Two-level Emitters Research Articles

Fate of the Mollow triplet in strongly coupled atomic arrays

Subwavelength arrays of quantum two-level emitters have emerged as an interesting platform displaying prominent collective effects that can be harnessed for applications. Here, we study such arrays under strong coherent driving, realizing an open quantum many-body problem in a strongly nonlinear regime. For this we introduce an approach to this problem in terms of a dynamical mean-field theory, paving the way for further studies. We show that the spectrum of scattered light, characterized by the famous Mollow triplet for a single atom, develops a characteristic line shape with flat sidebands determined by dipolar interactions and relevant for experiments. Remarkably, this is to some extent independent of the specific geometry, but is sensitive to the ordered arrangement of the atoms. This line shape therefore characterizes atomic arrays and distinguishes them from disordered ensembles and noninteracting emitters. Published by the American Physical Society 2024

Photon blockade in a high-damping cavity via a gain-type coupler

Abstract We propose a scheme to implement photon blockade in a non-Hermitian circuit quantum electrodynamics (circuit-QED) system where a single-mode cavity interacts with a two-level emitter through virtual photon excitation mediated by a coupler resonator. A damping compensation regime is introduced by the phase-lag arising from the medium mode, thereby the periodic exceptional points (EPs) are observed at which the system achieves gain-damping balance. This regime enables photon blockade to occur within the single-mode cavity with high-damping rate by controlling the gain circuit of the coupler, which breaks the limitation of a low-damping rate for photon blockade under weak drive and relaxes the stringent requirements on the quality of the cavity. The numerical simulations for the second-order correlation function, obtained using reported experimental parameters, exhibit excellent agreement with our analytical results. The findings of this study provide a circuit-QED solution for single-quantum devices based on the high-damping cavities, which is of great significance for integrated quantum computing networks.

Efficient, high-fidelity single-photon switch based on waveguide-coupled cavities

We demonstrate theoretically that waveguide-coupled cavities with embedded two-level emitters can act as a highly efficient, high-fidelity single-photon switch. The photon switch is an optical router triggered by a classical signal—the propagation direction of single input photons in the waveguide is controlled by changing the emitter-cavity coupling parameters , for example, using applied fields. The switch reflects photons in the weak emitter-cavity coupling regime and transmits photons in the strong coupling regime. By calculating transmission and reflection spectra using the input-output formalism of quantum optics and the transfer matrix approach, we obtain the fidelity and efficiency of the switch with a single-photon input in both regimes. We find that a single waveguide-coupled cavity can route input photon wave packets with near-unity efficiency and fidelity if the wave packet width is smaller than the cavity mode linewidth. We also find that using multiple waveguide-coupled cavities increases the switching bandwidth, allowing wider wave packets to be routed with high efficiency and fidelity. For example, an array of three waveguide-coupled cavities can reflect an input Gaussian wave packet with a full width at half-maximum of 1 nm (corresponding to a few-picosecond pulse) with an efficiency Er=96.4% and a fidelity Fr=97.7%, or transmit the wave packet with an efficiency Et=99.7% and a fidelity Ft=99.8%. Such efficient, high-fidelity single-photon routing is essential for scalable photonic quantum technologies. Published by the American Physical Society 2024

Telling different unravelings apart via nonlinear quantum-trajectory averages

The Gorini-Kossakowski-Sudarshan-Lindblad master equation (ME) governs the density matrix of open quantum systems (OQSs). When an OQS is subjected to weak continuous measurement, its state evolves as a stochastic quantum trajectory, whose statistical average solves the ME. The ensemble of such trajectories is termed an unraveling of the ME. We propose a method to operationally distinguish unravelings produced by the same ME in different measurement scenarios, using nonlinear averages of observables over trajectories. We apply the method to the paradigmatic quantum nonlinear system of resonance fluorescence in a two-level atom. We compare the Poisson-type unraveling, induced by direct detection of photons scattered from the two-level emitter, and the Wiener-type unraveling, induced by phase-sensitive detection of the emitted field. We show that a quantum-trajectory-averaged variance is able to distinguish these measurement scenarios. We evaluate the performance of the method, which can be readily extended to more complex OQSs, under a range of realistic experimental conditions. Published by the American Physical Society 2024

Experimental certification of level dynamics in single-photon emitters

Emitters of single photons are essential resources for emerging quantum technologies and developed within different platforms including nonlinear optics and atomic and solid-state systems. The energy-level structures of emission processes are critical for reaching and controlling high-quality sources. The most commonly applied test uses a Hanbury Brown and Twiss (HBT) setup to determine the emitter energy-level structure based on fitting temporal correlations of photon detection events. However, only partial information about the emission process is extracted from such detection, that might be followed by an inconclusive fitting of the data. This process predetermines our limited ability to quantify and understand the dynamics in the photon emission process that are of importance for the applications in communication, sensing, and computing. In this work, we present a complete analysis based on all normalized coincidences between detection and no-detection events recorded in the same HBT setup to certify expected properties of an emitted photonic state. As a proof of concept we apply our methodology to single nitrogen-vacancy centers in diamond, in which case the certification conclusively rejects a model based on a two-level emitter that radiates a photonic state mixed with any classical noise background. Published by the American Physical Society 2024

Superquantization rule for multistability in driven-dissipative quantum systems

Abstract We present a superquantization rule which indicates the possible robust stationary states of a generic driven-dissipative quantum system. Multistability in a driven cavity mode interacting with a qudit is revealed hence within a simple intuitive picture. The accuracy of the superquantization approach is confirmed by numerical simulations of the underlying quantum model. In the case when the qudit is composed of several two-level emitters coupled homogeneously to the cavity, we demonstrate the robustness of the superquantized steady states to single-emitter decay.

Dense dipole-dipole-coupled two-level systems in a thermal bath

The quantum dynamics of a dense and dipole-dipole-coupled ensemble of two-level emitters interacting via their environmental thermostat is investigated. The static dipole-dipole interaction strengths are being considered strong enough but smaller than the transition frequency. Therefore, the established thermal equilibrium of ensemble's quantum dynamics is described with respect to the dipole-dipole-coupling strengths. We have demonstrated the quantum nature of the spontaneously scattered light field in this process for weaker thermal baths as well as non-negligible dipole-dipole couplings compared to the emitter's transition frequency. Furthermore, the collectively emitted photon intensity suppresses or enhances depending on the environmental thermal baths' intensities. Published by the American Physical Society 2024

Purcell-modified Doppler cooling of quantum emitters inside optical cavities

Standard cavity cooling of atoms or dielectric particles is based on the action of dispersive optical forces in high-finesse cavities. We investigate here a complementary regime characterized by large cavity losses, resembling the standard Doppler cooling technique. For a single two-level emitter a modification of the cooling rate is obtained from the Purcell enhancement of spontaneous emission in the large cooperativity limit. This mechanism is aimed at cooling quantum emitters without closed transitions, which is the case for molecular systems, where the Purcell effect can mitigate the loss of population from the cooling cycle. We extend our analytical formulation to the many-particle case governed by small individual coupling, but exhibiting large collective coupling. Published by the American Physical Society 2024

Violation of Bell inequality by photon scattering on a two-level emitter

Entanglement, the non-local correlations present in multipartite quantum systems, is a key resource for quantum technologies. It is therefore a major priority to develop simple and energy-efficient methods for generating high-fidelity entangled states. In the case of light, entanglement can be realized by interactions with matter but the required nonlinear interaction is often impractically weak. Here we show how a single two-level emitter deterministically coupled to light in a nanophotonic waveguide can be used to realize photonic quantum entanglement by excitation at the single-photon level. Efficient optical coupling enables mediation of two-photon interactions by the emitter, creating a strong nonlinearity that leads to entanglement. We experimentally verify energy–time entanglement by violating a Bell inequality in an interferometric measurement of the two-photon scattering response. The on-chip two-level emitter acts as a passive scatterer, so that no advanced spin control is required. As such, our method may provide a more efficient approach to synthesizing photonic entangled states for quantum simulators or metrology.

Jaynes-Cummings interaction with a traveling light pulse

The Jaynes-Cummings model provides a simple and accurate description of the interaction between a two-level quantum emitter and a single mode of quantum radiation. Due to the multimode continuum of eigenmodes in free space and in waveguides, the Jaynes-Cummings model should not be expected to properly describe the interaction between an emitter and a traveling pulse of quantum radiation. In this article, we review a cascaded quantum system approach that accurately describes the interaction of a quantum system with an incident quantum pulse of radiation. When applied to the two-level system, different iterations of this approach lead to master equations with different Jaynes-Cummings-like Hamiltonians and damping terms.

Photon statistics analysis of h-BN quantum emitters with pulsed and continuous-wave excitation

We report on the quantum photon statistics of hexagonal boron nitride (h-BN) quantum emitters by analyzing the Mandel Q parameter. We have measured the Mandel Q parameter for h-BN quantum emitters under various temperature and pump power excitation conditions. Under pulsed excitation, we can achieve a Mandel Q of −0.002, and under continuous-wave excitation, this parameter can reach −0.0025. We investigate the effect of cryogenic temperatures on Mandel Q and conclude that the photon statistics vary weakly with temperature. Through the calculation of spontaneous emission from an excited two-level emitter model, we demonstrate good agreement between the measured and calculated Mandel Q parameters when accounting for the experimental photon collection efficiency. Finally, we illustrate the usefulness of Mandel Q in quantum applications by the example of random number generation and analyze the effect of Mandel Q on the speed of generating random bits via this method.

Band gap engineering and controlling transport properties of single photons in periodic and disordered Jaynes–Cummings arrays

We theoretically study the single-photon transport properties in periodic and position-disordered Jaynes–Cummings (or JC) arrays of waveguide-coupled microtoroidal ring resonators, each interacting with a single two-level quantum emitter. Employing the real-space formalism of quantum optics, we focus on various parameter regimes of cavity quantum electrodynamics (cQED) to gain better control of single-photon propagation in such a many-body quantum optical setting. As for some of the key findings, we observe that the periodic setting leads to the formation of the band structure in the photon transmission spectra, which is most evident in the strong coupling regime of cQED. However, under resonant conditions with no losses, the application of Bloch’s theorem indicates that the width of forbidden gaps can be altered by tuning the emitter-cavity coupling to small values. Moreover, in the disordered case, we find that the single-photon transmission curves show the disappearance of band formation. However, spectral features originating from cQED interactions observed for the single atom-cavity problem remain robust against weak-disordered conditions. The results of this work may find application in the study of quantum many-body effects in the optical domain as well as in different areas of quantum computation and quantum networking.

Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models

The Tavis-Cummings model is a paradigmatic central-mode model in which a set of two-level quantum emitters (spins) are coupled to a collective cavity mode. Here we study the eigenstate spectrum, its localization properties, and the effect on dynamics, focusing on the two-excitation sector relevant for nonlinear photonics. These models admit two sources of disorder: in the coupling between the spins and the cavity, and in the energy shifts of the individual spins. While this model was known to be exactly solvable in the limit of a homogeneous coupling and inhomogeneous energy shifts, we establish here the solvability in the opposite limit of a homogeneous energy shift and inhomogeneous coupling, presenting the exact solution and corresponding conserved quantities. We identify three different classes of eigenstates, exhibiting different degrees of multifractality and semilocalization closely tied to the integrable points, and we study their stability to perturbations away from these solvable points. The dynamics of the cavity occupation number away from equilibrium, exhibiting boson bunching and a two-photon blockade, is explicitly related to the localization properties of the eigenstates, and it illustrates how these models support a collective spin description despite the presence of disorder. Published by the American Physical Society 2024

Tunable chiral bound states in a dimer chain of coupled resonators

We study an excitation hopping on a one-dimensional (1D) dimer chain of coupled resonators with the alternate on-site photon energies, which interacts with a two-level emitter (TLE) by a coupling point or two adjacent coupling points. In the single-excitation subspace, this system not only possesses two energy bands with propagating states, but also possesses photonic bound states. The number of bound states depends on the coupling forms between the TLE and the dimer chain. It is found that when the TLE is locally coupled to one resonator of the dimer chain, the bound-state that has mirror reflection symmetry. When the TLE is nonlocally coupled to two adjacent resonators, three bound states with preferred direction arise due to the mirror symmetry breaking. By using chirality to measure the asymmetry, it is found that the chirality of these bound states can be tuned by changing the energy differences of single photon in the adjacent resonators, the coupling strengths and the transition energy of the TLE.

Surface Topological Plexcitons: Strong Coupling in a Bi2Se3 Topological Insulator Nanoparticle-Quantum Dot Molecule

Strong coupling of quantum states with electromagnetic modes of topological matter offer an interesting platform for the exploration of new physics and applications. In this work, we report a novel hybrid mode, a surface topological plexciton, arising from strong coupling between the surface topological plasmon mode of a Bi2Se3 topological insulator nanoparticle and the exciton of a two-level quantum emitter. We study the power absorption spectrum of the system by working within the dipole and rotating-wave approximations, using a density matrix approach for the emitter, and a classical dielectric-function approach for the topological-insulator nanoparticle. We show that a Rabi-type splitting can appear in the spectrum suggesting the presence of strong coupling. Furthermore, we study the dependence of the splitting on the separation of the two nanoparticles as well as the dipole moment of the quantum emitter. These results can be useful for exploring exotic phases of matter, furthering research in topological insulator plasmonics, as well as for applications in the far-infrared and quantum computing.

Electron-assisted probing of polaritonic light–matter states

Abstract Thanks to their exceptional spatial, spectral and temporal resolution, highly-coherent free-electron beams have emerged as powerful probes for material excitations, enabling their characterization even in the quantum regime. Here, we investigate strong light–matter coupling through monochromatic and modulated electron wavepackets. In particular, we consider an archetypal target, comprising a nanophotonic cavity next to a single two-level emitter. We propose a model Hamiltonian describing the coherent interaction between the passing electron beam and the hybrid photonic–excitonic target, which is constructed using macroscopic quantum electrodynamics and fully parameterized in terms of the electromagnetic dyadic Green’s function. Using this framework, we first describe electron-energy-loss and cathodoluminescence spectroscopies, and photon-induced near-field electron emission microscopy. Finally, we show the power of modulated electrons beams as quantum tools for the manipulation of polaritonic targets presenting a complex energy landscape of excitations.

Controlling atom-photon bound states in a coupled resonator array with a two-level quantum emitter.

We consider a one-dimensional (1D) coupled-resonator array (CRA), where a two-level quantum emitter (2LE) is electric-dipole coupled to the modes of two adjacent resonators. We investigate the energy spectrum, the photon probability distribution of the bound states, and the emission process of the 2LE into the CRA vacuum. A quantum phase transition is found which is characterized by the change of the number of the out-of-band discrete levels. The condition for this change is also presented. The photon wave functions of bound states are found to be asymmetry around the position of the 2LE when the coupling strengths between the 2LE and the resonator are not equal, and they have the same preferred directions which are primarily determined by the larger one among the coupling strengths. The presence of the atom-photon bound states is manifested in the form of a stationary oscillation or a non-vanishing constant in the long enough time.

Dynamics of a system of two-level emitters in the Dicke model taking into account small correlations between them

On the basis of our previous study of the quantum system of atoms and the electromagnetic field, a system of non-relativistic stationary and non-interacting small one-electron atoms located in a region much smaller in size than the characteristic wavelength of the field is considered. Atoms are considered in the two-level approximation and interact with the field by dipole-electric interaction. We carefully analyze the state space of the atom and the operators in it in the spin s = 1 / 2 formalism, which leads to the Dicke Hamiltonian in terms of the spin formalism. Non-equilibrium states of the system are investigated using the reduced description method and described by the occupation numbers of photon states ηαk , the degree of excitation of the atoms η1 , and the value of correlations between them η2. The basis of our consideration is the Peletminsky–Yatsenko model, the foundations of which and, in particular, the approach to solving the Cauchy problem, based on the notion of effective initial conditions, are thoroughly discussed. Since the Dicke model deals with the dynamics of a system of particles with spin, the technique of calculating the average values of products of spin operator proposed by Vax, Larkin, and Pikin is developed to a certain extent. Averages in a state with a statistical operator of a system of atoms with given excitations are considered. The obtained results are maximally simplified in the case of spin s = 1 / 2 . The impossibility of calculations with a quasi-local statistical operator when describing the state of the system with parameters ηαk , η1, η2 is overcome with using a somewhat simplified approach of our previous work, in which, instead of a parameter η2, the system is described by a small deviation δη2 = η2 - η20 of the parameter η2 from its value η20 when describing the system only by the parameters ηαk, η1. Developed approaches to calculations with spin operators are used to calculate the quasi-equilibrium statistical operator when choosing of the quantities ηαk, η1 , and δη2 as reduced description parameters and the right-hand sides of the time equations for these parameters.

Taking into account the influence of correlations on the system dynamics in the reduced description method

A complex of issues related to using the Peletminsky–Yatsenko model for the study of non-equilibrium processes is investigated. The problems are associated with the inability of performing the calculation of necessary averages when system states are described by a new, wider set of reduced description parameters, in particular, fluctuations. A matter system interacting with a non-equilibrium system of bosons is considered. The substance is described by two reduced description parameters η1 , η2 and calculations with the quasi-equilibrium statistical operator corresponding to these parameters are technically impossible; at the same time, the calculations can be performed with such operator in the case of the only parameter η1 . Overcoming this problem by considering only small values δη2 of the other reduced description parameter is proposed. An exact definition of δη2 is given, and the theory of perturbations by powers δη2 is developed for the calculation of the initial quasi-equilibrium statistical operator with accuracy up to second-order contributions. Since all further averages are calculated only with the named operator including only η1 , the simplified calculation procedure is carried out for it.On this basis, the theory of non-equilibrium processes in the system of two-level emitters interacting with the boson field is developed. The emitter system is described by excitation degree η1 and the value of emitter correlations η2. The system is considered as a system of spins. The mathematically identical Dicke model describing superradiance and Wagner model introduced for the analogous acoustic phenomenon description are studied. The quasi-equilibrium statistical operator calculation is constructed.

Phonon Mediated Collective Dynamics of Coherently Pumped Two-Level Emitters

"We investigate the collective quantum dynamics of an ensemble of two-level emitters, embedded in a crystal, and coherently pumped by a moderately intense, and externally applied coherent electromagnetic field. The ensemble is damped preponderantly via the surrounding phonon reservoir which mediates the inter-particle collective interactions. We have found that generally phonon transitions among the corresponding dressed states are taking place involving simultaneously many single emitters or pairs of two-level emitters, respectively. In both cases the phonon intensity can be proportional to the squared number of involved two-level emitters."