Erot Cavity Research Articles

Radiation pressure in finite Fabry–Pérot cavities

We study the effect of finite size and misalignment on a fundamental optomechanical setup: a Fabry-P\'erot cavity with one fixed and one moveable mirror. We describe in detail light confinement under these real world imperfections and compare the behaviour of the intracavity and output fields to the well-known ideal case. In particular, we show that it is possible to trace the motion of the movable mirror itself by measuring intensity changes in the output field even in the presence of fabrication shortcomings and thermal noise. Our result might be relevant to the transition from high precision research experiments to everyday commercial applications of optomechanics; such as high-precission stepmotor or actuator positioning.

Generation of three wide frequency bands within a single white-light cavity

We theoretically investigate the double-$\mathrm{\ensuremath{\Lambda}}$ scheme inside a Fabry-P\'erot cavity employing a weak probe beam and two strong driving fields together with an incoherent pumping mechanism. By generating analytical expressions for the susceptibility and applying the white-light cavity conditions, we devise a procedure that reaches the white-light condition at a smaller gas density than the values typically cited in similar previous studies. Further, when the intensities of the two driving fields are equal, a single giant white band is obtained, while for unequal driving fields three white bands can be present in the cavity. Two additional techniques are then advanced for generating three white bands and a method is described for displacing the center frequency of the bands. Finally, some potential applications are suggested.

Strong Exciton–Photon Coupling and Lasing Behavior in All-Inorganic CsPbBr3 Micro/Nanowire Fabry-Pérot Cavity

Macroscopic spontaneous coherence of exciton-polariton in semiconductor cavity is one important research field in condensed matter physics. All-inorganic micro/nanowire Fabry-P\'erot cavity with excellent optical performance makes it possible to realize strong coupling and lasing of exciton-photon at room temperature. In this work, we demonstrated strong coupling of exciton-photon and polariton lasing in CsPbBr3 micro/nanowires synthesized by CVD method. By exploring spatial resolved PL spectra of CsPbBr3 cavity, we observed mode volume dependent coupling strength , as well as significant increase in group index. Moreover, low threshold polariton lasing was achieved at room temperature within strong coupling regime; the polariton characteristic is confirmed by comparing lasing spectra with waveguided output spectra and the dramatically reduced lasing threshold. Our present results provide new avenues to achieve high coupling strengths potentially enabling application of exciting phenomena such as Bose-Einstein condensation of polaritons, efficient light-emitting diodes and lasers.

Fabry-Pérot Cavity Formed with Dielectric Metasurfaces in a Hollow-Core Fiber

We demonstrate a fiber-integrated Fabry-P\'erot cavity formed by attaching a pair of dielectric metasurfaces to the ends of a hollow-core photonic-crystal fiber segment. The metasurfaces consist of perforated membranes designed as photonic-crystal slabs that act as planar mirrors but can potentially allow injection of gases through their holes into the hollow core of the fiber. We have so far observed cavities with finesse of ~11 and Q factors of ~$4.5 \times 10^5$, but much higher values should be achievable with improved fabrication procedures. We expect this device to enable development of new fiber lasers, enhanced gas spectroscopy, and studies of fundamental light-matter interactions and nonlinear optics.

The OVAL experiment: a new experiment to measure vacuum magnetic birefringence using high repetition pulsed magnets

A new experiment to measure vacuum magnetic birefringence (VMB), the OVAL experiment, is reported. We developed an original pulsed magnet that has a high repetition rate and applies the strongest magnetic field among VMB experiments. The vibration isolation design and feedback system enable the direct combination of the magnet with a Fabry-P\'erot cavity. To ensure the searching potential, a calibration measurement with dilute nitrogen gas and a prototype search for vacuum magnetic birefringence are performed. Based on the results, a strategy to observe vacuum magnetic birefringence is reported.

Medium-finesse optical cavity for the stabilization of Rydberg lasers.

We describe the design, construction, and characterization of a medium-finesse Fabry-Perot cavity for simultaneous frequency stabilization of two lasers operating at 960 and 780 nm wavelengths, respectively. The lasers are applied in experiments with ultracold rubidium Rydberg atoms, for which a combined laser linewidth similar to the natural Rydberg linewidth (≈10 kHz) is desired. The cavity, with a finesse of ≈1500, is used to reduce the linewidth of the lasers to below this level. By using a spacer made of ultra low expansion (ULE) glass with active temperature stabilization, the residual frequency drift is limited to ≲1 MHz/day. The design optimizes for ease of construction, robustness, and affordability.

Microresonator-stabilized extended-cavity diode laser for supercavity frequency stabilization.

We demonstrate a simple, compact, and cost-effective laser noise reduction method for stabilizing an extended-cavity diode laser to a 3×105 finesse mirror Fabry-Perot (F-P) cavity, corresponding to a resonance linewidth of 10kHz, by using a crystalline MgF2 whispering gallery mode microresonator. The laser linewidth is reduced to sub-kilohertz such that a stable Pound-Drever-Hall error signal is built up. The wavelength of the pre-stabilized laser is tunable within a large bandwidth covering the high-reflection mirror coating of an F-P supercavity.

Probing spontaneous wave-function collapse with entangled levitating nanospheres

Wave function collapse models are considered as the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models make predictions, differently from those of standard quantum mechanics, that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments and hence efficient protocols for this kind of experiments are highly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-P\'erot cavity. We show that the collapse noise results in large reduction of the steady-state entanglement and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to unambiguously determine the effect of these models.

Analytical expression for Risken-Nummedal-Graham-Haken instability threshold in quantum cascade lasers.

We have obtained a closed-form expression for the threshold of Risken-Nummedal-Graham-Haken (RNGH) multimode instability in a Fabry-Pérot (FP) cavity quantum cascade laser (QCL). This simple analytical expression is a versatile tool that can easily be applied in practical situations which require analysis of QCL dynamic behavior and estimation of its RNGH multimode instability threshold. Our model for a FP cavity laser accounts for the carrier coherence grating and carrier population grating as well as their relaxation due to carrier diffusion. In the model, the RNGH instability threshold is analyzed using a second-order bi-orthogonal perturbation theory and we confirm our analytical solution by a comparison with the numerical simulations. In particular, the model predicts a low RNGH instability threshold in QCLs. This agrees very well with experimental data available in the literature.

Precision Interferometric Measurements of Mirror Birefringence in High-Finesse Optical Resonators.

High-finesse optical resonators found in ultrasensitive laser spectrometers utilize supermirrors ideally consisting of isotropic high-reflectivity coatings. Strictly speaking, however, the optical coatings are often non-uniformly stressed during the deposition process and therefore do possess some small amount of birefringence. When physically mounted the cavity mirrors can be additionally stressed in such a way that large optical birefringence is induced. Here we report a direct measurement of optical birefringence in a two-mirror Fabry-Pérot cavity with R = 99.99 % by observing TEM00 mode beating during cavity decays. Experiments were performed at a wavelength of 4.53 μm, with precision limited by both quantum and technical noise sources. We report a splitting of δν = 618(1) Hz, significantly less than the intrinsic cavity linewidth of δcav ≈ 3 kHz. With a cavity free spectral range of 96.9 MHz, the equivalent fractional change in mirror refractive index due to birefringence is therefore Δn/n = 6.38(1) × 10-6.

Determination of the hyperfine structure constants of theRb87andRb854D5/2state and the isotope hyperfine anomaly

The hyperfine structure (hfs) splittings of the $4{D}_{5/2}$ state for two isotopes of $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$ atoms are measured based on double-resonance optical pumping spectra in a $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{5/2}$ ladder-type atomic system. The frequency calibration is performed by employing a wideband fiber-pigtailed phase-type electro-optic modulator together with a Fabry-P\'erot cavity to cancel the error arising from nonlinear frequency scanning. The hfs magnetic dipole constant $A$ of the $4{D}_{5/2}$ state is determined to be \ensuremath{-}16.801 \ifmmode\pm\else\textpm\fi{} 0.005 MHz for $^{87}\mathrm{Rb}$ and \ensuremath{-}4.978 \ifmmode\pm\else\textpm\fi{} 0.004 MHz for $^{85}\mathrm{Rb}$. The hfs electric quadrupole constant $B$ of the $4{D}_{5/2}$ state is determined to be 3.645 \ifmmode\pm\else\textpm\fi{} 0.030 MHz for $^{87}\mathrm{Rb}$ and 6.560 \ifmmode\pm\else\textpm\fi{} 0.052 MHz for $^{85}\mathrm{Rb}$. The values of $A$ and $B$ for the $^{87}\mathrm{Rb}4{D}_{5/2}$ state are twice as accurate as previous work with thermal atoms using a femtosecond laser comb and the values of $A$ and $B$ for the $^{85}\mathrm{Rb}4{D}_{5/2}$ state are 3 times and 25 times more accurate than previous work in laser-cooled atoms using Fabry--P\'erot interferometer, respectively. According to this high precision of the hfs constants and the previously measured nuclear $g$ factors of the two isotopes, the value of the $d$-electron hyperfine anomaly $^{87}\mathrm{\ensuremath{\Delta}}{}^{85}(4{D}_{5/2})$ is derived to be \ensuremath{-}0.0041 \ifmmode\pm\else\textpm\fi{} 0.0009.

Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction.

We propose using optomechanical interaction to narrow the bandwidth of filter cavities for achieving frequency-dependent squeezing in advanced gravitational-wave detectors, inspired by the idea of optomechanically induced transparency. This can allow us to achieve a cavity bandwidth on the order of 100 Hz using small-scale cavities. Additionally, in contrast to a passive Fabry-Pérot cavity, the resulting cavity bandwidth can be dynamically tuned, which is useful for adaptively optimizing the detector sensitivity when switching amongst different operational modes. The experimental challenge for its implementation is a stringent requirement for very low thermal noise of the mechanical oscillator, which would need a superb mechanical quality factor and a very low temperature. We consider one possible setup to relieve this requirement by using optical dilution to enhance the mechanical quality factor.

Spin-orbit-coupled Bose-Einstein condensates in a cavity: Route to magnetic phases through cavity transmission

We study the spin orbit coupled ultra cold Bose-Einstein condensate placed in a single mode Fabry-P\'erot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized extended Bose Hubbard model whose zero temperature phase diagram can be controlled by tuning the cavity parameters. In the non-interacting limit, where the atom-atom interaction is set to zero, the resulting atomic dispersion shows interesting features such as bosonic analogue of Dirac points, cavity controlled Hofstadter spectrum which bears the hallmark of pseudo-spin-1/2 bosons in presence of Abelian and non-Abelian gauge field (the later due to spin-orbit coupling) in a cavity induced optical lattice potential. In the presence of atom-atom interaction, using a mapping to a generalized Bose Hubbard model of spin-orbit coupled bosons in classical optical lattice, we show that the system realizes a host of quantum magnetic phases whose magnetic order can be be detected from the cavity transmission. This provides an alternative approach for detecting quantum magnetism in ultra cold atoms. We discuss the effect of cavity induced optical bistability on this phases and their experimental consequences.

Quantum interference between Zeeman levels near structures made of left-handed materials and matched zero-index metamaterials

Quantum interference between Zeeman levels of atom placed in the structure containing left-handed materials (LHMs) and zero-index metamaterials (ZIMs) is investigated. Because of the existence of the LHM and ZIM, dipole radiation becomes highly anisotropic which is embodied by the high contrast between decay rates of the dipole component parallel to the surface and that normal to the surface. Furthermore, both decay rates are suppressed compared with those in free vacuum. Therefore, we propose the quantum interference between Zeeman levels accompanied by long lifetime. Two structures are designed to achieve such purpose. For the idealized LHM and ZIM without dissipation, a double-layer structure comprised of them is the right candidate. However, when we consider the dissipation of materials, a Fabry-P\'erot cavity made of matched ZIM slabs and LHM slabs is required. Results show that we get a high degree of quantum interference and low decay rates simultaneously.

Random lasing in an organic light‐emitting crystal and its interplay with vertical cavity feedback

The simultaneous vertical-cavity and random lasing emission properties of a blue-emitting molecular crystal are investigated. The 1,1,4,4-tetraphenyl-1,3-butadiene samples, grown by physical vapour transport, feature room-temperature stimulated emission peaked at about 430 nm. Fabry-P\'erot and random resonances are primed by the interfaces of the crystal with external media and by defect scatterers, respectively. The analysis of the resulting lasing spectra evidences the existence of narrow peaks due to both the built-in vertical Fabry-P\'erot cavity and random lasing in a novel, surface-emitting configuration and threshold around 500 microJ cm^-2. The anti-correlation between different modes is also highlighted, due to competition for gain. Molecular crystals with optical gain candidate as promising photonic media inherently supporting multiple lasing mechanisms.

Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction

We discuss the dynamics of a hybrid optomechanical setup where a dielectric nanosphere is levitated inside the Fabry-P\'erot cavity of a standard optomechanical system with one movable cavity mirror. The nanosphere is coupled to the cavity field and the movable mirror by the optomechanical and Casimir interactions with coupling strengths being dependent on the distance between the levitated nanosphere and cavity mirror. We investigate the steady-state characteristics of the system and the optical spring effect of the nanosphere in detail. We also analyze the effects of the distance-dependent optomechanical coupling and Casimir interaction on the cooling of the levitated nanosphere in the cases of a movable and of a fixed cavity mirror. It is found that in both cases, ground-state cooling of the levitated nanosphere can be approached in a certain range of parameters. Furthermore, in contrast to the case with the fixed mirror, the cooling of the levitated nanosphere with a movable mirror can be optimized with a properly chosen mirror oscillation frequency.

Enhanced optomechanical readout using optical coalescence

We present a scheme to strongly enhance the readout sensitivity of the squared displacement of a mobile scatterer placed in a Fabry-P\'erot cavity. We investigate the largely unexplored regime of cavity electrodynamics in which a highly reflective element positioned between the end mirrors of a symmetric Fabry-P\'erot resonator strongly modifies the cavity response function, such that two longitudinal modes with different spatial parity are brought close to frequency degeneracy and interfere in the cavity output field. In the case of a movable middle reflector we show that the interference in this generic "optical coalescence" phenomenon gives rise to an enhanced frequency shift of the peaks of the cavity transmission that can be exploited in optomechanics.

Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature

We demonstrate the analogue of electromagnetically induced transparency in a room temperature cavity optomechanics setup formed by a thin semitransparent membrane within a Fabry-P\'erot cavity. Due to destructive interference, a weak probe field is completely reflected by the cavity when the pump beam is resonant with the motional red sideband of the cavity. Under this condition we infer a significant slowing down of light of hundreds of microseconds, which is easily tuned by shifting the membrane along the cavity axis. We also observe the associated phenomenon of electromagnetically induced amplification which occurs due to constructive interference when the pump is resonant with the blue sideband.

Dressed photons in a nonlinear Fabry-Pérot cavity

The photo-polaron in a two-dimensional optical microcavity is investigated within the framework of quantum statistical mechanics. Our experimental setup is based on a planar Fabry-P\'erot cavity filled with a nonlinear nonpolar crystal. The Fabry-P\'erot cavity provides a chemical potential and an effective mass for a photon, making the system formally equivalent to a two-dimensional gas of number-conserving, massive bosons. The incident photons interact with the Raman phonons in the crystal and hence are converted into quasiparticles, which we refer to as photo-polarons. A photo-polaron is a photon dressed with a cloud of virtual transverse-optical phonons, namely, the dressed photon. One of the most important properties of photo-polaron is an increased inert mass. Because of the effect of photo-polarons, we find that the photon-photon interaction is enhanced greatly. The photo-polaron is a quantum effect of cavity nonlinear optics but its increased inert mass is a classical property.

Optically mediated nonlinear quantum optomechanics

We consider theoretically the optomechanical interaction of several mechanical modes with a single quantized cavity-field mode for linear and quadratic coupling. We focus specifically on situations where the optical dissipation is the dominant source of damping, in which case the optical field can be adiabatically eliminated, resulting in effective multimode interactions between the mechanical modes. In the case of linear coupling, the coherent contribution to the interaction can be exploited (e.g., in quantum state swapping protocols), while the incoherent part leads to significant modifications of cold damping or amplification from the single-mode situation. Quadratic coupling can result in a wealth of possible effective interactions including the analogs of second-harmonic generation and four-wave mixing in nonlinear optics, with specific forms depending sensitively on the sign of the coupling. The cavity-mediated mechanical interaction of two modes is investigated in two limiting cases: the resolved sideband and the Doppler regime. As an illustrative application of the formal analysis we discuss in some detail a two-mode system where a Bose-Einstein condensate is optomechanically linearly coupled to the moving end mirror of a Fabry-P\'erot cavity.