Two-level Emitters Research Articles

Interference-induced directional emission from an unpolarized two-level emitter into a circulating cavity

Chiral coupling between quantum emitters and evanescent fields allows directional emission into nanophotonic devices and is now considered to be a vital ingredient for the realization of quantum networks. However, such coupling requires a well-defined circular dipole moment for the emitter---something difficult to achieve for solid-state emitters at room temperature due to thermal population of available spin states. Here, we demonstrate that a two-level emitter with a randomly polarized dipole moment can be made to emit directionally into a circulating cavity if a separate emitter is chirally coupled to the same cavity, for the case when both emitter-cavity couplings are strong but in the bad-cavity regime. Our analysis of this system first considers a transient scenario, which highlights the physical mechanism giving rise to the directional emission of the two-level emitter into the cavity. An alternative setup involving a weak laser field continuously driving the system is also considered, where the directionality (our proposed figure of merit for this scheme) is shown to be significantly more robust against noise processes. The results presented here take the form of approximate analytical expressions backed by complete numerical simulations of the system.

Quantum limits to resolution and discrimination of spontaneous emission lifetimes

In this work we investigate the quantum information theoretical limits to several tasks related to lifetime estimation and discrimination of a two-level spontaneous optical emitter. We focus in particular on the model problem of resolving two mutually incoherent exponential decays with highly overlapping temporal probability profiles. Mirroring recent work on quantum-inspired super-resolution of point emitters, we find that direct lifetime measurement suffers from an analogue of "Rayleigh's Curse" when the time constants of the two decay channels approach one another. We propose alternative measurement schemes that circumvent this limit, and also demonstrate superiority to direct measurement for a related binary hypothesis test. Our findings add to a growing list of examples in which a quantum analysis uncovers significant information gains for certain tasks in opto-molecular metrology that do not rely on multiphoton interference, but evidently do benefit from a more thorough exploitation of the coherence properties of single photons.

Two emitters coupled to a bath with Kerr-like nonlinearity: Exponential decay, fractional populations, and Rabi oscillations

We consider two noninteracting two-level emitters that are coupled weakly to a one-dimensional nonlinear waveguide. Due to the Kerr-like nonlinearity, the waveguide considered supports---in addition to the scattering continuum---a two-body bound state. As such, the waveguide models a bath with nontrivial mode structure. Solving the time-dependent Schr\"odinger equation, the radiation dynamics of the two emitters, initially prepared in their excited states, is presented. Changing the emitter frequency such that the two-emitter energy is in resonance with one of the two-body bound states, radiation dynamics ranging from exponential decay to fractional populations to Rabi oscillations is observed. Along with the detuning, the dependence on the separation of the two emitters is investigated. Approximate reduced Hilbert-space formulations, which result in effective emitter separation and momentum dependent interactions, elucidate the underlying physical mechanisms and provide an avenue to showcase the features that would be absent if the one-dimensional waveguide did not contain a nonlinearity. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology. In addition, the weak-coupling Schr\"odinger equation based results provide critical guidance for the development of master equation approaches.

Selective mode excitations and spontaneous emission engineering in quantum emitter-photonic structure coupled systems.

We study the excitation conditions of the supported field modes, as well as the spontaneous decay property of a two-level quantum emitter coupled to photonic structures containing topological insulators (TIs) and left-handed materials. Within the proper field quantization scheme, the spontaneous decay rates of dipoles with different polarizations are expressed in forms of the Green's functions. We find that in the proposed structure, the variation in the topological magnetoelectric polarizability (TMP) has a deterministic effect on the excitation of different field modes. As the result, the spontaneous decay property of the quantum emitter can be engineered. For a dipole placed in different spatial regions, the spontaneous decay feature indicates a dominant contribution from the waveguide modes, the surface plasmon modes or the free vacuum modes. Moreover, a special kind of the surface plasmon modes displaying asymmetric density of states at the interfaces, becomes legal in the presence of nontrivial TIs. These phenomena manifest the feasibility in controlling dipole emissions via manipulations of the topological magnetoelectric (TME) effect. Our results have potential applications in quantum technologies relied on the accurate control over light-matter interactions.

Deterministic Photon Sorting in Waveguide QED Systems.

Sorting quantum fields into different modes according to their Fock-space quantum numbers is a highly desirable quantum operation. In this Letter, we show that a pair of two-level emitters, chirally coupled to a waveguide, may scatter single- and two-photon components of an input pulse into orthogonal temporal modes with a fidelity ≳0.9997. We develop a general theory to characterize and optimize this process and reveal that such a high fidelity is enabled by an interesting two-photon scattering dynamics: while the first emitter gives rise to a complex multimode field, the second emitter recombines the field amplitudes, and the net two-photon scattering induces a self-time reversal of the input pulse mode. The presented scheme can be employed to construct logic elements for propagating photons, such as a deterministic nonlinear-sign gate with a fidelity ≳0.9995.

Nonreciprocal Single-Photon Band Structure.

We study a single-photon band structure in a one-dimensional coupled-resonator optical waveguide that chirally couples to an array of two-level quantum emitters (QEs). The chiral interaction between the resonator mode and the QE can break the time-reversal symmetry without the magneto-optical effect and an external or synthetic magnetic field. As a result, nonreciprocal single-photon edge states, band gaps, and flat bands appear. By using such a chiral QE coupled-resonator optical waveguide system, including a finite number of unit cells and working in the nonreciprocal band gap, we achieve frequency-multiplexed single-photon circulators with high fidelity and low insertion loss. The chiral QE-light interaction can also protect one-way propagation of single photons against backscattering. Our work opens a new door for studying unconventional photonic band structures without electronic counterparts in condensed matter and exploring its applications in the quantum regime.

All-optical dynamic modulation of spontaneous emission rate in hybrid optomechanical emitter-cavity systems

Optomechanics is the study of the interaction between nano-objects and light fields through radiation pressure. Recent sophisticated optomechanical systems consist of strongly coupled mechanical and optical resonators and are made using semiconductor nanofabrication techniques. Although the optomechanical systems have exhibited their powerful capability of controlling photons, they are scarcely used to control the solid-state artificial atoms that emit photons. The main reason is that an efficient coupling mechanism remains unexplored. Here, we hybridize a silicon-integrated optomechanical resonator with two-level atom-like emitters to demonstrate an optomechanical cavity quantum electrodynamic (cQED) effect. With this system and the effect, we realize the dynamic modulation of the spontaneous emission rate. We choose copper dopants in silicon as the emitters for its narrow linewidth (0.3 nm) and long lifetime ( ∼ 30 n s ). Our judiciously designed coupled-nanobeam optomechanical resonator achieves a strong Purcell effect and high cavity-modulation performances. The optical cavity of the optomechanical resonator is dynamically coupled to the emission line and, as a result, on-demand sharp pulses (up to 9.5-fold intensity enhancement and 3.5 ns in duration, which is one ninth of the emission lifetime) appear along the photoluminescence decay. These experimental results are exactly explained with an analytical model that combines optomechanical and cQED theories. Considering that dopants in silicon are highly competitive qubits, we believe that our optomechanical cQED technology will find important applications in the quantum era.

Modulating the temporal dynamics of nonlinear ultrafast plasmon resonances

Surface plasmon-induced nonlinear optical resonances have shown immense potential in advanced optical imaging and nonlinear photonic devices. However, the ultrashort lifetime of these intense nonlinear fields inhibits their effective use in the vast applications of quantum plasmonics. Here, we propose enhancement in the lifetime of fast decaying second harmonic (SH) plasmon mode through a weak and pure resonant interaction with a two-level quantum emitter (QE). We compute the time evolution of SH response under a two-coupled oscillator model, in which we examine the interaction of short-lived SH mode supported by Au nanoparticle (AuNP) with long-lived dark mode (DM) or QE systems. To analyze the effect of spectral and temporal properties of DM and QE on the SH field, we evaluate the lifetime enhancement factor as a function of coupling strength and tuned resonant frequencies. The results show that tiny object like QE with sharp spectral bandwidth, small decay rate, and large oscillating strength is more efficient to control and probe the temporal dynamics of the SH field, as compared to DM which have a wide spectral bandwidth. Also, we control the lifetime of the SH mode after the natural decay time of the fundamental mode (FM), which distinguishes SH mode irrespective of its spatial convolution with elementary modes. Our proposed AuNP-QE coupled plasmonic system supporting nonlinear signal with enhanced temporal character paves its way for designing efficient on-chip nonlinear optical devices and can be a powerful tool in ultrahigh resolution nonlinear optical imaging.

Coherent perfect absorption in Tavis-Cummings models.

We theoretically study the conditions under which two laser fields can undergo Coherent Perfect Absorption (CPA) when shined on a single-mode bi-directional optical cavity coupled with two two-level quantum emitters (natural atoms, artificial atoms, quantum dots, qubits, etc.). In addition to being indirectly coupled through the cavity-mediated field, in our Tavis-Cummings model, the two quantum emitters (QEs) are allowed to interact directly via the dipole-dipole interaction (DDI). Under the mean-field approximation and low-excitation assumption, in this work, we particularly focus on the impact of DDI on the existence of CPA in the presence of decoherence mechanisms (spontaneous emission from the QEs and the leakage of photons from the cavity walls). We also present a dressed-state analysis of the problem to discuss the underlying physics related to the allowed polariton state transitions in the Jaynes-Tavis-Cummings ladder. As a key result, we find that in the strong-coupling regime of cavity quantum electrodynamics, the strong DDI and the emitter-cavity detuning can act together to achieve the CPA at two laser frequencies tunable by the inter-atomic separation which are not possible to attain with a single QE in the presence of detuning. Our CPA results are potentially applicable in building quantum memories that are an essential component in long-distance quantum networking.

Спектры поглощения пробного сигнала и резонансной флуоресценции для излучателей при их взаимодействии с локальным окружением в прозрачных средах

The current paper demonstrates theoretical analysis of two types of spectral curves for several configurations of system of two-level light emitters, considering the influence of local field and close environment inside a transparent medium. Probe field absorption spectra and resonant fluorescence spectra are calculated under excitation of a strong monochromatic cw laser. The sensitivity of absorption and emission optical spectroscopy method is compared for revealing the effects of the medium on individual emitters and their ensembles. Spectral curves were calculated for model emitters considering local field influence of a transparent dielectric medium and local electron-phonon interactions, which determined the response of the emitters to an external laser field and effective relaxation mechanisms. The calculation formalism is based on a semiclassical approach, while the relaxation processes associated with the phonon contribution are introduced phenomenologically with references to other studies.

Three methods for the single-photon transport in a chiral cavity quantum electrodynamics system

We investigate the single-photon transport problem in the system of a Whispering-Gallery mode microresonator directionally coupled with a two-level quantum emitter (QE). This QE-microresonator coupling system can usually be studied by cavity quantum electrodynamics and the single-photon transport methods. However, we find that if we treat a two-level QE as a single-photon phase-amplitude modulator, we can also deal with such systems using the transfer matrix method. Further, in theory, we prove that these three methods are equivalent. The corresponding relations of respective parameters among these approaches are precisely deduced. Our work can be extended to a multiple-resonator system interacting with two-level QEs in a chiral way. Therefore, the transfer matrix method may provide a convenient and intuitive form for exploring more complex chiral QE-resonator interaction systems.

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The current paper demonstrates theoretical analysis of two types of spectral curves for several configurations of system of two-level light emitters, considering the influence of local field and close environment inside a transparent medium. Probe field absorption spectra and resonant fluorescence spectra are calculated under excitation of a strong monochromatic cw laser. The sensitivity of absorption and emission optical spectroscopy method is compared for revealing the effects of the medium on individual emitters and their ensembles. Spectral curves were calculated for model emitters considering local field influence of a transparent dielectric medium and local electron-phonon interactions, which determined the response of the emitters to an external laser field and effective relaxation mechanisms. The calculation formalism is based on a semiclassical approach, while the relaxation processes associated with the phonon contribution are introduced phenomenologically with references to other studies.

Quantum interference effect in plasmonic transmission in the presence of quantum emitters

In this paper, we show how to enhance the transmission of the surface plasmon field using several interacting two-level quantum emitters placed in a plasmonic environment. Our model relies on quantum interference effect and, therefore, can be treated as a plasmonic analog of the electromagnetic induced transparency, usually referred to in the context of driven atomic systems. Moreover, our model with multiple interacting quantum emitters, similar to Ising spin chain, can be used for broadband transmission of the surface plasmon field.

Correlations in superradiance of a two-dimensional system

The process of cooperative spontaneous emission in a system of two-level emitters interacting via electromagnetic field is analyzed using the Bogolyubov reduced description method, which provides the possibility of studying the state of the generated field. Field macrostates are described with electric and magnetic field amplitudes and binary correlation functions of their components. Since the previously obtained set of differential equations describing the Dicke system evolution with considering field correlations is very cumbersome, we must find some way of simplifying the model to make it accessible for numerical modeling. The general picture of correlation development can be elucidated with using one- and two-dimensional models. The paper presents the set of evolution equations for Dicke system with fixed orientation of dipole moments of emitters forming a two-dimensional structure. The material equations and equilibrium correlations are discussed. The transition to the Cauchy problem for ordinary differential equations is proposed.

On the dissipative dynamics of entangled states in coupled-cavity quantum electrodynamics arrays

We examine the dissipative dynamics of N00N states with an arbitrary photon number N in two architectures of fiber-coupled optical ring resonators (RRs) interacting with two-level quantum emitters (QEs). One architecture consists of a two-way cascaded array of emitter–cavity systems, while in the other architecture, we consider two fiber-coupled RRs, each coupled to multiple dipole–dipole interacting (DDI) QEs. Our focus in this paper is to study how an initially prepared multiple excitation atomic N00N state transfers to the RRs and then how rapidly it decays in these open cavity quantum electrodynamics setups while varying the emitter–cavity coupling strengths, emitter–cavity detuning, and backscattering from cavity modes. We present a general theoretical formalism valid for any arbitrary numbers of QEs, RRs, and N numbers in the N00N state for both schemes. As examples, we discuss the cases of single- and two-excitation N00N states and report the comparison of our findings in both schemes. As one of the main results, we conclude that the array scheme tends to store N00N for longer times, while the DDI scheme supports higher fidelity values. The results of this study may find applications in designing new multiparty entanglement-based protocols in quantum metrology and quantum lithography.

Photon-emitter dressed states in a closed waveguide

We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the stable states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed states, that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field of quantum information.

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.

Low-frequency fluorescence spectrum of a laser driven polar quantum emitter damped by squeezed vacuum with finite bandwidth

A two-level quantum emitter with broken inversion symmetry driven by external semiclassical monochromatic high-frequency electromagnetic (e.g., laser) field and damped by squeezed vacuum reservoir with finite bandwidth is presented. The squeezed vacuum source is assumed to be either degenerate parametric oscillator (DPO) or a non-degenerate parametric oscillator (NDPO). It is shown that the shape of low-frequency fluorescence spectrum of the emitter can be effectively alternated by controlling the degree of the squeezed vacuum source degeneration and phase of the squeezing.

Stationary excitation waves and multimerization in arrays of quantum emitters

We explore the features of an equally-spaced array of two-level quantum emitters, that can be either natural atoms (or molecules) or artificial atoms, coupled to a field with a single continuous degree of freedom (such as an electromagnetic mode propagating in a waveguide). We investigate the existence and characteristics of bound states, in which a single excitation is shared among the emitters and the field. We focus on bound states in the continuum, occurring in correspondence of excitation energies in which a single excited emitter would decay. We characterize such bound states for an arbitrary number of emitters, and obtain two main results, both ascribable to the presence of evanescent fields. First, the excitation profile of the emitter states is a sinusoidal wave. Second, we discuss the emergence of multimers, consisting in subsets of emitters separated by two lattice spacings in which the electromagnetic field is approximately vanishing.

Quantum Optics in Nanostructures.

This review is devoted to the study of effects of quantum optics in nanostructures. The mechanisms by which the rates of radiative and nonradiative decay are modified are considered in the model of a two-level quantum emitter (QE) near a plasmonic nanoparticle (NP). The distributions of the intensity and polarization of the near field around an NP are analyzed, which substantially depend on the polarization of the external field and parameters of plasmon resonances of the NP. The effects of quantum optics in the system NP + QE plus external laser field are analyzed—modification of the resonance fluorescence spectrum of a QE in the near field, bunching/antibunching phenomena, quantum statistics of photons in the spectrum, formation of squeezed states of light, and quantum entangled states in these systems.