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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 19545–19553
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Coupling of ultrathin tapered fibers with high-Q microsphere resonators at cryogenic temperatures and observation of phase-shift transition from undercoupling to overcoupling

Masazumi Fujiwara, Tetsuya Noda, Akira Tanaka, Kiyota Toubaru, Hong-Quan Zhao, and Shigeki Takeuchi  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 19545-19553 (2012)
http://dx.doi.org/10.1364/OE.20.019545


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Abstract

We cooled ultrathin tapered fibers to cryogenic temperatures and controllably coupled them with high-Q microsphere resonators at a wavelength close to the optical transition of diamond nitrogen vacancy centers. The 310-nm-diameter tapered fibers were stably nanopositioned close to the microspheres with a positioning stability of approximately 10 nm over a temperature range of 7–28 K. A cavity-induced phase shift was observed in this temperature range, demonstrating a discrete transition from undercoupling to overcoupling.

© 2012 OSA

1. Introduction

Coupling diamond nitrogen vacancy (NV) centers with nanophotonic cavities such as microresonators and photonic crystals is currently of great importance for quantum information science [1

1. O. Benson, “Assembly of hybrid photonic architectures from nanophotonic constituents,” Nature (London) 480, 193–199 (2011). [CrossRef]

10

10. Y. F. Xiao, C. L. Zou, P. Xue, L. Xiao, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “Quantum electrodynamics in a whispering-gallery microcavity coated with a polymer nanolayer,” Phys. Rev. A 81, 053807 (2010). [CrossRef]

]. Such NV-coupled cavity quantum electrodynamics (cavity QED) systems can be used to develop coherent photonic quantum devices including quantum phase gates [11

11. K. Kojima, H. Hofmann, S. Takeuchi, and K. Sasaki, “Nonlinear interaction of two photons with a one-dimensional atom: Spatiotemporal quantum coherence in the emitted field,” Phys. Rev. A 68, 013803 (2003). [CrossRef]

, 12

12. K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate,” Phys. Rev. A 70, 013810 (2004). [CrossRef]

] and quantum memories [13

13. K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon-photon SWAP gate using a λ system,” Phys. Rev. A 82, 010301 (2010). [CrossRef]

, 14

14. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Physica Scripta T137, 014001 (2009). [CrossRef]

]. These applications exploit the narrow zero-phonon optical transitions of NV centers located at around λ = 637 nm, which appear only at cryogenic temperatures [6

6. C. Santori, P. Barclay, K. Fu, R. Beausoleil, S. Spillane, and M. Fisch, “Nanophotonics for quantum optics using nitrogen-vacancy centers in diamond,” Nanotechnology 21, 274008 (2010). [CrossRef] [PubMed]

]. To develop coherent quantum devices that employ NV centers, it is thus essential to couple NV optical transitions with these nanophotonic cavities in a cryogenic environment.

One of the most promising nanophotonic cavities is fiber-coupled microresonators that consist of high-Q silica microresonators and tapered fibers [15

15. S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature (London) 415, 621–623 (2002). [CrossRef]

24

24. 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, 15169–15173 (2010). [CrossRef] [PubMed]

]. Silica microresonators, such as microspheres or microtoroids, can support high-Q cavity modes (Q > 108) [15

15. S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature (London) 415, 621–623 (2002). [CrossRef]

], and tapered fibers act as efficient optical interfaces between these cavity modes and waveguide modes [25

25. M. Cai and K. Vahala, “Highly efficient optical power transfer to whispering-gallery modes by use of a symmetrical dual-coupling configuration,” Opt. Lett. 25, 260–262 (2000). [CrossRef]

]. To develop coherent quantum devices that use NV centers, the following two requirements should be realized in a cryogenic environment: (1) controllability of the input–output coupling efficiency between tapered fibers and microresonators [16

16. T. Aoki, B. Dayan, E. Wilcut, W. Bowen, A. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature (London) 443, 671–674 (2006). [CrossRef]

] and (2) well-behaved polarization characteristics adequate for measurement of a cavity-induced phase shift [26

26. M. Pototschnig, Y. Chassagneux, J. Hwang, G. Zumofen, A. Renn, and V. Sandoghdar, “Controlling the phase of a light beam with a single molecule,” Phys. Rev. Lett. 107, 63001 (2011). [CrossRef]

, 27

27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

].

Satisfaction of the second requirement can be demonstrated by investigating the cavity-induced phase-shift spectra. We recently obtained phase-shift spectra of fiber-coupled microsphere resonators at room temperature by using a polarization analysis technique [27

27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

]. However, the phase-shift spectra of such fiber-coupled microresonators have not been measured at cryogenic temperatures until now. Phase-shift spectrum measurements at cryogenic temperatures are particularly important because they directly demonstrate the potential of applying these fiber-coupled microresonators to coherent quantum information devices.

Here, we demonstrate cooling of 310-nm-diameter ultrathin tapered fibers down to 7 K and their fully controllable coupling with high-Q microsphere resonators at about λ = 637 nm. The tapered fibers were stably nanopositioned close to the microspheres with a positioning stability of less than 13 nm over at least 7 min over a temperature range of 7–28 K. A cavity-induced phase shift was observed. These observations clearly show a discrete transition from undercoupling to overcoupling [27

27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

, 28

28. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

]. In addition, 0.8-GHz frequency tuning of the cavity resonance was realized by increasing the temperature from 7 to 28 K while preserving near-critical coupling throughout this temperature range.

The present cavity system has high-Q factor of 1.9 × 107 (potentially up to 109 [29

29. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko“Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef] [PubMed]

]) in the visible wavelength region together with the full controllability of waveguide-cavity coupling condition, which makes it distinct from other cryogenic fiber-coupled microcavity systems recently reported [18

18. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Physics 4, 415–419 (2008). [CrossRef]

20

20. E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T.J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012). [CrossRef]

, 30

30. A.H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012). [CrossRef] [PubMed]

] in view that the present system can provide a testbed for quantum optics using stable solid-state quantum nanoemitters like diamond NV centers. The present demonstration is thus especially important for developing coherent quantum devices using those solid-state quantum nanoemitters.

2. Experiments

Ultrathin tapered fibers with diameters of ∼ 300 nm were fabricated from conventional single-mode optical fibers (Thorlabs, 630HP) by the method described elsewhere [31

31. M. Fujiwara, K. Toubaru, T. Noda, H. Zhao, and S. Takeuchi, “Highly efficient coupling of photons from nanoemitters into single-mode optical fibers,” Nano Lett. 11, 4362–4365 (2011). [CrossRef] [PubMed]

, 32

32. M. Fujiwara, K. Toubaru, and S. Takeuchi, “Optical transmittance degradation in tapered fibers,” Opt. Express 19, 8596–8601 (2011). [CrossRef] [PubMed]

]. Adiabatic tapering was confirmed as the transmittance was larger than 0.9 during fabrication. UV adhesives were used to attach the tapered fibers to a silica substrate [33

33. The overall transmittance of the tapered fibers (including the fiber coupling loss, the fiber connection loss, and the scattering loss at the UV adhesive) was 0.13 at room temperature. It decreased to 0.03 at 7 K, probably due to temperature-induced deformation of the UV adhesive. This reduction in transmittance does not essentially affect the present fiber–microsphere coupling experiment.

]. The tapered fibers used in the present experiments do not exhibit birefringence or depolarization in tapered region [35

35. H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, “Polarization-discriminated spectra of a fiber-microsphere system,” Appl. Phys. Lett. 89, 121107 (2006). [CrossRef]

], which ensures the polarization selectivity of cavity modes in fiber–microsphere coupling experiments. Microspheres were fabricated by melting the tips of silica fibers (S630-HP, Thorlabs) using a CO2 laser [34

34. Note that the microspheres fabricated from the silica fibers (S630-HP, Thorlabs) usually show Q factor of ∼ 107 due to impurities doped in the silica fibers. By using high-purity and low-OH silica for the starting material, we confirmed that the microspheres have Q factor of greater than 108. Note also that the cryogenic experiments do not affect the Q-factor of the microsphere as we already experimentally confirmed previously [24].

].

Using these ultrathin tapered fibers and microspheres, we performed transmittance and phase-shift measurements based on polarization analysis of the light in the fiber-coupled microsphere cavities. Figure 1 shows the experimental setup. The output of a tunable laser diode (λ = 638.8 nm) was coupled to a single-mode fiber, which was connected with a tapered fiber in the cryostat. Polarization controllers were inserted before and after the tapered fiber to compensate the fiber birefringence. The output light from the fiber was then sent to the polarization analysis setup that consisted of a half-wave plate, a quarter-wave plate, a polarizing beam splitter, and two photodetectors. The tapered fiber used in this experiment was 310 nm in diameter. The microsphere was 120 μm in diameter and its stem was 20 μm in diameter. It was mounted on a three-axis piezo stage [24

24. 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, 15169–15173 (2010). [CrossRef] [PubMed]

]. After cooling the cryostat, the microsphere was brought close to the fiber to couple the guided light and the cavity mode. The polarization analysis provided four Stokes parameters from S0 to S3, which can be used to calculate the phase shift (Δϕ) due to microsphere coupling [Δϕ = arctan(S3/S2)]. The experimental details of the phase-shift measurement are described in Ref. [27

27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

, 38

38. Equation (3) in Ref. [27] reads Δϕ = arctan(S3/S2) − argAX + argAY, where AX and AY are a orthogonal set of complex amplitudes of the input electric field. In the present experiment we input diagonal polarization light, which gives argAX = argAY = 1/2.

].

Fig. 1 Schematic diagram of experimental setup. LD: laser diode; HWP: half-wave plate; Pol. Ctrl.: polarization controller; QWP: quarter-wave plate; PBS: polarizing beam splitter; PD: photodetector. The photograph shows a critically coupled fiber–microsphere system at 7 K. Both ends of the tapered fiber were spliced with single-mode fibers. The input power to the tapered fiber was ∼ 10 nW.

3. Results and Discussions

Figures 2(a) and (b) show normalized transmittance (η) spectra of the cavity resonance measured at 10 K for taper–microsphere distances (D) of 390 and 250 nm, respectively. Here, η was normalized to the off-resonance transmittance of the cavity mode. The transmittance minimum and linewidth in Fig. 2(a) are respectively η = 0.152 and 77 MHz (Q = 6.1 × 106) and are respectively η = 0.395 and 220 MHz (Q = 2.1 × 106) in Fig. 2(b). The higher quality factors were obtained as the microsphere went away from the tapered fiber; e.g. Q = 1.2 × 107 (linewidth: 40 MHz) was observed at D = 1030 nm [see Fig. 2(f)].

Fig. 2 Transmittance and phase-shift spectra of the microsphere cavity resonance at 10 K measured at taper–microsphere distances D of (a, c) 390 nm and (b, d) 250 nm, respectively. Plots of the (e) transmittance minimum and (f) the linewidth of the cavity resonance dip as a function of D.

These two transmittance spectra exhibit different coupling conditions, namely undercoupling and overcoupling [27

27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

, 28

28. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

, 36

36. K. Totsuka and M. Tomita, “Slow and fast light in a microsphere-optical fiber system,” J. Opt. Soc. Am. B 23, 2194–2199 (2006). [CrossRef]

]. In Fig. 2(a), the microsphere is located far from the fiber and consequently the coupling strength is smaller than the cavity loss (the undercoupling regime). In contrast, the microsphere is near the fiber in Fig. 2(b) and the coupling strength is greater than the cavity loss (the overcoupling regime). Between these two regimes there is critical coupling for which the coupling strength equals the cavity loss. Critical coupling gives the highest coupling efficiency.

The striking difference between these two regimes can be clearly observed in their phase-shift spectra. The phase shift (Δϕ) exhibits a discrete transition between these two regimes [27

27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

, 36

36. K. Totsuka and M. Tomita, “Slow and fast light in a microsphere-optical fiber system,” J. Opt. Soc. Am. B 23, 2194–2199 (2006). [CrossRef]

]. Figures 2(c) and (d) show phase-shift spectra corresponding to Figs. 2(a) and (b), respectively. In the undercoupling regime, the phase shift caused by cavity resonance is less than π and the phase shift does not change between the lower frequency side of the cavity resonance and the higher side. In contrast, a phase shift of 2π is always obtained in the overcoupling regime and the phase shift changes by 2π as the frequency increases across the cavity resonance [36

36. K. Totsuka and M. Tomita, “Slow and fast light in a microsphere-optical fiber system,” J. Opt. Soc. Am. B 23, 2194–2199 (2006). [CrossRef]

]. The present observation of a discrete transition from undercoupling to overcoupling demonstrates the full controllability of taper–microsphere coupling in a cryogenic environment at λ ∼ 637 nm.

In addition to observing these drastic changes, we have controlled the coupling condition from undercoupling to overcoupling by varying the taper–microsphere distance. Figures 2(e) and (f) show plots of the transmittance minimum and the linewidth as a function of the taper–microsphere distance, respectively [37

37. The taper-microsphere distance was calibrated by the data of room-temperature coupling experiments using a 330-nm-diameter tapered fiber and a 125-μm-diameter microsphere with the quality factor of Q = 1.0 × 107.

]. As the microsphere approaches the fiber, the transmittance minimum decreases until D = 360 nm. Below D = 360 nm, the transmittance minimum increases until η ∼ 0.5 at D = 0 nm. At the same time, the linewidth of the cavity resonance dip increases rapidly below D = 360 nm. The positioning stability of the tapered fiber relative to the microsphere was estimated to be less than 13 nm over at least 7 minutes by calibrating the fluctuations in the transmittance minimum observed in 7 minutes with the distance dependence of the transmittance depicted in Fig. 2(e). Such coupling controllability is crucial for developing cavity QED systems [16

16. T. Aoki, B. Dayan, E. Wilcut, W. Bowen, A. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature (London) 443, 671–674 (2006). [CrossRef]

]. Thus, the present system can be effectively used for cavity QED studies using NV centers. Note that the nonzero transmittance minimum for critical coupling in Fig. 2(e) originates from the phase mismatch between the waveguide and cavity modes. This mismatch can be eliminated by optimizing the taper diameter to the microsphere coupling [28

28. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

, 39

39. B. Little, J. Laine, and H. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightw. Technol. 17, 704–715 (1999). [CrossRef]

].

This coupling controllability based on stable nanopositioning of the microsphere allows their efficient coupling over the temperature range of 7–28 K. Figure 3(a) shows the frequency shift of the cavity resonance as a function of the temperature from 7 to 28 K and Fig. 3(b) shows the corresponding several transmittance spectra that were measured at which the microsphere was positioned to the critical coupling position. As the temperature increases from 7 K, the central frequency of the cavity mode initially increases, but it starts to decrease at 20 K. Importantly, the transmittance minimum of the resonance dip remains constant over the entire temperature range, as shown in Fig. 3(b). This indicates that near-critical coupling was obtained over the whole temperature range.

Fig. 3 Cavity resonance frequency tuning by temperature change with preserving the critical coupling. (a) Frequency shift of the cavity resonance as a function of temperature. Each data plot has an experimental error of 14 MHz that comes from the frequency fluctuation of the laser. (b) Corresponding transmittance spectra at 28, 20, 14, and 8 K from top to bottom [indicated by arrows in (a)]. (c) Relative shift of 1ν0dν0dT, α, and 1neffdneffdT as a function of temperature from 7 to 28 K, which are indicated by black rectangle, red circle, blue triangle, respectively. The data of α is taken from Ref. [43, 44]. In (b), cavity mode A has the Q factor of 7.3 × 106 and cavity mode B 1.9 × 107.

The frequency shift of the resonance peak showed nonlinear temperature dependence in contrast to the linear frequency shift at room temperature (−2.6 GHz / K at room temperature [40

40. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Resonant frequency control of a microspherical cavity by temperature adjustment,” Jpn. J. Appl. Phys. 43, 6138–6141 (2004). [CrossRef]

]). As the temperature increased from 8 K the center frequency showed positive shift up to 20 K, and from there it switched to negative shift. It is known that the cavity resonance frequency shift is governed by thermal expansion coefficient of silica (α) and the effective refractive index of the cavity mode (neff) at cryogenic temperatures, which can be described as follows [41

41. O. Arcizet, R. Riviére, A. Schliesser, G. Antetsberger, and T. J. Kippenberg, “Cryogenic Properties of Optomechanical Silica Microcavities,” Phys. Rev. A 80, 021803 (2009). [CrossRef]

, 42

42. Y. Park and H. Wang, “Regenerative pulsation in silica microspheres,” Opt. Lett. 32, 3104–3106 (2007). [CrossRef] [PubMed]

],
1ν0dν0dT=α+1neffdneffdT.
(1)
Using the experimental values for 1ν0dν0dT and the literature data of α [43

43. G. K. White, “Thermal expansion of vitreous silica at low temperatures,” Phys. Rev. Lett. 34, 204–205 (1975). [CrossRef]

, 44

44. G. K. White, “Thermal expansion of reference materials: copper, silica and silicon,” J. Phys. D: Appl. Phys. 6, 2070–2078 (1973). [CrossRef]

], the variation in the effective refractive index ( 1neffdneffdT) is determined using this equation. Fig. 3(c) shows the plot of these three components. At room temperature, the neff term is known to be one order of magnitude greater than α, so that 1ν0dν0dT depends mostly on the neff term [40

40. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Resonant frequency control of a microspherical cavity by temperature adjustment,” Jpn. J. Appl. Phys. 43, 6138–6141 (2004). [CrossRef]

,41

41. O. Arcizet, R. Riviére, A. Schliesser, G. Antetsberger, and T. J. Kippenberg, “Cryogenic Properties of Optomechanical Silica Microcavities,” Phys. Rev. A 80, 021803 (2009). [CrossRef]

]. However, the neff term rapidly decreases as the temperature goes down to LHe temperature regime, thereby competing with the thermal coefficient α. The resultant frequency shift of the cavity resonance peak in Fig. 3(c) hence shows such a nonlinear behavior (reversal of the frequency shift).

The coupling of NV centers with microcavities at cryogenic temperatures has been the central issue in the recent solid-state cavity QED studies. Until now, several works have reported the coupling of single NV centers with microcavities (cavity only) at cryogenic temperature, demonstrating the NV-photon strong coupling [3

3. Y. Park, A. Cook, and H. Wang, “Cavity qed with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006). [CrossRef] [PubMed]

] or Purcell factor of F ∼ 70 [8

8. A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” arXiv:1202.0806v1 (2012).

]. However, these microcavities still do not have efficient optical access like tapered fibers. Forthcoming step to implement these NV-coupled cavity systems to the coherent quantum information devices is to provide the cavities with an efficient optical access. Thus our present demonstration of the fiber-coupled microsphere system at cryogenic temperatures is an important step towards the realization of coherent quantum devices using diamond NV centers.

The present fiber-coupled microsphere system is also distinct from other cryogenic fiber-coupled microcavity systems recently reported [18

18. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Physics 4, 415–419 (2008). [CrossRef]

20

20. E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T.J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012). [CrossRef]

,30

30. A.H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012). [CrossRef] [PubMed]

] in view that the system is optimized for the visible wavelength range necessary for the coherent excitation of the stable solid-state quantum nanoemitters, including diamond NV centers or CdSe/ZnS quantum dots, and has the full controllability of the waveguide-cavity coupling condition with high-Q factors. The cavity modes that we have shown above have the Q factor of 0.6–1.2 × 107 in the undercoupling regime [see Fig. 3(b) and cavity mode A in Fig. 3(b)]. We were also able to observe cavity modes that have Q factor of 107 in many cases; the cavity mode B in Fig. 3(b) showed Q = 1.9 × 107, for example. Furthermore, the microsphere-based cavity system can potentially provide Q factors up to 109 [29

29. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko“Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef] [PubMed]

]. The present system is therefore especially important for quantum optics experiments employing those promising solid-state nanoemitters.

4. Summary

We have demonstrated cooling of 310-nm-diameter ultrathin tapered fibers down to 7 K and fully controllable coupling with high-Q microsphere resonators at λ ∼ 637 nm in the vicinity of the zero-phonon optical transitions of diamond NV centers. Stable nanopositioning of the 310-nm-diameter tapered fibers in close proximity to the microsphere with a positioning stability of less than 13 nm over at least 7 min has been realized over the temperature range 7–28 K. A cavity-induced phase shift has been successfully obtained. The results clearly showed a discrete transition from undercoupling to overcoupling. In addition, 0.8-GHz frequency tuning of the cavity resonance by increasing the temperature from 7 to 28 K has been realized while preserving near-critical coupling over this temperature range. The present cavity systems have high-Q factor of Q = 1.9 × 107 in the visible wavelength region and therefore can be used for developing coherent quantum devices using diamond NV centers.

Acknowledgments

We thank Mr. Kamioka for his help with the fiber–microsphere coupling experiment at room temperature. We gratefully acknowledge financial support from MEXT-KAKENHI Quantum Cybernetics (No. 21101007), JSPS-KAKENHI (Nos. 20244062, 21840003, 23244079, and 23740228), JST-CREST, JSPS-FIRST, MIC-SCOPE, Project for Developing Innovation Systems of MEXT, G-COE Program, and the Research Foundation for Opto-Science and Technology.

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Y. F. Xiao, C. L. Zou, P. Xue, L. Xiao, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “Quantum electrodynamics in a whispering-gallery microcavity coated with a polymer nanolayer,” Phys. Rev. A 81, 053807 (2010). [CrossRef]

11.

K. Kojima, H. Hofmann, S. Takeuchi, and K. Sasaki, “Nonlinear interaction of two photons with a one-dimensional atom: Spatiotemporal quantum coherence in the emitted field,” Phys. Rev. A 68, 013803 (2003). [CrossRef]

12.

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate,” Phys. Rev. A 70, 013810 (2004). [CrossRef]

13.

K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon-photon SWAP gate using a λ system,” Phys. Rev. A 82, 010301 (2010). [CrossRef]

14.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Physica Scripta T137, 014001 (2009). [CrossRef]

15.

S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature (London) 415, 621–623 (2002). [CrossRef]

16.

T. Aoki, B. Dayan, E. Wilcut, W. Bowen, A. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature (London) 443, 671–674 (2006). [CrossRef]

17.

M. Larsson, K. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009). [CrossRef] [PubMed]

18.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Physics 4, 415–419 (2008). [CrossRef]

19.

A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the heisenberg uncertainty limit,” Nat. Physics 5, 509–514 (2009). [CrossRef]

20.

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T.J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012). [CrossRef]

21.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005). [CrossRef]

22.

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, “Fiber-microsphere laser with a sub-micrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus,” Appl. Phys. Lett. 90, 101103 (2007). [CrossRef]

23.

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, “Control of spontaneous emission coupling factor β in fiber-coupled microsphere resonators,” Appl. Phys. Lett. 92, 071115 (2008). [CrossRef]

24.

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, 15169–15173 (2010). [CrossRef] [PubMed]

25.

M. Cai and K. Vahala, “Highly efficient optical power transfer to whispering-gallery modes by use of a symmetrical dual-coupling configuration,” Opt. Lett. 25, 260–262 (2000). [CrossRef]

26.

M. Pototschnig, Y. Chassagneux, J. Hwang, G. Zumofen, A. Renn, and V. Sandoghdar, “Controlling the phase of a light beam with a single molecule,” Phys. Rev. Lett. 107, 63001 (2011). [CrossRef]

27.

A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express 19, 2278–2285 (2011). [CrossRef] [PubMed]

28.

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000). [CrossRef] [PubMed]

29.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko“Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef] [PubMed]

30.

A.H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012). [CrossRef] [PubMed]

31.

M. Fujiwara, K. Toubaru, T. Noda, H. Zhao, and S. Takeuchi, “Highly efficient coupling of photons from nanoemitters into single-mode optical fibers,” Nano Lett. 11, 4362–4365 (2011). [CrossRef] [PubMed]

32.

M. Fujiwara, K. Toubaru, and S. Takeuchi, “Optical transmittance degradation in tapered fibers,” Opt. Express 19, 8596–8601 (2011). [CrossRef] [PubMed]

33.

The overall transmittance of the tapered fibers (including the fiber coupling loss, the fiber connection loss, and the scattering loss at the UV adhesive) was 0.13 at room temperature. It decreased to 0.03 at 7 K, probably due to temperature-induced deformation of the UV adhesive. This reduction in transmittance does not essentially affect the present fiber–microsphere coupling experiment.

34.

Note that the microspheres fabricated from the silica fibers (S630-HP, Thorlabs) usually show Q factor of ∼ 107 due to impurities doped in the silica fibers. By using high-purity and low-OH silica for the starting material, we confirmed that the microspheres have Q factor of greater than 108. Note also that the cryogenic experiments do not affect the Q-factor of the microsphere as we already experimentally confirmed previously [24].

35.

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, “Polarization-discriminated spectra of a fiber-microsphere system,” Appl. Phys. Lett. 89, 121107 (2006). [CrossRef]

36.

K. Totsuka and M. Tomita, “Slow and fast light in a microsphere-optical fiber system,” J. Opt. Soc. Am. B 23, 2194–2199 (2006). [CrossRef]

37.

The taper-microsphere distance was calibrated by the data of room-temperature coupling experiments using a 330-nm-diameter tapered fiber and a 125-μm-diameter microsphere with the quality factor of Q = 1.0 × 107.

38.

Equation (3) in Ref. [27] reads Δϕ = arctan(S3/S2) − argAX + argAY, where AX and AY are a orthogonal set of complex amplitudes of the input electric field. In the present experiment we input diagonal polarization light, which gives argAX = argAY = 1/2.

39.

B. Little, J. Laine, and H. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightw. Technol. 17, 704–715 (1999). [CrossRef]

40.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Resonant frequency control of a microspherical cavity by temperature adjustment,” Jpn. J. Appl. Phys. 43, 6138–6141 (2004). [CrossRef]

41.

O. Arcizet, R. Riviére, A. Schliesser, G. Antetsberger, and T. J. Kippenberg, “Cryogenic Properties of Optomechanical Silica Microcavities,” Phys. Rev. A 80, 021803 (2009). [CrossRef]

42.

Y. Park and H. Wang, “Regenerative pulsation in silica microspheres,” Opt. Lett. 32, 3104–3106 (2007). [CrossRef] [PubMed]

43.

G. K. White, “Thermal expansion of vitreous silica at low temperatures,” Phys. Rev. Lett. 34, 204–205 (1975). [CrossRef]

44.

G. K. White, “Thermal expansion of reference materials: copper, silica and silicon,” J. Phys. D: Appl. Phys. 6, 2070–2078 (1973). [CrossRef]

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(350.3950) Other areas of optics : Micro-optics
(140.3945) Lasers and laser optics : Microcavities
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Quantum Optics

History
Original Manuscript: May 29, 2012
Revised Manuscript: July 23, 2012
Manuscript Accepted: August 3, 2012
Published: August 10, 2012

Citation
Masazumi Fujiwara, Tetsuya Noda, Akira Tanaka, Kiyota Toubaru, Hong-Quan Zhao, and Shigeki Takeuchi, "Coupling of ultrathin tapered fibers with high-Q microsphere resonators at cryogenic temperatures and observation of phase-shift transition from undercoupling to overcoupling," Opt. Express 20, 19545-19553 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-19545


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References

  1. O. Benson, “Assembly of hybrid photonic architectures from nanophotonic constituents,” Nature (London)480, 193–199 (2011). [CrossRef]
  2. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vuckovic, H. Park, and M. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett.10, 3922–3926 (2010). [CrossRef] [PubMed]
  3. Y. Park, A. Cook, and H. Wang, “Cavity qed with diamond nanocrystals and silica microspheres,” Nano Lett.6, 2075–2079 (2006). [CrossRef] [PubMed]
  4. O. Arcizet, V. Jacques, A. Siria, P. Poncharal, P. Vincent, and S. Seidelin, “A single nitrogen-vacancy defect coupled to a nanomechanical oscillator,” Nat. Physics7, 879–883 (2011). [CrossRef]
  5. P. E. Barclay, C. Santori, K.-M. Fu, R. G. Beausoleil, and O. Painter, “Coherent interference effects in a nano-assembled diamond NV center cavity-QED system,” Opt. Express17, 8081–8097 (2009). [CrossRef] [PubMed]
  6. C. Santori, P. Barclay, K. Fu, R. Beausoleil, S. Spillane, and M. Fisch, “Nanophotonics for quantum optics using nitrogen-vacancy centers in diamond,” Nanotechnology21, 274008 (2010). [CrossRef] [PubMed]
  7. 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. Photonics5, 301–305 (2011). [CrossRef]
  8. A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” arXiv:1202.0806v1 (2012).
  9. Y. C. Liu, Y. F. Xiao, B. B. Li, X. F. Jiang, Y. Li, and Q. Gong, “Coupling of a single diamond nanocrystal to a whispering-gallery microcavity: Photon transport benefitting from Rayleigh scattering,” Phys. Rev. A84, 011805 (2011). [CrossRef]
  10. Y. F. Xiao, C. L. Zou, P. Xue, L. Xiao, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “Quantum electrodynamics in a whispering-gallery microcavity coated with a polymer nanolayer,” Phys. Rev. A81, 053807 (2010). [CrossRef]
  11. K. Kojima, H. Hofmann, S. Takeuchi, and K. Sasaki, “Nonlinear interaction of two photons with a one-dimensional atom: Spatiotemporal quantum coherence in the emitted field,” Phys. Rev. A68, 013803 (2003). [CrossRef]
  12. K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate,” Phys. Rev. A70, 013810 (2004). [CrossRef]
  13. K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon-photon SWAP gate using a λ system,” Phys. Rev. A82, 010301 (2010). [CrossRef]
  14. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Physica ScriptaT137, 014001 (2009). [CrossRef]
  15. S. Spillane, T. Kippenberg, and K. Vahala, “Ultralow-threshold raman laser using a spherical dielectric microcavity,” Nature (London)415, 621–623 (2002). [CrossRef]
  16. T. Aoki, B. Dayan, E. Wilcut, W. Bowen, A. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature (London)443, 671–674 (2006). [CrossRef]
  17. M. Larsson, K. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett.9, 1447–1450 (2009). [CrossRef] [PubMed]
  18. A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Physics4, 415–419 (2008). [CrossRef]
  19. A. Schliesser, O. Arcizet, R. Rivière, G. Anetsberger, and T. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the heisenberg uncertainty limit,” Nat. Physics5, 509–514 (2009). [CrossRef]
  20. E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T.J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London)482, 63–67 (2012). [CrossRef]
  21. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005). [CrossRef]
  22. H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, “Fiber-microsphere laser with a sub-micrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus,” Appl. Phys. Lett.90, 101103 (2007). [CrossRef]
  23. H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, “Control of spontaneous emission coupling factor β in fiber-coupled microsphere resonators,” Appl. Phys. Lett.92, 071115 (2008). [CrossRef]
  24. 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. Express18, 15169–15173 (2010). [CrossRef] [PubMed]
  25. M. Cai and K. Vahala, “Highly efficient optical power transfer to whispering-gallery modes by use of a symmetrical dual-coupling configuration,” Opt. Lett.25, 260–262 (2000). [CrossRef]
  26. M. Pototschnig, Y. Chassagneux, J. Hwang, G. Zumofen, A. Renn, and V. Sandoghdar, “Controlling the phase of a light beam with a single molecule,” Phys. Rev. Lett.107, 63001 (2011). [CrossRef]
  27. A. Tanaka, T. Asai, K. Toubaru, H. Takashima, M. Fujiwara, R. Okamoto, and S. Takeuchi, “Phase shift spectra of a fiber-microsphere system at the single photon level,” Opt. Express19, 2278–2285 (2011). [CrossRef] [PubMed]
  28. M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000). [CrossRef] [PubMed]
  29. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko“Ultimate Q of optical microsphere resonators,” Opt. Lett.21, 453–455 (1996). [CrossRef] [PubMed]
  30. A.H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett.108, 033602 (2012). [CrossRef] [PubMed]
  31. M. Fujiwara, K. Toubaru, T. Noda, H. Zhao, and S. Takeuchi, “Highly efficient coupling of photons from nanoemitters into single-mode optical fibers,” Nano Lett.11, 4362–4365 (2011). [CrossRef] [PubMed]
  32. M. Fujiwara, K. Toubaru, and S. Takeuchi, “Optical transmittance degradation in tapered fibers,” Opt. Express19, 8596–8601 (2011). [CrossRef] [PubMed]
  33. The overall transmittance of the tapered fibers (including the fiber coupling loss, the fiber connection loss, and the scattering loss at the UV adhesive) was 0.13 at room temperature. It decreased to 0.03 at 7 K, probably due to temperature-induced deformation of the UV adhesive. This reduction in transmittance does not essentially affect the present fiber–microsphere coupling experiment.
  34. Note that the microspheres fabricated from the silica fibers (S630-HP, Thorlabs) usually show Q factor of ∼ 107 due to impurities doped in the silica fibers. By using high-purity and low-OH silica for the starting material, we confirmed that the microspheres have Q factor of greater than 108. Note also that the cryogenic experiments do not affect the Q-factor of the microsphere as we already experimentally confirmed previously [24].
  35. H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, “Polarization-discriminated spectra of a fiber-microsphere system,” Appl. Phys. Lett.89, 121107 (2006). [CrossRef]
  36. K. Totsuka and M. Tomita, “Slow and fast light in a microsphere-optical fiber system,” J. Opt. Soc. Am. B23, 2194–2199 (2006). [CrossRef]
  37. The taper-microsphere distance was calibrated by the data of room-temperature coupling experiments using a 330-nm-diameter tapered fiber and a 125-μm-diameter microsphere with the quality factor of Q = 1.0 × 107.
  38. Equation (3) in Ref. [27] reads Δϕ = arctan(S3/S2) − argAX + argAY, where AX and AY are a orthogonal set of complex amplitudes of the input electric field. In the present experiment we input diagonal polarization light, which gives argAX = argAY = 1/2.
  39. B. Little, J. Laine, and H. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightw. Technol.17, 704–715 (1999). [CrossRef]
  40. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Resonant frequency control of a microspherical cavity by temperature adjustment,” Jpn. J. Appl. Phys.43, 6138–6141 (2004). [CrossRef]
  41. O. Arcizet, R. Riviére, A. Schliesser, G. Antetsberger, and T. J. Kippenberg, “Cryogenic Properties of Optomechanical Silica Microcavities,” Phys. Rev. A80, 021803 (2009). [CrossRef]
  42. Y. Park and H. Wang, “Regenerative pulsation in silica microspheres,” Opt. Lett.32, 3104–3106 (2007). [CrossRef] [PubMed]
  43. G. K. White, “Thermal expansion of vitreous silica at low temperatures,” Phys. Rev. Lett.34, 204–205 (1975). [CrossRef]
  44. G. K. White, “Thermal expansion of reference materials: copper, silica and silicon,” J. Phys. D: Appl. Phys.6, 2070–2078 (1973). [CrossRef]

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