We present a blueprint for a maser with a single three-level transmon superconducting artificial atom. The system can be pumped coherently via a two-photon process, and to achieve high population inversion, the relaxation rate of the metastable state is increased via an auxiliary low-$Q$ cavity coupled to a transition between the transmon excited states. We show numerically that such a maser can operate both in the intermediate-coupling regime with super-Poissonian photon statistics and in the strong-coupling regime, where the statistics is sub-Poissonian. For the former the maser exhibits thresholdless behavior, and for the latter there is a well-defined pumping threshold. A useful side effect of the auxiliary resonator is that it allows to overcome the photon blockade effect for the pump, which would otherwise prevent a high photon population. Finally, we observe the bistability of the steady-state Wigner function and the self-quenching effect for some parameters.

The character of evolution of an open quantum system is often encoded in the correlation function of the environment or, equivalently, in the spectral density function of the interaction. When the environment is heterogeneous, e.g., consists of several independent subenvironments with different spectral functions, one of the subenvironments can be considered auxiliary and used to control decoherence of the open quantum system in the remaining part of the environment. The control can be realized, for example, by adjusting the character of interaction with the subenvironment via suitable parameters of its spectral density. We investigate non-Markovian evolution of a two-level system (qubit) under influence of three independent decoherence channels: two of them have classical nature and originate from interaction with a stochastic field, and the third is a quantum channel formed by interaction with a bosonic bath. By modifying spectral densities of the channels, we study their impact on steady states of the two-level system, evolution of its density matrix, and the equilibrium emission spectra. Additionally, we investigate the impact of the rotation-wave approximation applied to the bath channel on accuracy of the results.

The decay rate of an interstitial two-level spin impurity, located in the center of a unit cell of an anisotropic ferromagnetic lattice subjected to an external magnetic field, is derived. The impurity is coupled to nearest-neighbor spins through a Heisenberg $XY$ interaction. By mapping the lattice spin operators using the Holstein-Primakoff transformation, we establish the similarity with the Fano-Anderson model at low temperatures, and we calculate the retarded Green's function in one and two dimensions analytically for arbitrary coupling strength. It is shown that the reduced density matrix of the impurity satisfies an exact master equation in Lindblad form, from which the decay rate and the Lamb shift are deduced. The evolution in time of the latter together with the excited-state occupation probability is investigated and its dependence on the applied magnetic field is discussed. It is found that there exists a critical resonance-like value of the magnetic field around which the behavior of the decay rate and the density matrix changes drastically. The Markovian decay law, as given by the Fermi golden rule, does not hold in the weak-coupling regime unless the magnetic field is weak, typically less than the critical value. The weak-coupling regime is further treated perturbatively up to second order, and the obtained results are compared with the exact solution. We also discuss the Zeno regime of the dynamics, where it is shown that, at short times, the effective decay rate is twice as small as the exact decay rate, and that when the impurity energy lies outside the lattice continuum, the measurement speeds up the decay of the survival probability.

Continuous-variable codes are an expedient solution for quantum information processing and quantum communication involving optical networks. Here we characterize the squeezed comb, a finite superposition of equidistant squeezed coherent states on a line, and its properties as a continuous-variable encoding choice for a logical qubit. The squeezed comb is a realistic approximation to the ideal code proposed by Gottesman et al. [D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001)], which is fully protected against errors caused by the paradigmatic types of quantum noise in continuous-variable systems: damping and diffusion. This is no longer the case for the code space of finite squeezed combs, and noise robustness depends crucially on the encoding parameters. We analyze finite squeezed comb states in phase space, highlighting their complicated interference features and characterizing their dynamics when exposed to amplitude damping and Gaussian diffusion noise processes. We find that squeezed comb states are more suitable and less error prone when exposed to damping, which speaks against standard error-correction strategies that employ linear amplification to convert damping into easier-to-describe isotropic diffusion noise.

Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination, and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness-constructing method, which are also used to estimate the robustness of coherence, the $l_1$ norm, and the $l_2$ norm of coherence measures. Furthermore, we compare one of our coherence witnesses with a previously introduced witness by proving that our witness is strictly stronger than that previous witness. We also present an application of coherence in a quantum metrology task, in which we estimate an unknown parameter by measuring our coherence witness.

We consider the optical dipole potential energy, which arises from the interaction of a two-level atom with a circularly polarized Laguerre-Gaussian laser beam of small waist. The beam is characterized by the existence of a longitudinal electric field component which is responsible for the appearance of a chiral term in the optical dipole potential energy. This term reverses sign if either the winding number or the wave polarization of the beam reverses sign. We propose a scheme of a bi-chromatic vortex interaction with the two-level atom in which the resulting optical dipole potential is fully chiral.

We apply the theory of the inhomogeneous Kibble-Zurek mechanism to understand the quench dynamics in the transition from a Mott insulator to a superfluid in a cold Bose gas confined in both a two-dimensional optical lattice and a harmonic trap. The local quench time and the resulting Kibble-Zurek diabatic-adiabatic boundary take a nontrivial positional dependence due to the Mott-lobe structure of the ground-state phase diagram of the Bose-Hubbard model. We demonstrate the quench dynamics through the time-dependent Gutzwiller simulations, revealing inhomogeneous properties of the growth of the superfluid order parameter. The inhomogeneous Kibble-Zurek theory is applicable to the shallow harmonic trap.

Brewster reflection of a postparaxial optical beam at a plane dielectric interface unravels fundamentally significant optical singularity dynamics. We express the simulated field-component profiles of a Brewster-reflected postparaxial beam field via empirical functions, using which we demonstrate optical beam-shifts and formation of phase singularities. These occurrences naturally reveal the presence and complex transitional dynamics of generic polarization singularities, which we observe via simulation and experiments. A single reflection being the core process, our method becomes a fundamentally appealing way to generate optical singularities and to study their dynamics.

In this paper we discuss two strategies to achieve wideband light generation through intermodal nonlinear parametric processes in multimode integrated waveguides. We outline how the interplay among intermodal interactions and high dispersion may lead to the generation of light characterized by substantial power spectral density if compared to supercontinuum sources. These results are valid independently of the waveguide material; however, our numerical simulations focus on silicon waveguides, which are nowadays at the core of integrated photonics. The long-term vision is that by exploiting an adequate number of intermodal processes, widely tunable radiation having high-power spectral density can be generated in a broad portion of the transparency window of silicon.

We analyze the consequences of dissipative heating in driven Kerr microresonators theoretically and numerically, using a thermal Lugiato-Lefever model. We show that thermal sensitivity modifies the stability range of continuous waves in a way that blocks direct access to broadband frequency-comb-forming waveforms, and we propose a deterministic access path that bypasses the thermal instability barrier. We describe a thermal instability that leads to thermo-optical oscillations via a Hopf bifurcation.

A quantum Kerr-nonlinear oscillator is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. We theoretically study the echo phenomenon in a single impulsively excited (“kicked”) Kerr-nonlinear oscillator. We reveal two types of echoes, “quantum” and “classical” ones, emerging on the long and short time scales, respectively. The mechanisms of the echoes are discussed, and their sensitivity to dissipation is considered. These echoes may be useful for studying decoherence processes in a number of systems related to quantum information processing.

We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert-space dimension with the number of particles. For a constant Hamiltonian system of Hilbert-space dimension $n$ with frequencies ranging from $f_{min}$ to $f_{max}$, we show via a proper orthogonal decomposition that for a run time $T$ the dominant dynamics are compressed in the neighborhood of a subspace whose dimension is the smallest integer larger than the time-bandwidth product $\mathrm{\Delta }=(f_{max}-f_{min})T$. We also show how the distribution of initial states can further compress the system dimension. Under the stated conditions, the time-bandwidth estimate reveals the existence of an effective compressed model whose dimension is derived solely from system properties and not dependent on the particular implementation of a variational simulator, such as a machine learning system, or quantum device, or possibly even specially adapting traditional methods of solving the time-dependent Schrödinger equation. However, finding an efficient solution procedure $\mathit{is}$ dependent on the simulator implementation, which is not discussed in this paper. In addition, we show that the compression rendered by the proper orthogonal decomposition encoding method can be further strengthened via a multilayer autoencoder. Finally, we present numerical illustrations to affirm the compression behavior in time-varying Hamiltonian dynamics in the presence of external fields. The essential time-bandwidth product is also simply estimated for a wide class of physical systems, where typically localized high-frequency motion occurs at or around each of the many particles, and with low-frequency dynamics associated with globally distributed characteristic degrees of freedom. This estimate for the bandwidth has a generic character indicating the wide significance of expected quantum system dynamics compression. We also discuss the potential implications of the findings for machine learning tools to efficiently solve the many-body or other high-dimensional Schrödinger equations.

We propose an approach to distribute high-fidelity long-range entanglement in a quantum network assisted by the entanglement supplied by auxiliary short-range paths between the network nodes. Entanglement assistance in the form of shared catalyst states is utilized to maximize the efficiency of entanglement concentration transformations over the edges of the network. The catalyst states are recycled for use in adaptive operations at the network nodes and replenished periodically using the auxiliary short-range paths. The rate of long-range entanglement distribution using such entanglement assistance is found to be significantly higher than possible without using entanglement assistance.

Capturing the discontinuous shift by $\mathrm{\Delta }$ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap $E_{\mathrm{g}}$ from the Kohn-Sham (KS) gap ${\varepsilon }_{\mathrm{g}}$ within KS density functional theory (DFT) as $E_{\mathrm{g}}={\varepsilon }_{\mathrm{g}}+\mathrm{\Delta }$, yet this discontinuity is absent from existing approximations. The “$N$-centered” formulation of ensemble DFT artificially maintains a total electron number $N$ in order to yield $E_{\mathrm{g}}$ not through a discontinuous shift in the xc potential but via the ensemble-weight derivative of the xc energy. Within the $N$-centered approach, we calculate exact xc potentials for a one-dimensional finite system and show analytically that $\mathrm{\Delta }$ can in fact be interpreted as a discontinuous shift in the exact $N$-centered ensemble xc potential, thereby extending to charged excitations an exact property of uncharged excitations. We show that applying the Levy-Zahariev “shift-in-potential” procedure in this context relocates the discontinuous shift to the unimportant periphery of the system, so that the exact xc potential in effect is free of discontinuities and thus the inability of a local functional to capture discontinuous behavior is inconsequential.

We theoretically investigate the phenomenon of modulation instability for systems obeying the nonlinear Schrödinger equation, which are under the influence of an external homogeneous synthetic magnetic field. For an initial condition, the instability is detected numerically by comparing dynamics with and without a small initial perturbation; the perturbations are characterized in a standard fashion by wave vectors in momentum space. We demonstrate that the region of (in)stability in momentum space, as well as time evolution in real space, for identical initial conditions, depend on the choice of the gauge (i.e., vector potential) used to describe the homogeneous synthetic magnetic field. This superficially appears as if the gauge invariance is broken, but this is not true. When the system is evolved from an identical initial condition in two different gauges, it is equivalent to suddenly turning on the synthetic magnetic field at $t=0$. This gives rise, via Faraday's law, to an initial instantaneous kick of a synthetic electric field to the wave packet, which can differ for gauges yielding an identical uniform magnetic field for $t>0$.

We study how intensity fluctuations in transmission through a disordered slab change depending on the regime of wave transport. A system with large (compared to the wavelength of light) inhomogeneities is considered. Within a diagrammatic approach, the variance of the total transmission coefficient is calculated numerically beyond the diffusion approximation. A great enhancement of fluctuations is found in the crossover from the ballistic to the diffusive transport at the grazing angles of incidence on the sample surface. The effect originates from the reflection of waves that propagate nearly parallel to the sample boundaries and experience scattering through small angles, and reveals itself both in transmission and reflection and in correlations between the transmitted and reflected fluxes.

The time-bandwidth limit is a mathematical tenet that affects all reciprocal resonators, stating that the product of the spectral bandwidth that can couple into a resonant system and its characteristic energy decay time is always equal to 1. Here, we develop an analytical and numerical model to show that introducing nonreciprocal coupling to a generalized resonator changes the power balance between the reflected and intracavity fields, which consequently overcomes the time-bandwidth limit of the resonant system. By performing a full evaluation of the time-bandwidth product (TBP) of the modeled resonator, we show that it represents a measure of the increased delay imparted to a light wave, with respect to what the bandwidth of the reciprocal resonant structure would allow to the same amount of in-coupled power. No longer restricted to the value 1, we show that the TBP can instead be used as a figure of merit of the improvement in intracavity power enhancement due to the nonreciprocal coupling.

We propose a variational principle to compute a quantum adiabatic brachistochrone (QAB) for open systems. Using the notion of “adiabatic speed” based on the energy gaps, we derive a Lagrangian associated to the functional measuring the time spent to achieve adiabatic behavior, which in turn allows us to perform the optimization. The QAB is illustrated for the nonunitary dynamics of a stimulated Raman adiabatic passage process, the Deutsch-Jozsa quantum computing algorithm, and of a transmon qutrit. A numerical protocol is devised, which allows one to compute the QAB for arbitrary quantum systems for which exact simulations can be afforded. We also establish sufficient conditions for the equivalence between the Lagrangians, and thus the QAB, of open and closed systems.

One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreover, using this notion and the majorization relation, we obtain a necessary condition for the conversion of general quantum states by means of incoherent operations. These results generalize the necessary conditions of conversions for pure states given in the literature, and show that the tools of the majorization lattice are useful also in the general case. Finally, we introduce a family of coherence quantifiers by considering concave and symmetric functions applied to the generalized coherence vector. We compare this proposal with the convex roof measure of coherence and others quantifiers given in the literature.

Manipulation and control of the complex quantum system with high precision are essential for achieving universal fault-tolerant quantum computing. For a physical system with restricted control resources, it is a challenge to control the dynamics of the target system efficiently and precisely under disturbances. Here we propose a multilevel dissipative quantum control framework and show that deep reinforcement learning provides an efficient way to identify the optimal strategies with restricted control parameters of the complex quantum system. This framework can be generalized to be applied to other quantum control models. Compared with the traditional optimal control method, this deep reinforcement learning algorithm can realize efficient and precise control for multilevel quantum systems with different types of disturbances.