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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6354–6365
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Coupling slot-waveguide cavities for large-scale quantum optical devices

Chun-Hsu Su, Mark P. Hiscocks, Brant C. Gibson, Andrew D. Greentree, Lloyd C. L. Hollenberg, and François Ladouceur  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6354-6365 (2011)
http://dx.doi.org/10.1364/OE.19.006354


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Abstract

By offering effective modal volumes significantly less than a cubic wavelength, slot-waveguide cavities offer a new in-road into strong atom-photon coupling in the visible regime. Here we explore two-dimensional arrays of coupled slot cavities which underpin designs for novel quantum emulators and polaritonic quantum phase transition devices. Specifically, we investigate the lateral coupling characteristics of diamond-air and GaP-air slot waveguides using numerically-assisted coupled-mode theory, and the longitudinal coupling properties via distributed Bragg reflectors using mode-propagation simulations. We find that slot-waveguide cavities in the Fabry-Perot arrangement can be coupled and effectively treated with a tight-binding description, and are a suitable platform for realizing Jaynes-Cummings-Hubbard physics.

© 2011 OSA

1. Introduction

Quantum emulation with controllable quantum systems [1

1. R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21(6-7), 467–488 (1982). [CrossRef]

] is an important field as it offers efficient means to study computationally-hard problems. The numerical roadblock arises because of the exponential growth in quantum systems with linear increase in the number of quantum particles, and so quantum emulation is expected to be important in many disciplines including atomic physics, quantum chemistry, condensed-matter physics, material engineering, high-energy physics and cosmology. There are now many platforms being explored for implementing quantum emulators using various quantum systems such as neutral atoms, ions, photons and electrons. These efforts are matched by fast and striking experimental advances and now the level of coherent controlling these systems required for the physical realization of quantum simulation is within reach [2

2. I. Buluta and F. Nori, “Quantum simulators,” Science 326(5949), 108–111 (2009). [CrossRef] [PubMed]

].

Photonic bandgap (PBG) cavities offer a promising route to large-scale solid-state cavity-QED applications. The reason for this derives from the great technological advancements in photonic structure fabrication and the ability to create wavelength-sized, high-Q cavities [8

8. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]

]. In the appropriate media, these can be doped with impurities on the surface of the cavity, e.g. optical defect centres in diamond [9

9. A. D. Greentree, B. A. Fairchild, F. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today 11(9), 22–31 (2008). [CrossRef]

,10

10. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010). [CrossRef] [PubMed]

], donor-bound electrons [11

11. K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, “Coherent population trapping of electron spins in a high-purity n-type GaAs semiconductor,” Phys. Rev. Lett. 95(18), 187405 (2005). [CrossRef] [PubMed]

] and quantum dots [12

12. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

] in gallium-arsenide semiconductors. Prospects for large-scale integration in photonic crystals are promising, and over 100 PBG cavities have been coupled resonantly via a common line-defect to demonstrate ultraslow waveguiding [13

13. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008). [CrossRef]

].

Slot-waveguide cavities (SWCs) are another promising implementation [14

14. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]

,15

15. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

]. Slot waveguides allow in principle lossless transmission along a narrow region (i.e. slot) defined by two regions (rods) of higher refractive index via large dielectric discontinuities. SWCs are then formed as a micro-ring or in a Fabry-Perot (FP) arrangement by combining a slot waveguide with mirrors, PBG or distributed Bragg reflectors (DBRs) [16

16. C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express 13(25), 10092–10101 (2005). [CrossRef] [PubMed]

]. A critical advantage of SWCs over PBG cavities in the quantum-emulator engineering context is that the cavity mode volumes of SWCs can be up to 2 orders of magnitude smaller [17

17. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005). [CrossRef] [PubMed]

19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

], allowing stronger intracavity interactions, and thereby reducing the Q limitations to demonstrate strong atom-photon coupling. As the maximum of the optical field is in the central low dielectric (ideally air) region, they are compatible with high-dipole moment emissive nanoparticles that can infiltrate the slot. In particular, we have explored coupling of the SWC to an optically-active defect centre in diamond [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

] – negatively-charged nitrogen-vacancy (NV) centre – which is a promising quantum system for single-photon emission [20

20. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85(2), 290–293 (2000). [CrossRef] [PubMed]

], quantum computing [21

21. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004). [CrossRef] [PubMed]

,22

22. T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2(6), 408–413 (2006). [CrossRef]

], quantum control [23

23. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “High-speed quantum gates with cavity quantum electrodynamics,” Phys. Rev. A 78(6), 062336 (2008). [CrossRef]

,24

24. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: single photons and qudits,” Phys. Rev. A 80(3), 033811 (2009). [CrossRef]

], and communication [25

25. A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. 89(18), 187901 (2002). [CrossRef] [PubMed]

].

To date, most investigations into SWCs have focused on their confinement properties for a single cavity. Here we consider the optical coupling between spatially separated identical SWCs in array configurations. We find that SWCs in the FP arrangement can be coupled laterally and end-to-end, and that in certain regimes this coupling can be effectively treated with a tight-binding type interaction. Through these characterizations, we also determine the DBR specifications for achieving subwavelength confinement in FP-based SWCs. Our results demonstrate the potential of SWCs for building large-scale integrated quantum-optical devices that take advantage of the ultra-small mode volumes of SWCs, and the availability of strong and coherent dipoles such as diamond optical centres, quantum dots and nanorods.

2. Slot-waveguide cavity array

In the tight-binding model, photons are tightly-confined within individual resonators and can propagate only by hopping between adjacent cavities via evanescent fields of one cavity tunneling into the other [26

26. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999). [CrossRef]

]. Here we want to achieve a device in which the interaction between cavity sites is effectively mimicking a tight-binding model and hence operating in the most commonly-discussed regime of quantum emulation.

For slot waveguides, the high refractive index contrast at rod-slot interfaces enables ideally lossless light guiding along the central slot. To be compatible with high-dipole moment emitters as part of the construction of cavity-QED systems in the visible regime, diamond and gallium phosphide (GaP) are suitable materials for the rods because they have high transparency at this wavelength range [27

27. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983). [CrossRef]

] and have high refractive indices (n = 2.4 for diamond and 3.3 for GaP). On these structures, an air-slot and waveguiding patterns can be fabricated using electron beam [15

15. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

] or optical lithography [28

28. K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide,” Appl. Phys. Lett. 93(23), 234107 (2008). [CrossRef]

] combined with masking/dry etching techniques [29

29. M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express 16(24), 19512–19519 (2008). [CrossRef] [PubMed]

].

Light confinement along the z-direction (slot direction) to form a slot-waveguide cavity (SWC) is achieved by appending the ends of the waveguide with reflective boundaries such as mirrors, PBG or DBRs. Using narrow slots of wS = 20 nm width and an optimal wR × h = 140 × 110 nm diamond rods, the fundamental quasi-TE modes of the structure occupies a cavity mode volume of 0.1λ3/n , where λ is the operating wavelength of 637 nm and the mode is assumed to span over a cavity length of λ/2. The mode volume reduces to 0.02λ3/n when replaced with 5 nm slot or a 110 × 70 nm GaP rods. Further reduction is possible using angled sidewalls for the slot [30

30. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007). [CrossRef] [PubMed]

,31

31. A. Säynätjoki, T. Alasaarela, A. Khanna, L. Karvonen, P. Stenberg, M. Kuittinen, A. Tervonen, and S. Honkanen, “Angled sidewalls in silicon slot waveguides: conformal filling and mode properties,” Opt. Express 17(23), 21066–21076 (2009). [CrossRef] [PubMed]

]. Considering the special case of a NV in diamond with dipole moment on the zero phonon transition line of 10−30 Cm and emission wavelength 637 nm, the single-photon Rabi frequency Ω, can in theory reach as high as Ω = 1011 rad/s [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

]. This is an order of magnitude stronger than the intracavity, atom-photon coupling that can be realized by wavelength-sized PBG counterparts.

3. Lateral inter-cavity coupling

To describe the system in a tight-binding model, it is useful to determine the single-photon hopping or coupling rate J (coupling energy ħJ). Given that the solution of classical Maxwell’s equations can be reinterpreted as a precise quantum description of a one-photon state, we use the classical results and write down the relation for lateral coupling,
JL=2cκmnneffk
(5)
where the subscript L is used to distinguish lateral coupling from end-to-end coupling (JE) discussed in Sec. 4. The propagating field sees an effective refractive index n eff of the combined system that we approximate to that of an individual waveguide in isolation.

3.1. Cladding-separated configuration

We use the optimal diamond-air and GaP-air vertical slot arrangements previously discussed in Sec. 2 and first consider waveguide arrays with varying width of the separating claddingregion. We first consider a two-waveguide system in Fig. 2
Fig. 2 Ex-field distribution of the TE-supermodes of a coupled diamond-air slot-waveguide system with dimensions {wS, wR, h} = {20, 140, 110} nm for (a,b) wG = 200 nm or d = 500 μm) and (c,d) 1 μm (d = 1.3 μm). Strong E-field localization is found within the slots. The even supermodes are shown in (a,c) and the odd in (b,d). The predicted coupling strength between the waveguides is shown in Fig. 3.
, showing its even and odd supermodes (with respective propagation constants χ + and χ ) and a strong E-field within each slot region. In the limit of large separations, the effective indices and propagation constants of these modes approach the parameter values of the single waveguide n eff = 1.31 and β = 12.91 rad/μm for diamond-air, and 1.34 and 13.22 rad/μm for GaP-air slots. Applying NA-CMT analysis to the mode solutions of the diamond-air system with centre-to-centre separation distance d = 500 nm, we arrive at a matrix with Mnnβ 2 = 0.1460 and Mmn = 2.6442, in units of rad2/μm2. The self-coupling is much weaker than the inter-cavity coupling. In particular, with χ + > β >χ , κmn = Mmn with JL = 1.2 × 1014 rad/s for a centre-to-centre separation distance of d = 500 nm. This rate falls off exponentially with distance as shown in Fig. 3
Fig. 3 Lateral coupling rate JL between two slot waveguides in cladding-separated configuration, plotted as a function of centre-to-centre separation between the waveguides. Circles (Crosses) denote the calculated results for coupled diamond-air (GaP-air) slots. The coupling strength exponentially decreases with the separation.
and the contribution of (Mnnβ 2) approaches zero. At 1.5 μm separation, JL = 1.7 × 1010 rad/s is commensurate with the strength of the intracavity coupling of diamond colour centres to subwavelength-sized SWCs [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

] On the other hand, for d < 400 nm, the cladding region between the waveguides begins to act as a slot, altering the number of effective cavities. The resulting geometry becomes akin the shared-rod configuration, which as we will see in Sec. 3.2 is not suitable for realizing tight-binding systems.

3.2. Shared-rod configuration

M=(241.57821.0760.8202.35027 .712228.49729 .8545 .1245.02630.684226 .75330 .6781.1845.19829 .803228 .677    1.3091 .1685 .10227 .676  1.201  2.110  0.429   21.461  241.212).
(7)

4. Longitudinal end-to-end coupling

JE/2π=lnRτ.
(10)

To estimate the grating length necessary for achieving high reflectivity, we use FIMMPROP [38

38. FIMMPROP, Photon Design, http://www.photond.com.

] to simulate field propagation (in 3D) along a single SWC in its fundamental TE-mode to determine the reflected power at a DBR. As we require high reflection over short lengths, gratings that use small perturbations to the slot-waveguide dimensions, e.g., an increase in rod width wR of 10 nm as in Ref. [39

39. J. Mu, H. Zhang, and W.-P. Huang, “A theoretical investigation of slot waveguide Bragg gratings,” IEEE J. Quantum Electron. 44(7), 622–627 (2008). [CrossRef]

], are insufficient, requiring more than 200 periods to achieve reflectivity more than 90%. Instead we use a high-contrast grating as in Ref. [40

40. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. 32(5), 533–535 (2007). [CrossRef] [PubMed]

], for example, in our case leaving the material slab unetched to give a large index contrast between the air slot and rectangular rod, and use a 50/50 duty cycle, as shown in Fig. 6
Fig. 6 (a) Schematic for a distributed Bragg reflector with 4.5 periods that separates two SWCs. The grating alternates between solid rectangular guide and slot regions. The respective E-field distributions of their fundamental modes are shown in (b) and (c).
. Due to the high contrast and nanometre-sized geometries involved, the simulations yield good indications of the reflection strengths, although the raw output shows numerical artifacts where reflected power slightly exceeds unity. To remove these artifacts, we invoke the conservation relation that T + R = 1 to plot the renormalized reflection spectra for different number of grating periods NP in Fig. 7(a)
Fig. 7 (a) Reflection coefficient R of a diamond-air DBR [Fig. 6(a)] appended to a diamond-air slot waveguide. The coefficient is associated to its fundamental TE-mode and is calculated for different grating periods P and number of periods Np. The maximal reflectivity is observed at P = 220 nm and these specifications are selected for (b) plotting longitudinal end-to-end coupling rate JE. In both figures, markers indicate simulation data points, and the lines are guides and are used to predict the coupling rate at larger Np.
. The maximum reflection occurs at the grating period P of 220 nm that satisfies the relation that P = λ/2n DBR where we estimate n DBR = 1.45 using the weighted average of the diamond-air slot (with an effective refractive index of 1.31) and diamond core (index 1.6).

Given these results, we expect that a grating with 14.5 periods and length 3.18 μm produces a high reflectivity of 1 – R = 10−2 and an effective grating length of L eff = 560 nm. By increasing the number of periods to 19.5, the reflectivity improves to 1 – R = 10−3 while L eff hardly changes (570 nm). It is therefore worthwhile to point out that the effective length remains relatively constant around 0.6 μm because the denominator of Eq. (8) increases very slowly with increasing R. Consequently, since the minimum value of the cavity length Lc is limited only by the size of the atomic system inside the cavity, we can set the overall index N effn DBR and L^c2Leff as the fundamental limit. Applying these values to Eqs. (8) and (10) we plot the expected coupling rate for different grating periods in Fig. 7(b). Apart from showing an exponential scaling, achieving a coupling strength in the range of 109–1011 rad/s is possible with structures with 24.5 < NP < 39.5 and 200 < P < 240 nm. Moreover, following Eq. (9), we can expect that a dielectric-based grating design would only increase the cavity mode volume of a λ/2-long SWC reported in Ref. [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

]. by a factor of (2L eff)/(λ/2) = 3.7. The resultant cavity mode volumes are therefore still well below the dimensions of the wavelength of light.

5. Conclusions

The use of slot-waveguide cavities for implementing multi-cavity quantum-optical devices takes advantage of the extremely strong atom-photon interactions inside the cavities made possible by their subwavelength-sized cavity mode volumes. This effort to study and optimize the confinement properties of such cavities in various materials and designs is matched by our effort to investigate the coupling properties between multiple cavities arranged in parallel and in series. Amongst the three coupling configurations considered in this work, the arrangements of cladding-separated slots in parallel and DBR-separated slots connected end-to-end are ideal for implementing a tight-binding model.

We have shown that the strength of inter-cavity coupling in the lateral direction can be tailored from as large as 1014 rad/s to arbitrarily small values by introducing cladding separation of 500 nm or more. Similarly, the coupling rate in the longitudinal direction can be reduced from 5 × 1014 rad/s by introducing 5 or more Bragg periods. Specifically, there is exponential scaling of coupling strength against these setup parameters. Our DBR analysis furthermore extends and validates the work of Ref. [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

] by relaxing the hard-boundary assumption used in the calculation of cavity mode volumes of diamond-air and GaP-air slot-waveguide cavities.

These results, which along with Refs. [17

17. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005). [CrossRef] [PubMed]

,19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

], represent a blueprint for building a cavity-QED based quantum simulator to study strongly-correlated many-body systems. A very wide parameter space for the Hubbard-like inter-site interactions in JCH model is experimentally accessible in the proposed platform. For instance, the second-excitation Mott-insulator lobe of the quantum phase in JCH model can be physically simulated in a NV-doped cavity-array that supports a uniform inter-cavity coupling of 109 rad/s [4

4. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2(12), 856–861 (2006). [CrossRef]

]. This can be achieved with a lateral slot separation of 1.8 μm and 39.5 Bragg periods for the DBRs. More generally, our results support the suitability of slot designs as a promising and superior alternative to PBG cavities in the quantum-optical applications and large-scaled solid-state cavity-QED.

Acknowledgments

This project is supported by the Australian Research Council under the Discovery Scheme (DP0770715, DP0880466, and DP0877871) and the Centre of Excellence Scheme (CE0348250). CHS acknowledges the support of the Albert Shimmins Memorial Fund. The authors thank Photon Design support for their assistance with simulations.

References and links

1.

R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21(6-7), 467–488 (1982). [CrossRef]

2.

I. Buluta and F. Nori, “Quantum simulators,” Science 326(5949), 108–111 (2009). [CrossRef] [PubMed]

3.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2(12), 849–855 (2006). [CrossRef]

4.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2(12), 856–861 (2006). [CrossRef]

5.

D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76(3), 031805 (2007). [CrossRef]

6.

J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED based photon lattices,” Phys. Rev. A 82(4), 043811 (2010). [CrossRef]

7.

J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “A new class of dynamic quantum metamaterials,” http://arxiv.org/abs/1009.4867 (2010).

8.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]

9.

A. D. Greentree, B. A. Fairchild, F. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today 11(9), 22–31 (2008). [CrossRef]

10.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010). [CrossRef] [PubMed]

11.

K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, “Coherent population trapping of electron spins in a high-purity n-type GaAs semiconductor,” Phys. Rev. Lett. 95(18), 187405 (2005). [CrossRef] [PubMed]

12.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

13.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008). [CrossRef]

14.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]

15.

Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

16.

C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express 13(25), 10092–10101 (2005). [CrossRef] [PubMed]

17.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005). [CrossRef] [PubMed]

18.

A. Gondarenko and M. Lipson, “Low modal volume dipole-like dielectric slab resonator,” Opt. Express 16(22), 17689–17694 (2008). [CrossRef] [PubMed]

19.

M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]

20.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85(2), 290–293 (2000). [CrossRef] [PubMed]

21.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004). [CrossRef] [PubMed]

22.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2(6), 408–413 (2006). [CrossRef]

23.

C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “High-speed quantum gates with cavity quantum electrodynamics,” Phys. Rev. A 78(6), 062336 (2008). [CrossRef]

24.

C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: single photons and qudits,” Phys. Rev. A 80(3), 033811 (2009). [CrossRef]

25.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. 89(18), 187901 (2002). [CrossRef] [PubMed]

26.

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999). [CrossRef]

27.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983). [CrossRef]

28.

K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide,” Appl. Phys. Lett. 93(23), 234107 (2008). [CrossRef]

29.

M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express 16(24), 19512–19519 (2008). [CrossRef] [PubMed]

30.

F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007). [CrossRef] [PubMed]

31.

A. Säynätjoki, T. Alasaarela, A. Khanna, L. Karvonen, P. Stenberg, M. Kuittinen, A. Tervonen, and S. Honkanen, “Angled sidewalls in silicon slot waveguides: conformal filling and mode properties,” Opt. Express 17(23), 21066–21076 (2009). [CrossRef] [PubMed]

32.

W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11(3), 963–983 (1994). [CrossRef]

33.

A. W. Synder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 2000), Chap. 29.

34.

M. L. Cooper and S. Mookherjea, “Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides,” Opt. Express 17(3), 1583–1599 (2009). [CrossRef] [PubMed]

35.

E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. 9(4), 125–127 (1984). [CrossRef] [PubMed]

36.

FIMMWAVE, Photon Design, http://www.photond.com.

37.

Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]

38.

FIMMPROP, Photon Design, http://www.photond.com.

39.

J. Mu, H. Zhang, and W.-P. Huang, “A theoretical investigation of slot waveguide Bragg gratings,” IEEE J. Quantum Electron. 44(7), 622–627 (2008). [CrossRef]

40.

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. 32(5), 533–535 (2007). [CrossRef] [PubMed]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.5750) Optical devices : Resonators
(230.7380) Optical devices : Waveguides, channeled
(230.4555) Optical devices : Coupled resonators
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Integrated Optics

History
Original Manuscript: November 29, 2010
Manuscript Accepted: February 17, 2011
Published: March 21, 2011

Citation
Chun-Hsu Su, Mark P. Hiscocks, Brant C. Gibson, Andrew D. Greentree, Lloyd C. L. Hollenberg, and François Ladouceur, "Coupling slot-waveguide cavities for large-scale quantum optical devices," Opt. Express 19, 6354-6365 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6354


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References

  1. R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21(6-7), 467–488 (1982). [CrossRef]
  2. I. Buluta and F. Nori, “Quantum simulators,” Science 326(5949), 108–111 (2009). [CrossRef] [PubMed]
  3. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2(12), 849–855 (2006). [CrossRef]
  4. A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2(12), 856–861 (2006). [CrossRef]
  5. D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76(3), 031805 (2007). [CrossRef]
  6. J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED based photon lattices,” Phys. Rev. A 82(4), 043811 (2010). [CrossRef]
  7. J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “A new class of dynamic quantum metamaterials,” http://arxiv.org/abs/1009.4867 (2010).
  8. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]
  9. A. D. Greentree, B. A. Fairchild, F. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today 11(9), 22–31 (2008). [CrossRef]
  10. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010). [CrossRef] [PubMed]
  11. K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, “Coherent population trapping of electron spins in a high-purity n-type GaAs semiconductor,” Phys. Rev. Lett. 95(18), 187405 (2005). [CrossRef] [PubMed]
  12. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]
  13. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008). [CrossRef]
  14. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]
  15. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]
  16. C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express 13(25), 10092–10101 (2005). [CrossRef] [PubMed]
  17. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005). [CrossRef] [PubMed]
  18. A. Gondarenko and M. Lipson, “Low modal volume dipole-like dielectric slab resonator,” Opt. Express 16(22), 17689–17694 (2008). [CrossRef] [PubMed]
  19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express 17(9), 7295–7303 (2009). [CrossRef] [PubMed]
  20. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. 85(2), 290–293 (2000). [CrossRef] [PubMed]
  21. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004). [CrossRef] [PubMed]
  22. T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2(6), 408–413 (2006). [CrossRef]
  23. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “High-speed quantum gates with cavity quantum electrodynamics,” Phys. Rev. A 78(6), 062336 (2008). [CrossRef]
  24. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: single photons and qudits,” Phys. Rev. A 80(3), 033811 (2009). [CrossRef]
  25. A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. 89(18), 187901 (2002). [CrossRef] [PubMed]
  26. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999). [CrossRef]
  27. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983). [CrossRef]
  28. K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide,” Appl. Phys. Lett. 93(23), 234107 (2008). [CrossRef]
  29. M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express 16(24), 19512–19519 (2008). [CrossRef] [PubMed]
  30. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007). [CrossRef] [PubMed]
  31. A. Säynätjoki, T. Alasaarela, A. Khanna, L. Karvonen, P. Stenberg, M. Kuittinen, A. Tervonen, and S. Honkanen, “Angled sidewalls in silicon slot waveguides: conformal filling and mode properties,” Opt. Express 17(23), 21066–21076 (2009). [CrossRef] [PubMed]
  32. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11(3), 963–983 (1994). [CrossRef]
  33. A. W. Synder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 2000), Chap. 29.
  34. M. L. Cooper and S. Mookherjea, “Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides,” Opt. Express 17(3), 1583–1599 (2009). [CrossRef] [PubMed]
  35. E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. 9(4), 125–127 (1984). [CrossRef] [PubMed]
  36. FIMMWAVE, Photon Design, http://www.photond.com .
  37. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]
  38. FIMMPROP, Photon Design, http://www.photond.com .
  39. J. Mu, H. Zhang, and W.-P. Huang, “A theoretical investigation of slot waveguide Bragg gratings,” IEEE J. Quantum Electron. 44(7), 622–627 (2008). [CrossRef]
  40. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. 32(5), 533–535 (2007). [CrossRef] [PubMed]

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