Abstract

We experimentally realize an optical fiber ring resonator that includes a tapered section with a subwavelength-diameter waist. In this section, the guided light exhibits a significant evanescent field which allows for efficient interfacing with optical emitters. A commercial tunable fiber beam splitter provides simple and robust coupling to the resonator. Key parameters of the resonator such as the out-coupling rate, free spectral range, and birefringence can be adjusted. Thanks to the low taper- and coupling-losses, the resonator exhibits an unloaded finesse of F=75±1, sufficient for reaching the regime of strong coupling for emitters placed in the evanescent field. The system is ideally suited for trapping ensembles of laser-cooled atoms along the nanofiber section. Based on measured parameters, we estimate that the system can serve as a platform for optical multimode strong coupling experiments. Finally, we discuss the possibilities of using the resonator for applications based on chiral quantum optics.

© 2016 Optical Society of America

Over the past years, significant research effort has been devoted to interfacing quantum emitters, such as molecules, quantum dots, color centers, and neutral atoms, with fiber-guided light fields. Suitable light–matter interfaces are considered to be key elements for future quantum networks [1]. One way to realize such an interface consists of coupling emitters to the evanescent fields surrounding the nanofiber waist of a tapered optical fiber, that is, a fiber section with sub-wavelength diameter. Such systems already provide absorption probabilities for single fiber-guided photons of about 25% for a single emitter located on the nanofiber surface [2] and about 5% at a distance of 200 nm, typical for cold atoms in nanofiber-based optical dipole traps [3,4].

One way to further enhance the light–matter coupling strength is to increase the number of emitters in the evanescent field and to take advantage of the collective coupling [5]. Another option relies on confining the light in an optical resonator, which allows one to even reach the regime of strong coupling in the sense of cavity quantum electrodynamics (CQED) [6]. There, the coherent emitter-light interaction strength dominates over the incoherent decay channels. In this context, optical nanofibers are a versatile platform, as they allow one to combine both approaches and, in this way, to reach very strong light–matter coupling in a fiber-integrated environment.

Different nanofiber-based Fabry–Perot resonator schemes have been developed, for example, based on Bragg structures created using ion beam milling [7,8] or laser ablation [9] of the fiber waist. A nanofiber placed on an optical grating has been demonstrated, and Purcell enhancement of single quantum emitters coupled to this system has been observed [10]. Tapered optical fibers have been combined with conventional fiber Bragg gratings to form a Fabry–Perot resonator [11] for which strong coupling has been demonstrated with Cesium (Cs) atoms trapped close to the nanofiber surface [12]. Running-wave type resonators, such as nanofiber knot and loop resonators [13] and a nanofiber-segment tapered fiber closed to a ring via a 50:50 beam splitter [14], have also been demonstrated, albeit so far with smaller finesse than the Fabry–Perot counterparts.

Here, we demonstrate a tapered fiber-based ring resonator with optical characteristics that are compatible with entering the regime of single-atom strong coupling. We experimentally reach a finesse of F=75±1, which corresponds to a single-atom cooperativity of C1. Our implementation offers easy tuning of the resonator eigenpolarizations and out-coupling rate as well as straightforward adjustment of the free spectral range of the resonator. Our system is compatible with established nanofiber-based schemes for the optical trapping of laser-cooled atoms. This would enable a controlled coupling of large ensembles of atoms to the resonator field which then gives rise to extremely large collective atom-resonator interaction strengths. Furthermore, the evanescent fields around the nanofiber exhibit an inherent link between the local polarization and the propagation direction of the guided light [15]. This gives rise to a direction-dependent light-emitter coupling [16,17] which renders this resonator distinct from traditional Fabry–Perot or ring resonators. In particular, this allows one to implement chiral quantum optics effects [18]. Finally, the optical path length of such a tapered fiber ring (TFR) resonator can be significantly increased without reducing cooperativity. This makes this system a prime candidate for experimentally exploring the regime of optical multimode strong coupling where the atoms simultaneously couple strongly to many longitudinal resonator modes [19,20].

Our ring resonator consists of a tapered optical fiber with a nanofiber waist connected to an adjustable fiber beam splitter (Newport F-CPL-830-N-FA), see Fig. 1(a), whose splitting ratio can be continuously adjusted between 0% and 100%. The tapered fiber, shown schematically in Fig. 1(b), is fabricated from a standard step-index silica fiber (Fiber Core SM 800) using a heat-and-pull process [21,22]. The fiber waist has a length of 5 mm and a diameter of 500 nm. Light guided in such a subwavelength-diameter optical fiber exhibits a pronounced evanescent field [Fig. 1(c)] and enables efficient, homogeneous coupling of optical emitters to the guided mode. The standard fiber ends of the tapered fiber are spliced to the fiber beam splitter, yielding a TFR resonator with a total resonator length of l=2.35±0.01  m. The remaining two outputs of the fiber beam splitter then constitute the coupling fiber that allows us to interface the resonator.

 figure: Fig. 1.

Fig. 1. (a) Sketch of the experimental setup: a tapered optical fiber with a nanofiber waist forms a fiber ring resonator. An adjustable fiber beam splitter allows one to couple light into and out of the resonator. The characterization of the system is carried out by recording transmission spectra through the coupling fiber around a center wavelength of about 850 nm. The polarization of the input light field can be adjusted using a half and a quarter wave plate. (b) Schematic of the tapered optical fiber section with a nanofiber waist. A waist with a diameter of 500 nm and a length of 5 mm was used in the experiment. (c) Normalized intensity profile of a quasi-linearly polarized nanofiber-guided light field. The pronounced evanescent part of the guided light allows efficient interfacing with optical emitters (parameters: nanofiber radius 250 nm; vacuum optical wavelength 852 nm; and fiber refractive index 1.45).

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We optically characterize the TFR resonator by recording transmission spectra through the coupling fiber. To this end, we send light from a tunable, narrow-band diode laser into the coupling fiber and align the polarization of the probe light with one of the principle polarization axes of the resonator using wave plates (see below). The transmitted power is recorded with a photodiode as a function of the laser–resonator detuning. The wavelength of the light is about 850 nm, close to the Cs D2 line. By changing the splitting ratio of the beam splitter, we can continuously adjust the fiber–resonator coupling rate κext from the undercoupled regime (κext<κ0) to critical coupling (κext=κ0) and to the overcoupled regime (κext>κ0). Here, κ0 is the unloaded field decay rate of the uncoupled TFR resonator. Figure 2 shows example spectra for the three different coupling regimes. In each case, the laser is scanned over three consecutive resonances. Narrow transmission dips are clearly apparent with a free spectral range (FSR) of νFSR=87.5±0.4  MHz, demonstrating a high optical finesse and indicating a small internal resonator field decay rate κ0.

 figure: Fig. 2.

Fig. 2. Measured coupling fiber transmission (gray) as a function of the laser detuning for the (a) undercoupled regime (κext<κ0), (b) critically coupling (κext=κ0), and (c) overcoupled regime (κext>κ0). The red dashed lines are Lorentzian fits to the data.

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The resonator is produced from a non-polarization maintaining optical fiber and is subject to birefringence. The TFR resonator has two eigenpolarizations and the corresponding eigenfrequencies are, in general, different from each other. The eigenpolarizations are these two (orthogonal) polarization states that exactly reproduce themselves after one resonator round trip. In the experiment, we added an intra-resonator fiber paddle polarization controller (Thorlabs FPC) into the resonator fiber. This controller adds additional stress-induced birefringence to the fiber which allows us to adjust the resonator eigenpolarizations. In this way, we were able to fully tune the TFR resonator polarization eigenmodes from the point of degeneracy (same eigenfrequencies) to the point of maximum birefringence (eigenfrequencies of the two polarization eigenmodes are separated by half a FSR). For the data presented in Fig. 2, the resonator was set such that the two modes were clearly separated. The polarization of the probe light field was always adjusted to couple to only one of the resonator polarization modes by optimizing the wave plate settings in the coupling beam path.

Close to a cavity resonance, the field transmission t through the coupling fiber as a function of the frequency of the probe light is given by the Lorentzian [23]:

t=κ0κext+i(ωω0)κ0+κext+i(ωω0),
and is related to the power transmission T by T=|t|2. Here, (ωω0) is the detuning between the laser frequency ω and the resonator frequency ω0. In order to precisely determine the unloaded resonator loss rate, we record transmission spectra for a total of 12 different settings of the fiber beam splitter. For each setting, the laser is scanned over three consecutive resonances. All spectra and all resonances are then fit with the Lorentzian in Eq. (1) from which we obtain the overall field decay rate κ=κ0+κext and the on-resonance transmission Tr. This dataset, {κ,Tr}, is shown as blue dots in Fig. 3. By adjusting the splitting ratio of the fiber beam splitter and, thus, increasing κ, we clearly observe the transition from undercoupling to critical coupling and to overcoupling. In order to infer the unloaded field decay rate of the resonator κ0, we fit the theoretical prediction in Eq. (1) to the data in Fig. 3 with κ0 as the only free parameter. The fit shows excellent agreement with the data, which demonstrates that the fiber beam splitter does not introduce significant parasitic losses. From the fit, we obtain κ0=2π×0.58±0.01  MHz, which yields an unloaded finesse of F=πνFSR/κ0=75±1 and a quality factor of about Q=3×108. We note that these values give an upper bound on the resonator performance. Depending on the application and the chosen setting of κext, the resulting finesse and quality factor can be obtained from the intrinsic values by multiplication with a factor κ0/κ.

The intrinsic decay rate κ0 in our experiment corresponds to round trip power losses of L=exp(2κ0nl/c)7.9%, where n is the silica refractive index and c the vacuum speed of light. For our resonator length, these losses have two main contributions: one originates from the insertion loss of the fiber beam splitter, specified by the manufacturer to be below 0.1 dB, which corresponds to a loss of 2.3%. The remaining loss stems from the finite tapered fiber transmission, which we estimate to be about 94%. This is slightly lower than typical transmissions of our home-made tapered fibers (about 98%), presumably due to dust that accumulated in the fiber waist during the experiment.

Based on our system parameters and the results of the spectral characterization of the resonator, we now estimate the potential for the realization of a light–matter interface and for experiments in the realm of CQED. We discuss the typical example of interfacing an ensemble of laser-cooled Cs133 atoms to the evanescent field present around the nanofiber section of the TFR resonator [3]. The closed optical transition |F=4,mF=4|F=5,mF=5 from the 6S1/2 ground to the 6P3/2 excited state (wavelength λ=852  nm, dipole decay rate γ=2π×2.6  MHz) is σ+-polarized. For a suitably chosen quantization axis, this optical transition has almost unit polarization overlap with the nanofiber-guided light [16]. In order to calculate the coupling strength g, we recall that this quantity corresponds to the single-photon optical Rabi frequency of the driven atom inside the resonator. Using the explicit solution for the evanescent fields of the nanofiber [15], we can calculate the local electric field at the position of the atom. From the electric field associated with the optical power of one single photon circulating the resonator and the atomic dipole moment of the above-mentioned transition, we then obtain a coupling strength of g=2π×1.5  MHz for an atom located 200 nm away from the nanofiber surface, that is, at a typical atom–surface separation realized with nanofiber-based traps [3]. This corresponds to a single-atom cooperativity C0=g2/(2κγ)=0.74, close to the regime of strong coupling. For comparison, for an atom at the surface, we find a coupling strength of gsurf=2π×5  MHz, which is high enough to enter the strong coupling regime, that is, C0,surf4.4>1. The increase of γ due to the close proximity of the atomic dipole to the surface is taken into account in the calculation [25]. By employing established techniques, it should be feasible to optically trap about N=2000 atoms close to the nanofiber [3]. This would realize a large collective interaction between the atomic ensemble and the light in the resonator, yielding a collective cooperativity of Ccoll=NC01500, which sets the system far in the strong coupling regime.

We now estimate how the resonator and coupling parameters change with the resonator length. Diffraction effects make it challenging to maintain a small mode area (and, thus, large coupling strength) for long resonators build from free-space optical components. However, for both Fabry–Perot and ring-type fiber-based resonators, the light is guided and the mode cross section is independent of the resonator length. Then, the atom-resonator coupling strength scales as gl1/2 with the length l of the resonator. At the same time, the cumulative propagation losses in the standard fiber part are typically much smaller than the losses that occur when the light propagates through the tapered section. In this case, the unloaded resonator decay rate κ0 depends on the length as κ0l1. Consequently, the cooperativity is then independent of the resonator length. Remarkably, it is thus possible to maintain large cooperativities also for large resonator lengths. For our experimental system, Fig. 3 shows the predicted behavior of the collective cooperativity Ccoll as well as collective coupling strength gcoll=Ng and FSR νFSR as a function of the geometrical resonator length of the TFR resonator. The calculation takes fiber propagation losses into account. For fiber lengths l of more than 4 m, the collective coupling strength gcoll exceeds the FSR, and the system enters the regime of multimode strong coupling [19]. In this regime of CQED, the atomic ensemble is simultaneously strongly coupled to several non-degenerate longitudinal resonator modes. So far, this has only been realized in the microwave domain [26]. Multimode strong coupling enables atom-mediated interactions between different optical modes and results in a nonlinear quantum dynamics that is not present in the single-mode regime [20]. Atom-mediated mode coupling has recently also been considered for implementing photonic quantum simulation protocols [27].

 figure: Fig. 3.

Fig. 3. (a) Transmission through the coupling fiber as a function of the total field decay rate of the resonator κ=κext+κ0. From small to large values of κ, the regimes of undercoupling, critical coupling, and overcoupling are observed. The curve is a fit using Eq. (1). Error bars, indicating the standard deviation of the {κ,Tr} fit values, are small and hardly visible. (b) Expected collective coupling strength gcoll (blue dashed line), free spectral range νFSR (red dashed-dotted line), and cooperativity Ccoll (black solid line) of the TFR resonator as a function of the resonator length. The plot is calculated for fiber losses of 1.5 dB/km for optical fibers at a wavelength of about 850 nm [24] and for the case of a state-of-the-art nanofiber trap loaded with 2000 atoms [3]. The dashed vertical line indicates the length at which the gcoll exceeds the free spectral range, and the atom-resonator system enters the regime of multimode strong coupling.

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Apart from the large possible collective coupling strength and the intrinsic fiber integration, a TFR resonator differs from other resonator types because of the extremely tight confinement of the light in the nanofiber section. This confinement gives rise to an inherent link between the local polarization and the propagation direction of the light. In conjunction with suitable quantum emitters, such as spin-polarized atoms, NV-centers or quantum dots, which can exhibit polarization dependent scattering cross-sections, this gives rise to strong direction-dependent light–matter interaction strengths [16,17], similar to the case of whispering-gallery-mode resonators [28]. This renders the TFR resonator a conceptually novel type of optical resonator for which collectively enhanced chiral light–matter interaction [18] provides novel quantum functionalities [29] and that can, for example, be employed to realize optical nonreciprocal devices with significantly higher efficiency that also work for light levels that are higher than in previous implementations [30,31]. Moreover, it enables the study of chiral interactions and the consequences of collective effects such as sub- and super-radiance in the regime of multimode strong coupling, that is, where the dynamics of the system is neither that expected for a conventional CQED system nor that of an open waveguide.

In summary, we realized a TFR resonator that incorporates a nanofiber section, and identified two key areas of application. The high optical finesse, the tight confinement of the light in the nanofiber section, and the compatibility with homogeneously coupling to large ensembles of optical emitters render this system well suited for protocols that require strong light–matter interaction. By taking additional precautions against the pollution of the nanofiber waist, we expect to be able to reduce the transmission losses in this section and, thus, to further enhance the finesse and cooperativity of the system. Our experimental approach also offers practical advantages such as a simple tuning of key system parameters. Both, the chiral light–matter interactions present in our resonator and the option to enter the regime of multimode strong coupling, make TFR resonators a powerful platform for future experiments in classical and quantum photonics.

Funding

Austrian Science Fund (FWF) (F 4908-N23).

REFERENCES

1. H. J. Kimble, Nature 453, 1023 (2008). [CrossRef]  

2. R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012). [CrossRef]  

3. E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010). [CrossRef]  

4. A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012). [CrossRef]  

5. M. Tavis and F. W. Cummings, Phys. Rev. 188, 692 (1969). [CrossRef]  

6. P. Berman, Cavity Quantum Electrodynamics (Academic, 1994).

7. M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011). [CrossRef]  

8. K. P. Nayak, F. L. Kien, Y. Kawai, K. Hakuta, K. Nakajima, H. T. Miyazaki, and Y. Sugimoto, Opt. Express 19, 14040 (2011). [CrossRef]  

9. K. P. Nayak, P. Zhang, and K. Hakuta, Opt. Lett. 39, 232 (2014). [CrossRef]  

10. R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014). [CrossRef]  

11. C. Wuttke, M. Becker, S. Brückner, M. Rothhardt, and A. Rauschenbeutel, Opt. Lett. 37, 1949 (2012). [CrossRef]  

12. S. Kato and T. Aoki, Phys. Rev. Lett. 115, 093603 (2015). [CrossRef]  

13. G. Brambilla, J. Opt. 12, 043001 (2010). [CrossRef]  

14. D. E. Jones, G. T. Hickman, J. D. Franson, and T. B. Pittman, Opt. Lett. 41, 3683 (2016). [CrossRef]  

15. F. Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014). [CrossRef]  

16. R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014). [CrossRef]  

17. J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).

18. P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

19. J. Parker and C. R. Stroud, Phys. Rev. A 35, 4226 (1987). [CrossRef]  

20. D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014). [CrossRef]  

21. T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992). [CrossRef]  

22. F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).

23. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Vol. 1.

24. D. R. Goff, Fiber Optic Reference Guide (Focal, 2013).

25. S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015). [CrossRef]  

26. N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

27. N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016). [CrossRef]  

28. C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013). [CrossRef]  

29. I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014). [CrossRef]  

30. C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

31. M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

References

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  1. H. J. Kimble, Nature 453, 1023 (2008).
    [Crossref]
  2. R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
    [Crossref]
  3. E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
    [Crossref]
  4. A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
    [Crossref]
  5. M. Tavis and F. W. Cummings, Phys. Rev. 188, 692 (1969).
    [Crossref]
  6. P. Berman, Cavity Quantum Electrodynamics (Academic, 1994).
  7. M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011).
    [Crossref]
  8. K. P. Nayak, F. L. Kien, Y. Kawai, K. Hakuta, K. Nakajima, H. T. Miyazaki, and Y. Sugimoto, Opt. Express 19, 14040 (2011).
    [Crossref]
  9. K. P. Nayak, P. Zhang, and K. Hakuta, Opt. Lett. 39, 232 (2014).
    [Crossref]
  10. R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014).
    [Crossref]
  11. C. Wuttke, M. Becker, S. Brückner, M. Rothhardt, and A. Rauschenbeutel, Opt. Lett. 37, 1949 (2012).
    [Crossref]
  12. S. Kato and T. Aoki, Phys. Rev. Lett. 115, 093603 (2015).
    [Crossref]
  13. G. Brambilla, J. Opt. 12, 043001 (2010).
    [Crossref]
  14. D. E. Jones, G. T. Hickman, J. D. Franson, and T. B. Pittman, Opt. Lett. 41, 3683 (2016).
    [Crossref]
  15. F. Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).
    [Crossref]
  16. R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
    [Crossref]
  17. J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).
  18. P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).
  19. J. Parker and C. R. Stroud, Phys. Rev. A 35, 4226 (1987).
    [Crossref]
  20. D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
    [Crossref]
  21. T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
    [Crossref]
  22. F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).
  23. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Vol. 1.
  24. D. R. Goff, Fiber Optic Reference Guide (Focal, 2013).
  25. S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
    [Crossref]
  26. N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).
  27. N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
    [Crossref]
  28. C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
    [Crossref]
  29. I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
    [Crossref]
  30. C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).
  31. M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

2016 (2)

D. E. Jones, G. T. Hickman, J. D. Franson, and T. B. Pittman, Opt. Lett. 41, 3683 (2016).
[Crossref]

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

2015 (4)

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
[Crossref]

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

S. Kato and T. Aoki, Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

2014 (7)

D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
[Crossref]

F. Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).
[Crossref]

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).

K. P. Nayak, P. Zhang, and K. Hakuta, Opt. Lett. 39, 232 (2014).
[Crossref]

R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014).
[Crossref]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

2013 (1)

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

2012 (3)

C. Wuttke, M. Becker, S. Brückner, M. Rothhardt, and A. Rauschenbeutel, Opt. Lett. 37, 1949 (2012).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

2011 (2)

2010 (2)

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

G. Brambilla, J. Opt. 12, 043001 (2010).
[Crossref]

2008 (2)

H. J. Kimble, Nature 453, 1023 (2008).
[Crossref]

F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).

1992 (1)

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[Crossref]

1987 (1)

J. Parker and C. R. Stroud, Phys. Rev. A 35, 4226 (1987).
[Crossref]

1969 (1)

M. Tavis and F. W. Cummings, Phys. Rev. 188, 692 (1969).
[Crossref]

Albrecht, B.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

Alton, D. J.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Aoki, T.

S. Kato and T. Aoki, Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

Bartholomäus, T.

F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).

Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

Becker, M.

Berman, P.

P. Berman, Cavity Quantum Electrodynamics (Academic, 1994).

Birks, T. A.

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[Crossref]

Brambilla, G.

M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011).
[Crossref]

G. Brambilla, J. Opt. 12, 043001 (2010).
[Crossref]

Brückner, S.

Buhmann, S. Y.

S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
[Crossref]

Choi, K. S.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Clausen, C.

S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
[Crossref]

Cummings, F. W.

M. Tavis and F. W. Cummings, Phys. Rev. 188, 692 (1969).
[Crossref]

Dawkins, S. T.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Dayan, B.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

Ding, D.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Ding, M.

M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011).
[Crossref]

Franson, J. D.

Goban, A.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Goff, D. R.

D. R. Goff, Fiber Optic Reference Guide (Focal, 2013).

Gromov, A.

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

Guendelman, G.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

Hakuta, K.

R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014).
[Crossref]

K. P. Nayak, P. Zhang, and K. Hakuta, Opt. Lett. 39, 232 (2014).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

K. P. Nayak, F. L. Kien, Y. Kawai, K. Hakuta, K. Nakajima, H. T. Miyazaki, and Y. Sugimoto, Opt. Express 19, 14040 (2011).
[Crossref]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Vol. 1.

Hickman, G. T.

Hilico, A.

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

Houck, A. A.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Jones, D. E.

Junge, C.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

Kato, S.

S. Kato and T. Aoki, Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

Kawai, Y.

Kien, F. L.

Kimble, H. J.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

H. J. Kimble, Nature 453, 1023 (2008).
[Crossref]

Krimer, D. O.

D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
[Crossref]

Lacroûte, C.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Le Kien, F.

F. Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

Lee, T.

M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011).
[Crossref]

Li, Y. W.

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[Crossref]

Liertzer, M.

D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
[Crossref]

Liu, Y.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Lodahl, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Lovsky, Y.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

Mahmoodian, S.

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Malekakhlagh, M.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Mitsch, R.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

Miyazaki, H. T.

Morinaga, M.

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

Nakajima, K.

Nayak, K. P.

O’shea, D.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

Parker, J.

J. Parker and C. R. Stroud, Phys. Rev. A 35, 4226 (1987).
[Crossref]

Petersen, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).

Pichler, H.

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Pittman, T. B.

Pototschnig, M.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Rauschenbeutel, A.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).

F. Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).
[Crossref]

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

C. Wuttke, M. Becker, S. Brückner, M. Rothhardt, and A. Rauschenbeutel, Opt. Lett. 37, 1949 (2012).
[Crossref]

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

Reitz, D.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Rosenblum, S.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

Rothhardt, M.

Rotter, S.

D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
[Crossref]

Ryou, A.

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

Sadgrove, M.

R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014).
[Crossref]

Sadri, D.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Sagué, G.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Sayrin, C.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

Scheel, S.

S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
[Crossref]

Scheucher, M.

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

Schine, N.

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

Schmidt, R.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Schneeweiss, P.

S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
[Crossref]

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Shomroni, I.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

Simon, J.

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

Sommer, A.

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

Stern, N. P.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Stobbe, S.

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Stroud, C. R.

J. Parker and C. R. Stroud, Phys. Rev. A 35, 4226 (1987).
[Crossref]

Sugimoto, Y.

Sundaresan, N. M.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Szöcs, L. J.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Tavis, M.

M. Tavis and F. W. Cummings, Phys. Rev. 188, 692 (1969).
[Crossref]

Thiele, T.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Türeci, H. E.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
[Crossref]

Underwood, D. L.

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Vetsch, E.

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

Volz, J.

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Wang, P.

M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011).
[Crossref]

Warken, F.

F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).

Will, E.

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

Wuttke, C.

Yalla, R.

R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

Zhang, P.

Zoller, P.

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

Appl. Phys. Lett. (1)

M. Ding, P. Wang, T. Lee, and G. Brambilla, Appl. Phys. Lett. 99, 051105 (2011).
[Crossref]

J. Lightwave Technol. (1)

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[Crossref]

J. Opt. (1)

G. Brambilla, J. Opt. 12, 043001 (2010).
[Crossref]

Nat. Commun. (1)

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Nat. Commun. 5, 5713 (2014).
[Crossref]

Nature (2)

H. J. Kimble, Nature 453, 1023 (2008).
[Crossref]

N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Nature 534, 671 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Photon. Spectra (1)

F. Warken, A. Rauschenbeutel, and T. Bartholomäus, Photon. Spectra 42, 3 (2008).

Phys. Rev. (1)

M. Tavis and F. W. Cummings, Phys. Rev. 188, 692 (1969).
[Crossref]

Phys. Rev. A (4)

F. Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).
[Crossref]

J. Parker and C. R. Stroud, Phys. Rev. A 35, 4226 (1987).
[Crossref]

D. O. Krimer, M. Liertzer, S. Rotter, and H. E. Türeci, Phys. Rev. A 89, 033820 (2014).
[Crossref]

S. Scheel, S. Y. Buhmann, C. Clausen, and P. Schneeweiss, Phys. Rev. A 92, 043819 (2015).
[Crossref]

Phys. Rev. Lett. (6)

C. Junge, D. O’shea, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 110, 213604 (2013).
[Crossref]

S. Kato and T. Aoki, Phys. Rev. Lett. 115, 093603 (2015).
[Crossref]

R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014).
[Crossref]

R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012).
[Crossref]

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).
[Crossref]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
[Crossref]

Phys. Rev. X (2)

C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O’shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Phys. Rev. X 5, 041036 (2015).

N. M. Sundaresan, Y. Liu, D. Sadri, L. J. Szöcs, D. L. Underwood, M. Malekakhlagh, H. E. Türeci, and A. A. Houck, Phys. Rev. X 5, 021035 (2015).

Science (2)

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, Science 345, 903 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 1257671 (2014).

Other (5)

P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller, “Chiral quantum optics,” arXiv:1608.00446 (2016).

P. Berman, Cavity Quantum Electrodynamics (Academic, 1994).

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Science (2016), doi: 10.1126/science.aaj2118.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984), Vol. 1.

D. R. Goff, Fiber Optic Reference Guide (Focal, 2013).

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Figures (3)

Fig. 1.
Fig. 1. (a) Sketch of the experimental setup: a tapered optical fiber with a nanofiber waist forms a fiber ring resonator. An adjustable fiber beam splitter allows one to couple light into and out of the resonator. The characterization of the system is carried out by recording transmission spectra through the coupling fiber around a center wavelength of about 850 nm. The polarization of the input light field can be adjusted using a half and a quarter wave plate. (b) Schematic of the tapered optical fiber section with a nanofiber waist. A waist with a diameter of 500 nm and a length of 5 mm was used in the experiment. (c) Normalized intensity profile of a quasi-linearly polarized nanofiber-guided light field. The pronounced evanescent part of the guided light allows efficient interfacing with optical emitters (parameters: nanofiber radius 250 nm; vacuum optical wavelength 852 nm; and fiber refractive index 1.45).
Fig. 2.
Fig. 2. Measured coupling fiber transmission (gray) as a function of the laser detuning for the (a) undercoupled regime ( κ ext < κ 0 ), (b) critically coupling ( κ ext = κ 0 ), and (c) overcoupled regime ( κ ext > κ 0 ). The red dashed lines are Lorentzian fits to the data.
Fig. 3.
Fig. 3. (a) Transmission through the coupling fiber as a function of the total field decay rate of the resonator κ = κ ext + κ 0 . From small to large values of κ , the regimes of undercoupling, critical coupling, and overcoupling are observed. The curve is a fit using Eq. (1). Error bars, indicating the standard deviation of the { κ , T r } fit values, are small and hardly visible. (b) Expected collective coupling strength g coll (blue dashed line), free spectral range ν FSR (red dashed-dotted line), and cooperativity C coll (black solid line) of the TFR resonator as a function of the resonator length. The plot is calculated for fiber losses of 1.5 dB/km for optical fibers at a wavelength of about 850 nm [24] and for the case of a state-of-the-art nanofiber trap loaded with 2000 atoms [3]. The dashed vertical line indicates the length at which the g coll exceeds the free spectral range, and the atom-resonator system enters the regime of multimode strong coupling.

Equations (1)

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t = κ 0 κ ext + i ( ω ω 0 ) κ 0 + κ ext + i ( ω ω 0 ) ,

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