Normal Mode Splitting Research Articles

A Green’s function approach to the linear response of a driven dissipative optomechanical system

In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green’s function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.

Multimode Nonlinear Coupling Induced by Internal Resonance in a Microcantilever Resonator.

Coupled resonators represent a generic model for many physical systems. In this context, a microcantilever is a multimode resonator clamped at one end, and it finds extensive application in high-precision metrology and is expected to be of great potential use in emerging quantum technologies. Here, we explore the microcantilever as a flexible platform for realizing multimode nonlinear interactions. Multimode nonlinear coupling is achieved by (1:2) internal resonance (IR) and parametric excitation with efficient coherent energy transfer. Specifically, we demonstrate abundant tunable parametric behaviors via frequency and voltage sweeps; these behaviors include mode veering, degenerate four-wave mixing (D4WM) with satellite resonances, partial amplitude suppression, acoustic frequency comb (AFC) generation, mechanically induced transparency (MIT), and normal-mode splitting. The experiments depict a new scheme for manipulating multimode microresonators with IR and parametric excitation.

Strong optomechanical coupling at room temperature by coherent scattering

Quantum control of a system requires the manipulation of quantum states faster than any decoherence rate. For mesoscopic systems, this has so far only been reached by few cryogenic systems. An important milestone towards quantum control is the so-called strong coupling regime, which in cavity optomechanics corresponds to an optomechanical coupling strength larger than cavity decay rate and mechanical damping. Here, we demonstrate the strong coupling regime at room temperature between a levitated silica particle and a high finesse optical cavity. Normal mode splitting is achieved by employing coherent scattering, instead of directly driving the cavity. The coupling strength achieved here approaches three times the cavity linewidth, crossing deep into the strong coupling regime. Entering the strong coupling regime is an essential step towards quantum control with mesoscopic objects at room temperature.

HALL CONDUCTIVITY ESTIMATES FROM MAGNETOTELLURIC SOUNDING DATA

Many minerals have semiconductor properties. It is known that petroleum reservoir rocks permeated with hydrocarbon fluids can sometimes behave as semiconductors. In the Earth’s magnetic field, the electrical conductivity of such materials becomes anisotropic, and the Hall effect is quite possible in rocks in natural conditions and detectable by magnetotelluric sounding. In the anisotropic medium, the field is subject to normal mode splitting, and its components show different attenuation coefficients and phase velocities. The modes differ due to polarization and rotation of the field vectors (clockwise in one mode, and counterclockwise in another). With account of the Hall effect, responses of the medium can be different when the medium is excited by a single normal wave. To detect the Hall effect in MTS surveys, we use the polarization analysis method and select the spectra of modes with right and left circular polarization. Special experiments were carried out to detect the contribution of the Hall effect during the MTS surveys. This article presents the first estimates of the Hall conductivity for the studied rocks.

Photonic molecules stacked on multicore optical fiber for vapor sensing

We designed and fabricated photonic molecules on the tiny end facet of a multicore optical fiber. The photonic molecules are three pairs of coupled polymer micro-ring resonators, which are stacked on the fiber in three layers. The normal mode splitting of the photonic molecules is simulated and observed experimentally. It is shown that if the absorption of vapors causes both the radii and refractive index changes of the rings, the two branches of the split resonant modes show different wavelength shifts. The photonic molecules were fabricated by the two-photon lithography technology and show good sensitivity to various organic vapors.

Polariton relaxation and polariton nonlinearities in nonresonantly cw-pumped III-nitride slab waveguides

Polariton lasers are mostly based on planar cavities. Here we focus on an alternative configuration with slab waveguide modes strongly coupled to excitons confined in GaN/AlGaN quantum wells. We study experimentally and theoretically polariton relaxation at temperatures ranging from 4 to 200 K. We observe a good robustness of the lower polariton population peak energy position against temperature changes due to a balance between the shift of the exciton energy and the change in the normal mode splitting, a promising feature for future applications such as lasers and amplifiers where a small temperature drift in the emission wavelength is a desired asset. Finally, at $T=4\phantom{\rule{4pt}{0ex}}\mathrm{K}$ we observe the signature of polariton nonlinearities occurring in the continuous wave regime that are assigned to an optical parametric oscillation process.

Observation of normal mode splitting in THz Fabry–Pérot microcavity made of wire grid structures containing cut wire metamaterials

In this study, we realize normal mode splitting in Fabry–Pérot (FP) microcavity structures containing cut wire (CW) metamaterials inside the cavity layer in the terahertz (THz) region. We used a wire grid (WG) structure to mirror the microcavity. To verify this concept, we analyzed the reflection and transmission properties of WG, CW, WG cavity (WGC), and microcavity containing CW (CWWGC) using transmission line theory. Consequently, we discovered that when the resonance frequencies of the CW and WGC matched, normal mode splitting occurred and anti-crossing is observed in the dispersion relation in the CWWGC. The samples are designed by the finite difference time domain method and were fabricated via photolithography. We measured the transmission spectrum of the fabricated samples by THz time domain spectroscopy. Finally, we observed a large splitting of the transmission peak owing to mode coupling between the light mode of the FP microcavity and the electric dipole mode of a single CW in the CWWGC.

Controllable bistable optical switch and normal mode splitting in hybrid optomechanical semiconductor microcavity containing single quantum dot driven by amplitude modulated field

We theoretically explore optical bistability for the possible signature of all-optical switching and their performance in a hybrid quantum optomechanical system comprising of two semiconductor microcavities coupled optically. One of the cavity is driven by an external amplitude-modulated pump laser while the second cavity, which contains a quantum dot (QD), is indirectly driven by light transmitted from the first cavity and a transverse optical field. The generated bistable behavior due to optomechanical nonlinearity shows a typical optical switching behavior and it can be controlled by changing the laser power, QD cavity coupling, modulating amplitude/frequency and the optomechanical coupling. A clear signature of energy exchange between the mechanical and optical modes is visible from the mechanical displacement spectrum. These results suggest that the present system can be used in sensitive optical switches and optical sensors.

Optical switching and normal mode splitting in hybrid semiconductor microcavity containing quantum well and Kerr medium driven by amplitude-modulated field

ABSTRACTWe theoretically investigate optical bistability/multistability for all optical switching signature in a hybrid semiconductor microcavity system comprising a quantum well and a Kerr nonlinear substrate. The system is essentially two optically coupled microcavities with one of the microcavity being driven by an external amplitude-modulated pump laser. We show that the switching between bistable and multistable behaviour is influenced by the modulated pump laser, Kerr nonlinearity and the optical coupling between the two microcavities. We further investigate the intracavity spectrum of quantum fluctuations which exhibit the well-known normal mode splitting (NMS). The NMS behaviour is also found to be influenced by the system parameters. These results demonstrate that the present hybrid nonlinear system can be used in designing sensitive optical devices.

Quantum capacitance mediated carbon nanotube optomechanics

Cavity optomechanics allows the characterization of a vibration mode, its cooling and quantum manipulation using electromagnetic fields. Regarding nanomechanical as well as electronic properties, single wall carbon nanotubes are a prototypical experimental system. At cryogenic temperatures, as high quality factor vibrational resonators, they display strong interaction between motion and single-electron tunneling. Here, we demonstrate large optomechanical coupling of a suspended carbon nanotube quantum dot and a microwave cavity, amplified by several orders of magnitude via the nonlinearity of Coulomb blockade. From an optomechanically induced transparency (OMIT) experiment, we obtain a single photon coupling of up to g0 = 2π ⋅ 95 Hz. This indicates that normal mode splitting and full optomechanical control of the carbon nanotube vibration in the quantum limit is reachable in the near future. Mechanical manipulation and characterization via the microwave field can be complemented by the manifold physics of quantum-confined single electron devices.

Normal-mode splitting and ponderomotive squeezing in a nonlinear optomechanical system assisted by an atomic ensemble

We theoretically investigate the displacement spectrum of a movable mirror and squeezing spectrum of the cavity quadrature field in a hybrid optomechanical system (OMS), which contains a degenerate optical parametric amplifier (OPA) and N two-level cold atoms. In comparison with the bare OMS, when there is only an OPA in the optical cavity, with the increasing nonlinear gain of the OPA, peak separation of the normal-mode splitting (NMS) in the displacement spectrum and degree of the squeezing spectrum for the cavity quadrature field increase. Further, the simultaneous presence of both OPA and the atomic ensemble in the optical cavity ensures wider spacing in the NMS and greater degree of the squeezing spectrum than the OMS with just an OPA or an atomic ensemble. Further, a decrease in temperature ends the peak in the squeezing spectrum due to a reduction in mechanical thermal noise.

Transparency and tunable slow-fast light in a hybrid cavity optomechanical system.

We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon in a hybrid optomechanical system composing of an optomechanical cavity and a traditional one. A Kerr medium is inserted in the optomechanical cavity and the other traps the atomic ensemble. We demonstrate the appearance of electromagnetically and optomechanically induced transparency when there is only Kerr medium or atoms in the system. We give an explicit explanation for the mechanism of the transparency. Moreover, we set up new scheme for the measurement of Kerr coefficient and the single atom-photon coupling strength. It is shown that Kerr nonlinearity can inhibit the normal mode splitting (NMS) when the tunnel strength is strong coupling. Furthermore, in the output field, slow light and fast light are converted to realize the tunable switch from slow light to fast light. This study has some important guiding significance in the fields of the high precision measurement and quantum information processing.

Strong Coupling of a Single Ion to an Optical Cavity.

Strong coupling between an atom and an electromagnetic resonator is an important condition in cavity quantum electrodynamics. While strong coupling in various physical systems has been achieved so far, it remained elusive for single atomic ions. Here, we achieve a coupling strength of 2π×(12.3±0.1) MHz between a single ^{40}Ca^{+} ion and an optical cavity, exceeding both atomic and cavity decay rates which are 2π×11.5 and 2π×(4.1±0.1) MHz, respectively. We use cavity assisted Raman spectroscopy to precisely characterize the ion-cavity coupling strength and observe a spectrum featuring the normal mode splitting in the cavity transmission due to the ion-cavity interaction. Our work paves the way towards new applications of cavity quantum electrodynamics utilizing single trapped ions in the strong coupling regime for quantum optics and quantum technologies.

Normal-mode splitting in a linear and quadratic optomechanical system with an ensemble of two-level atoms

We theoretically calculate normal-mode splitting (NMS) in a linear and quadratic optomechanical system (OMS) with an ensemble of two-level atoms, where the interaction between the mechanical membrane and the optical cavity includes linear optomechanical coupling and quadratic optomechanical coupling (QOC). In the presence of atomic ensemble, a negative QOC strength is instrumental for generating NMS, while the positive QOC restricts NMS, and eventually it disappears. Further, for the hybrid OMS assisted with the atomic ensemble, the displacement spectrum of the mechanical resonator displays three peaks, where the middle peak results from the effective coupling strength between the cavity field and the atomic ensemble. Here the negative QOC strength and the effective ensemble-field coupling can provide an efficient control of the amplitude and position of the three peaks.

Collective Multimode Vacuum Rabi Splitting.

We report the experimental observation of collective multimode vacuum Rabi splitting in free space. In contrast to optical cavities, the atoms couple to a continuum of modes, and the optical thickness of the cloud provides a measure of this coupling. The splitting, also referred as normal mode splitting, is monitored through the Rabi oscillations in the scattered intensity, and the results are fully explained by a linear-dispersion theory.

Normal-mode splitting in coupled high-Q microwave cavities

Three-dimensional radio frequency cavities demonstrate excellent frequency selectivity and, as such, are known for their use in RF filters. These cavities have potential applications in quantum information science, precision displacement metrology, and quantum electrodynamics. Additionally, coupled cavities that form a spectral doublet allow for parametric gain when incorporating mechanical elements. Here, we investigate normal-mode splitting in a pair of quarter-wave stub microwave cavities at room temperature and cryogenic environments in order to identify coupling mechanics for normal and superconducting systems. Superconducting quarter-wave stub cavities with a resonant frequency of 10 GHz are made from reactor-grade niobium and exhibit Q ranging from 105 to 109. We varied cavity-to-cavity coupling to observe several normal-mode splittings of increasing peak separation until we observed a mode crossing. The minimum observed peak separation was 7 MHz for room temperature tests and 200 kHz for cryogenic tests. We also report on values of an intrinsic quality factor for the tuning cavity as a dielectric rod is translated along its symmetry axis. The realization of coupled superconducting radio frequency (SRF) cavities of this type is a necessary step toward implementation of parametric SRF-mechanical gain.

Manifestation of classical nonlinear dynamics in optomechanical entanglement with a parametric amplifier

Cavity optomechanical system involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the former regime, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regular periodic oscillation to period-doubling motion, in which cases the light-mechanical entanglement can be well studied by the logarithm negativity and can manifest the dynamical transition in the classical nonlinear dynamics. Moreover, the optomechanical entanglement shows a second-order transition characteristic at the critical parametric gain. For the latter regime, the kind of normal mode splitting comes up in the laser detuning dependence of optomechanical entanglement, which is induced by the squeezing of the optical and mechanical hybrid modes and finds no classical correspondence. The OPA assisted optomechanical systems therefore offer a simple way to study and exploit quantum manifestations of classical nonlinear dynamics.

Cooling of a Mechanical Oscillator and Normal Mode Splitting in Optomechanical Systems with Coherent Feedback

The ground state cooling of a mechanical oscillator and strong optomechanical coupling are necessary prerequisites for realizing quantum control of the macroscopic mechanical oscillator. Here, we show that the resolved-sideband cooling of a mechanical oscillator in an optomechanical system can be enhanced by a simple coherent feedback scheme, in which a portion of the output field from the cavity is fed back into the cavity using an asymmetric beam splitter. Moreover, we show that the normal mode splitting in the spectra of the movable mirror and the output field in a weakly coupled optomechanical system can be induced by the feedback scheme due to a reduced effective cavity decay rate. We find that the peak separation becomes larger and two peaks of the spectra become narrower and higher with increasing the reflection coefficient r of the beam splitter.

Dynamic suppression of Rayleigh backscattering in dielectric resonators

The ultimate limits of performance for any classical optical system are set by sub-wavelength fluctuations within the host material, which may be frozen-in or even dynamically induced. The most common manifestation of such subwavelength disorder is Rayleigh light scattering, which is observed in nearly all waveguiding technologies today and can lead to both irreversible radiative losses as well as undesirable intermodal coupling. While it has been shown that backscattering from disorder can be suppressed by breaking the time-reversal symmetry in magneto-optic and topological insulator materials, common optical dielectrics possess neither of these properties. Here, we demonstrate an optomechanical approach for dynamically suppressing Rayleigh backscattering within dielectric resonators. We achieve this by locally breaking the time-reversal symmetry in a silica resonator through a Brillouin scattering interaction that is available in all materials. Near-complete suppression of Rayleigh backscattering is experimentally confirmed through two independent measurements—the elimination of a commonly seen normal-mode splitting or “doublet” effect and by measurement of the reduction in intrinsic optical loss. Additionally, a reduction of the back-reflections caused by disorder is also observed. Our results provide new evidence that it is possible to dynamically suppress Rayleigh backscattering within any optical dielectric medium using time-reversal symmetry breaking, for achieving robust light propagation in spite of scatterers or defects.

The occurrence of multistability and normal mode splitting in an optomechanical system

We provide a theoretical technique to study the occurrence of multistability and normal mode splitting in an optomechanical system driven by a single mode cavity field. For this purpose, we consider the position-dependent mass mechanical resonator (PDMR) which produces the nonlinearity in the system. This shifts the system from monostable to bistable regime and bistable to a multistable regime at different conditions of the nonlinearity. Further, we use the Fourier transform technique to find out the fluctuation in the position of the nano-mechanical resonator and their energy spectrum as well. Moreover, we used the input-output theory to analyze the transmitted field spectrum as well as x and y quadratures spectra of the output field. We explain the effect of the non-linearity on the normal mode splitting of the former and later spectra. In addition, we also explain the normal mode splitting as a function of cavity decay rate and laser power, respectively.