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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2278–2285
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Phase shift spectra of a fiber–microsphere system at the single photon level

Akira Tanaka, Takeshi Asai, Kiyota Toubaru, Hideaki Takashima, Masazumi Fujiwara, Ryo Okamoto, and Shigeki Takeuchi  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2278-2285 (2011)
http://dx.doi.org/10.1364/OE.19.002278


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Abstract

We succeeded in measuring phase shift spectra of a micro-sphere cavity coupled with a tapered fiber using a weak coherent probe light at the single photon level. We utilized a tapered fiber with almost no depolarization and constructed a very stable phase shift measurement scheme based on polarization analysis using photon counting. Using a very weak probe light ( = 0.41), we succeeded in observing the transition in the phase shift spectrum between undercoupling and overcoupling (at gap distances of 500 and 100 nm, respectively). We also used quantum state tomography to obtain a ‘purity spectrum’. Even in the overcoupling regime, the average purity was 0.982±0.024 (minimum purity: 0.892), suggesting that the coherence of the fiber–microsphere system was well preserved. Based on these results, we believe this system is applicable to quantum phase gates using single light emitters such as diamond nitrogen vacancy centers.

© 2011 Optical Society of America

1. Introduction

Microsphere resonators coupled with tapered optical fibers [1

1. G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, “Morphology-dependent resonances of a microsphere-optical fiber system,” Opt. Lett. 21, 695–697 (1996). [CrossRef] [PubMed]

, 2

2. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

] have been attracting interest because of their ultrahigh quality factors [3

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

], small mode volumes [4

4. J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003). [CrossRef]

], polarization selective coupling [5

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

], and highly efficient single-spatial-mode input-output [6

6. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]

]. Following the pioneering demonstrations of coupling between a microcavity and a tapered fiber [1

1. G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, “Morphology-dependent resonances of a microsphere-optical fiber system,” Opt. Lett. 21, 695–697 (1996). [CrossRef] [PubMed]

, 2

2. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

], applications to lasers [7

7. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430–1432 (2000). [CrossRef]

9

9. 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]

], biosensors [10

10. F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974–1979 (2003). [CrossRef] [PubMed]

], and nonlinear optics [11

11. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007). [CrossRef]

] have been reported. When a single light emitter is deposited on the cavity, the interaction between the light emitter and photons is enhanced due to confinement in the small mode volume. Thus, this system is an ideal testbed for cavity quantum electrodynamics(QED) experiments [12

12. 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]

]. Examples of applications include a nonlinear sign shift gate [13

13. H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003). [CrossRef]

15

15. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase-shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995). [CrossRef] [PubMed]

] for photonic quantum computation [16

16. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001). [CrossRef]

] and quantum memory [17

17. T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” N. J. Phys. 8, 184 (2006). [CrossRef]

] for long-distance quantum communication. We are currently interested in realizing such devices using a fiber–microsphere system with a coupled single light emitter, e.g. nitrogen-vacancy (NV) centers in diamond [18

18. A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18, 191–196 (2002). [CrossRef]

].

To characterize such photonic quantum devices, the probe input light has to be very weak (i.e., single photon level). It is also essential to analyze the phase change of the probe light to evaluate the coherence properties of quantum devices. The first step toward performing such evaluations is observing the phase shift of an empty microsphere cavity coupled with a tapered fiber using a probe light at the single photon level [19

19. 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]

].

A phase shift spectrum was recently obtained by interfering the bright coherent signal output from a fiber–microsphere system with a reference light [20

20. M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, “Observation of normal and anomalous dispersions in a microsphere taper fiber system,” J. Phys. Soc. Jpn. 78, 035001 (2009). [CrossRef]

]. However, it is technically very difficult to stabilize the optical phase between signal and reference lights that have different optical paths, especially when using a very faint probe light.

Furthermore, we need to characterize the depolarization of an output photon from a fiber–microsphere system. For this purpose, we performed frequency-dependent quantum state tomography [22

22. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]

] of an output photon and derived the purity spectrum, which is important for characterizing the depolarization of the system. This method involves reconstructing an output state as a density matrix ρ̂(ω) from the output spectra for three different polarization bases for a polarization input consisting of a combination of two orthogonal polarization modes, X and Y. Quantum state tomography is able to accurately estimate the coherence even when there are statistical fluctuations, which is significant when a very weak probe light is used. From ρ̂(ω), we obtained purity spectra that indicate the decoherence (i.e. the depolarization) in the fiber–microsphere system. The average purity was 0.982±0.024 (minimum purity: 0.892), indicating that our fiber–microsphere system can maintain coherence and is thus suitable for quantum coherent devices. Such an observation of the purity spectrum will be essential in future cavity QED experiments.

2. Experimental setup

A tapered fiber was fabricated from a commercial single-mode fiber (Thorlab, 780HP). The fiber was heated using a ceramic heater [23

23. 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]

] and stretched at about 1330°C. To generate a large evanescent field strength, a tapered fiber was fabricated with a diameter of 410 nm in the tapered region, as measured by scanning electron microscopy (Keyence, VE9800). The total transmittance of the tapered fiber used in the experiment was 30% (the values of the transmittance given below were compensated by this value). A microsphere cavity with a stem [24

24. L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993). [CrossRef]

] was fabricated by melting the tip of a tapered fiber (fused silica) by focusing a carbon dioxide laser beam (output power: 4–8 W; wavelength: 1.55 μm) on the tip. Optical microscopy observations revealed that the microsphere cavity has a diameter of 43.3 μm.

Figure 1 shows the measurement setup. The probe light is generated by a tunable laser diode (New Focus, Velocity 6312), whose frequency was swept by a function generator about the resonance frequency of the microsphere cavity. We set the sweeping range to 150 and 300 MHz; these frequencies correspond to the two coupling conditions. To calibrate the frequency, we measured the absorption spectrum of a rubidium gas cell. The laser output was attenuated by three neutral density filters to a weak with ≤ 1. After a polarizing filter, a half-wave plate was used to prepare a combination of X and Y modes at the coupling region in the tapered fiber. Two quarter-wave plates and a half-wave plate were used for precompensation of the birefringence in a single-mode fiber. The probe was then coupled to the single-mode fiber, which was connected to the tapered fiber. The intensity of the probe light was measured at the connector. After the tapered fiber, we used an additional polarization controller for postcompensation of the birefringence. The microsphere was set close to the fiber in the tapered region. To control the coupling with the cavity, the stem of the microsphere was fixed onto a metal jig of a three-axis piezoelectric transducer (PI, NanoCube) to enable the distance between the cavity and the tapered fiber to be varied in 20 nm steps. The output was sent to the polarization measurement region, which consists of a half-wave plate, a quarter-wave plate, a polarizing beam splitter, two fiber-coupled single-photon counting modules (Parkin Elmer, SPCM-AQR-14) and two photon counters (Stanford Research Systems, SR400). The analog outputs of the photon counters (per 1 ms) were sent to an oscilloscope (Tektronix, DPO 4104). Photon counting spectra, which indicate the coupling of individual polarizations with the microsphere cavity mode, were displayed on the oscilloscope. The typical photon count was 800counts per 1ms and the dark count of SPCMs were below 0.3counts per 1ms. The origin of the signal level on the oscilloscope was set when the probe laser was off.

Fig. 1 Experimental setup. HWP: half wave plate; QWP: quarter wave plate; PBS: polarizing beam splitter; SMF: single mode fiber; PD: photodiode; PZT: piezoelectric transducer; SPCM: single photon counting module.

3. Gap distance dependence of transmittance spectrum

Fig. 2 (a) Minimum transmittance, (c) phase shift, and (e) purity spectra obtained at a gap distance of 500 nm; (b), (d), and (f) spectra obtained at a gap distance of 100 nm. Solid curves in (a) to (d) are theoretical fits based on coupled-mode theory.

Figure 3 shows the minimum transmittance Tmin of the probe light as a function of the distance d between the tapered fiber and the microsphere cavity. In this experiment, we used a 1 μW input probe light and a calibrated photodiode, which has placed after the tapered fiber. The horizontal axis represents the distance d between the tapered fiber and the surface of the microsphere cavity. The left vertical axis is the minimum transmittance Tmin at the resonance frequency (indicated by the red triangles). Since the spectrum did not change when the microsphere was moved toward the tapered fiber, we believe that the microsphere was in contact with the tapered fiber at d = 0. As the microsphere was moved toward the tapered fiber (from approximately 800 nm), Tmin decreases for d > 300 nm. Tmin has a minimum near d = dc ≃ 300nm. As d is further reduced, Tmin tends to increase, as predicted by theory [19

19. 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 region where d is larger (smaller) than dc is called the under(over)coupling regime [19

19. 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]

, 26

26. N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, “Eroded monomode optical-fiber for whispering-gallery mode excitation in fused-silica microspheres,” Opt. Lett. 20, 813–815 (1995). [CrossRef] [PubMed]

]. Figure 2(a) was obtained at d = 500 nm, where there is undercoupling. To study the effect of the coupling condition, another transmittance spectrum was obtained at d = 100 nm (overcoupling) (see Fig. 2(b)). Note that the scan range of Fig. 2(b) (200MHz) is much larger larger than Fig. 2(a) (60MHz). The full width at half maximum (FWHM) of the dip in Fig. 2(b) is three times greater than that in Fig. 2(a), due to the large damping of the cavity mode in the tapered fiber in the overcoupling regime.

Fig. 3 Dependences of (red) minimum transmittance and (green) quality factor on gap distance. Black arrows indicate gap distances used to measure the spectra in Fig. 2.

For reference, we calculated the quality factor Q = 2πf0/δf from the FWHM δf of the resonance dip. Q indicates the degree of confinement of the probe light in the cavity. The calculated Q for different d is indicated by the green triangles in Fig. 3. As a result, the quality factor (right vertical axis) decreases continuously from 3.0 × 107 at d = 800 nm to 1.1 × 106 at d = 0 nm, as predicted by theory. The effect of the small parasitic dip at −50 MHz in Fig. 2(b) is discussed below.

4. Phase shift spectrum at the single photon level

We then measured phase shift spectra for both coupling conditions. As stated earlier, the phase shift is measured using reference polarization mode Y, which does not couple with the cavity mode; in contrast, X mode couples with the cavity mode, giving a phase shift θX(ω) described by Eq. (1). We represent the X(Y)-polarized complex amplitude of the input electric field by A0X(0Y). Here, we consider the case when only A0X couples with the cavity resonance mode with a transmittance TallTX(ω) and a phase shift θX(ω). Tall is the total transmittance of both polarization modes. The output electric field of the fiber–microsphere system then obeys the following transformation:
A0X(ω)AX(ω)=TallTX(ω)eiθX(ω)A0X(ω),A0Y(ω)AY(ω)=TallA0Y(ω)
(2)
The phase shift θX(ω) is obtained as follows:
θX(ω)=Tan1(S3(ω)S2(ω))ArgA0X+ArgA0Y
(3)
where S2(ω) = IP(ω) − IM(ω) and S3(ω) = IR(ω) − IL(ω) are Stokes parameters at the frequency ω. IP(ω) and IM(ω) are respectively the intensities of diagonal/antidiagonal polarization modes, and IR(ω) and IL(ω) are respectively the intensities of right/left circular polarization modes, where X and Y are taken to be horizontal and vertical polarization modes. Note that IP(ω) is given by [27

27. A. Yariv, Optical Electronics in Modern Communications, pp. 12 (Oxford, 1997).

]
IP(ω)=|AP(ω)|22η=12η|AX(ω)+AY(ω)2|2
(4)
where η=μ0/ɛ0 is vacuum impedance. Similarly, IM(ω), IR(ω), and IL(ω) are found using AM(ω)=(AX(ω)AY(ω))/2, AR(ω)=(AX(ω)iAY(ω)/2, and AL(ω)=(AX(ω)+iAY(ω)/2.

Figures 2(c) and 2(d) are phase shift spectra obtained for undercoupling (Fig. 2(a)) and overcoupling (Fig. 2(b)), respectively. The vertical axis indicates the phase shift θX (ω). We subtracted a constant phase shift due to the small birefringence of the fiber (0.9 rad in Figs. 2(c) and 2(d)). The phase shift asymptotically approaches 0 rad in the highly detuned region in the undercoupling condition, whereas it approaches ±π in the overcoupling condition (±2.9rad at ±100MHz). Thus, the transition of the phase shift spectrum from undercoupling to overcoupling [20

20. M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, “Observation of normal and anomalous dispersions in a microsphere taper fiber system,” J. Phys. Soc. Jpn. 78, 035001 (2009). [CrossRef]

, 21

21. T. Asai, H. Konishi, H. Takashima, H. Fujiwara, S. Takeuchi, and K. Sasaki, “Optical phase shift observed in a resonance mode of a tapered-fiber coupled with a microsphere resonator,” in Meeting Abstracts of the Phys. Soc. of Japan, (Academic, Osaka, Japan, 2008) 63, 23pQD-13, pp. 152.

] is clearly observed using a probe light with = 0.41. Note that the parasitic dip at −50 MHz in Fig. 2(b) caused a small step-like change at −50MHz in Fig. 2(d). The change is small (0.3rad) maybe because it is still in the undercoupling condition with small coupling efficiency κ.

5. Purity spectrum of the fiber–microsphere system

6. Conclusion

We succeeded in measuring phase shift spectra of a microsphere cavity coupled with a tapered fiber using a weak coherent probe light at the single photon level. We utilized a tapered fiber with almost no depolarization and constructed a very stable phase shift measurement scheme based on polarization analysis using photon counting. Using a very weak probe light ( = 0.41), we succeeded in observing the transition in the phase shift spectrum between undercoupling and overcoupling (at gap distances of 500 and 100 nm, respectively). We also used quantum state tomography to obtain a ’purity spectrum’. Even in the overcoupling regime, the average purity was 0.982±0.024 (minimum purity: 0.892), suggesting that the coherence of the fiber–microsphere system was well preserved. Based on these results, we believe this system is applicable to quantum phase gates using single light emitters such as diamond nitrogen vacancy centers.

Acknowledgments

The current work was supported in part by the program “R&D Support Scheme for Funding Selected IT Proposals” of the Ministry of Public Management, Home Affairs, Posts and Telecommunications, a Grant-in-Aid from the Japan Society for the Promotion of Science, the 21st Century COE Program, CREST Project, Japan Science and Technology Agency, JSPS-Grant in Aid for Scientific Research on Innovative areas ‘Quantum Cyberneticsf, Funding Program for World-Leading Innovative R&D on Science and Technology, and Special Coordination Funds for Promoting Science and Technology.

References and links

1.

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, “Morphology-dependent resonances of a microsphere-optical fiber system,” Opt. Lett. 21, 695–697 (1996). [CrossRef] [PubMed]

2.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

3.

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

4.

J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A 67, 033806 (2003). [CrossRef]

5.

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

6.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]

7.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430–1432 (2000). [CrossRef]

8.

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

9.

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]

10.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974–1979 (2003). [CrossRef] [PubMed]

11.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007). [CrossRef]

12.

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]

13.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218–221 (2003). [CrossRef]

14.

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]

15.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase-shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995). [CrossRef] [PubMed]

16.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52 (2001). [CrossRef]

17.

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” N. J. Phys. 8, 184 (2006). [CrossRef]

18.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, “Room temperature stable single-photon source,” Eur. Phys. J. D 18, 191–196 (2002). [CrossRef]

19.

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]

20.

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, “Observation of normal and anomalous dispersions in a microsphere taper fiber system,” J. Phys. Soc. Jpn. 78, 035001 (2009). [CrossRef]

21.

T. Asai, H. Konishi, H. Takashima, H. Fujiwara, S. Takeuchi, and K. Sasaki, “Optical phase shift observed in a resonance mode of a tapered-fiber coupled with a microsphere resonator,” in Meeting Abstracts of the Phys. Soc. of Japan, (Academic, Osaka, Japan, 2008) 63, 23pQD-13, pp. 152.

22.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]

23.

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]

24.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993). [CrossRef]

25.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22, 1129–1131 (1997). [CrossRef] [PubMed]

26.

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, “Eroded monomode optical-fiber for whispering-gallery mode excitation in fused-silica microspheres,” Opt. Lett. 20, 813–815 (1995). [CrossRef] [PubMed]

27.

A. Yariv, Optical Electronics in Modern Communications, pp. 12 (Oxford, 1997).

OCIS Codes
(140.3948) Lasers and laser optics : Microcavity devices
(060.5565) Fiber optics and optical communications : Quantum communications
(270.5565) Quantum optics : Quantum communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 20, 2010
Revised Manuscript: January 18, 2011
Manuscript Accepted: January 18, 2011
Published: January 24, 2011

Citation
Akira Tanaka, Takeshi Asai, Kiyota Toubaru, Hideaki Takashima, Masazumi Fujiwara, Ryo Okamoto, and Shigeki Takeuchi, "Phase shift spectra of a fiber–microsphere system at the single photon level," Opt. Express 19, 2278-2285 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2278


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References

  1. G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996). [CrossRef] [PubMed]
  2. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997). [CrossRef] [PubMed]
  3. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996). [CrossRef] [PubMed]
  4. J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003). [CrossRef]
  5. H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006). [CrossRef]
  6. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]
  7. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000). [CrossRef]
  8. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002). [CrossRef]
  9. H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007). [CrossRef]
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