Finite Linewidth Research Articles

Quantum correlations, mixed states, and bistability at the onset of lasing

We derive a model for a single-mode laser that includes all two-particle quantum correlations between photons and electrons. In contrast to the predictions of semiclassical models, we find that lasing takes place in the presence of quantum bistability between a nonlasing and a nonclassical coherent state. The coherent state is characterized by a central frequency and a finite linewidth and emerges with finite amplitude from a saddle-node bifurcation together with an unstable coherent state. Hence coherent emission in nanolasers originates through a mixing of lasing and nonlasing states. In the limit of a macrolaser with a large number of emitters and nonresonant modes, the laser threshold approaches the prediction of the semiclassical theory, but with the important difference that lasing can be achieved only in the presence of finite-size perturbations. Published by the American Physical Society 2025

Monolithically integrated EP-based optical isolator.

Exceptional points (EPs) display peculiar degeneracies, where complex eigenvalues and associated eigenvectors coalesce simultaneously, resulting in a defective Hamiltonian. Meanwhile, the negative imaginary part of the energy eigenvalues related to a finite spectral linewidth at the resonant energy, which could provide a solution to tackle the isolation bandwidth limitation of MRR-based optical isolators without sacrificing the insertion loss. Here, a second-order EP2 system constructed by SiN-based cascaded racetrack resonators is proposed, while the metal strip operating as an integrated electromagnet provides magnetic fields required for non-reciprocal phase shifting (NRPS). Owing to the existence of the NRPS perturbation, the system is pushed away from EP and consequently triggers complex frequency splitting, resulting in the isolation bandwidth proportional to the square-root perturbation instead. The results show that the isolation bandwidth of the EP isolator is increased by 163% and 22% compared to single-racetrack and cascaded-racetrack isolators with 2.85 dB insertion loss and 34.3 dB isolation ratio, respectively. The presented EP-based optical isolator shows tremendous potential for high-density monolithic integration and packaging.

Optomagnonically tunable whispering gallery cavity laser wavelength conversion

We achieve laser wavelength conversion in an optomagnonical whispering gallery cavity by adjusting the strength of the applied static magnetic field. Numerical simulations are carried out on a yttrium iron garnet (YIG) sphere under different cavity quality factors or coupling strength. It is found that a high cavity quality factor will not always mean a high cavity excitation field for Gaussian lasers with finite linewidth. On state of the art, the high cavity quality factor will always mean the higher lightwave conversion rate. In addition, we also find that increasing the mode coupling strength is beneficial to the conversion of the laser. Our study provides new insights into generation of highly precise tunable coherent light.

Analytical theory of frequency-modulated combs: generalized mean-field theory, complex cavities, and harmonic states.

Frequency-modulated (FM) combs with a linearly-chirped frequency and nearly constant intensity occur naturally in certain laser systems; they can be most succinctly described by a nonlinear Schrödinger equation with a phase potential. In this work, we perform a comprehensive analytical study of FM combs in order to calculate their salient properties. We develop a general procedure that allows mean-field theories to be constructed for arbitrary sets of master equations, and as an example consider the case of reflective defects. We derive an expression for the FM chirp of arbitrary Fabry-Perot cavities-important for most realistic lasers-and use perturbation theory to show how they are affected by finite gain bandwidth and linewidth enhancment in fast gain media. Lastly, we show that an eigenvalue formulation of the laser's dynamics can be useful for characterizing all of the stable states of the laser: the fundamental comb, the continuous-wave solution, and the harmonic states.

Second‐Order Autocorrelation Function of Spectrally Filtered Light From an Incoherently Pumped Two‐Level System

AbstractLight with zero second‐order autocorrelation function, g(2)(0), emitted by single‐photon source (SPS), for example, two‐level system (TLS), is usually considered as being in a Fock state with one photon in a certain electromagnetic mode of free space. However, real SPSs have finite linewidths and excite all modes lying within the linewidth. It is shown that the zero value of g(2)(0) of light emitted by an incoherently pumped TLS is a consequence of the quantum interference of electromagnetic modes lying within the linewidth. Applying the quantum regression theorem for out‐of‐time‐ordered correlation functions, an analytical expression for g(2)(0) is obtained for the light emitted by a TLS and passed through a spectral filter. It is shown that narrowing the spectral width of the band‐pass filter inevitably leads to an increase in g(2)(0). is found and it is demonstrated that certain spectral filters lead to its nonmonotonic time dependence. These results open up the possibility of controlling the statistics of the emitted light using a spectral filter, which can find applications in quantum communication and cryptography.

Quantum size effects in the magnetic susceptibility of a metallic nanoparticle

We theoretically study quantum size effects in the magnetic response of a spherical metallic nanoparticle (e.g. gold). Using the Jellium model in spherical coordinates, we compute the induced magnetic moment and the magnetic susceptibility for a nanoparticle in the presence of a static external magnetic field. Below a critical magnetic field the magnetic response is diamagnetic, whereas above such field the magnetization is characterized by sharp, step-like increases of several tenths of Bohr magnetons, associated with the Zeeman crossing of energy levels above and below the Fermi sea. We quantify the robustness of these regimes against thermal excitations and finite linewidth of the electronic levels. Finally, we propose two methods for experimental detection of the quantum size effects based on the coupling to superconducting quantum interference devices.

Dynamical torque from Shiba states ins-wave superconductors

Magnetic impurities inserted in a $s$-wave superconductor give rise to spin-polarized in-gap states called Shiba states. We study the back-action of these induced states on the dynamics of the classical moments. We show that the Shiba state pertains to both reactive and dissipative torques acting on the precessing classical spin that can be detected through ferromagnetic resonance measurements. Moreover, we highlight the influence of the bulk states as well as the effect of the finite linewidth of the Shiba state on the magnetization dynamics. Finally, we demonstrate that the torques are a direct measure of the even and odd frequency triplet pairings generated by the dynamics of the magnetic impurity. Our approach offers non-invasive alternative to the STM techniques used to probe the Shiba states.

Polariton response in the presence of Brownian dissipation from molecular vibrations.

We study the elastic response of a stationarily driven system of a cavity field strongly coupled with molecular excitons, taking into account the main dissipation channels due to the finite cavity linewidth and molecular vibrations. We show that the frequently used coupled oscillator model fails in describing this response especially due to the non-Lorentzian dissipation of the molecules to their vibrations. Signatures of this failure are the temperature dependent minimum point of the polariton peak splitting, the uneven polariton peak height at the minimum splitting, and the asymmetric shape of the polariton peaks even at the experimentally accessed "zero-detuning" point. Using a rather generic yet representative model of molecular vibrations, we predict the polariton response in various conditions, depending on the temperature, molecular Stokes shift and vibration frequencies, and the size of the Rabi splitting. Our results can be used as a sanity check of the experiments trying to "prove" results originating from strong coupling, such as vacuum-enhanced chemical reaction rate.

Quantum expander for gravitational-wave observatories

The quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. Over the past 30 years, techniques for squeezing the quantum uncertainty, as well as for enhancing gravitational-wave signals with optical resonators have been invented. Resonators, however, have finite linewidths, and the high signal frequencies that are produced during the highly scientifically interesting ring-down of astrophysical compact-binary mergers still cannot be resolved. Here, we propose a purely optical approach for expanding the detection bandwidth. It uses quantum uncertainty squeezing inside one of the optical resonators, compensating for the finite resonators’ linewidths while keeping the low-frequency sensitivity unchanged. This quantum expander is intended to enhance the sensitivity of future gravitational-wave detectors, and we suggest the use of this new tool in other cavity-enhanced metrological experiments.

Impact of Fundamental Temperature Fluctuations on the Frequency Stability of Metallo- Dielectric Nanolasers

The capability of nanolasers to generate coherent light in small volume resonators has made them attractive to be implemented in future ultra-compact photonic integrated circuits. However, compared to conventional lasers, nanolasers are also known for their broader spectral linewidths, that are usually on the order of 1 nm. While it is well known that the broad linewidths in light emitters originate from various noise sources, there has been no rigorous study on evaluating the origins of the linewidth broadening for nanolasers to date to the best of our knowledge. In this manuscript, we investigate the impact of fundamental thermal fluctuations on the nanolaser linewidth. We show that such thermal fluctuations are one of the intrinsic noise sources in a sub-wavelength metal-clad nanolaser inducing significant linewidth broadening. We further show that with the reduction of the nanolaser’s dimensions, i.e., mode volume, and the increase of the ambient temperature, such linewidth broadening is enhanced, due to the effect of more pronounced fundamental thermal fluctuation. Specifically, we show that the finite linewidths induced by the thermal fluctuations at room temperature are 1.14nm and 0.16nm, for nanolasers with core radii of 250nm and 750nm, respectively. Although our study was performed on a metallo-dielectric nanolaser, it is reasonable to assume that, in general, other nanolaser architectures are also more prone to thermal fluctuations, and hence exhibit larger finite linewidths than conventional large mode volume lasers.

Generation of high-average-power ultra-broadband infrared radiation

High-average-power ultra-broadband mid-IR radiation can be generated by illuminating a nonlinear medium with a multi-line laser radiation. Propagation of a multi-line pulsed CO2 laser beam in a nonlinear medium, e.g., gallium arsenide or chalcogenide, can generate directed broadband IR radiation in the atmospheric window (2–13 μm). A 3D laser code for propagation in a nonlinear medium has been developed to incorporate extreme spectral broadening resulting from the beating of several wavelengths. The code has the capability to treat coupled forward and backward-propagating waves, as well as transverse and full linear dispersion effects. Methods for enhancing the spectral broadening are proposed and analyzed. Grading the refractive index radially or using a cladding will tend to guide the CO2 radiation and extend the interaction distance, allowing for enhanced spectral broadening. Nonlinear coupling of the CO2 laser beam to a backward-propagating reflected beam can increase the rate of spectral broadening in the anomalous dispersion regime of a medium. Laser phase noise associated with the finite CO2 linewidths can significantly enhance the spectral broadening, as well. In a dispersive medium, laser phase noise results in laser intensity fluctuations. These intensity fluctuations result in spectral broadening due to the self-phase modulation mechanism. Finally, we present propagation through a chalcogenide fiber as an alternative for extreme spectral broadening of a frequency-doubled CO2 multi-line laser beam.

Dzyaloshinskii-Moriya interaction induced extrinsic linewidth broadening of ferromagnetic resonance

For a thin ferromagnetic film with the Dzyaloshinskii-Moriya interaction (DMI), we derive an expression of the extrinsic ferromagnetic resonance (FMR) linewidth in a quantum mechanical way, taking into account scatterings from structural inhomogeneity. In the presence of the DMI, the magnon dispersion exhibits rich resonant states, especially in small external magnetic fields and strong DMI strength. It is found that the FMR linewidth shows several characteristic features such as a finite linewidth at zero frequency and peaks in the low frequency range.

Probing Homogeneous Line Broadening in CdSe Nanocrystals Using Multidimensional Electronic Spectroscopy.

The finite spectral line width of an ensemble of CdSe nanocrystals arises from size and shape inhomogeneity and the single-nanocrystal spectrum itself. This line width directly limits the performance of nanocrystal-based devices, yet most optical measurements cannot resolve the underlying contributions. We use two-dimensional electronic spectroscopy (2D ES) to measure the line width of the band-edge exciton of CdSe nanocrystals as a function of radii and surface chemistry. We find that the homogeneous width decreases for increasing nanocrystal radius and that surface chemistry plays a critical role in controlling this line width. To explore the hypothesis that unpassivated trap states serve to broaden the homogeneous line width and to explain its size-dependence, we use 3D ES to identify the spectral signatures of exciton-phonon coupling to optical and acoustic phonons. We find enhanced coupling to optical phonon modes for nanocrystals that lack electron-passivating ligands, suggesting that localized surface charges enhance exciton-phonon coupling via the Fröhlich interaction. Lastly, the data reveal that spectral diffusion contributes negligibly to the homogeneous line width on subnanosecond time scales.

Investigation of Tolerable Laser Linewidth for Different Modulation Formats in CO-OFDM Systems

The ideal behavior of communication system requires a single frequency carrier. In optical communication system, light is used as a carrier. Practical laser source has a finite linewidth due to variations in the frequency of operation, hence, resulting in undesired phase perturbations in the signal whereas the ideal requirement is the delta function spectral shape at the carrier frequency. The spectral shape gets broadened due to phase noise and is modeled as lorentzian shape. Linewidth is a measure of stability of laser phase noise with time. Coherent Optical Orthogonal frequency division multiplexing (CO-OFDM) along with the spectrally efficient Quadrature Amplitude Modulation (QAM) formats is emerging as one of the best solutions for future high speed fiber transmission systems. Though the coherent, receivers have advantages in terms of sensitivity and selectivity, laser phase noise is the main limitation of such systems as the laser phase noise further causes common phase rotation of all the subcarriers per symbol and also results in inter carrier interference. QAM formats are also susceptible to laser phase noise. Phase noise in coherent systems is governed by laser linewidth. Hence, it is very important to investigate the impact of laser linewidth in CO-OFDM systems. This paper investigates the tolerable laser linewidths for different QAM formats in a 40 Gbps COOFDM system.

Numerical Study of the Dynamics of Laser Lineshape and Linewidth

give no information about the dynamics of lineshape and linewidth. Second, their way of calculating lineshape and linewidth leads through the implicit assumption that the laser field can be represented by a complex amplitude oscillating at the resonance frequency of the pure cavity, which is equivalent to requiring the solutions for the laser field to be self-consistent. In this context, the finite linewidth of the laser radiation is not related to the existence of solutions at frequencies other than the resonance frequency, it is just the fingerprint of the statistical fluctuations of the complex amplitude when transformed into the frequency domain. The Fokker‐Plank equation divides these statistical fluctuations into a drift term and a diusion term. The former is assigned the coherent

Investigation of the unidirectional spin heat conveyer effect in a 200 nm thin Yttrium Iron Garnet film.

We have investigated the unidirectional spin wave heat conveyer effect in sub-micron thick yttrium iron garnet (YIG) films using lock-in thermography (LIT). Although the effect is small in thin layers this technique allows us to observe asymmetric heat transport by magnons which leads to asymmetric temperature profiles differing by several mK on both sides of the exciting antenna, respectively. Comparison of Damon-Eshbach and backward volume modes shows that the unidirectional heat flow is indeed due to non-reciprocal spin-waves. Because of the finite linewidth, small asymmetries can still be observed when only the uniform mode of ferromagnetic resonance is excited. The latter is of extreme importance for example when measuring the inverse spin-Hall effect because the temperature differences can result in thermovoltages at the contacts. Because of the non-reciprocity these thermovoltages reverse their sign with a reversal of the magnetic field which is typically deemed the signature of the inverse spin-Hall voltage.

Influence of the finite linewidth of the laser radiation spectrum on the shape of the coherent population trapping resonance line in an optically dense medium with a buffer gas

The theory of coherent population trapping resonance is developed for the finite linewidth of the laser radiation spectrum in an optically dense medium of Λ atoms in a cell with a buffer gas. Equations are derived for the atomic density matrix and laser emission spectrum transfer in a cell with working and buffer gases at a finite temperature. The dependence of the quality factor of coherent population trapping resonance on the linewidth of the laser radiation spectrum is studied by measuring transmitted radiation and fluorescence signals.

Study of field shifts of Ramsey resonances on ultracold atoms and ions

The effect of the finite laser radiation line width and spontaneous relaxation of levels on the efficiency of the suppression of the field shift of the central resonance for the generalized Ramsey scheme with pulses of different lengths and with a phase jump in the second pulse has been considered. The optimal parameters of the scheme corresponding to the minimum frequency shift and maximum amplitude of the resonance have been determined.

Jaynes-Cummings dynamics in mesoscopic ensembles of Rydberg-blockaded atoms

We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of a Rydberg blockade where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg-blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps, we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interaction strengths and a finite laser linewidth on the visibility of the revivals. We have shown that observation of collapses and revivals of Rabi oscillations can be used as a signature of the Rydberg blockade without the need to measure the exact number of Rydberg atoms.

Plasmon Line Width in Liquid Metals

With the recent development of synchrotron radiation sources and the instrumentations, inelastic X-ray scattering (IXS) has become an important tool for observing plasmons in materials. One of the significant advantages of IXS is that it can be applied to liquid samples, which is considerably difficult for electron energy loss spectroscopy. Thus far, the IXS study of plasmons in liquid samples has been performed for several systems such as liquid lithium, liquid aluminum, or lithium ammonia solutions. However, the properties of plasmons in the liquid phase are less clearly understood than those in the crystalline phase. One of such properties is the plasmon line width. For the solid state, the finite line width observed in experiments can be evaluated using the formulations derived in previous theoretical studies, in which the effect of interband transitions, phonon-assisted intraband (or interband) transitions, and the excitations of two electron–hole (e–h) pairs are considered. These effects should also play an important role in liquid, because a finite line width is also observed in liquid samples. The effects of phonon and two e–h pairs are readily extended to liquid systems, since these effects can be calculated without using information on the ionic structure. On the other hand, the effect of interband transitions is difficult to extend to the liquid state, because it strongly depends on the ionic structure. In this work, we show the derivation of a formula for evaluating the plasmon line width at the zero momentum transfer, q 1⁄4 0, in metallic liquid. The formula describes how the ionic structure influences the plasmon line width for metallic liquid. The application of the formula to liquid alkali metals is also shown. The plasmon line width at q 1⁄4 0, E1=2ð0Þ, is written as E1=2ð0Þ 1⁄4 h !p Im ð!pÞ; ð1Þ