Normal Mode Splitting Research Articles

Coupling mechanical motion of a single atom to a micromechanical cantilever

We design and analyze a hybrid optomechanical setup to achieve an effective coupling between the mechanical motions of a micromechanical cantilever and a single atom trapped inside a cavity, which is mediated by a direct interaction between the micromechanical cantilever and the atomic internal state via the quantum vacuum effect. Moreover, the optomechanical coupling between the mechanical motion of the cantilever and the cavity field can be mediated by the interaction with the atom. Their couplings are demonstrated in detail by analyzing the normal-mode splitting of the mechanical motion and the optical response of the hybrid optomechanical system. It is found that double optomechanically-induced transparency can be observed in the output probe field in the presence of the mediated coupling. In particular, both the width of the splitting peaks and the separation between the two absorption dips increase with the increasing strength of the vacuum coupling and with the decreasing trapped position of the atom. These characteristics can be used to study the strong coupling between a single atom and a massive micromechanical cantilever.

Cavity enhanced interference of orthogonal modes in a birefringent medium

Interference of orthogonal modes in a birefringent crystal mediated by a rotator is known to lead to interesting physical effects (Solli et al., 2003). In this paper we show that additional feedback offered by a Fabry–Perot cavity (containing the birefringent crystal and the rotator) can lead to a novel strong interaction regime. Usual signatures of the strong interaction regime like the normal mode splitting and avoided crossings, sensitive to the rotator orientation, are reported. A high finesse cavity is shown to offer an optical setup for measuring small angles. The results are based on direct calculations of the cavity transmissions along with an analysis of its dispersion relation.

Room-temperature cavity quantum electrodynamics with strongly coupled Dicke states

The strong coupling regime is essential for efficient transfer of excitations between states in different quantum systems on timescales shorter than their lifetimes. The coupling of single spins to microwave photons is very weak but can be enhanced by increasing the local density of states by reducing the magnetic mode volume of the cavity. In practice, it is difficult to achieve both small cavity mode volume and low cavity decay rate, so superconducting metals are often employed at cryogenic temperatures. For an ensembles of N spins, the spin–photon coupling can be enhanced by sqrt N through collective spin excitations known as Dicke states. For sufficiently large N the collective spin–photon coupling can exceed both the spin decoherence and cavity decay rates, making the strong-coupling regime accessible. Here we demonstrate strong coupling and cavity quantum electrodynamics in a solid-state system at room-temperature. We generate an inverted spin-ensemble with N ~ 1015 by photo-exciting pentacene molecules into spin-triplet states with spin dephasing time T_2^*sim 3 μs. When coupled to a 1.45 GHz TE01δ mode supported by a high Purcell factor strontium titanate dielectric cavity (V_{mathrm{m}}sim 0.25 cm3, Q ~ 8,500), we observe Rabi oscillations in the microwave emission from collective Dicke states and a 1.8 MHz normal-mode splitting of the resultant collective spin–photon polariton. We also observe a cavity protection effect at the onset of the strong-coupling regime which decreases the polariton decay rate as the collective coupling increases.

Controllable double electromagnetically induced transparency in a closed four-level-loop cavity–atom system**Project supported by the National Natural Science Foundation of China (Grant No. 11174109).

We present a theoretical study of an optical cavity coupled with single four-level atoms in closed loop formed via applied control lasers. The transmitted probe field from the cavity is analyzed. We show that the electromagnetically induced transparency (EIT) in the cavity and the normal mode splitting will be very different with changing the closed interaction phase and the intensity of the free-space control laser. This coupled cavity–atom system presents a variational double-EIT that comes from modulating the splitting of the dark state, which means that we could realize the gradual transfer between one EIT peak and two EIT peaks by adjusting the applied control lasers, and the normal mode splitting sidebands will shift slightly by changing the free-space control laser. This means that we could control the output cavity probe field more freely and it is easer to realize optical switch controlled by more parameters. We also depict the angular dispersion of the intracavity probe field in different free-space control laser. The large phase shift () of the reflected intracavity probe field will be very useful for optical temporal differentiation and quantum phase gate.

Effects of cross-Kerr coupling and parametric nonlinearity on normal mode splitting, cooling, and entanglement in optomechanical systems

We study the influence of cross-Kerr (CK) coupling and optical parametric amplifier (OPA) on the effective frequency, damping, normal mode splitting, ground state cooling, and steady state entanglement of an optomechanical system formed by one fixed mirror and one movable mirror. The CK coupling could increase the damping of the movable mirror. The normal mode splitting of the output field is observed due to the CK coupling. The combination of the CK coupling and OPA decreases the minimum attainable phonon number and the effective temperature of the movable mirror. The amount of stationary entanglement between the mechanical and cavity modes can be enhanced by the weak CK coupling. In particular, we find the stationary entanglement becomes more robust against thermal fluctuations of the movable mirror in the presence of the weak CK coupling.

Coherent coupling between an optomechanical membrane and an interacting photon Bose–Einstein condensate

In this paper, we study theoretically the optomechanical interaction of an interacting condensate of photons with an oscillating mechanical membrane in a microcavity. We show that in the Bogoliubov approximation, due to the large number of photons in the condensate, there is a linear strong effective coupling between the Bogoliubov mode of the photonic Bose–Einstein condensate (BEC) and the mechanical motion of the membrane which depends on the photon–photon scattering potential. This coupling leads to the cooling of the mechanical motion, the normal mode splitting (NMS), the squeezing of the output field and the entanglement between the excited mode of the cavity and the mechanical mode. Since the photon condensation occurs at room temperature, this hybrid system can be potentially considered as a room temperature source of squeezed light as well as a suited candidate for exploring the quantum effects. We show that, on one hand, the non-linearity of the photon gas increases the degree of the squeezing of the output field of the microcavity and the efficiency of the cooling process at high temperatures. On the other hand, it reduces the NMS in the displacement spectrum of the oscillating membrane and the degree of the optomechanical entanglement. In addition, the temperature of the photonic BEC can be used to control the above-mentioned phenomena.

Demonstration of the Jaynes-Cummings ladder with Rydberg-dressed atoms

We observe the nonlinearity of the Jaynes-Cummings (JC) ladder in the Autler-Townes spectroscopy of the hyperfine ground states for a Rydberg-dressed two-atom system. Here the role of the two-level system in the JC model is played by the presence or absence of a collective Rydberg excitation, and the bosonic mode manifests as the number $n$ of single atom spin flips, symmetrically distributed between the atoms. We measure the normal-mode splitting and $\sqrt{n}$ nonlinearity as a function of detuning and Rabi frequency, thereby experimentally establishing the isomorphism with the JC model.

Adjustable quantum coherence effects in a hybrid optomechanical system**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574092, 61378012, 91121023, and 60978009), the National BasicResearch Program of China (Grant No. 2013CB921804), and the Innovative Research Team in University, China (Grant No. IRT1243).

We propose a system for achieving some adjustable quantum coherence effects, including the normal-mode splitting (NMS), the optomechanically induced transparency (OMIT), and the optomechanically induced absorption (OMIA). In this system, two tunnel-coupled optomechanical cavities are each driven by a coupling field and coupled to an atomic ensemble. Besides, one of the cavities is also injected with a probe field. When the system works under different conditions, we can obtain the NMS, the OMIT, and the OMIA, respectively. These effects can be flexibly adjusted by the tunnel coupling between the two cavities, the power of the coupling lasers, and the coupling strength between the atomic ensembles and the cavity fields. Furthermore, we can realize the OMIT even if the oscillating mirrors have relatively larger decay rates.

Control of the Stokes Shift with Strong Coupling

Strong coupling of excitons in macroscopic ensembles of quantum emitters and cavities (or surface plasmons) can lead to dramatic change of the optical properties and modification of the dispersion curves, characterized by the normal mode splitting of the order of 1 eV. Such gigantic alteration of the hybrid energy states enables scores of unparalleled physical phenomena and functionalities, ranging from enhancement of electrical conductivity to control of chemical reactions. While coupling of single emitters to a cavity is a pure quantum mechanical phenomenon, the origin of the strong coupling involving large ensembles of molecules is the subject of controversy. In this work, the strong coupling of rhodamine 6G dye molecules with silver Fabry–Perot cavities is studied and the significant increase of the Stokes shift between the excitation and the emission bands of hybridized molecules is demonstrated. The proposed empirical model of the underlying physics calls for the quantum mechanical parity selection rule.

Controllable Bistability and Normal Mode Splitting in an Optomechanical System Assisted by an Atomic Ensemble

We consider a system consisting of a standard optomechanical cavity and a trapped atomic ensemble. In such a system, we mainly focus on the features of optomechanical bistability and normal mode splitting with the presence of atomic ensemble. The results show that the energy of laser directly coupling the atomic ensemble can be enhanced effectively, and using this laser is more convenient and easier to realize the bistability and normal mode splitting than the traditional means. Besides, we find that atom-cavity field detuning also has a significant impact on optomechanical bistability, which offers us an important method to adjust and control the cavity mean photon number. At last, the numerical results show that atom-cavity field detuning and atom-cavity field coupling strength have an opposite effect on the normal mode splitting because they have different contributions to the effective cavity field decay rate.

Strong coupling and ultrafast dynamics in organic semiconductor/metal hybrid nanostructures

Active plasmonics, as an important branch of Plasmonics, is growing rapidly over the last decades. The main principle of active plasmonics is to combine surface plasmon polaritons (SPPs) with ‘active’ materials to com-penstate intrinsic weak optical nonlinearities and short propagation lengths of SPPs, so that external manipula-tion and coherent control of SPPs can be realized. Here, we give a brief review of the studies in the area of active plasmonics. In particular, we focus on hybrid J-aggregate/metal nanostructures consisting of J-aggregate excitons and surface plasmon polaritons supported by metallic nanostructures. Two experimental methods: chrip-compensated spectral interferometry and nonlinear pump-probe spectroscopy are introduced. The strong coupling between J-aggregate excitons and SPPs is studied in details by probing both the static optical properties and ultrasfast dynamics of the strongly coupled X-SPP systems. The results reveal that two different energy transfer channels: a coherent resonant dipole-dipole interaction and an incoherent exchange of photons, are coexisting in the hybrid system. Coherent energy exchange, that is, Rabi oscillations between the excitonic and the SPP systems in real time are also investigated. It is found that coherent X-SPP population transfer induces transient oscillations in exciton density, leading to a periodic modulation of the normal mode splitting and thus optical nonlinearity on a 10 fs timescale.

Observing coherence effects in an overdamped quantum system

It is usually considered that the spectrum of an optical cavity coupled to an atomic medium does not exhibit a normal-mode splitting unless the system satisfies the strong coupling condition, meaning the Rabi frequency of the coherent coupling exceeds the decay rates of atom and cavity excitations. Here we show that this need not be the case, but depends on the way in which the coupled system is probed. Measurements of the reflection of a probe laser from the input mirror of an overdamped cavity reveal an avoided crossing in the spectrum that is not observed when driving the atoms directly and measuring the Purcell-enhanced cavity emission. We understand these observations by noting a formal correspondence with electromagnetically induced transparency of a three-level atom in free space, where our cavity acts as the absorbing medium and the coupled atoms play the role of the control field.

Polaritonic normal-mode splitting and light localization in a one-dimensional nanoguide

Propagation of light through dielectrics lies at the heart of optics. However, this ubiquitous process is commonly described using phenomenological dielectric function $\varepsilon$ and magnetic permeability $\mu$, i.e. without addressing the quantum graininess of the dielectric matter. Here, we present a theoretical study where we consider a one-dimensional ensemble of atoms in a subwavelength waveguide (nanoguide) as fundamental building blocks of a model dielectric. By exploring the roles of the atom-waveguide coupling efficiency, density, disorder, and dephasing, we establish connections among various features of polaritonic light-matter states such as localization, super and subradiance, and strong coupling. In particular, we show that coherent multiple scattering of light among atoms that are coupled via a single propagating mode can gives rise to Rabi splitting. These results provide important insight into the underlying physics of strong coupling reported by recent room-temperature experiments with microcavities and surface plasmons.

Steady-state entanglement between distant quantum dots in photonic crystal dimers

We show that two spatially separated semiconductor quantum dots under resonant and continuous-wave excitation can be strongly entangled in the steady-state, thanks to their radiative coupling by mutual interaction through the normal modes of a photonic crystal dimer. We employ a quantum master equation formalism to quantify the steady-state entanglement by calculating the system {\it negativity}. Calculations are specified to consider realistic semiconductor nanostructure parameters for the photonic crystal dimer-quantum dots coupled system, determined by a guided mode expansion solution of Maxwell equations. Negativity values of the order of 0.1 ($20\%$ of the maximum value) are shown for interdot distances that are larger than the resonant wavelength of the system. It is shown that the amount of entanglement is almost independent of the interdot distance, as long as the normal mode splitting of the photonic dimer is larger than their linewidths, which becomes the only requirement to achieve a local and individual qubit addressing. Considering inhomogeneously broadened quantum dots, we find that the steady-state entanglement is preserved as long as the detuning between the two quantum dot resonances is small when compared to their decay rates. The steady-state entanglement is shown to be robust against the effects of pure dephasing of the quantum dot transitions. We finally study the entanglement dynamics for a configuration in which one of the two quantum dots is initially excited and find that the transient negativity can be enhanced by more than a factor of two with respect to the steady-state value. These results are promising for practical applications of entangled states at short time scales.

An electromechanical displacement transducer

Two modes of an electromechanical resonator are coupled through the strain inside the structure with a cooperativity as high as 107, a state-of-the-art value for purely mechanical systems, which enables the observation of normal-mode splitting. This coupling is exploited to transduce the resonator’s fundamental mode into the bandwidth of the second flexural mode, which is 1.4 MHz higher in frequency. Thus, an all-mechanical heterodyne detection scheme is implemented that can be developed into a high-precision displacement sensor.

Seismic shear waves as Foucault pendulum

AbstractEarth's rotation causes splitting of normal modes. Wave fronts and rays are, however, not affected by Earth's rotation, as we show theoretically and with observations made with USArray. We derive that the Coriolis force causes a small transverse component for P waves and a small longitudinal component for S waves. More importantly, Earth's rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum. The polarization plane of shear waves counteracts Earth's rotation and rotates clockwise in the Northern Hemisphere. The rotation rate is independent of the wave frequency and is purely geometric, like the Berry phase. Using the polarization of ScS and ScS2 waves, we show that the Foucault‐like rotation of the S wave polarization can be observed. This can affect the determination of source mechanisms and the interpretation of observed SKS splitting.

Spectral engineering of coupled open‐access microcavities

Open‐access microcavities are emerging as a new approach to confine and engineer light at mode volumes down to the λ3 regime. They offer direct access to a highly confined electromagnetic field while maintaining tunability of the system and flexibility for coupling to a range of matter systems. This article presents a study of coupled cavities, for which the substrates are produced using Focused Ion Beam milling. Based on experimental and theoretical investigation the engineering of the coupling between two microcavities with radius of curvature of 6 m is demonstrated. Details are provided by studying the evolution of spectral, spatial and polarisation properties through the transition from isolated to coupled cavities. Normal mode splittings up to 20 meV are observed for total mode volumes around . This work is of importance for future development of lab‐on‐a‐chip sensors and photonic open‐access devices ranging from polariton systems to quantum simulators. image

Optical Bistability and Normal-Mode Splitting of Two-Species Bose-Einstein Condensates in An Optical Cavity

We investigate the optical bistable behavior for a weakly interacting two-species Bose-Einstein condensates inside a pumped optical cavity by considering the two possible regimes- the phase mixed regime and the phase segregated regime. We find that the cavity-pump detuning plays a significant role in controlling the threshold of the optical bistability and the constrast between the bistability values depending upon the state we are working in. We also demonstrate the occurence of normal mode splitting in the optical spectrum for both the regimes which further showing the position and amplitude discrepancies in the spectral peaks.

Optomechanical Entanglement Between an Ion and an Optical Cavity Field

We study an optomechanical system in which the mechanical motion of a single trapped ion is coupled to a cavity field for the realization of a strongly quantum correlated two-mode system. We show that for large pump intensities the steady state photon number exhibits bistable behaviour. We further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the ion motion which indicates a coherent energy exchange. We also find that in the parameter regime where NMS exists, the steady state of the system shows continuous variable entanglement. Such a two-mode optomechanical system can be used for the realization of continuous variable quantum information interfaces and networks.

Optical Control of Mechanical Mode-Coupling within a MoS2 Resonator in the Strong-Coupling Regime.

Two-dimensional (2-D) materials including graphene and transition metal dichalcogenides (TMDs) are an exciting platform for ultrasensitive force and displacement detection in which the strong light-matter coupling is exploited in the optical control of nanomechanical motion. Here we report the optical excitation and displacement detection of a ∼ 3 nm thick MoS2 resonator in the strong-coupling regime, which has not previously been achieved in 2-D materials. Mechanical mode frequencies can be tuned by more than 12% by optical heating, and they exhibit avoided crossings indicative of strong intermode coupling. When the membrane is optically excited at the frequency difference between vibrational modes, normal mode splitting is observed, and the intermode energy exchange rate exceeds the mode decay rate by a factor of 15. Finite element and analytical modeling quantifies the extent of mode softening necessary to control intermode energy exchange in the strong coupling regime.