We experimentally demonstrate the mechanical tuning of whispering gallery modes in a 40 μm diameter silica microsphere at 10K, over a tuning range of 450 GHz and with a resolution less than 10 MHz. This is achieved by mechanically stretching the stems of a double-stemmed silica microsphere with a commercially available piezo-driven nano-positioner. The large tuning range is made possible by the millimeter long slip-stick motion of the nano-positioner. The ultrafine tuning resolution, corresponding to sub-picometer changes in the sphere diameter, is enabled by the use of relatively long and thin fiber stems, which reduces the effective Poisson ratio of the combined sphere-stem system to approximately 0.0005. The mechanical tuning demonstrated here removes a major obstacle for the use of ultrahigh Q-factor silica microspheres in cavity QED studies of solid state systems and, in particular, cavity QED studies of nitrogen vacancy centers in diamond.
©2011 Optical Society of America
Whispering gallery mode (WGM) silica microresonators feature ultrahigh optical Q-factors along with relatively small mode volume, making them uniquely suitable for cavity QED studies in the high-Q regime [1,2]. These resonators, including microspheres and microtoroids, have been used in cavity QED studies of atomic systems with remarkable success . Silica microspheres have also been exploited for cavity QED studies of atomic-like solid state systems such as semiconductor nanocrystals and, more recently, nitrogen vacancy (NV) centers in diamond [4,5]. Among the variety of microcavity systems of NV centers [5–13], systems based on the use of silica resonators are especially promising for reaching the strong-coupling regime of cavity QED [5,14].
An essential requirement for experimental cavity QED studies is the matching of the cavity resonance with the resonance of the relevant optical dipole transition. For the use of ultrahigh-Q optical resonators in solid state cavity QED systems, it is highly desirable to tune the optical resonance over a significant fraction of the free spectral range (FSR) with a spectral resolution that is better than the optical cavity linewidth. The need for a broad tuning range is dictated by the large environmentally-induced variations in the transition frequencies of an artificial atom. Since solid state cavity QED studies need to be carried out at low and, in most cases, liquid helium temperatures, the tuning of the cavity resonance needs to be implemented in a cryogenic environment.
The inability to realize a precise and broad-range tuning of WGM resonances in silica microresonators at cryogenic temperatures has thus far hindered the successful use of these resonators in solid state cavity QED systems. Though temperature tuning has been used in earlier cavity QED studies involving NV centers coupled to a silica microsphere at temperatures below 10 K, the tuning range is limited to only a few hundred MHz . Additionally, temperature tuning is not desirable in experiments where one needs to maintain as low a temperature as possible in order to minimize phonon-related decoherence. Note that for optical resonators that feature comparatively small optical Q-factors, such as photonic crystals and micro-rings, a buffer gas approach has been developed for the tuning of optical resonances . This approach, however, cannot meet the precision or resolution needed for ultrahigh-Q silica resonators. In addition, at liquid helium temperatures, buffer gases spoil the ultrahigh Q-factors of silica microresonators.
Earlier experimental studies have developed techniques for tuning WGM resonances of a silica microsphere by mechanically stretching or compressing the sphere with a piezoelectric transducer [16–19]. This approach has led to the mechanical tuning of WGM resonances at room temperature, with a tuning range nearing the FSR of the resonator. Mechanical tuning at cryogenic temperatures, however, has not been realized previously. This is due in part to the greatly reduced travel range of piezoelectric transducers at low temperature and in part to the fact that silica microspheres are very fragile. Cooling a mechanically-loaded silica microsphere from 300K to liquid helium temperatures often induces irreversible damage to the microresonator. Such damage includes breakage of the fiber stems attached to the microsphere.
In this paper, we demonstrate experimentally the mechanical tuning of WGM resonances in a silica microsphere at 10K. We have used a commercially available piezo-driven nano-positioner to stretch a silica sphere with fiber stems attached to both poles of the sphere. The slip-stick motion of the nano-positioner enables millimeter long travel ranges at cryogenic temperatures. This results in a broad spectral tuning range on the order of 450 GHz. The direct expansion and contraction of the piezo element inside the nano-positioner enables mechanical displacement with sub-nanometer resolution. Continuous frequency tuning with a resolution better than 10 MHz is achieved with the use of relatively long and thin fiber stems. These remarkable experimental successes remove a major obstacle toward the successful development of a well-controlled solid state cavity QED system that couples artificial atoms, such as NV centers in diamond, to the WGMs in a silica microsphere.
2. Sample fabrication and experimental setup
We used a deformed double-stemmed microsphere (DDSS) to implement the mechanical tuning of the WGM resonances. For a solid-state cavity QED system utilizing a silica microsphere, the artificial atoms (e.g. NV centers) are in the evanescent field of the WGMs. As demonstrated in an earlier study, a slight deformation in a microsphere can result in a much greater evanescent decay length, thus enhancing the relevant light-matter interactions [20,21]. The first step in fabricating a DDSS is to fabricate two conventional silica microspheres with the use of a CO2 laser. Each sphere is attached to a thin fiber stem with a diameter near 5 μm. Fusing the two spheres together, while cutting off the stem of one of the spheres, leads to the formation of a deformed sphere. The degree of deformation of the final microsphere can be controlled by repeated heating with the CO2 laser, until the desired deformation (~2%) is achieved . Finally, the tip of a bare fiber is slightly heated and then quickly attached to the bottom of the deformed microsphere. Figure 1a shows an example of a DDSS with a diameter near 35 μm.
A commercially available piezo-driven nano-positioner (Attocube Systems, model ANPz51) is used for the mechanical stretching of a silica microsphere. The Attocube positioner can be used in two different operating modes needed for mechanical displacement at cryogenic temperatures. One mode uses a DC offset to expand and contract a piezo element inside the positioner, allowing one to generate mechanical displacement with sub-nanometer resolution. The second mode utilizes the slip-stick motion of the positioner. This can produce a mechanical displacement as large as a few millimeters.
Figure 1b shows a schematic of the experimental setup, with a photo of the actual setup shown in Fig. 1c. In this setup, one of the stems is clamped in a modified fiber chuck. The other is mounted to the top of an Attocube positioner via a custom-made fiber clamp. Note that only the z-positioner in the figure is used for the mechanical stretching of a DDSS. To avoid breaking the DDSS while transferring it into the cryostat, and during the cooling of the system, extra slack is given to the two stems after mounting the DDSS into the tuning system.
A free-space evanescent excitation technique is used for the excitation of WGM resonances in a DDSS . As is depicted in Fig. 2a , a single frequency tunable laser (either a New Focus Velocity 304H or a frequency-stabilized Coherent 899-21 ring laser with wavelengths near 637 nm) is focused with a microscope objective onto an equatorial region (within 1μm of the sphere surface) that is 45° away from a symmetry axis. The emission from the excited WGM is collected with the same microscope objective. Figure 2b shows as an example a WGM resonance for a 40 μm diameter DDSS under tension with a linewidth of 65MHz.
The DDSS and the tuning setup were cooled in a helium flow optical cryostat (Janis Research) to 10 K with a temperature stability near 0.1K. After reaching the desired temperature, the extra slack is removed from the two stems by stepping the z-positioner while the DDSS is excited and the WGM frequency is monitored. Once the slack has been removed and the motion of the z-positioner begins to stretch the DDSS, a shift in the resonance frequency of the WGM occurs. After the observation of this initial resonance frequency shift, further mechanical displacement can be taken with the z-positioner to coarsely tune the resonance frequency of the WGM. For a precise frequency tuning, the DC offset function of the Attocube z-positioner is used.
3. Experimental results
Experimental results presented in this section were obtained at T = 10 K and from the same WGM of a DDSS. The DDSS features a diameter of d = 40 μm and a deformation of approximately 2%. The length of each fiber stem (from the sphere surface to the mechanical clamping point) is nearly 3 mm. Figure 3 shows the experimental result of coarse mechanical tuning of the WGM resonance. For this experiment, the Attocube positioner was operated in the slip-stick (step) mode, with an applied voltage per step of 25 volts. The WGM resonance was measured with a tunable diode laser. The average tuning step size is estimated to be 1.37 GHz. A total of 183 steps were taken to achieve an overall resonance shift of 250 GHz as shown in Fig. 3. A total resonance shift greater than 450 GHz was achieved with 329 steps of the nano-positioner. For comparison, the FSR of the microsphere is approximately 1.6 THz.
Figures 4 and 5 show the experimental result for the fine mechanical tuning of the WGM resonance when the Attocube positioner is operated in the DC-offset mode. These results were obtained after the frequency of the WGM resonance was shifted by more than 100 GHz with the step tuning approach discussed above. The WGM resonance was measured with a frequency-stabilized tunable ring dye laser. For Fig. 4a, a 10 V increment in the DC offset was used, resulting in an approximate frequency shift of 500 MHz per step. For Fig. 4b, a 1 V increment in the DC offset was used, resulting in an approximate frequency shift of 50 MHz per step. Note that the corresponding mechanical displacement of the nano-positioner is plotted as the top axis in Figs. 4a and 4b.
To achieve a finer frequency shift of the WGMs, we further reduced the DC offset step size to 0.1 V. As shown in Fig. 5, the resulting frequency shift for the WGM resonance has a step size less than 10 MHz. Note that this was achieved with an Attocube controller. Smaller step sizes in the frequency shift can be achieved with an external voltage source.
Both the coarse and fine tuning processes are reversible as well as stable. We noticed that for both processes, there was little, “backlash” in shifting the resonance frequency of the WGM back to a previous position. We also found that the clamping or stretching of the two stems did not alter the Q-factor of the WGM. For the WGM resonance used in the above experiment, the linewidth was 65 MHz, corresponding to a Q-factor of approximately 7.2x106.
The frequency shift of the WGM resonance, Δν, induced by mechanical stretching is due in part to a change in the geometrical shape of the resonator and in part to a change in the refractive index of fused silica. As shown in an earlier study, the frequency shift due to the index change is small compared with that due to the shape change [16–18]. To the lowest order in mechanical displacement, we have:
where Δd is the strain-induced increase in the sphere diameter. The linear slope shown in Figs. 3, 4a, 4b, and 5 indicates that the strain-induced change in the sphere diameter is linearly proportional to the mechanical displacement of the nano-positioner. Using Eq. (1) and the experimentally observed slope, we obtain an effective Poisson ratio for the combined sphere and fiber stem system, Δd/Δz = 0.0005 where Δz is the mechanical displacement of the nano-positioner. In comparison, for fused silica at room temperature, the Poisson ratio is 0.17. The use of long and thin fiber stems greatly reduces the effective Poisson ratio of the combined system, enabling a more precise mechanical control of the sphere diameter and thus the frequency of the WGM resonance.
For ν = 470957 GHz and with d = 40 μm, a frequency shift of 10 MHz corresponds to a change in the sphere diameter of 0.85 pm. In this context, it is remarkable that the stretching of the silica microsphere enables the continuous tuning of the WGM resonance with a resolution better than 10 MHz and with excellent reproducibility. The ratio of the frequency shift over the nano-positioner mechanical displacement, Δv/Δz, for our system is 6 MHz/nm, as can be derived from Figs. 4a, 4b and 5. This ratio is considerably smaller than the ratio on the order of 100 MHz/nm used in an earlier experimental study, which featured short and thick, instead of long and thin, fiber stems .
There are a number of advantages for having a relatively small shift/displacement ratio. First of all, MHz frequency tuning can be realized with sub-nanometer, instead of picometer, mechanical displacement. Secondly, fluctuations in the mechanical system lead to a relatively small fluctuation in the frequency of the WGM resonance. Additionally, the long stems also make it easier to accommodate other essential requirements in the cavity QED setup, for example, the precise positioning of a diamond nanopillar for cavity QED studies with NV centers .
The ability to tune the resonance frequency of a WGM in a silica microsphere over a spectral range of several hundred GHz with MHz resolution at cryogenic temperatures overcomes a major hurdle for the use of these ultrahigh-Q optical resonators in solid state cavity QED systems. The importance of resonance tuning cannot be understated since it is extremely difficult, if not impossible, to control the resonance frequency of the WGMs while the resonators are being fabricated. The techniques developed in our work, including the use of piezo-driven nano-positioner for mechanical tuning and the reduction of the Poisson ratio, may also be extended to other types of optical resonators.
This work is supported by NSF under grant no. PHY-1005499 and by DARPA. K. N. Dinyari acknowledges support by the NSF-IGERT program under grant no. DGE-0549503.
References and links
1. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and non-linear properties of optical whispering-gallery modes,” Phys. Lett. A 137(7-8), 393–397 (1989). [CrossRef]
4. X. Fan, P. Palinginis, S. Lacey, H. Wang, and M. C. Lonergan, “Coupling semiconductor nanocrystals to a fused-silica microsphere: a quantum-dot microcavity with extremely high Q factors,” Opt. Lett. 25(21), 1600–1602 (2000). [CrossRef] [PubMed]
6. C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91(20), 201112 (2007). [CrossRef]
7. S. Schietinger, T. Schröder, and O. Benson, “One-by-one coupling of single defect centers in nanodiamonds to high-Q modes of an optical microresonator,” Nano Lett. 8(11), 3911–3915 (2008). [CrossRef] [PubMed]
8. H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, “Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers,” Opt. Express 18(14), 15169–15173 (2010). [CrossRef] [PubMed]
9. K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers in diamond to a gap waveguide,” Appl. Phys. Lett. 93(23), 234107 (2008). [CrossRef]
11. P. E. Barclay, K. M. C. Fu, C. Santori, and R. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95(19), 191115 (2009). [CrossRef]
12. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10(10), 3922–3926 (2010). [CrossRef] [PubMed]
13. A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5(5), 301–305 (2011). [CrossRef]
15. S. Mosor, J. Hendrickson, B. C. Richards, J. Sweet, G. Khitrova, H. M. Gibbs, T. Yoshie, A. Scherer, O. B. Shchekin, and D. G. Deppe, “Scanning a photonic crystal slab nanocavity by condensation of xenon,” Appl. Phys. Lett. 87(14), 141105 (2005). [CrossRef]
16. V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145(1-6), 86–90 (1998). [CrossRef]
17. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26(3), 166–168 (2001). [CrossRef] [PubMed]
18. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” N. J. Phys. 3, 14 (2001). [CrossRef]
21. R. J. Barbour, K. N. Dinyari, and H. Wang, “A composite microcavity of diamond nanopillar and deformed silica microsphere with enhanced evanescent decay length,” Opt. Express 18(18), 18968–18974 (2010). [CrossRef] [PubMed]