Abstract

The goal in designing mode-evolution based devices is to realise short and high-fidelity components. The counterdiabatic protocol in coherent quantum state control can be used to cancel unwanted coupling between adiabatic modes in mode evolution but is not directly realisable in the coupled-waveguide system. By finding alternative coupled-mode equations that links to the same interaction picture dynamical equation as the counterdiabatic protocol via unitary transformations, we have derived a universal formalism for the design of short and high-fidelity mode-evolution based coupled-waveguide devices. Starting from a traditional adiabatic device design, the counterdiabatic protocol leads to a high-fidelity device, with its evolution following the adiabatic modes exactly even when the adiabatic condition is violated. Tolerance analysis shows that the countera-diabatic devices combine the advantages of adiabatic and resonant devices. The formalism is used to design asymmetric waveguide couplers.

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References

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  1. R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett.4, 1135–1138 (1992).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. S. Guérin, S. Thomas, and H. R. Jauslin, “Optimization of population transfer by adiabatic passage,” Phys. Rev. A65, 023409 (2002).
    [CrossRef]
  6. M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
    [CrossRef]
  7. B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequence of chirped pulses,” Phys. Rev. Lett.106, 233001 (2011).
    [CrossRef]
  8. R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
    [CrossRef]
  9. M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A107, 9937–9945 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, “Mode conversion using optical analogy of shortcut to adiabatic passage in engineered multimode waveguides,” Opt. Express20, 24085–24092 (2012).
[CrossRef] [PubMed]

2011

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequence of chirped pulses,” Phys. Rev. Lett.106, 233001 (2011).
[CrossRef]

2010

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

S.-Y. Tseng and M.-C. Wu, “Mode conversion/splitting by optical analogy of multistate stimulated Raman adiabatic passage in multimode waveguides,” J. Lightwave Technol.28, 3529–3534 (2010).

2009

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev.3, 243–261 (2009).
[CrossRef]

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor.42, 365303 (2009).
[CrossRef]

X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett.34, 280–282 (2009).
[CrossRef] [PubMed]

2006

2005

M. R. Watts, H. A. Haus, and E. P. Ippen, “Integrated mode-evolution-based polarization splitter,” Opt. Lett.30, 967–969 (2005).
[CrossRef] [PubMed]

M. Demirplak and S. A. Rice, “Assisted adiabatic passage revisited,” J. Phys. Chem. B109, 6838–6844 (2005).
[CrossRef]

2003

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A107, 9937–9945 (2003).
[CrossRef]

2002

S. Guérin, S. Thomas, and H. R. Jauslin, “Optimization of population transfer by adiabatic passage,” Phys. Rev. A65, 023409 (2002).
[CrossRef]

1998

1997

R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
[CrossRef]

1992

R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett.4, 1135–1138 (1992).
[CrossRef]

1990

M. V. Berry, “Histories of adiabatic quantum transitions,” Proc. R. Soc. Lond. A429, 61–72 (1990).
[CrossRef]

1986

S. K. Korotky, “Three-space representation of phase-mismatch switching in coupled two-state optical systems,” IEEE J. Quantum Electron.22, 952–958 (1986).
[CrossRef]

1973

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9, 919–933 (1973).
[CrossRef]

Al-Bader, S.

Arimondo, E.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Bai, Y.

Bason, M. G.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Bergmann, K.

R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
[CrossRef]

Berry, M. V.

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor.42, 365303 (2009).
[CrossRef]

M. V. Berry, “Histories of adiabatic quantum transitions,” Proc. R. Soc. Lond. A429, 61–72 (1990).
[CrossRef]

Chen, X.

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

Chiang, K. S.

Ciampini, D.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Demirplak, M.

M. Demirplak and S. A. Rice, “Assisted adiabatic passage revisited,” J. Phys. Chem. B109, 6838–6844 (2005).
[CrossRef]

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A107, 9937–9945 (2003).
[CrossRef]

Fazio, R.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Giovannetti, V.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Guérin, S.

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequence of chirped pulses,” Phys. Rev. Lett.106, 233001 (2011).
[CrossRef]

S. Guérin, S. Thomas, and H. R. Jauslin, “Optimization of population transfer by adiabatic passage,” Phys. Rev. A65, 023409 (2002).
[CrossRef]

Guéry-Odelin, D.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

Haus, H. A.

Hsiao, F.-C.

Hu, C.

Huillery, P.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Ibáñez, S.

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

Ippen, E. P.

Jauslin, H. R.

S. Guérin, S. Thomas, and H. R. Jauslin, “Optimization of population transfer by adiabatic passage,” Phys. Rev. A65, 023409 (2002).
[CrossRef]

Jhang, Y.-W.

Kawano, K.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).
[CrossRef]

Kitoh, T.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).
[CrossRef]

Korotky, S. K.

S. K. Korotky, “Three-space representation of phase-mismatch switching in coupled two-state optical systems,” IEEE J. Quantum Electron.22, 952–958 (1986).
[CrossRef]

Lin, T.-Y.

Liu, H.-C.

Liu, Q.

Lizuain, I.

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev.3, 243–261 (2009).
[CrossRef]

Lor, K. P.

Malossi, N.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Mannella, R.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Morsch, O.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Muga, J. G.

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides(Academic, 2006).

Rice, S. A.

M. Demirplak and S. A. Rice, “Assisted adiabatic passage revisited,” J. Phys. Chem. B109, 6838–6844 (2005).
[CrossRef]

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A107, 9937–9945 (2003).
[CrossRef]

Ruschhaupt, A.

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

Schneider, V. M.

Shore, B. W.

R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
[CrossRef]

Sun, X.

Syahriar, A.

Syms, R. R. A.

R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett.4, 1135–1138 (1992).
[CrossRef]

Thomas, S.

S. Guérin, S. Thomas, and H. R. Jauslin, “Optimization of population transfer by adiabatic passage,” Phys. Rev. A65, 023409 (2002).
[CrossRef]

Torosov, B. T.

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequence of chirped pulses,” Phys. Rev. Lett.106, 233001 (2011).
[CrossRef]

Torrontegui, E.

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

Tseng, S.-Y.

Unanyan, R. G.

R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
[CrossRef]

Vitanov, N. V.

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequence of chirped pulses,” Phys. Rev. Lett.106, 233001 (2011).
[CrossRef]

Viteau, M.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Watts, M. R.

Wu, M.-C.

Yariv, A.

Yatsenko, L. P.

R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
[CrossRef]

IEEE J. Quantum Electron.

S. K. Korotky, “Three-space representation of phase-mismatch switching in coupled two-state optical systems,” IEEE J. Quantum Electron.22, 952–958 (1986).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9, 919–933 (1973).
[CrossRef]

IEEE Photon. Technol. Lett.

R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon. Technol. Lett.4, 1135–1138 (1992).
[CrossRef]

J. Lightwave Technol.

J. Phys. A: Math. Theor.

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor.42, 365303 (2009).
[CrossRef]

J. Phys. Chem. A

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A107, 9937–9945 (2003).
[CrossRef]

J. Phys. Chem. B

M. Demirplak and S. A. Rice, “Assisted adiabatic passage revisited,” J. Phys. Chem. B109, 6838–6844 (2005).
[CrossRef]

Laser and Photon. Rev.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev.3, 243–261 (2009).
[CrossRef]

Nature Phys.

M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, “High-fidelity quantum driving,” Nature Phys.8, 147–152 (2012).
[CrossRef]

Opt. Commun.

R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, “Laser-induced adiabatic atomic reorientation with control of diabatic losses,” Opt. Commun.139, 48–54 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Guérin, S. Thomas, and H. R. Jauslin, “Optimization of population transfer by adiabatic passage,” Phys. Rev. A65, 023409 (2002).
[CrossRef]

Phys. Rev. Lett.

B. T. Torosov, S. Guérin, and N. V. Vitanov, “High-fidelity adiabatic passage by composite sequence of chirped pulses,” Phys. Rev. Lett.106, 233001 (2011).
[CrossRef]

X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, “Shortcut to adiabatic passage in two- and three-level atoms,” Phys. Rev. Lett.105, 123003 (2010).
[CrossRef] [PubMed]

S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, “Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity,” Phys. Rev. Lett.109, 100403 (2012).
[CrossRef]

Proc. R. Soc. Lond. A

M. V. Berry, “Histories of adiabatic quantum transitions,” Proc. R. Soc. Lond. A429, 61–72 (1990).
[CrossRef]

Other

K. Okamoto, Fundamentals of Optical Waveguides(Academic, 2006).

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equations (Wiley, 2001).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic of the mode-evolution coupled-waveguide system.

Fig. 2
Fig. 2

Fractional power evolution in the two waveguides for different device lengths. (a) 5 mm, (b) 10 mm, (c) 20 mm, and (d) 50 mm. Dash-dotted lines show the adiabatic coupler corresponding to H0. Solid lines show the counterdiabatic coupler corresponding to κsσx + Δsσz. The solid lines also overlay the theoretical eigenmode power evolution curves given by [cos2(θ/2), sin2(θ/2)].

Fig. 3
Fig. 3

κs and Δs for the four device lengths considered in Fig. 2. (a) 5 mm, (b) 10 mm, (c) 20 mm, and (d) 50 mm. Red solid lines indicate the coupling coefficients for the counterdiabatic couplers. Black solid lines indicate the waveguide mismatch for the counterdiabatic couplers. Red dashed lines are the coupling coefficients for the adiabatic couplers. Black dashed lines are the waveguide mismatch for the adiabatic couplers.

Fig. 4
Fig. 4

Coupling efficiency as a function of the device length L. (Dash-dotted line) adiabatic coupler. (Solid line) counterdiabatic coupler.

Fig. 5
Fig. 5

Coupling efficiency against coupling coefficient variations for couplers designed using (a) adiabatic, (b) counterdiabatic, and (c) resonant coupling schemes.

Fig. 6
Fig. 6

(a) Waveguide geometry and BPM simulation of light propagation in a 5 mm adiabatic coupler. Solid white lines indicate the waveguide cores. (b) Fractional power evolution in the two waveguides.

Fig. 7
Fig. 7

(a) Waveguide geometry and BPM simulation of light propagation in a 5 mm counterdiabatic coupler designed by applying the counterdiabatic formalism to the adiabatic coupler in Fig. 6(a). Solid white lines indicate the waveguide cores. (b) Fractional power evolution in the two waveguides.

Fig. 8
Fig. 8

(a) Waveguide geometry and BPM simulation of light propagation in a 500 μm adiabatic coupler. Solid white lines indicate the waveguide cores. (b) Waveguide geometry and BPM simulation of light propagation in the corresponding 500 μm counterdiabatic coupler. Solid white lines indicate the waveguide cores.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

d d z [ A 1 A 2 ] = i [ Δ κ κ Δ ] [ A 1 A 2 ] = i H 0 [ A 1 A 2 ] ,
H c d = i h ¯ U ˙ U = 1 2 [ 0 i κ a ( z ) i κ a ( z ) 0 ] = 1 2 κ a σ y ,
H 0 + H c d = [ Δ k e i ϕ k e i ϕ Δ ] ,
U z = [ e i ϕ / 2 0 0 e i ϕ / 2 ] ,
U z ( H 0 + H c d i h ¯ U ˙ z U z ) U z = κ s σ x + Δ s σ z ,

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