Abstract

Rare earth ions are known as promising candidates for building quantum light-matter interface. However, tunable photonic cavity access to rare earth ions in their desired host crystal remains challenging. Here, we demonstrate the integration of erbium doped yttrium orthosilicate (Er3+:Y2SiO5) with thin-film lithium niobate photonic circuit by plasma-activated direct flip chip bonding. Resonant coupling to erbium ions is realized by on-chip electro-optically tuned high Q lithium niobate micro-ring resonators. Fluorescence and absorption of erbium ions at 1536.48 nm are measured in the waveguides, while the collective ion-cavity cooperativity with micro-ring resonators is assessed to be 0.36. This work presents a versatile scheme for future rare earth ion integrated quantum devices.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Incorporating solid-state emitters in integrated photonic circuits has been shown to be favorable for quantum information processing including quantum memory [1,2], microwave-to-optical transduction [3], and single photon generation [4]. Thanks to their narrow optical and spin linewidth, rare earth ions (REIs) are particularly appealing for these applications. To date, direct incorporation of REIs into photonic waveguides has been realized by means of ion implantation [57], smart-cut technique [8], and in-diffusion [9]. Since the properties of REI species in different host materials vary considerably, it is critical to choose ion-specific host materials which are often difficult to pattern into waveguides. Among all the REIs, erbium (Er) ion has drawn great attention due to its optical transition in the telecommunication band, which permits long-range transmission through optical fibers. Yttrium orthosilicate (YSO) is a commonly used crystalline host for erbium ions and exhibits excellent properties. Homogeneous linewidth down to 73 Hz [10] has been measured in erbium doped yttrium orthosilicate (Er$^{3+}$:Y$_2$SiO$_5$), while the inhomogeneous linewidth can be narrower than 1 GHz [11]. As a comparison, the inhomogeneous linewidth of Er doped in lithium niobate is as large as 180 GHz [12].

Methods of integrating REI native crystals include deposition of waveguide layers [13,14] and focused ion beam shaping [15]. In these approaches, however, the choices of photonic waveguides are often limited by available material growth technique or compatibility in fabrication process. In this work, we demonstrate the coupling of Er$^{3+}$:Y$_2$SiO$_5$ and thin-film lithium niobate (LN) waveguides and resonators by direct flip chip bonding [16]. Direct flip chip bonding allows the joining of two heterogeneous materials with flat surfaces without intermediate layers. Plasma treatment [17] is often used to obtain large surface energies, which allows direct bonding at room temperature by the van der Waals forces. This method has been applied in silicon photonics for realizing heterostructure devices [18,19]. Due to the universality of the bonding method, it would be applicable to various REI doped materials and integrated photonic platforms, providing a flexible basis for REI integrated device development.

As a material with excellent opto-mechanical [20], electro-optic [21], and nonlinear optical [22] properties, LN finds a great variety of applications in modern photonics. The recent breakthrough in thin-film LN nano-fabrication enables low-loss waveguides and high-Q optical resonators [23], ideally suitable for realizing enhanced light-matter interaction. Here, by using direct bonding, we are able to harness both the advantages of thin-film LN photonics and Er$^{3+}$:Y$_2$SiO$_5$. Micro-ring resonators with quality factor as high as a million are fabricated and characterized. Utilizing the electro-optic property of LN, we further incorporate on-chip metal electrodes to tune the resonator wavelength at a rate of 2.25 pm/V. The Er ion signal in LN waveguides is observed in fluorescence and absorption measurements. The collective coupling strength of Er ensemble and micro-ring resonator is assessed subsequently and characterized by the ion-cavity collective cooperativity.

2. Device fabrication and characterization

For device fabrication, we use 600-nm-thick x-cut lithium niobate on silicon dioxide (LNOI) thin-film wafers. The fabrication process includes three steps. First, in order to mask sufficient bonding areas, a 1-$\mu$m-thick silicon dioxide (SiO$_2$) layer is deposited on the LNOI film via plasma-enhanced chemical vapor deposition (PECVD). Windows are opened in the oxide layer with electron beam lithography (EBL) using CSAR as a positive resist, followed by fluorine-based reactive ion etching (RIE) to reveal the LN surface. A second EBL exposure is applied in the exposed windows using hydrogen silsesquioxan (HSQ) to pattern waveguides and micro-ring resonators, followed by RIE with argon plasma to half-etch 350 nm into the LN layer. Finally, electrodes consist of 5 nm chromium (Cr), used as adhesion layer, and 50 nm gold (Au) are thermally evaporated next to the micro-ring resonators, with a lift-off process using polymethyl methacrylate (PMMA). For flip chip bonding, a 50 ppm Er$^{3+}$:Y$_2$SiO$_5$ crystal (5 mm $\times$ 5 mm $\times$ 500 $\mu$m, from Scientific Materials) is polished by an Allied High Tech tabletop polisher to prepare a smooth surface. The polishing procedure starts with diamond lapping films ranging from 15 $\mu$m to 1 $\mu$m. 0.05 $\mu$m colloidal silica suspension is then used for final polishing. After polishing, the rms roughness of the crystal is reduced to less than 1 nm. The Er$^{3+}$:Y$_2$SiO$_5$ crystal and fabricated LNOI devices then go through a series of cleaning process using acetone, isopropanol, and piranha (H$_2$SiO$_4$:H$_2$O$_2$=2:1). The as-cleaned surfaces are activated by 200 W oxygen plasma at 350 mT for 50 s. The two films are immediately put in contact at room temperature after the process. Since the film surfaces are thoroughly cleaned and activated to be hydrophilic, a direct bond between them will be formed upon contacting [24].

An overall optical image of the device is shown in the bottom panel of Fig. 1(a), together with a zoomed-in SEM image of the micro-ring resonator shown on the top. The micro-ring has a radius of 70 $\mu$m and a width of 1.6 $\mu$m. It is coupled by a 0.8 $\mu$m wide bus waveguide, connected by a pair of grating couplers for fiber-optic coupling. The gap between two metal electrodes are designed to be 6 $\mu$m to avoid perturbing the optical mode. A probe station is made in contact with the electrodes to apply voltage for resonance tuning. Both metal wires and waveguides are made to be sufficiently long so that the coupling components are outside the bonded crystal. The cross section of the micro-ring resonator is drawn in Fig. 1(b), together with the simulated optical mode profile of the fundamental transverse-electric (TE) mode. A portion of the electric field goes into the top YSO layer, enabling optical dipolar coupling to the Er ions.

 figure: Fig. 1.

Fig. 1. (a) Optical micrograph (bottom panel) and zoom-in SEM image (upper panel) of a micro-ring device. (b) Schematic drawing of the device cross section after bonded with Er$^{3+}$:Y$_2$SiO$_5$. Shown on the right is the electric field profile of the fundamental TE mode in the micro-ring, with arrows marking the direction of the electric field.

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The bonded device was then cooled down to 4 K in a Montana Instruments cryostation fitted with a fiber array setup for characterization. A set of Attocube Nanopositioners, installed on the sample stage, are used for aligning and screening of devices at cryogenic temperature. A typical grating coupler transmission spectrum is shown in Fig. 2(a). The peak coupling efficiency for the device was estimated to be 4 %. For the spectrum scan we used 1 mW laser power. A fundamental TE mode resonance around 1537 nm is shown in the right panel. Lorentzian fit of the resonance indicates a quality factor (Q) of 1.09 million. It is worth to note that device Q measured before and after bonding is similar, suggesting that the optical Q can be preserved after the cleaning and bonding process.

 figure: Fig. 2.

Fig. 2. (a) The transmission spectrum of the micro-ring device. The overall transmission envelope is determined by the grating couplers. Fundamental TE, TM and first-order TE modes of the resonator can be seen in the spectrum. The right panel shows a Lorentzian fit of a fundamental TE mode resonance yielding Q of 1.09 M. (b) The resonance shift in response to the applied DC voltage. The linear fit indicates a tuning rate of 2.25 pm/V. The inset shows resonance at two applied voltages, 20 V (blue) and 80 V (orange). All data were taken at 4K.

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The inhomogeneous linewidth of Er ions in YSO is usually around 1 GHz (or 8 pm), while the free spectrum range (FSR) of the micro-ring resonator is 2.3 nm. Thus, it is important to have the ability of tuning the resonance frequency in order to align the resonance with the Er transition line. Here, we leverage the electro-optic effect of LN, in which the refractive index of the resonator can be modified by static electric field. The electric field is applied along the z-axis of LN so that the largest electro-optic coefficient $r_{33}=31$ pm/V [25] is utilized. We measured the resonance wavelength tunability to be 2.25 pm/V at cryogenic temperature, as shown in Fig. 2(b). Two resonance curves under different voltage in the inset of Fig. 1 verify that the Q is not impacted by the tuning. The electric breakdown of lithium niobate could be observed when applying voltage up to around 300 V. This translates to a maximal tuning range of 1.3 nm, exceeding 50 % of the FSR.

3. Characterization of Er coupling

3.1 Fluorescence measurements in the waveguides

To demonstrate the coupling of Er ions and LN waveguides, the fluorescence decay of Er ions was first measured. The experimental setup is shown in Fig. 3(a). We used an acousto-optic modulator (AOM) to generate a pump pulse from a continuous-wave tunable laser to excite the erbium ions coupled to the waveguide. After the pump pulse, The fluorescence that traveled in the reverse direction transmitted through an optical circulator and was gated by another AOM. The fluorescence signal was collected by a power detector with noise floor around -95dBm after the AOM. Meanwhile, another power meter at the other end of the device was utilized to monitor the transmission spectrum.

Figure 3(b) shows the transmission spectrum of the waveguide around 1536.48 nm, where a clear dip due to erbium absorption can be seen, with around 2% of the light absorbed. The red cross marks the wavelength that the fluorescence was measured at, corresponding to the emission wavelength of site 1 Er in YSO host. By changing the delay between the pump pulse and the detection window, an exponential decay of the fluorescence intensity could be extracted, as shown in Fig. 3(c). The fluorescence lifetime was fitted to be 11.5 ms, consistent with the bulk result 11.4 ms [11].

 figure: Fig. 3.

Fig. 3. (a) Schematic setup for measuring Er fluorescence decay. A tunable laser was used to excite the Er ions. Two AOMs were used to generate pump pulse and gate detection window, respectively. An optical circulator was utilized to collect the fluorescence in the reverse direction of the pump. The emission at different delays was measured by an optical power detector. Another detector at the other end of the device recorded the waveguide transmission. (b) The waveguide transmission spectrum around 1536.48nm. The dip arises from erbium absorption, with the red cross marking the wavelength for fluorescence measurement. (c) The fluorescence decay of site 1 Er ions at 1536.48 nm measured in the waveguide. The red line is an exponential fit of the signal, yielding a lifetime of 11.5 ms.

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3.2 Characterization of ion-cavity collective coupling

Incorporation of optical resonator is important when coupling to REIs due to their weak oscillator strength [26], which is the origin of their excellent coherence properties. Under electric dipolar interaction approximation, the coupling rate between an optical cavity and a REI can be denoted as

$$g(\vec{r})=\frac{\mu}{n_\textrm{mode}}\sqrt{\frac{\omega}{2\epsilon_0\hbar V_\textrm{mode}}}\frac{|E(\vec{r})|}{|E_{\mathrm{max}}|},$$
where $\mu$, $n_\textrm {mode}$, and $V_\textrm {mode}=\frac {\int dV \epsilon (\vec {r}) |E(\vec {r})|^2}{\mathrm {max}(\epsilon (\vec {r})|E(\vec {r})|^2)}$ are the transition dipole moment, refractive index of the optical mode and the mode volume. The coupling strength is also weighted by the ratio between resonator electric field at the ion position and the maximum field strength. Here, we are interested in the collective coupling between Er ensemble and micro-ring resonator, $G=[\int _{YSO}g^2(\vec {r})\rho dV]^{1/2}$, with $\rho$ being the number concentration of the ions. By defining the filling factor as $F=\frac {\int _{YSO} dV \epsilon (\vec {r}) |E(\vec {r})|^2}{\int dV \epsilon (\vec {r}) |E(\vec {r})|^2}$, which denotes the percentage of electric field energy in the YSO crystal, we can rewrite the collective coupling strength as
$$G=\frac{\mu}{n_\textrm{mode}}\sqrt{ \frac{F \rho \omega}{2\epsilon_0\hbar}}.$$
Note that the single-ion coupling rate is inversely proportional to the square root of the optical mode volume, while the collective coupling only depends on the ion density and the filling factor. Using the input-output theorem, the resonator transmission when coupled to an inhomogeneously broadened ensemble can be written as [27]
$$T(\omega)=\left|1-\frac{i\kappa_{ex}}{\omega-\omega_0+i\kappa_0/2-\frac{G^2}{\omega-\omega_\textrm{ions}+i\gamma/2}}\right|^2,$$
where $\omega _0$, $\kappa _{ex}$, and $\kappa _0$ are the frequency, external coupling rate, and energy decay rate of the resonator. $\omega _\textrm {ions}$ and $\gamma$ are the center frequency and full width at half maximum (FWHM) of the ensemble inhomogeneous line. Here we assume a Lorentzian shape of the ensemble, which is a commonly used approximation for REIs [11]. In the case where the collective coupling strength $G$ is smaller than the inhomogeneous linewidth $\gamma$, the coupling is shown as a broadening of the resonance. The linewidth of the resonator when coupled to the ion ensemble is
$$\kappa=\kappa_{0}+\frac{G^2\gamma}{\Delta^2+(\gamma/2)^2},$$
where $\Delta =\omega _0-\omega _\textrm {ions}$ is the detuning between the resonator frequency and ensemble center frequency. The strength of the coupling is evaluated by the collective cooperativity $C=\frac {4G^2}{\kappa _0\gamma }$.

To extract the collective cooperativity of ion-cavity coupling, we chose a resonance near 1536 nm and scanned the resonance across the Er transition line. For the resonance used in the measurement, DC voltage around 100 V was applied for tuning to erbium transition wavelength. For each voltage applied, we measured the resonator transmission and fitted its linewidth. To accurately fit the quality factor, in the measurement we used a single sideband modulator (SSBM) to generate a weak sideband to probe the resonance. As shown in Fig. 4, the resonator linewidth increases at 1536.48 nm, which coincides with the Er absorption wavelength. Three transmission curves for the Er on-resonance and off-detuned cases are also shown. A Lorentizian fit of the resonance’s linewidth broadening yields the collective coupling rate $G=98$ MHz, the inhomogeneous linewidth $\gamma =480$ MHz, and the resonator linewidth $\kappa _0=225$ MHz. This gives a collective cooperativity $C=0.36$.

 figure: Fig. 4.

Fig. 4. Resonator linewidth measurement when the resonator is tuned across the erbium transition wavelength. Insets: Three resonance curves represent Er on-resonance case and off-detuned cases, taken at wavelengths correponding to the blue, orange and cyan points. A Lorentian fitting to the linewidth change is shown by the red curve, yielding a collective coupling cooperativity of 0.36.

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The filling factor in Eq. (2) is calculated to be $F=1.5$ % by substituting the measured $G=98$ MHz and transition dipole moment $\mu = 2\times 10^{-32}\,$C $\cdot$ m, $n_\textrm {mode}=2.2$ and $\rho =4.68\times 10^{23}$ /m$^3$ for 50 ppm Er concentration. With a zero bonding gap, the mode profile simulation predicts a filling factor $F=7$ %. For the measured results, however, the gap between YSO and LN film is estimated to be around 150 nm. We attribute this discrepancy to the thermal expansion coefficient difference of YSO and LN. Since the bonding is done at room temperature, during cooldown it could be weakened by the large temperature traverse, causing an enlarged bonding gap at cryogenic temperature. It is possible to mitigate this problem by using stronger bonding methods. For example, atomic layer deposition (ALD) of $\sim$10-nm-thick alumina is often used in semiconductor wafer bonding [28], which also shows good device performance at cryogenic temperature [29]. We anticipate a more than 3 fold increase of cooperativity if this approach is implemented. Other efforts to increase the cooperativity will include the use of thinner and narrower waveguides. The filling factor is expected to be twice larger if the waveguide is thinned down to 400 nm from 600 nm. Applying these improvements will reasonably allow us to get to the strong coupling regime, where the cooperativity is larger than unity.

4. Discussion and conclusion

In conclusion, we have fabricated thin film LNOI micro-ring resonator with Q of a million after flip-bonded with Er$^{3+}$:Y$_2$SiO$_5$ crystal. With appropriate polishing, cleaning, and surface activation steps, a direct bond between them can be formed at room temperature and maintained at 4 K. To match the resonance with erbium transition wavelength, electro-optic tuning of the resonance frequency is applied. Measured tuning rate of 2.25 pm/V allows us to cover more than 50% of the resonator FSR before breakdown. Fluorescence and absorption of Er in site 1 of YSO is seen at 1536.48 nm, in good agreements with the bulk results. Coupling with the micro-ring resonator is characterized by the linewidth broadening at the Er transition wavelength. A collective cooperativity of 0.36 is obtained. The bonding method can be well-suited for other REI doped materials and on-chip photonic platforms such as silicon, silicon nitride, and aluminum nitride. Future device engineering can be included to meet various applications. For example, changing the LNOI resonator scheme to ones with smaller mode volume like photonic crystal cavity [30] (PhC) or micro-disk resonator [31] will enable detection and control of fewer or single ions. Superconducting microwave resonator can be integrated to realize the microwave-to-optical conversion [32,33] using REIs. Our results provide a widely-applicable platform for on-chip quantum device development with REIs integrated.

Funding

U.S. Department of Energy (DE-SC0019406).

Acknowledgments

The authors would like to thank Dr. Charles Thiel at Montana State University (MSU) for useful discussions about Er$^{3+}$:Y$_2$SiO$_5$ material properties. The authors would like to thank Dr. Yong Sun, Sean Rinehart, Kelly Woods, and Dr. Michael Rooks for their assistance provided in the device fabrication. The fabrication of the devices was done at the Yale School of Engineering & Applied Science (SEAS) Cleanroom and the Yale Institute for Nanoscience and Quantum Engineering (YINQE).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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References

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  1. T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
    [Crossref]
  2. A. Tiranov, J. Lavoie, A. Ferrier, P. Goldner, V. B. Verma, S. W. Nam, R. P. Mirin, A. E. Lita, F. Marsili, H. Herrmann, C. Silberhorn, N. Gisin, M. Afzelius, and F. Bussières, “Storage of hyperentanglement in a solid-state quantum memory,” Optica 2(4), 279–287 (2015).
    [Crossref]
  3. J. G. Bartholomew, J. Rochman, T. Xie, J. M. Kindem, A. Ruskuc, I. Craiciu, M. Lei, and A. Faraon, “On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo 4,” Nat. Commun. 11(1), 3266 (2020).
    [Crossref]
  4. A. Dibos, M. Raha, C. Phenicie, and J. D. Thompson, “Atomic source of single photons in the telecom band,” Phys. Rev. Lett. 120(24), 243601 (2018).
    [Crossref]
  5. D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
    [Crossref]
  6. S. Wang, L. Yang, R. Cheng, Y. Xu, M. Shen, R. L. Cone, C. W. Thiel, and H. X. Tang, “Incorporation of erbium ions into thin-film lithium niobate integrated photonics,” Appl. Phys. Lett. 116(15), 151103 (2020).
    [Crossref]
  7. D. Pak, H. An, A. Nandi, X. Jiang, Y. Xuan, and M. Hosseini, “Ytterbium-implanted photonic resonators based on thin film lithium niobate,” J. Appl. Phys. 128(8), 084302 (2020).
    [Crossref]
  8. S. Dutta, E. A. Goldschmidt, S. Barik, U. Saha, and E. Waks, “Integrated photonic platform for rare-earth ions in thin film lithium niobate,” Nano Lett. 20(1), 741–747 (2020).
    [Crossref]
  9. J. Jones, J. De Sandro, M. Hempstead, D. Shepherd, A. Large, A. Tropper, and J. Wilkinson, “Channel waveguide laser at 1 μm in yb-indiffused linbo 3,” Opt. Lett. 20(13), 1477–1479 (1995).
    [Crossref]
  10. T. Böttger, C. Thiel, R. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in er 3+: Y 2 sio 5,” Phys. Rev. B 79(11), 115104 (2009).
    [Crossref]
  11. T. Böttger, Y. Sun, C. Thiel, and R. Cone, “Spectroscopy and dynamics of er 3+: Y 2 si o 5 at 1.5 μ m,” Phys. Rev. B 74(7), 075107 (2006).
    [Crossref]
  12. C. Thiel, T. Böttger, and R. Cone, “Rare-earth-doped materials for applications in quantum information storage and signal processing,” J. Lumin. 131(3), 353–361 (2011).
    [Crossref]
  13. S. Marzban, J. G. Bartholomew, S. Madden, K. Vu, and M. J. Sellars, “Observation of photon echoes from evanescently coupled rare-earth ions in a planar waveguide,” Phys. Rev. Lett. 115(1), 013601 (2015).
    [Crossref]
  14. E. Miyazono, I. Craiciu, A. Arbabi, T. Zhong, and A. Faraon, “Coupling erbium dopants in yttrium orthosilicate to silicon photonic resonators and waveguides,” Opt. Express 25(3), 2863–2871 (2017).
    [Crossref]
  15. T. Zhong, J. M. Kindem, E. Miyazono, and A. Faraon, “Nanophotonic coherent light–matter interfaces based on rare-earth-doped crystals,” Nat. Commun. 6(1), 8206 (2015).
    [Crossref]
  16. D. Tulli, D. Janner, and V. Pruneri, “Room temperature direct bonding of linbo3 crystal layers and its application to high-voltage optical sensing,” J. Micromech. Microeng. 21(8), 085025 (2011).
    [Crossref]
  17. S. N. Farrens, J. R. Dekker, J. K. Smith, and B. E. Roberds, “Chemical free room temperature wafer to wafer direct bonding,” J. Electrochem. Soc. 142(11), 3949–3955 (1995).
    [Crossref]
  18. Y. S. Lee, G.-D. Kim, W.-J. Kim, S.-S. Lee, W.-G. Lee, and W. H. Steier, “Hybrid si-linbo 3 microring electro-optically tunable resonators for active photonic devices,” Opt. Lett. 36(7), 1119–1121 (2011).
    [Crossref]
  19. Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood Jr, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
    [Crossref]
  20. M. Shen, J. Xie, C.-L. Zou, Y. Xu, W. Fu, and H. X. Tang, “High frequency lithium niobate film-thickness-mode optomechanical resonator,” Appl. Phys. Lett. 117(13), 131104 (2020).
    [Crossref]
  21. M. Li, J. Ling, Y. He, U. A. Javid, S. Xue, and Q. Lin, “Lithium niobate photonic-crystal electro-optic modulator,” Nat. Commun. 11(1), 4123 (2020).
    [Crossref]
  22. J. Lu, J. B. Surya, X. Liu, A. W. Bruch, Z. Gong, Y. Xu, and H. X. Tang, “Periodically poled thin-film lithium niobate microring resonators with a second-harmonic generation efficiency of 250, 000%/w,” Optica 6(12), 1455–1460 (2019).
    [Crossref]
  23. M. Zhang, C. Wang, R. Cheng, A. Shams-Ansari, and M. Lončar, “Monolithic ultra-high-q lithium niobate microring resonator,” Optica 4(12), 1536–1537 (2017).
    [Crossref]
  24. A. Plößl and G. Kräuter, “Wafer direct bonding: tailoring adhesion between brittle materials,” Mater. Sci. Eng., R 25(1-2), 1–88 (1999).
    [Crossref]
  25. E. Turner, “High-frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8(11), 303–304 (1966).
    [Crossref]
  26. D. McAuslan, J. J. Longdell, and M. Sellars, “Strong-coupling cavity qed using rare-earth-metal-ion dopants in monolithic resonators: What you can do with a weak oscillator,” Phys. Rev. A 80(6), 062307 (2009).
    [Crossref]
  27. I. Diniz, S. Portolan, R. Ferreira, J. Gérard, P. Bertet, and A. Auffeves, “Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum memories,” Phys. Rev. A 84(6), 063810 (2011).
    [Crossref]
  28. H. K. Sahoo, L. Ottaviano, Y. Zheng, O. Hansen, and K. Yvind, “Low temperature bonding of heterogeneous materials using al2o3 as an intermediate layer,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(1), 011202 (2018).
    [Crossref]
  29. F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, and S. Abel, “An integrated optical modulator operating at cryogenic temperatures,” Nat. Mater. 19(11), 1164–1168 (2020).
    [Crossref]
  30. H. Liang, R. Luo, Y. He, H. Jiang, and Q. Lin, “High-quality lithium niobate photonic crystal nanocavities,” Optica 4(10), 1251–1258 (2017).
    [Crossref]
  31. C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Lončar, “Integrated high quality factor lithium niobate microdisk resonators,” Opt. Express 22(25), 30924–30933 (2014).
    [Crossref]
  32. Y. Xu, A. A. Sayem, L. Fan, S. Wang, R. Cheng, C.-L. Zou, W. Fu, L. Yang, M. Xu, and H. X. Tang, “Bidirectional electro-optic conversion reaching 1% efficiency with thin-film lithium niobate,” arXiv preprint arXiv:2012.14909 (2020).
  33. L. A. Williamson, Y.-H. Chen, and J. J. Longdell, “Magneto-optic modulator with unit quantum efficiency,” Phys. Rev. Lett. 113(20), 203601 (2014).
    [Crossref]

2020 (7)

J. G. Bartholomew, J. Rochman, T. Xie, J. M. Kindem, A. Ruskuc, I. Craiciu, M. Lei, and A. Faraon, “On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo 4,” Nat. Commun. 11(1), 3266 (2020).
[Crossref]

S. Wang, L. Yang, R. Cheng, Y. Xu, M. Shen, R. L. Cone, C. W. Thiel, and H. X. Tang, “Incorporation of erbium ions into thin-film lithium niobate integrated photonics,” Appl. Phys. Lett. 116(15), 151103 (2020).
[Crossref]

D. Pak, H. An, A. Nandi, X. Jiang, Y. Xuan, and M. Hosseini, “Ytterbium-implanted photonic resonators based on thin film lithium niobate,” J. Appl. Phys. 128(8), 084302 (2020).
[Crossref]

S. Dutta, E. A. Goldschmidt, S. Barik, U. Saha, and E. Waks, “Integrated photonic platform for rare-earth ions in thin film lithium niobate,” Nano Lett. 20(1), 741–747 (2020).
[Crossref]

M. Shen, J. Xie, C.-L. Zou, Y. Xu, W. Fu, and H. X. Tang, “High frequency lithium niobate film-thickness-mode optomechanical resonator,” Appl. Phys. Lett. 117(13), 131104 (2020).
[Crossref]

M. Li, J. Ling, Y. He, U. A. Javid, S. Xue, and Q. Lin, “Lithium niobate photonic-crystal electro-optic modulator,” Nat. Commun. 11(1), 4123 (2020).
[Crossref]

F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, and S. Abel, “An integrated optical modulator operating at cryogenic temperatures,” Nat. Mater. 19(11), 1164–1168 (2020).
[Crossref]

2019 (1)

2018 (2)

H. K. Sahoo, L. Ottaviano, Y. Zheng, O. Hansen, and K. Yvind, “Low temperature bonding of heterogeneous materials using al2o3 as an intermediate layer,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 36(1), 011202 (2018).
[Crossref]

A. Dibos, M. Raha, C. Phenicie, and J. D. Thompson, “Atomic source of single photons in the telecom band,” Phys. Rev. Lett. 120(24), 243601 (2018).
[Crossref]

2017 (4)

2016 (1)

D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
[Crossref]

2015 (3)

A. Tiranov, J. Lavoie, A. Ferrier, P. Goldner, V. B. Verma, S. W. Nam, R. P. Mirin, A. E. Lita, F. Marsili, H. Herrmann, C. Silberhorn, N. Gisin, M. Afzelius, and F. Bussières, “Storage of hyperentanglement in a solid-state quantum memory,” Optica 2(4), 279–287 (2015).
[Crossref]

T. Zhong, J. M. Kindem, E. Miyazono, and A. Faraon, “Nanophotonic coherent light–matter interfaces based on rare-earth-doped crystals,” Nat. Commun. 6(1), 8206 (2015).
[Crossref]

S. Marzban, J. G. Bartholomew, S. Madden, K. Vu, and M. J. Sellars, “Observation of photon echoes from evanescently coupled rare-earth ions in a planar waveguide,” Phys. Rev. Lett. 115(1), 013601 (2015).
[Crossref]

2014 (2)

2011 (4)

Y. S. Lee, G.-D. Kim, W.-J. Kim, S.-S. Lee, W.-G. Lee, and W. H. Steier, “Hybrid si-linbo 3 microring electro-optically tunable resonators for active photonic devices,” Opt. Lett. 36(7), 1119–1121 (2011).
[Crossref]

I. Diniz, S. Portolan, R. Ferreira, J. Gérard, P. Bertet, and A. Auffeves, “Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum memories,” Phys. Rev. A 84(6), 063810 (2011).
[Crossref]

C. Thiel, T. Böttger, and R. Cone, “Rare-earth-doped materials for applications in quantum information storage and signal processing,” J. Lumin. 131(3), 353–361 (2011).
[Crossref]

D. Tulli, D. Janner, and V. Pruneri, “Room temperature direct bonding of linbo3 crystal layers and its application to high-voltage optical sensing,” J. Micromech. Microeng. 21(8), 085025 (2011).
[Crossref]

2009 (2)

T. Böttger, C. Thiel, R. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in er 3+: Y 2 sio 5,” Phys. Rev. B 79(11), 115104 (2009).
[Crossref]

D. McAuslan, J. J. Longdell, and M. Sellars, “Strong-coupling cavity qed using rare-earth-metal-ion dopants in monolithic resonators: What you can do with a weak oscillator,” Phys. Rev. A 80(6), 062307 (2009).
[Crossref]

2008 (1)

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood Jr, “Magneto-optical isolator with silicon waveguides fabricated by direct bonding,” Appl. Phys. Lett. 92(7), 071117 (2008).
[Crossref]

2006 (1)

T. Böttger, Y. Sun, C. Thiel, and R. Cone, “Spectroscopy and dynamics of er 3+: Y 2 si o 5 at 1.5 μ m,” Phys. Rev. B 74(7), 075107 (2006).
[Crossref]

1999 (1)

A. Plößl and G. Kräuter, “Wafer direct bonding: tailoring adhesion between brittle materials,” Mater. Sci. Eng., R 25(1-2), 1–88 (1999).
[Crossref]

1995 (2)

S. N. Farrens, J. R. Dekker, J. K. Smith, and B. E. Roberds, “Chemical free room temperature wafer to wafer direct bonding,” J. Electrochem. Soc. 142(11), 3949–3955 (1995).
[Crossref]

J. Jones, J. De Sandro, M. Hempstead, D. Shepherd, A. Large, A. Tropper, and J. Wilkinson, “Channel waveguide laser at 1 μm in yb-indiffused linbo 3,” Opt. Lett. 20(13), 1477–1479 (1995).
[Crossref]

1966 (1)

E. Turner, “High-frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8(11), 303–304 (1966).
[Crossref]

Abel, S.

F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, and S. Abel, “An integrated optical modulator operating at cryogenic temperatures,” Nat. Mater. 19(11), 1164–1168 (2020).
[Crossref]

Afzelius, M.

An, H.

D. Pak, H. An, A. Nandi, X. Jiang, Y. Xuan, and M. Hosseini, “Ytterbium-implanted photonic resonators based on thin film lithium niobate,” J. Appl. Phys. 128(8), 084302 (2020).
[Crossref]

Arbabi, A.

Atikian, H. A.

Auffeves, A.

I. Diniz, S. Portolan, R. Ferreira, J. Gérard, P. Bertet, and A. Auffeves, “Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum memories,” Phys. Rev. A 84(6), 063810 (2011).
[Crossref]

Barik, S.

S. Dutta, E. A. Goldschmidt, S. Barik, U. Saha, and E. Waks, “Integrated photonic platform for rare-earth ions in thin film lithium niobate,” Nano Lett. 20(1), 741–747 (2020).
[Crossref]

Barreto, J.

F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, and S. Abel, “An integrated optical modulator operating at cryogenic temperatures,” Nat. Mater. 19(11), 1164–1168 (2020).
[Crossref]

Bartholomew, J. G.

J. G. Bartholomew, J. Rochman, T. Xie, J. M. Kindem, A. Ruskuc, I. Craiciu, M. Lei, and A. Faraon, “On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo 4,” Nat. Commun. 11(1), 3266 (2020).
[Crossref]

T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
[Crossref]

S. Marzban, J. G. Bartholomew, S. Madden, K. Vu, and M. J. Sellars, “Observation of photon echoes from evanescently coupled rare-earth ions in a planar waveguide,” Phys. Rev. Lett. 115(1), 013601 (2015).
[Crossref]

Bauters, J. F.

D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
[Crossref]

Bertet, P.

I. Diniz, S. Portolan, R. Ferreira, J. Gérard, P. Bertet, and A. Auffeves, “Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum memories,” Phys. Rev. A 84(6), 063810 (2011).
[Crossref]

Bettinelli, M.

T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
[Crossref]

Beyer, A. D.

T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
[Crossref]

Böttger, T.

C. Thiel, T. Böttger, and R. Cone, “Rare-earth-doped materials for applications in quantum information storage and signal processing,” J. Lumin. 131(3), 353–361 (2011).
[Crossref]

T. Böttger, C. Thiel, R. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in er 3+: Y 2 sio 5,” Phys. Rev. B 79(11), 115104 (2009).
[Crossref]

T. Böttger, Y. Sun, C. Thiel, and R. Cone, “Spectroscopy and dynamics of er 3+: Y 2 si o 5 at 1.5 μ m,” Phys. Rev. B 74(7), 075107 (2006).
[Crossref]

Bouwmeester, D.

D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
[Crossref]

Bowers, J. E.

D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
[Crossref]

Bruch, A. W.

Burek, M. J.

Bussières, F.

Caimi, D.

F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, and S. Abel, “An integrated optical modulator operating at cryogenic temperatures,” Nat. Mater. 19(11), 1164–1168 (2020).
[Crossref]

Cavalli, E.

T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
[Crossref]

Chen, Y.-H.

L. A. Williamson, Y.-H. Chen, and J. J. Longdell, “Magneto-optic modulator with unit quantum efficiency,” Phys. Rev. Lett. 113(20), 203601 (2014).
[Crossref]

Cheng, R.

S. Wang, L. Yang, R. Cheng, Y. Xu, M. Shen, R. L. Cone, C. W. Thiel, and H. X. Tang, “Incorporation of erbium ions into thin-film lithium niobate integrated photonics,” Appl. Phys. Lett. 116(15), 151103 (2020).
[Crossref]

M. Zhang, C. Wang, R. Cheng, A. Shams-Ansari, and M. Lončar, “Monolithic ultra-high-q lithium niobate microring resonator,” Optica 4(12), 1536–1537 (2017).
[Crossref]

Y. Xu, A. A. Sayem, L. Fan, S. Wang, R. Cheng, C.-L. Zou, W. Fu, L. Yang, M. Xu, and H. X. Tang, “Bidirectional electro-optic conversion reaching 1% efficiency with thin-film lithium niobate,” arXiv preprint arXiv:2012.14909 (2020).

Cone, R.

C. Thiel, T. Böttger, and R. Cone, “Rare-earth-doped materials for applications in quantum information storage and signal processing,” J. Lumin. 131(3), 353–361 (2011).
[Crossref]

T. Böttger, C. Thiel, R. Cone, and Y. Sun, “Effects of magnetic field orientation on optical decoherence in er 3+: Y 2 sio 5,” Phys. Rev. B 79(11), 115104 (2009).
[Crossref]

T. Böttger, Y. Sun, C. Thiel, and R. Cone, “Spectroscopy and dynamics of er 3+: Y 2 si o 5 at 1.5 μ m,” Phys. Rev. B 74(7), 075107 (2006).
[Crossref]

Cone, R. L.

S. Wang, L. Yang, R. Cheng, Y. Xu, M. Shen, R. L. Cone, C. W. Thiel, and H. X. Tang, “Incorporation of erbium ions into thin-film lithium niobate integrated photonics,” Appl. Phys. Lett. 116(15), 151103 (2020).
[Crossref]

Craiciu, I.

J. G. Bartholomew, J. Rochman, T. Xie, J. M. Kindem, A. Ruskuc, I. Craiciu, M. Lei, and A. Faraon, “On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo 4,” Nat. Commun. 11(1), 3266 (2020).
[Crossref]

T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
[Crossref]

E. Miyazono, I. Craiciu, A. Arbabi, T. Zhong, and A. Faraon, “Coupling erbium dopants in yttrium orthosilicate to silicon photonic resonators and waveguides,” Opt. Express 25(3), 2863–2871 (2017).
[Crossref]

de Dood, M. J.

D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
[Crossref]

De Sandro, J.

Dekker, J. R.

S. N. Farrens, J. R. Dekker, J. K. Smith, and B. E. Roberds, “Chemical free room temperature wafer to wafer direct bonding,” J. Electrochem. Soc. 142(11), 3949–3955 (1995).
[Crossref]

Dibos, A.

A. Dibos, M. Raha, C. Phenicie, and J. D. Thompson, “Atomic source of single photons in the telecom band,” Phys. Rev. Lett. 120(24), 243601 (2018).
[Crossref]

Ding, D.

D. Ding, L. M. Pereira, J. F. Bauters, M. J. Heck, G. Welker, A. Vantomme, J. E. Bowers, M. J. de Dood, and D. Bouwmeester, “Multidimensional purcell effect in an ytterbium-doped ring resonator,” Nat. Photonics 10(6), 385–388 (2016).
[Crossref]

Diniz, I.

I. Diniz, S. Portolan, R. Ferreira, J. Gérard, P. Bertet, and A. Auffeves, “Strongly coupling a cavity to inhomogeneous ensembles of emitters: Potential for long-lived solid-state quantum memories,” Phys. Rev. A 84(6), 063810 (2011).
[Crossref]

Dutta, S.

S. Dutta, E. A. Goldschmidt, S. Barik, U. Saha, and E. Waks, “Integrated photonic platform for rare-earth ions in thin film lithium niobate,” Nano Lett. 20(1), 741–747 (2020).
[Crossref]

Eltes, F.

F. Eltes, G. E. Villarreal-Garcia, D. Caimi, H. Siegwart, A. A. Gentile, A. Hart, P. Stark, G. D. Marshall, M. G. Thompson, J. Barreto, J. Fompeyrine, and S. Abel, “An integrated optical modulator operating at cryogenic temperatures,” Nat. Mater. 19(11), 1164–1168 (2020).
[Crossref]

Fan, L.

Y. Xu, A. A. Sayem, L. Fan, S. Wang, R. Cheng, C.-L. Zou, W. Fu, L. Yang, M. Xu, and H. X. Tang, “Bidirectional electro-optic conversion reaching 1% efficiency with thin-film lithium niobate,” arXiv preprint arXiv:2012.14909 (2020).

Faraon, A.

J. G. Bartholomew, J. Rochman, T. Xie, J. M. Kindem, A. Ruskuc, I. Craiciu, M. Lei, and A. Faraon, “On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo 4,” Nat. Commun. 11(1), 3266 (2020).
[Crossref]

T. Zhong, J. M. Kindem, J. G. Bartholomew, J. Rochman, I. Craiciu, E. Miyazono, M. Bettinelli, E. Cavalli, V. Verma, S. W. Nam, F. Marsili, M. D. Shaw, A. D. Beyer, and A. Faraon, “Nanophotonic rare-earth quantum memory with optically controlled retrieval,” Science 357(6358), 1392–1395 (2017).
[Crossref]

E. Miyazono, I. Craiciu, A. Arbabi, T. Zhong, and A. Faraon, “Coupling erbium dopants in yttrium orthosilicate to silicon photonic resonators and waveguides,” Opt. Express 25(3), 2863–2871 (2017).
[Crossref]

T. Zhong, J. M. Kindem, E. Miyazono, and A. Faraon, “Nanophotonic coherent light–matter interfaces based on rare-earth-doped crystals,” Nat. Commun. 6(1), 8206 (2015).
[Crossref]

Farrens, S. N.

S. N. Farrens, J. R. Dekker, J. K. Smith, and B. E. Roberds, “Chemical free room temperature wafer to wafer direct bonding,” J. Electrochem. Soc. 142(11), 3949–3955 (1995).
[Crossref]

Ferreira, R.

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Y. Xu, A. A. Sayem, L. Fan, S. Wang, R. Cheng, C.-L. Zou, W. Fu, L. Yang, M. Xu, and H. X. Tang, “Bidirectional electro-optic conversion reaching 1% efficiency with thin-film lithium niobate,” arXiv preprint arXiv:2012.14909 (2020).

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (4)

Fig. 1.
Fig. 1. (a) Optical micrograph (bottom panel) and zoom-in SEM image (upper panel) of a micro-ring device. (b) Schematic drawing of the device cross section after bonded with Er $^{3+}$ :Y $_2$ SiO $_5$ . Shown on the right is the electric field profile of the fundamental TE mode in the micro-ring, with arrows marking the direction of the electric field.
Fig. 2.
Fig. 2. (a) The transmission spectrum of the micro-ring device. The overall transmission envelope is determined by the grating couplers. Fundamental TE, TM and first-order TE modes of the resonator can be seen in the spectrum. The right panel shows a Lorentzian fit of a fundamental TE mode resonance yielding Q of 1.09 M. (b) The resonance shift in response to the applied DC voltage. The linear fit indicates a tuning rate of 2.25 pm/V. The inset shows resonance at two applied voltages, 20 V (blue) and 80 V (orange). All data were taken at 4K.
Fig. 3.
Fig. 3. (a) Schematic setup for measuring Er fluorescence decay. A tunable laser was used to excite the Er ions. Two AOMs were used to generate pump pulse and gate detection window, respectively. An optical circulator was utilized to collect the fluorescence in the reverse direction of the pump. The emission at different delays was measured by an optical power detector. Another detector at the other end of the device recorded the waveguide transmission. (b) The waveguide transmission spectrum around 1536.48nm. The dip arises from erbium absorption, with the red cross marking the wavelength for fluorescence measurement. (c) The fluorescence decay of site 1 Er ions at 1536.48 nm measured in the waveguide. The red line is an exponential fit of the signal, yielding a lifetime of 11.5 ms.
Fig. 4.
Fig. 4. Resonator linewidth measurement when the resonator is tuned across the erbium transition wavelength. Insets: Three resonance curves represent Er on-resonance case and off-detuned cases, taken at wavelengths correponding to the blue, orange and cyan points. A Lorentian fitting to the linewidth change is shown by the red curve, yielding a collective coupling cooperativity of 0.36.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

g ( r ) = μ n mode ω 2 ϵ 0 V mode | E ( r ) | | E m a x | ,
G = μ n mode F ρ ω 2 ϵ 0 .
T ( ω ) = | 1 i κ e x ω ω 0 + i κ 0 / 2 G 2 ω ω ions + i γ / 2 | 2 ,
κ = κ 0 + G 2 γ Δ 2 + ( γ / 2 ) 2 ,

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