Wave propagation through rapidly but continuously varying media is surprisingly subtle, and in a pair of recent papers [Horsley et al., J. Opt. 18, 044016 (2016); Longhi, Eur. Phys. Lett. 112, 64001 (2015)] it was found that planar media with a spatially varying permittivity $\epsilon \left(x\right)$ obeying the spatial Kramers-Kronig relations do not reflect waves incident from one side, however rapid the changes in $\epsilon \left(x\right)$. Within this large class of media there are some examples where the dissipation or gain is not asymptotically negligible and it has been pointed out [Longhi, Eur. Phys. Lett. 112, 64001 (2015)] that it is impossible to define meaningful reflection and transmission coefficients in such cases. Here we show—using an exactly soluble example—that despite the lack of any meaningful reflection and transmission coefficients, these profiles are still reflectionless from one side in the sense that the profile generates no counterpropagating wave for incidence from one side. This finding is demonstrated through examining the propagation of pulses through the profile, where from one side we find that no second reflected pulse is generated, while from the other there is. We conclude with a discussion of the effect of truncating these infinitely extended profiles, illustrating how the reflectionless behavior may be retained over a wide range of incident angles.

By employing the full counting statistics formalism, we characterize the first moment of energy that is exchanged during a generally non-Markovian evolution in nondriven continuous-variable systems. In particular, we focus on the evaluation of the energy flowing back from the environment into the open quantum system. We apply these results to the quantum Brownian motion, where these quantities are calculated both analytically, under the weak-coupling assumption, and numerically also in the strong-coupling regime. Finally, we characterize the non-Markovianity of the reduced dynamics through a recently introduced witness based on the so-called Gaussian interferometric power and we discuss its relationship with the energy backflow measure.

Real photon-photon scattering is a long-predicted phenomenon that is being searched for in experiment in the form of a birefringent vacuum at optical and x-ray frequencies. We present results of calculations and numerical simulations for a scenario to measure this effect using multi-MeV photons generated in the collision of electrons with a laser pulse. We find that the birefringence of the vacuum should be measurable using experimental parameters attainable in the near future.

We study analytically the superfluid flow of a Bose-Einstein condensate in a ring geometry in the presence of a rotating barrier. We show that a phase transition breaking a parity symmetry among two topological phases occurs at a critical value of the height of the barrier. Furthermore, a discontinuous (accompanied by hysteresis) phase transition is observed in the ordered phase when changing the angular velocity of the barrier. At the critical point where the hysteresis area vanishes, the chemical potential of the ground state develops a cusp (a discontinuity in the first derivative). Along this path, the jump between the two corresponding states having a different winding number shows analogies with a topological phase transition. We finally study the current-phase relation of the system and compare some of our calculations with published experimental results.

Feasible setup for pulsed quantum nondemolition interaction between two distant mechanical oscillators through an optical or microwave mediator is proposed. The proposal uses homodyne measurement of the mediator and feedforward control of the mechanical oscillators to reach the interaction. To verify the quantum nature of the interaction, we investigate the Gaussian entanglement generated in the mechanical modes. We evaluate it under influence of mechanical bath and propagation loss for the mediator and propose ways to optimize the interaction. Finally, both currently available optomechanical and electromechanical platforms are numerically analyzed. The analysis shows that implementation is already feasible with current technology.

We propose a method of producing steady-state coherent light with negative Wigner functions in nonlinear media combined with feedback control. While the nonlinearities are essential to produce the Wigner negativities, this alone is insufficient to stabilize steady-state light with negativities. Using feedback control to control the phase in the cavity, we find that this produces significant total negativities for reasonable experimental parameters. The negative Wigner function is produced continuously and does not appear to be restricted to low-amplitude light. The technique is applicable to systems such as exciton-polaritons, where strong natural nonlinearities are present.

We present a formula for the spectroscopically accessible level shifts and decay rates of an atom moving at an arbitrary angle relative to a surface. Our Markov formulation leads to an intuitive analytic description whereby the shifts and rates are obtained from the coefficients of the Heisenberg equation of motion for the atomic flip operators but with complex Doppler-shifted (velocity-dependent) transition frequencies. Our results conclusively demonstrate that for the limiting case of parallel motion the shifts and rates are quadratic or higher in the atomic velocity. We show that a stronger, linear velocity dependence is exhibited by the rates and shifts for perpendicular motion, thus opening the prospect of experimentally probing the Markovian approach to the phenomenon of quantum friction.

We theoretically investigate a hybrid optomechanical system including two coupled optomechanical cavities in the presence of two strong pump fields and a weak probe field. The photon-hopping coupling of the cavities gives rise to two cavity supermodes whose resonant frequencies can be obtained in the probe transmission spectrum. In a strong photon-hopping coupling regime, there is a large coupling rate between the probe field and one of the two cavity supermodes that is called a bright mode. The optomechanical couplings between the bright mode and two mechanical resonators can cause double optomechanically induced transparency (OMIT), which can be employed to both separately and simultaneously store two weak probe pulses with different central frequencies. We obtain the group delay (light storage time) of the probe field in the hybrid optomechanical system. The results suggest that compared with that of a single cavity optomechanical system, the maximum value of the storage time roughly quadrupled in a particular case. The physical origin of the results is discussed. The hybrid optomechanical system opens an avenue of light storage in cavity optomechanics.

We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical, and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double-well symmetry-breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry-breaking states, in the form of a bistable pair, are associated with the single-cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry-breaking states and bistability disappear due to the quantum fluctuations. In the quantum trajectory picture, we observe enhanced quantum jumps and switching, which indicate the presence of the underlying semiclassical symmetry-breaking states. Finally, we present a set of analytical solutions for the steady-state correlation functions by using the complex $P$ representation and discuss its regime of validity.

The analytical and numerical study of the radiation self-action in a system of coupled light guides is fulfilled on the basis of the discrete nonlinear Schrödinger equation (DNSE). We develop a variational method for qualitative study of DNSE and classify self-action modes. We show that the diffraction of narrow (in grating scale) wave beams weakens in discrete media and, consequently, the “collapse” of the one-dimensional wave field with power exceeding the critical value occurs. This results in the ability to self-channel radiation in the central fiber. Qualitative analytical results were confirmed by numerical simulation of DNSE, which also shows the stability of the collapse mode.

The non-Markovian dynamics of open quantum systems is still a challenging task, particularly in the nonperturbative regime at low temperatures. While the stochastic Liouville–von Neumann equation (SLN) provides a formally exact tool to tackle this problem for both discrete and continuous degrees of freedom, its performance deteriorates for long times due to an inherently nonunitary propagator. Here we present a scheme that combines the SLN with projector operator techniques based on finite dephasing times, gaining substantial improvements in terms of memory storage and statistics. The approach allows for systematic convergence and is applicable in regions of parameter space where perturbative methods fail, up to the long-time domain. Findings are applied to the coherent and incoherent quantum dynamics of two- and three-level systems. In the long-time domain sequential and superexchange transfer rates are extracted and compared to perturbative predictions.

A resource theory of quantum coherence attempts to characterize the quantum coherence that exists in a given quantum system. Many different approaches to a resource theory of coherence have recently been proposed, with their differences lying primarily in the identification of “free” or “incoherent” operations. In this article, we compare a number of these operational classes. In particular, the recently introduced class of dephasing-covariant operations is analyzed, and we characterize the Kraus operators of such maps. A number of coherence measures are introduced based on relative Rényi entropies, and we study incoherent state transformations under different operational classes. In particular, we show that the incoherent Schmidt rank can be increased arbitrarily large by certain noncoherence generating operations. The distinction between asymmetry-based versus basis-dependent notions of coherence theory is clarified, and we further develop the resource theory of $N$ asymmetry, where $N$ is the group of all diagonal incoherent unitaries.

We theoretically investigate the implementation of a quantum controlled-phase gate in a system constituted by a single atom inside an optical cavity, based on the electromagnetically induced transparency effect. First we show that a probe pulse can experience a $\pi$ phase shift due to the presence or absence of a classical control field. Considering the interplay of the cavity-EIT effect and the quantum memory process, we demonstrated a controlled-phase gate between two single photons. To this end, first one needs to store a (control) photon in the ground atomic states. In the following, a second (target) photon must impinge on the atom-cavity system. Depending on the atomic state, this second photon will be either transmitted or reflected, acquiring different phase shifts. This protocol can then be easily extended to multiphoton systems, i.e., keeping the control photon stored, it may induce phase shifts in several single photons, thus enabling the generation of multipartite entangled states. We explore the relevant parameter space in the atom-cavity system that allows the implementation of quantum controlled-phase gates using the recent technologies. In particular, we have found a lower bound for the cooperativity of the atom-cavity system which enables the implementation of phase shift on single photons. The induced shift on the phase of a photonic qubit and the controlled-phase gate between single photons, combined with optical devices, enable one to perform universal quantum computation.

This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by tuning a model parameter $\alpha$. We provide analytic solutions to the quantum walks for the star and circulant graph classes that are valid for an arbitrary value of the number of nodes $N$, time $t$, and the model parameter $\alpha$. We discuss quantitative and qualitative aspects of quantum walks based on directed graphs and their undirected counterparts. Numerical simulations of quantum walks on circulant graphs show complex interference phenomena and how complete suppression of transport is achieved near $\alpha =\pi /2$. By proving two mirror symmetries around $\alpha =0$ and $\pi /2$ we show that these quantum walks have a period of $\pi$ in $\alpha$. We show that undirected edges lose their effect on the quantum walk at $\alpha =\pi /2$ and present non-bipartite graphs that exhibit suppression of transport. Finally, we analytically compute the Hamiltonians of quantum walks on the directed ring graph.

Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The model consists of a network of elementary dissipation-generated modules and it is in principle scalable. In particular, we demonstrate the ability to dissipatively prepare all single-qubit gates, and the controlled-not gate; prerequisites for universal quantum computing. We also show a way to implement a type of quantum memory in a dissipative environment, whereby we can arbitrarily control the loss in both coherence, and concurrence, over the evolution. Moreover, our dissipation-assisted modular construction exhibits a degree of inbuilt robustness to Hamiltonian and, indeed, Lindbladian errors, and as such is of potential practical relevance.

Recent experimental progress in creating and controlling singular electron beams that carry orbital angular momentum allows for new types of local spectroscopies. We investigate theoretically the twisted-electron-energy-loss spectroscopy (EELS) from the ${\mathrm{C}}_{60}$ fullerene. Of particular interest are the strong multipolar collective excitations and their selective response to the orbital angular momentum of the impinging electron beam. Based on ab initio calculations for the collective response, we compute EELS signals with twisted-electron beams, particularly in a transmission electron microscopy setup, and uncover the interplay between the plasmon polarity and the amount of angular momentum transfer.

We propose the use of stimulated Raman adiabatic passage to offer a fast high fidelity method of performing SU(2) rotations on spinor Bose-Einstein condensates (BECs). Past demonstrations of BECs optical control suffer from difficulties arising from collective enhancement of spontaneous emission and inefficient two-photon transitions originating from selection rules. We present here a scheme which allows for arbitrary coherent rotations of two-component BECs while overcoming these issues. Numerical tests of the method show that for BECs of ${}^{87}\mathrm{Rb}$ with up to ${10}^4$ atoms and gate times of $1\mu \mathrm{s}$, decoherence due to spontaneous emission can be suppressed to negligible values.

The global coupling of few-level quantum systems (“spins”) to a discrete set of bosonic modes is a key ingredient for many applications in quantum science, including large-scale entanglement generation, quantum simulation of the dynamics of long-range interacting spin models, and hybrid platforms for force and spin sensing. We present a general numerical framework for treating the out-of-equilibrium dynamics of such models based on matrix product states. Our approach applies for generic spin-boson systems: it treats any spatial and operator dependence of the two-body spin-boson coupling and places no restrictions on relative energy scales. We show that the full counting statistics of collective spin measurements and infidelity of quantum simulation due to spin-boson entanglement, both of which are difficult to obtain by other techniques, are readily calculable in our approach. We benchmark our method using a recently developed exact solution for a particular spin-boson coupling relevant to trapped ion quantum simulators. Finally, we show how decoherence can be incorporated within our framework using the method of quantum trajectories, and study the dynamics of an open-system spin-boson model with spatially nonuniform spin-boson coupling relevant for trapped atomic ion crystals in the presence of molecular ion impurities.

We model the dynamics of attractively interacting ultracold bosonic atoms in a quasi-one-dimensional wave guide with additional harmonic trapping. Initially, we prepare the system in its ground state and then shift the zero of the harmonic trap and switch on an additional narrow scattering potential near the center of the trap. After colliding with the barrier twice, we propose to measure the number of atoms opposite the initial condition. Quantum-enhanced interferometry with quantum bright solitons allows us to predict detection of an offset of the scattering potential with considerably increased precision as compared to single-particle experiments. In a future experimental realization this might lead to measurement of weak forces caused, for example, by small horizontal gradients in the gravitational potential—with a resolution of several micrometers given essentially by the size of the solitons. Our numerical simulations are based on the rigorously proved effective potential approach developed in previous papers [Phys. Rev. Lett. 102, 010403 (2009) and Phys. Rev. Lett. 103, 210402 (2009)]. We choose our parameters such that the prerequisite of the proof (that the solitons cannot break apart, for energetic reasons) is always fulfilled, thus exploring a parameter regime inaccessible to the mean-field description via the Gross-Pitaevskii equation due to Schrödinger-cat states occurring in the many-particle quantum dynamics.

The generalized Gross-Pitaevskii equation (gGPE) is an effective phenomenological description for the dynamics of incoherently pumped exciton-polariton condensates. However, a brute force numerical simulation of the gGPE provides little physical insight into condensate formation under arbitrary pumping configurations, and is demanding in terms of computational resources. We introduce in this paper a modal description of polariton condensation under incoherent pumping of arbitrary spatial profile, based on eigenmodes of the non-Hermitian generator of the linearized dynamics. A pump-dependent basis is then introduced to formulate a temporal coupled-mode theory that captures condensate dynamics in the presence of all nonlinear interactions. Simulations using a single set of modes for a given pumping and trapping configuration agree very well with a full integration of the gGPE in diverse dynamical regimes, supporting the validity of this modal description, while also providing a speedup in simulation times.