The present paper theoretically investigates features of quantum dynamics for localized plasmons in three-particle or four-particle spaser systems consisting of metal nanoparticles and semiconductor quantum dots. In the framework of the mean field approximation, the conditions for the observation of stable stationary regimes for single-particle plasmons in spaser systems are revealed, and realization of these regimes is discussed. The strong dipole-dipole interaction between adjacent nanoparticles for the four-particle spaser system is investigated. We show that this interaction can lead to the decreasing of the autocorrelation function values for plasmons. The generation of entangled plasmons in a three-particle spaser system with nonlinear plasmon-exciton interaction is predicted. For the first time the use of an external magnetic field is proposed for control of the cross-correlation between plasmons in the three-particle spaser system.
We present a unified approach to describe spasing in plasmonic systems modeled by quantum emitters interacting with resonant plasmon mode. We show that spaser threshold implies detailed energy transfer balance between the gain and plasmon mode and derive explicit spaser condition valid for arbitrary plasmonic systems. By defining carefully the plasmon mode volume relative to the gain region, we show that the spaser condition represents, in fact, the standard laser threshold condition extended to plasmonic systems with dispersive dielectric function. For extended gain region, the saturated mode…
At the plasmon resonance, high Joule losses in a metal nanoparticle of a spaser result in its low Q-factor. Due to the latter, to achieve the spasing regime, in which the number of coherent plasmons exceeds the number of incoherent plasmons, unsustainably high pump rates may be required. We show that under the condition of loss compensation by a spaser driven by an external optical wave, the number of coherent plasmons increases dramatically, and the quantum noise is suppressed. Since the compensation of losses of the driving wave may occur even near the spasing threshold, the number of cohere…
In this work, a new structure is suggested for spasing. The presented spaser is made up of a graphene nanosphere, which supports localized surface plasmon modes, and a quantum dot array, acting as a gain medium. The gain medium is pumped by an external laser source. Since all the plasmons are carried on a graphene platform, the structure features coherent surface plasmons with high confinement and large life time. All the structure is analyzed theoretically using full quantum mechanical description. The main advantage of the proposed spaser is the simple tuning capability of it by changing gra…
We study the effect of off-resonant plasmon modes on spaser threshold in nanoparticle-based spasers. We develop an analytical semiclassical model and derive spaser threshold condition accounting for gain coupling to higher-order plasmons. We show that such a coupling originates from inhomogeneity of gain distribution near the metal surface and leads to an upward shift of spaser frequency and population inversion threshold. This effect is similar, albeit significantly weaker, to quenching of plasmon-enhanced fluorescence near metal nanostructures due to excitation of off-resonant modes with wid…
In the approach to the stationary regime, a spaser exhibits complicated and highly nonlinear dynamics with anharmonic oscillations.1 We demonstrate that these oscillations are due to Rabi oscillations of the quantum dot in the field of the nanoparticle. We show that the oscillations may or may not arise dependent on the initial conditions.
We show that net amplification of surface plasmons is achieved in channel in a metal plate due to nonradiative excitation by quantum dots. This makes possible lossless plasmon transmission lines in the channel as well as the amplification and generation of coherent surface plasmons. As an example, a ring channel spaser is considered.
We present an electrodynamical model of a novel quantum plasmonic device - magneto-optical spaser. It is shown that a spherical gain nanoparticle coated with a metallic magneto-optical shell can operate as a spaser amplifying circularly polarized surface plasmons. The magneto-optical spaser may be used in design of optical isolator in plasmonic transmission lines as well as in spaser spectrometry of chiral molecules.
We demonstrate that the conditions of spaser generation and the full loss compensation in a resonant plasmonic-gain medium (metamaterial) are identical. Consequently, attempting the full compensation or overcompensation of losses by gain will lead to instability and a transition to a spaser state. This will limit (clamp) the inversion and lead to the limitation on the maximum loss compensation achievable. The criterion of the loss overcompensation, leading to the instability and spasing, is given in a analytical and universal (independent from system's geometry) form.
A novel type of spaser with the net amplification of surface plasmons (SPs) in doped graphene nanoribbon is proposed. The plasmons in THz region can be generated in a dopped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon is obtained. The dependence of the minimal population inversion on the surface plasmon wavevector, graphene nanoribbon width, doping and damping parameters necessary for the ampli…
Colloidal quantum dots are robust, efficient, and tunable emitters now used in lighting, displays, and lasers. Consequently, when the spaser, a laser-like source of surface plasmons, was first proposed, quantum dots were specified as the ideal plasmonic gain medium. Subsequent spaser designs, however, have required a single material to simultaneously provide gain and define the plasmonic cavity, an approach ill-suited to quantum dots and other colloidal nanomaterials. Here we develop a more open architecture that decouples the gain medium from the cavity, leading to a versatile class of quantu…
In this paper a surface plasmon polariton laser (spaser), which generates surface plasmons in graphene nanoflake, is considered. The peculiarities of spaser, such as strong material dispersion, require revision of basic laser equations. We provide a full derivation of equations of the spaser dynamics starting from the Maxwell-Bloch equations. Optical Bloch equations and rate equations are obtained and the relation of the equation parameters through the physical ones is given. In the case of graphene realization, the numerical parameter values are estimated.
A new method for high-sensitivity subwavelength spectromicroscopy is proposed based on the usage of a spaser (near-field laser) in the form of a scanning probe microscope tip. The high spatial resolution is defined by the tip's curvature, as is the case for apertureless scanning near-field optical microscopy. In contrast to the latter method, we suggest using radiationless plasmon pumping by neighbouring quantum dots instead of irradiation of the tip by an external laser beam. The spaser generation spectrum is analyzed. The plasmon generation is suppressed due to absorption at the transition f…
We theoretically study a nanospaser system, which consists of a spherical silver nanoparticle embedded inside a sphere composed of dye molecules. The gain of the system, dye molecules, are described by a three-level model, where the transition frequency between the lowest two energy levels is close to the surface plasmon frequency of the nanosphere. Contrary to a two-level model of spaser, the three-level model takes into account finite relaxation time between the high energy levels of the gain medium. These relaxation processes affect both the spaser threshold and the number of generated plas…
Loss is a crucial problem in plasmonic integrated optical circuits and metamaterials. The Er, Yb codoped gain material is introduced into a magnetic plasmon waveguide composed of a chain of nanosandwiches in order to solve the loss problem in such subwavelength waveguide. The magnetic plasmon mode and a higher order mode are chosen as the signal and pump light to enhance the radiation and pump efficiencies. The signal light propagating in the waveguide is investigated with different Er3+ doping concentration and signal decay time. It is shown that the gain effect can not only compensate the lo…
We consider theoretically the spaser excited electrically via a nanowire with ballistic quantum conductance. We show that in the extreme quantum regime, i.e., for a single conductance-quantum nanowire, the spaser with the core made of common plasmonic metals, such as silver and gold, is fundamentally possible. For ballistic nanowires with multiple-quanta or non-quantized conductance, the performance of the spaser is enhanced in comparison with the extreme quantum limit. The electrically-pumped spaser is promising as an optical source, nanoamplifier, and digital logic device for optoelectronic …
A numerically exact solution to the many emitter -- cavity problem as an open many body system is presented. The solution gives access to the full, nonperturbative density matrix and thus the full quantum statistics and quantum correlations. The numerical effort scales with the third power in the number of emitters. Notably the solution requires none of the common approximations like good/bad cavity limit. As a first application the recently discussed concept of coherent surface plasmon amplification -- spaser -- is addressed: A spaser consists of a plasmonic nanostructure that is driven by a …
We demonstrate that when the frequency of the external field differs from the lasing frequency of an autonomous spaser, the spaser exhibits stochastic oscillations at low field intensity. The plasmon oscillations lock to the frequency of the external field only when the field amplitude exceeds a threshold value. We find a region of values of the external field amplitude and the frequency detuning (the Arnold tongue) for which the spaser synchronizes with the external wave.
Plasmons, quantized collective oscillations of electrons, have been observed in metals and semiconductors. Such massive electrons have been the basic ingredients of research in plasmonics and optical metamaterials.1 Also, Dirac plasmons have been observed in graphene, two-dimensional electron systems and topological insulators (TIs). A nontrivial Z2 topology of the bulk valence band leads to the emergence of massless Dirac fermions on the surface in TIs.2,3 Although Dirac plasmons can be formed through additional grating or patterning, their characteristics promise novel plasmonic metamaterial…
Due to their many potential applications, there is an increasing interest in studying hybrid systems composed of optically active media and plasmonic metamaterials. In this work we focus on a particular system which consists of an optically active silica core covered by a gold shell. We find that the spaser (surface plasmon amplification by stimulated emission of radiation) conditions can be found at the poles of the scattering cross section of the system, a result that remains valid beyond the geometry studied. We explored a wide range of parameters that cover most of the usual experimental c…
We present a quantum theory of a spaser-based nanolaser, under the bad-cavity approximation. We find first- and second-order correlation functions $g^{(1)} (τ)$ and $g^{(2)}(τ)$ below and above the generation threshold, and obtain the average number of plasmons in the cavity. The latter is shown to be of the order of unity near the generation threshold, where the spectral line narrows considerably. In this case the coherence is preserved in a state of active atoms in contradiction to the good-cavity lasers, where the coherence is preserved in a state of photons. The damped oscillations in $g^{…
We show that graphene monolayer coupled to multi-quantum well system can form a graphene spaser, which is a coherent quantum generator of surface plasmons in graphene. The active element of graphene spaser is a multi-quantum well system with a design similar to the design of an active element of quantum cascade laser. Under realistic parameters of the multi-quantum well system, the spasing in graphene monolayer can be achieved at a finite doping of graphene and at a plasmon frequency, 0.15 eV, close to the typical frequency of intersubband transitions in multi-quantum well systems.
Nanoplasmonics has recently experienced explosive development with many novel ideas and dramatic achievements in both fundamentals and applications. The spaser has been predicted and observed experimentally as an active element -- generator of coherent local fields. Even greater progress will be achieved if the spaser could function as a ultrafast nanoamplifier -- an optical counterpart of the MOSFET (metal-oxide-semiconductor field-effect transistor). A formidable problem with this is that the spaser has the inherent feedback causing quantum generation of nanolocalized surface plasmons and sa…
We study numerically the effect of mode mixing and direct dipole-dipole interactions between gain molecules on spasing in a small composite nanoparticles with a metallic core and a dye-doped dielectric shell. By combining Maxwell-Bloch equations with Green's function formalism, we calculate lasing frequency and threshold population inversion for various gain densities in the shell. We find that gain coupling to nonresonant plasmon modes has a negligible effect on spasing threshold. In contrast, the direct dipole-dipole coupling, by causing random shifts of gain molecules' excitation frequencie…
The novel effect of self-excitation of surface plasmons (SESP) in a plasmonic nanocavity is predicted and its theory is developed from first principles. It is assumed that the cavity is formed by a nanogap between two metals and contains polarizable inclusions. Basing on the dyadic Green's function of the structure, the equations for the field in the cavity are investigated. It is shown that under certain conditions the field becomes unstable that leads to its self-excitation. The threshold criterion for self-excitation as well as the frequency of self-oscillation are derived in an analytical …
Emission of photon pairs by metal-dielectric interface in case of a superluminally propagating laser-induced nonlinear polarization is considered. Using oblique incidence of the laser wave it is possible to tune frequencies of generated photons due to the Doppler effect. For every frequency smaller than frequency of induced polarization there exist an excitation angle when singular enhancement of the emission takes place. Emitted photon pairs are in the polarization entangled state. The yield of emission is estimated.
We investigate the two-plasmon spontaneous decay of a quantum emitter near single-walled carbon nanotubes (SWCNT) and graphene-coated wires (GCWs). We demonstrate efficient, enhanced generation of two-plasmon entangled states in SWCNTs due to the strong coupling between tunable guided plasmons and the quantum emitter. We predict two-plasmon emission rates more than twelve orders of magnitude higher than in free-space, with average lifetimes of a few dozens of nanoseconds. Given their low dimensionality, these systems could be more efficient for generating and detecting entangled plasmons in co…
In a previous study, we have discovered that nonlinear processes can be enhanced several orders of magnitude due to the path interference effects which are introduced by Fano resonances. Emergence of this phenomenon has been demonstrated also in 3-dimensional solutions of Maxwell equations. However, enhancement has been found to be limited by the decay rate of the plasmonic oscillations. In the present work, we demonstrate that such a limitation can be lifted o? when the path interference from two quantum emitters to a plasmonic resonator (second harmonic converter) is considered. Enhancement …
We show that a strong infrared laser beam obliquely incident on graphene can experience a parametric instability with respect to decay into lower-frequency (idler) photons and THz surface plasmons. The instability is due to a strong in-plane second-order nonlinear response of graphene which originates from its spatial dispersion. The parametric decay leads to efficient generation of THz plasmons and gives rise to quantum entanglement of idler photons and surface plasmon states. A similar process can be supported by surface states of topological insulators such as Bi$_2$Se$_3$.
We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The …
We investigate coherent single surface-plasmon transport in a metal nanowire strongly coupled to two colloidal quantum dots. Analytical expressions are obtained for the transmission and reflection coefficients by solving the corresponding eigenvalue equation. Remote entanglement of the wave functions of the two quantum dots can be created if the inter-dot distance is equal to a multiple half-wavelength of the surface plasmon. Furthermore, by applying classical laser pulses to the quantum dots, the entangled states can be stored in metastable states which are decoupled from the surface plasmons…
We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tri-state entanglement are realized near the parametric resonances in a coupled system. The model includes decoherence effects due to coupl…
Quantum plasmonics experiments have on multiple occasions reported the observation of quantum coherence of discrete plasmons, which exhibit remarkable preservation of quantum interference visibility, a seemingly surprising feature for systems mixing light and matter with high ohmic losses during propagation. However, most experiments to date used essentially weakly-confined plasmons, which experience limited light-matter hybridization, thus limiting the potential for decoherence. Here, we report quantum coherence of plasmons near the surface plasmon polariton (SPP) resonance frequency, where p…
Intense efforts have been made in recent years to realize nonlinear optical interactions at the single-photon level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other quantum emitters while the possibility of achieving strong second-order nonlinearities remains unexplored. Here, we describe a novel technique to realize such nonlinearities using graphene, exploiting the strong per-photon fields associated with tightly confined graphene plasmons in combination with spatially nonlocal nonlinear optical interactions. We show that i…
We study the potential for controlled transfer of population to the biexciton state of a semiconductor quantum dot coupled with a metal nanoparticle, under the influence of an electromagnetic pulse with hyperbolic secant shape, and derive analytical solutions of the density matrix equations, for both zero and nonzero biexciton energy shift. These solutions lead to efficient transfer to the biexciton state, for various interparticle distances, including relatively small values. In certain cases, when the distance between the two particles is small, the transfer of population is strongly modifie…
