stationary states despite the exchange of particles with the environment. In the mean-field approximation this is described by the $\mathcal{PT}$-symmetric Gross-Pitaevskii equation with real eigenvalues. In this work we study the role of stationary states in the appropriate many-particle description. It is shown that without particle interaction there exist two nonoscillating trajectories which can be interpreted as the many-particle equivalent of the stationary $\mathcal{PT}$-symmetric mean-field states. Furthermore, the system has a nonequilibrium steady state which acts as an attractor in the oscillating regime. This steady state is a pure condensate for strong gain and loss contributions if the interaction between the particles is sufficiently weak.

Experimental evidence indicates that high-repetition-rate ultrafast pulsed excitation is more efficient in optical trapping of dielectric nanoparticles as compared with continuous-wave excitation at the same average power. The physics behind the different nature of force under these two excitation conditions remained deceptive until quite recently when it was theoretically explained, in the dipole limit, as a combined effect of (1) repetitive instantaneous momentum transfer and (2) optical Kerr nonlinearity. The role of optical Kerr effect was theoretically studied for larger dielectric spherical particles, in the ray optics limit, also. However, a theoretical underpinning is yet to be established as to whether the effect of optical nonlinearity is omnipresent across different particle sizes, which we investigate here. Using localized approximation of generalized Lorenz-Mie theory, we theoretically analyze the nature of force (and potential) and provide a detailed comparative discussion between this generalized scattering formulation with dipole scattering formulation for dielectric nanoparticles.

Based on the relation between a plane phased array and plane waves we show that a spherical current layer or a current sphere proportional to a multipole electric field and situated in a uniform medium generates the same multipole field in all space. We calculate TE and TM multipoles inside and outside the spherical layer. The $l=1$ TM multipoles are localized at the origin with a focal spot with full width at half maximum of $0.4\lambda$ in the lateral axes and $0.58\lambda$ in the vertical axis. The multipole fields near the origin are prescriptions for the current distributions required to generate those multipole fields. A spherical layer can couple to a multipole source since the oscillation of the electrons in the layer due to the multipole field generates the multipole field in all space, which in turn can drive the multipole currents. Exciting a multipole in a polarizable sphere or spherical layer can couple it to another polarizable sphere or spherical layer.

It is known that placing a mechanical oscillator in a superposition of coherent states allows, in theory, a measurement of a linear force whose sensitivity increases with the amplitude of the mechanical oscillations, a uniquely quantum effect. Further, entangled versions of these states across a network of $n$ mechanical oscillators enable a measurement whose sensitivity increases linearly with $n$, thus improving the classical scaling by $\sqrt{n}$. One of the key challenges in exploiting this effect is processing the signal so that it can be readily measured; linear processing is insufficient. Here we show that a Kerr oscillator will not only create the necessary states, but also perform the required processing, transforming the quantum phase imprinted by the force signal into a shift in amplitude measurable with homodyne detection. This allows us to design a relatively simple quantum electromechanical circuit that can demonstrate the core quantum effect at the heart of this scheme, namely amplitude-dependent force sensitivity. We derive analytic expressions for the performance of the circuit, including thermal mechanical noise and photon loss. We discuss the experimental challenges in implementing the scheme with near-term technology.

We present a powerful computational approach to simulate the threshold behavior of photonic-crystal quantum-dot (QD) lasers. Using a finite-difference time-domain (FDTD) technique, Maxwell-Bloch equations representing a system of thousands of statistically independent and randomly positioned two-level emitters are solved numerically. Phenomenological pure dephasing and incoherent pumping is added to the optical Bloch equations to allow for a dynamical lasing regime, but the cavity-mediated radiative dynamics and gain coupling of each QD dipole (artificial atom) is contained self-consistently within the model. These Maxwell-Bloch equations are implemented by using Lumerical's flexible material plug-in tool, which allows a user to define additional equations of motion for the nonlinear polarization. We implement the gain ensemble within triangular-lattice photonic-crystal cavities of various length $N$ (where $N$ refers to the number of missing holes), and investigate the cavity mode characteristics and the threshold regime as a function of cavity length. We develop effective two-dimensional model simulations which are derived after studying the full three-dimensional passive material structures by matching the cavity quality factors and resonance properties. We also demonstrate how to obtain the correct point-dipole radiative decay rate from Fermi's golden rule, which is captured naturally by the FDTD method. Our numerical simulations predict that the pump threshold plateaus around cavity lengths greater than $N=9$, which we identify as a consequence of the complex spatial dynamics and gain coupling from the inhomogeneous QD ensemble. This behavior is not expected from simple rate-equation analysis commonly adopted in the literature, but is in qualitative agreement with recent experiments. Single-mode to multimode lasing is also observed, depending on the spectral peak frequency of the QD ensemble. Using a statistical modal analysis of the average decay rates, we also show how the average radiative decay rate decreases as a function of cavity size. In addition, we investigate the role of structural disorder on both the passive cavity and active lasers, where the latter show a general increase in the pump threshold for cavity lengths greater than $N=7$, and a reduction in the nominal cavity mode volume for increasing amounts of disorder.

In this paper we analyze the evolution of generalized Pauli channels governed by the memory kernel master equation. We provide necessary and sufficient conditions for the memory kernel to give rise to legitimate (completely positive and trace-preserving) quantum evolution. In particular, we analyze a class of kernels generating the quantum semi-Markov evolution, which is a natural generalization of the Markovian semigroup. Interestingly, the convex combination of Markovian semigroups goes beyond the semi-Markov case. Our analysis is illustrated with several examples.