Abstract

Quantum state transfer in optical microcavities plays an important role in quantum information processing and is essential in many optical devices such as optical frequency converters and diodes. Existing schemes are effective and realized by tuning the coupling strengths between modes. However, such approaches are severely restricted due to the small amount of strength that can be tuned and the difficulty performing the tuning in some situations, such as in an on-chip microcavity system. Here we propose a novel approach that realizes the state transfer between different modes in optical microcavities by tuning the frequency of an intermediate mode. We show that for typical functions of frequency tuning, such as linear and periodic functions, the state transfer can be realized successfully with different features. To optimize the process, we use the gradient descent technique to find an optimal tuning function for a fast and perfect state transfer. We also showed that our approach has significant nonreciprocity with appropriate tuning variables, where one can unidirectionally transfer a state from one mode to another, but the inverse direction transfer is forbidden. This work provides an effective method for controlling the multimode interactions in on-chip optical microcavities via simple operations, and it has practical applications in all-optical devices.

© 2020 Chinese Laser Press

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References

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2020 (1)

2019 (6)

2018 (5)

2017 (8)

X. Jiang, L. Shao, S.-X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y.-F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358, 344–347 (2017).
[Crossref]

C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing,” Rev. Mod. Phys. 89, 035002 (2017).
[Crossref]

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

N. Zhang, Z. Gu, S. Liu, Y. Wang, S. Wang, Z. Duan, W. Sun, Y.-F. Xiao, S. Xiao, and Q. Song, “Far-field single nanoparticle detection and sizing,” Optica 4, 1151–1156 (2017).
[Crossref]

Z.-H. Zhou, C.-L. Zou, Y. Chen, Z. Shen, G.-C. Guo, and C.-H. Dong, “Broadband tuning of the optical and mechanical modes in hollow bottle-like microresonators,” Opt. Express 25, 4046–4053 (2017).
[Crossref]

X. Zhou, B.-J. Liu, L. Shao, X.-D. Zhang, and Z.-Y. Xue, “Quantum state conversion in opto-electro-mechanical systems via shortcut to adiabaticity,” Laser Phys. Lett. 14, 095202 (2017).
[Crossref]

B.-C. Ren and F.-G. Deng, “Robust hyperparallel photonic quantum entangling gate with cavity qed,” Opt. Express 25, 10863–10873 (2017).
[Crossref]

M. C. Kuzyk and H. Wang, “Controlling multimode optomechanical interactions via interference,” Phys. Rev. A 96, 023860 (2017).
[Crossref]

2016 (5)

J.-Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116, 163602 (2016).
[Crossref]

Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10, 657–661 (2016).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref]

A. Baksic, H. Ribeiro, and A. A. Clerk, “Speeding up adiabatic quantum state transfer by using dressed states,” Phys. Rev. Lett. 116, 230503 (2016).
[Crossref]

X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 023001 (2016).
[Crossref]

2015 (6)

Y. Liang, Q.-C. Wu, S.-L. Su, X. Ji, and S. Zhang, “Shortcuts to adiabatic passage for multiqubit controlled-phase gate,” Phys. Rev. A 91, 032304 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

X.-Y. Lü, H. Jing, J.-Y. Ma, and Y. Wu, “PT-symmetry-breaking chaos in optomechanics,” Phys. Rev. Lett. 114, 253601 (2015).
[Crossref]

M. Gao, F.-C. Lei, C.-G. Du, and G.-L. Long, “Self-sustained oscillation and dynamical multistability of optomechanical systems in the extremely-large-amplitude regime,” Phys. Rev. A 91, 013833 (2015).
[Crossref]

F.-C. Lei, M. Gao, C. Du, Q.-L. Jing, and G.-L. Long, “Three-pathway electromagnetically induced transparency in coupled-cavity optomechanical system,” Opt. Express 23, 11508–11517 (2015).
[Crossref]

X. Jiang, M. Wang, M. C. Kuzyk, T. Oo, G.-L. Long, and H. Wang, “Chip-based silica microspheres for cavity optomechanics,” Opt. Express 23, 27260–27265 (2015).
[Crossref]

2014 (7)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

H. Jing, S. Özdemir, X.-Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity–time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators,” Nat. Photonics 8, 524–529 (2014).
[Crossref]

T.-J. Wang and C. Wang, “Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator,” Phys. Rev. A 90, 052310 (2014).
[Crossref]

Y.-H. Chen, Y. Xia, Q.-Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

2013 (6)

W. Chen, K. M. Beck, R. Bücker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V. Vuletić, “All-optical switch and transistor gated by one stored photon,” Science 341, 768–770 (2013).
[Crossref]

H.-R. Wei and F.-G. Deng, “Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities,” Phys. Rev. A 88, 042323 (2013).
[Crossref]

R. Henze, J. M. Ward, and O. Benson, “Temperature independent tuning of whispering gallery modes in a cryogenic environment,” Opt. Express 21, 675–680 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, and J. C. Gates, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

K. Xia and J. Twamley, “All-optical switching and router via the direct quantum control of coupling between cavity modes,” Phys. Rev. X 3, 031013 (2013).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110, 153606 (2013).
[Crossref]

2012 (4)

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

L. Tian, “Adiabatic state conversion and pulse transmission in optomechanical systems,” Phys. Rev. Lett. 108, 153604 (2012).
[Crossref]

Y.-D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. 108, 153603 (2012).
[Crossref]

Y.-D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14, 105010 (2012).
[Crossref]

2011 (2)

2010 (3)

D. A. Miller, “Are optical transistors the logical next step?” Nat. Photonics 4, 3–5 (2010).
[Crossref]

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

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

2009 (1)

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

2007 (1)

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488–490 (2007).
[Crossref]

2006 (1)

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[Crossref]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

2001 (2)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763–809 (2001).
[Crossref]

W. Von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26, 166–168 (2001).
[Crossref]

2000 (1)

C. Hood, T. Lynn, A. Doherty, A. Parkins, and H. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287, 1447–1453 (2000).
[Crossref]

1998 (2)

K. Bergmann, H. Theuer, and B. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

V. Ilchenko, P. Volikov, V. Velichansky, F. Treussart, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Strain-tunable high-Q optical microsphere resonator,” Opt. Commun. 145, 86–90 (1998).
[Crossref]

1997 (1)

J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997).
[Crossref]

Ai, Q.

S.-S. Chen, H. Zhang, Q. Ai, and G.-J. Yang, “Phononic entanglement concentration via optomechanical interactions,” Phys. Rev. A 100, 052306 (2019).
[Crossref]

H. Zhang, X.-K. Song, Q. Ai, H. Wang, G.-J. Yang, and F.-G. Deng, “Fast and robust quantum control for multimode interactions using shortcuts to adiabaticity,” Opt. Express 27, 7384–7392 (2019).
[Crossref]

G.-Y. Wang, T. Li, Q. Ai, A. Alsaedi, T. Hayat, and F.-G. Deng, “Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems,” Phys. Rev. Appl. 10, 054058 (2018).
[Crossref]

X.-K. Song, H. Zhang, Q. Ai, J. Qiu, and F.-G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 023001 (2016).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Schematic diagram for the model of multimode interactions in optical microcavities. All the modes have very narrow linewidths. A mode in one cavity couples to two different optical modes (a) in the same cavity and (b) in two different cavities separately. (c) Resonance frequency tuning of the intermediate cavity to induce state transfer. The tuning domain is divided into three parts labelled I, II, and III.
Fig. 2.
Fig. 2. Result of FIST between a1 and a2 by linearly tuning the resonance frequency of at. The speed is chosen as 0.08δ2. The inset is the plot of tuning function, and the unit of time t is δ1.
Fig. 3.
Fig. 3. Simulation of final population of mode a2 affected by tuning variables. The units d and v are chosen as δ and δ2, respectively. (a) Population P versus tuning range d with v=0.27δ2. All Δ0 are chosen as Δ0=(δd)/2. (b) Population P versus tuning speed v with d=2.65δ and Δ0=0.825δ. (c) Population P versus tuning range d and tuning speed v. The dashed line shows all the points of evolution time with 10δ1.
Fig. 4.
Fig. 4. Population change with respect to evolution time via sine tuning function. Lines labeled with a1, a2, and at are the populations of the corresponding modes.
Fig. 5.
Fig. 5. Simulation of fast FIST from a1 to a2 by using the gradient descent technique. The parameters are the cross points of Fig. 3(c) with d=2.65δ, v=0.27δ2. (a) Result of the optimized population transfer process. (b) Corresponding optimal tuning function of the intermediate mode. The unit of time here is δ1.
Fig. 6.
Fig. 6. Nonreciprocal state transfer between modes a1 and a2. (a) Populations of modes a1 and a2 versus tuning speed. The tuning range is d=14δ. (b) Populations of modes a1 and a2 versus tuning range. The tuning speed is v=0.1δ2. (c) Order difference between the populations of a2 and a1, log10[P(a2)]log10[P(a1)], in the parameter spaces of tuning speed and tuning range.
Fig. 7.
Fig. 7. All-optical on-chip microcavity structures. (a) One-dimensional microcavity array. (b) Two-dimensional optical microcavity lattice.

Equations (8)

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H1=δa2a2+Δ(t)atat+g1a1at+g2a2at+H.c.,
M(t)=[0g10g1Δ(t)g20g2δ].
a(t)=U(t,0)a(0),
a(t1)=U(Δ1,,Δn;t1,0)a(0).
L(a,t1)=L(Δ1,,Δn;t1,0).
L=(L1,,Ln),
Li=L(,Δi+δΔ,;t1,0)L(Δ1,,Δn;t1,0)δΔ.
ΔII(t)=Asin[(Ωt+θ)+C1](eγt+C2),