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Acta Physica Sinica

Precision measurement of resonate frequency and the effective cavity length of the high finesse optical micro-cavity

Jinjin Du, LI Wen-fang, Ruijuan Wen, Gang Li, Tiancai Zhang

Published Jan 1, 2013• 8 citations
Publisher

Abstract

Ultra-high finesse micro-resonator plays an important role in realizing the interaction between atoms and cavity field in the study of cavity quantum electrodynamics (QED) system, weak optical nonlinear effects and micro-optic devices. By measuring basic parameters of the microcavity, the atom-cavity coupling coefficient and the cavity decay rate can be determined precisely. It is also useful for exploring the dynamic characteristics of the system. However, it has difficulty in determining resonate frequency and effective cavity length due to the structure of the ultra-high finesse optical microcavity itself and the characteristics of multilayer coating. In this paper, we demonstrate the precision measurement of effective cavity length under different resonant frequencies which our cavity mirror is coated with 37 layers of dielectric film. The theoretical expectation when using the revised model of the multilayer coating agrees well with that of the experiment; and the measurement error for longitudinal mode interval is below 0.004 nm which is two orders of magnitude better than that obtained in previous unrevised model. The tiny depths into mirror coatings that the standing-wave light field inside the cavity penetrates are given for different mode numbers. This method may be applied to other micro resonator in the precision measurement.

DOI
10.7498/aps.62.194203

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Summary form only given. Optical microcavities with high quality factors Q are of great interest in integrated micro- and nanophotonics. Their narrow resonance and long photon lifetime (τcav) can be used in fundamental physics, sensing applications, microwave signal optical processing or for optical delay line and memory miniaturization [1]. Considering a Lorentzian resonance profile, the quality factor and the photon lifetime of a microcavity with a resonant angular frequency ωο = 2·πε/λ0reads: Q = ω0τcab= nG(ω0)LF/λ0, (1) where ngis the group index of the material constituting the microcavity, F is the finesse and L is the cavity round-trip length. The usual method to obtain ultra-high quality factors consists in optimizing the manufacturing process to reach high finesse values. Following this approach record quality factors up to 1011have been measured in millimetric CaF2 whispering gallery mode (WGM) resonators [2]. Otherwise, Eq. (1) shows that for a given finesse, the use of resonators made with slow-light materials displaying high group indices can also increase the quality factor. This method has already been successfully implemented in bulky resonators including a highly dispersive slow-light medium [3]. We have recently demonstrated that this approach can be applied to solid-state optical micro-resonators [4]. The slow-light effect was introduced thanks to population oscillations in an Er3+doped WGM fluoride glass microsphere (diameter 100 μm). Since the lifetime of the4I13/2level is very long (T ≈ 10 ms) strong group index up to 106can be obtained. Using a cavity-ring-down method (see Fig. 1) in a pump probe configuration, we have measured a photon lifetime of 2.5 ms at 1530 nm corresponding to a quality factor of 3 × 1012[4].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•0 citations
Ultra-high finesse micro-resonator plays an important role in realizing the interaction between atoms and cavity field in the study of cavity quantum electrodynamics (QED) system, weak optical nonlinear effects and micro-optic devices. By measuring basic parameters of the microcavity, the atom-cavity coupling coefficient and the cavity decay rate can be determined precisely. It is also useful for exploring the dynamic characteristics of the system. However, it has difficulty in determining resonate frequency and effective cavity length due to the structure of the ultra-high finesse optical microcavity itself and the characteristics of multilayer coating. In this paper, we demonstrate the precision measurement of effective cavity length under different resonant frequencies which our cavity mirror is coated with 37 layers of dielectric film. The theoretical expectation when using the revised model of the multilayer coating agrees well with that of the experiment; and the measurement error for longitudinal mode interval is below 0.004 nm which is two orders of magnitude better than that obtained in previous unrevised model. The tiny depths into mirror coatings that the standing-wave light field inside the cavity penetrates are given for different mode numbers. This method may be applied to other micro resonator in the precision measurement.
We characterize a high-finesse Fabry-Perot resonator for coupling with single neutral atoms. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters' uncertainty is solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Moreover, the technique with two lasers consists of a vital approach for determining geometric parameters of a short cavity, with a free spectral range on the order of THz. Our system operates in the strong atom-cavity coupling regime that allows us to explore fundamental quantum optics and implement quantum network protocols.
We evaluate the exact dipole coupling strength between a single emitter and the radiation field within an optical cavity, taking into account the effects of multilayer dielectric mirrors. Our model allows one to freely vary the resonance frequency of the cavity, the frequency of light or atomic transition addressing it, and the design wavelength of the dielectric mirror. The coupling strength is derived for an open system with unbound frequency modes. For very short cavities, the effective length used to determine their mode volume and the lengths defining their resonances are different, and also found to diverge appreciably from their geometric length, with the radiation field being strongest within the dielectric mirror itself. Only for cavities much longer than their resonant wavelength does the mode volume asymptotically approach that normally assumed from their geometric length.
Cavity-based quantum node is a competitive platform for distributed quantum networks. Here, we characterize a high-finesse Fabry-Pérot optical resonator for coupling single or few atomic quantum registers. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters’ uncertainties are solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Our scheme makes it possible to quantify the atom-cavity coupling constant up to four significant figures, the most precise and accurate estimation so far, which would become a key ingredient for benchmarking a cavity-based quantum node. Furthermore, the distortion of polarized photonic qubits would be minimized owing to the small birefringent splitting, below 4.9% of the cavity linewidth. Our system should operate in the intermediate atom-cavity coupling regime that would allow us to implement various quantum network protocols.
Effective models to describe the dynamics of an open cavity have been extensively discussed in the literature. In many of these models the cavity leakage to the outside is treated as a loss introduced phenomenologically. In contrast to these, we focus here on characterizing the outgoing photon using a novel approach where the outside is treated as part of the system. In such a global system, in order to separately characterize the photon inside and outside cavity, we demonstrate a first-principle derivation of a coherent cavity-reservoir coupling function for cavities with mirrors consisting of a stack of dielectric layers. In particular, we show that due to the effects induced by the multilayer nature of the cavity mirror, even in the standardly defined high-finesse cavity regime, the cavity-reservoir system description might differ from the one where the structure of the mirror is neglected. Based on this, we define a generalized cavity response function and a cavity-reservoir coupling function, which account for the longitudinal geometric structure of the cavity mirror. This allows us to define an effective reflectivity for the cavity with a multilayer mirror as if it was sitting in a well-defined effective mirror plane. We estimate the error of such a definition by considering cavities of different lengths and mirror structures. Finally, we apply this model to characterize the dynamics of a single photon produced in such a cavity and propagating outside.
Summary form only given. Optical microcavities with high quality factors Q are of great interest in integrated micro- and nanophotonics. Their narrow resonance and long photon lifetime (τcav) can be used in fundamental physics, sensing applications, microwave signal optical processing or for optical delay line and memory miniaturization [1]. Considering a Lorentzian resonance profile, the quality factor and the photon lifetime of a microcavity with a resonant angular frequency ωο = 2·πε/λ0reads: Q = ω0τcab= nG(ω0)LF/λ0, (1) where ngis the group index of the material constituting the microcavity, F is the finesse and L is the cavity round-trip length. The usual method to obtain ultra-high quality factors consists in optimizing the manufacturing process to reach high finesse values. Following this approach record quality factors up to 1011have been measured in millimetric CaF2 whispering gallery mode (WGM) resonators [2]. Otherwise, Eq. (1) shows that for a given finesse, the use of resonators made with slow-light materials displaying high group indices can also increase the quality factor. This method has already been successfully implemented in bulky resonators including a highly dispersive slow-light medium [3]. We have recently demonstrated that this approach can be applied to solid-state optical micro-resonators [4]. The slow-light effect was introduced thanks to population oscillations in an Er3+doped WGM fluoride glass microsphere (diameter 100 μm). Since the lifetime of the4I13/2level is very long (T ≈ 10 ms) strong group index up to 106can be obtained. Using a cavity-ring-down method (see Fig. 1) in a pump probe configuration, we have measured a photon lifetime of 2.5 ms at 1530 nm corresponding to a quality factor of 3 × 1012[4].