Two-level Emitters Research Articles

Strong nonlinearity-induced correlations for counterpropagating photons scattering on a two-level emitter

We analytically treat the scattering of two counter-propagating photons on a two-level emitter embedded in an optical waveguide. We find that the non-linearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quantified via a reduction in coincident clicks in a Hong-Ou-Mandel measurement setup, analogous to a linear beam splitter. Changes to the spectra and phase of the scattered photons, however, would lead to reduced interference with other photons when implemented in a larger optical circuit. We introduce suitable fidelity measures which account for these changes, and find that high values can still be achieved even when accounting for all properties of the scattered photonic state.

Quantum Emitters near Layered Plasmonic Nanostructures: Decay Rate Contributions

We introduce a numerical framework for calculating decay rate contributions when excited two-level quantum emitters are located near layered plasmonic nanostructures, particularly emphasizing the case of plasmonic nanostructures atop metal substrates where three decay channels exist: free space radiation, Ohmic losses, and excitation of surface plasmon polaritons (SPPs). The calculation of decay rate contributions is based on Huygen’s equivalence principle together with a near-field to far-field transformation of the local electric field, thereby allowing us to discern the part of the electromagnetic field associated with free propagating waves rather than SPPs. The methodology is applied to the case of an emitter inside and near a gap-plasmon resonator, emphasizing strong position and orientation dependencies of the total decay rate, contributions of different decay channels, radiation patterns, and directivity of SPP excitation.

Time-dependent highly correlated photons

Enhanced time-dependent photon–photon correlations are shown to occur in a setup consisting of a spontaneously damped and strongly laser-pumped two-level emitter embedded in a leaking optical micro-resonator. The nonlinear effects arising for intense qubit-cavity couplings are responsible for increasing the photon correlations and their intensity. Particularly, the photon correlations at certain time-intervals are larger than those in the steady-state.

Quantum spin dimers from chiral dissipation in cold-atom chains.

We consider the nonequilibrium dynamics of a driven dissipative spin chain with chiral coupling to a one-dimensional (1D) bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasicondensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left- and right-moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.

Quantum dynamics of a two-level emitter with a modulated transition frequency

The resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency of modulation is selected to be of the order of the bare-state spontaneous decay rate. In this way, one can induce quantum interference effects and, consequently, quantum coherences among multiple decaying transition pathways. Depending on the modulation depth and its absolute phase, both the spontaneous emission and the frequency shift may be conveniently modified and controlled.

Cavity-output-field control via interference effects

We show how interference effects are responsible for manipulating the output electromagnetic field of an optical micro-resonator in the good-cavity limit. The system of interest consists in a moderately strongly pumped two-level emitter embedded in the optical cavity. When an additional weaker laser of the same frequency is pumping the combined system through one of the resonator's mirrors then the output cavity electromagnetic field can be almost completely suppressed or enhanced. This is due to the interference among the scattered light by the strongly pumped atom into the cavity mode and the incident weaker laser field. The result applies to photonic crystal environments as well.

Large and well-defined Rabi splitting in a semiconductor nanogap cavity.

We propose a nanogap structure composed of semiconductor nanoparticles forming an optical cavity. The resonant excitation of excitons in the nanoparticles can generate a localized strong light field in the gap region, also called "hot spot". The spectral width of the hot spot is significantly narrow because of the small exciton damping and the dephasing at low temperature, so the semiconductor nanogap structure acts as a high-Q cavity. In addition, the interaction between light and matter at the nanogap is significantly larger than that in a conventional microcavity, because the former has a small cavity-mode volume beyond the diffraction limit. We theoretically demonstrate the large and well-defined vacuum-Rabi splitting of a two-level emitter placed inside the semiconductor nanogap cavity: the Rabi splitting energy of 1.7 meV for the transition dipole moment of the emitter (25 Debye) is about 6.3 times larger than the spectral width. An optical cavity providing such a large and well-defined Rabi splitting is highly suited for studying characteristic features of the cavity quantum electrodynamics and for the development of new applications.

Spontaneous collective coherence in driven dissipative cavity arrays

We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay exponentially with distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous build-up of collective coherence in the system.

Analytical Expression for the Relaxation Rate of Emitter-Near-Metal Nanoparticles

We present a simple analytical expression for the full relaxation rate of the excited state of the two-level resonant emitter placed close to a metal nanoparticle with localized plasmon resonance excited by the emitter. We take into account the interaction of the emitter with all multipole polarization modes and the radiation absorption in the nanoparticle. Analytical and numerical estimations of the full relaxation rate are in good agreement. Thus, only two modes are sufficient for describing the electromagnetic interaction of the dipole emitter and the metal nanoparticle, namely, the dipole mode and the mode related to the emitter image under the nanoparticle surface. Such “two-mode” approximation can simplify the analysis of optical properties of nanoplasmonic structures. In particular, the proposed expression for the full relaxation rate is helpful in the modeling of plasmonic nanolasers.

Quantum Langevin model for nonequilibrium condensation

We develop a quantum model for nonequilibrium Bose-Einstein condensation of photons and polaritons in planar microcavity devices. The model builds on laser theory and includes the spatial dynamics of the cavity field, a saturation mechanism, and some frequency dependence of the gain: quantum Langevin equations are written for a cavity field coupled to a continuous distribution of externally pumped two-level emitters with a well-defined frequency. As an example of application, the method is used to study the linearized quantum fluctuations around a steady-state condensed state. In the good-cavity regime, an effective equation for the cavity field only is proposed in terms of a stochastic Gross-Pitaevskii equation. Perspectives in view of a full quantum simulation of the nonequilibrium condensation process are finally sketched.

Estimation of atomic interaction parameters by photon counting

Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon-counting signals can be exploited to optimally extract information about the physical parameters that govern the dynamics of the emitter. For a simple two-level emitter subject to photon counting, we show that the Fisher information and the Cram\'er-Rao sensitivity bound based on the full detection record can be evaluated from the waiting-time distribution in the fluorescence signal which can, in turn, be calculated for both perfect and imperfect detectors by a quantum trajectory analysis. We provide an optimal estimator achieving that bound.

Strong anisotropic lifetime orientation distributions of a two-level quantum emitter around a plasmonic nanorod.

Spontaneous emission lifetime orientation distributions of a two-level quantum emitter in metallic nanorod structures are theoretically investigated by the rigorous electromagnetic Green function method. It was found that spontaneous emission lifetime strongly depended on the transition dipole orientation and the position of the emitter. The anisotropic factor defined as the ratio between the maximum and minimum values of the lifetimes along different dipole orientations can reach up to 103. It is much larger than those in dielectric structures which are only several times usually. Our results show that the localized plasmonic resonance effect provides a new degree of freedom to effectively control spontaneous emission by the dipole orientation of the quantum emitters.

Single-photon quantum router with multiple output ports.

The routing capability is a requisite in quantum network. Although the quantum routing of signals has been investigated in various systems both in theory and experiment, the general form of quantum routing with many output terminals still needs to be explored. Here we propose a scheme to achieve the multi-channel quantum routing of the single photons in a waveguide-emitter system. The channels are composed by the waveguides and are connected by intermediate two-level emitters. By adjusting the intermediate emitters, the output channels of the input single photons can be controlled. This is demonstrated in the cases of one output channel, two output channels and the generic N output channels. The results show that the multi-channel quantum routing of single photons can be well achieved in the proposed system. This offers a scheme for the experimental realization of general quantum routing of single photons.

Optical cavity quantum electrodynamics with dark-state polaritons

We present a theoretical scheme to study optical cavity quantum electrodynamics using dark-state polaritons. Exploiting the highly tunable lifetimes of the photons in the form of cavity dark-state polaritons, we push the strong coupling of single optical photons to an effective two-level emitter in a Rydberg-blockade atomic ensemble to an unprecedented regime. The resulting Jaynes\char21{}Cummings model with extremely strong coupling is of fundamental interest. We discuss applications in controlled quantum Rabi oscillation, nonlinear spectroscopy of the Jaynes-Cummings ladder, as well as the generation of nonclassical states, all based on light-matter interactions in the optical domain.

Superluminal surface polaritonic solitons at weak light level via coherent population oscillation

We investigate the possibility of generating nonlinear surface polaritons at the interface between a negative-index metamaterial and a dielectric doped with two-level quantum emitters by means of coherent population oscillation (CPO) working at room temperature. Based on the CPO and the strong confinement of the optical field near the interface, we find that the system can possess a giant Kerr nonlinearity. We demonstrate that it is possible to obtain a type of surface polaritonic solitons which is not only robust during propagation but also has ultraweak generation power and superluminal propagating velocity.

Roles of the vacuum field bath in a cavity QED system beyond the Weisskopf-Wigner approximation: Coupling renormalization, off-resonance assisted feeding, and pure dephasing

We present nonperturbative treatment of the vacuum field bath for two cases, a two-level emitter (TLE) in free space and a lossy TLE coupled to a cavity mode (CM), and the condition that guarantees the validity of the perturbative treatment in both cases is studied. It is shown that the perturbative treatment in the first case is always valid for a real system. In the second case, nevertheless, the perturbative treatment ignores a coupling term, which can bring effects similar to a phonon bath, e.g., coupling renormalization, off-resonance assisted feeding, and pure dephasing inside the resonance region. All of these effects are important for understanding the experimental observations, including the far-off-resonance cavity fluorescence and the additional CM line inside the resonance region in the strong coupling regime.

Stochastic excitation during the decay of a two-level emitter subject to homodyne and heterodyne detection

We study the dynamics of an atomic two-level system decaying by spontaneous emission of light. Subject to continuous detection of the radiated field, the system tends with certainty to the ground state in the long time limit, but at initial times the excited state population exhibits non-trivial stochastic behavior. Employing methods from Ito calculus, we characterize this behavior, and we show, for example, that the emitter, as a result of in-phase homodyne measurements, may become fully excited during the decay process while heterodyne and out of phase homodyne measurements do not drive the atom completely into the excited state.

Cooling a two-level emitter in photonic-crystal environments

We investigate the resonant cooling phenomena of a driven two-level radiator embedded in a photonic-crystal structure. We find that cooling occurs even at laser-atom-frequency resonance. This happens due to atomic dressed-state coupling with different strengths, resulting in population redistribution and cooling. Furthermore, for off-resonant driving the two-level particle can be in either the ground or excited bare state. This may help in the engineering of different amplified optical devices as well as highly coherent light sources.

Dynamical Properties of Nanolasers Based on Few Discrete Emitters

We investigate the dynamical properties of nanolasers comprising a few two-level emitters coupled to an optical cavity. A set of rate equations is derived, which agree very well with a solution of the full master equation model and makes it simple to investigate the properties of the system. Using a linearized version of these rate equations, we can analytically express the response of the nanolaser to a modulation of the pumping rate. These results are compared to the modulation response obtained directly from the master equation using a novel method. Using the rate equation method, we calculate the modulation bandwidth and show that, contrary to conventional semiconductor lasers, the nanolaser is typically over-damped and displays a dip in the modulation bandwidth as the two-level systems become inverted. Both these features can be traced back to the modeling of the emitters as two-level systems that are incoherently pumped.

Theory and simulation of cavity quantum electro-dynamics in multi-partite quantum complex systems

The cavity quantum electrodynamics of various complex systems is here analyzed using a general versatile code developed in this research. Such quantum multi-partite systems normally consist of an arbitrary number of quantum dots in interaction with an arbitrary number of cavity modes. As an example, a nine-partition system is simulated under different coupling regimes, consisting of eight emitters interacting with one cavity mode. Two-level emitters (e.g. quantum dots) are assumed to have an arrangement in the form of a linear chain, defining the mutual dipole–dipole interactions. It was observed that plotting the system trajectory in the phase space reveals a chaotic behavior in the so-called ultrastrong-coupling regime. This result is mathematically confirmed by detailed calculation of the Kolmogorov entropy, as a measure of chaotic behavior. In order to study the computational complexity of our code, various multi-partite systems consisting of one to eight quantum dots in interaction with one cavity mode were solved individually. Computation run times and the allocated memory for each system were measured.