Perfect optomechanically induced transparency in two-cavity optomechanics

doi:10.1007/s11467-023-1279-1

Front. Phys.

2023, Vol. 18

Issue (5) : 52301 https://doi.org/10.1007/s11467-023-1279-1

RESEARCH ARTICLE

Perfect optomechanically induced transparency in two-cavity optomechanics

Lai-Bin Qian, Xiao-Bo Yan(

)

School of Physics and Electronic Engineering, Northeast Petroleum University, Daqing 163318, China

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Abstract

Here, we study the controllable optical responses in a two-cavity optomechanical system, especially on the perfect optomechanically induced transparency (OMIT) in the model which has never been studied before. The results show that the perfect OMIT can still occur even with a large mechanical damping rate, and at the perfect transparency window the long-lived slow light can be achieved. In addition, we find that the conversion between the perfect OMIT and optomechanically induced absorption can be easily achieved just by adjusting the driving field strength of the second cavity. We believe that the results can be used to control optical transmission in modern optical networks.

Keywords perfect optomechanically induced transparency slow light optomechanically induced absorption cavity optomechanics

Corresponding Author(s): Xiao-Bo Yan

Issue Date: 07 April 2023

Cite this article:

Lai-Bin Qian,Xiao-Bo Yan. Perfect optomechanically induced transparency in two-cavity optomechanics[J]. Front. Phys. , 2023, 18(5): 52301.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1279-1
https://academic.hep.com.cn/fop/EN/Y2023/V18/I5/52301

Fig.1 Sketch of a two-cavity optomechanical system consists of a mechanical membrane with frequency

ω m

interacted with cavity

a^1

and

a^2

via radiation pressure. The cavity

a^1

is driven by a coupling field

ε c

with frequency

ω c

and a weak probe field

ε p

with frequency

ω p

. The cavity

a^2

is driven by a driving field

ε d

with frequency

ω d

Fig.2 The real part

Re [ε T]

(red-solid) vs. frequency detuning

x

with parameters

ω m = κ 1 = κ 2 = 104

γ m = 1

β 1 = 3 × 104

and

β 2 = 1250

according to Eq. (9). The blue-dashed line indicates width

Γ OMIT

. The inset shows the OMIT profile in a large scale.

Fig.3 The real part

Re [ε T]

vs. frequency detuning

x

for large mechanical damping rate

γ m = 10

(red-solid) with

β 1 = 3 × 105

and

β 2 = 1.25 × 104

according to Eq. (9), and for

γ m = 100

(blue-dashed) with

β 1 = 3 × 106

and

β 2 = 1.25 × 105

according to Eq. (9). The other parameters are same as Fig.2.

Fig.4 The imaginary part

Im [ε T]

vs. frequency detuning

x

with the same parameters as those in Fig.3.

Fig.5 The real part

Re [ε T]

vs. frequency detuning

x

for

κ 2 = 10

with parameters

ω m = 104

κ 1 = 4 × 103

γ m = 1

β 1 = 105

and

β 2 = 5.91

. The inset shows a zoom-in of the transparency window at

x ≃ − 5.55

Fig.6 The time delay

τ

vs. frequency detuning

x

for

γ m = 1

(red-solid) with

β 1 = 3 × 104

and

β 2 = 1250

(same as Fig.2), and for

γ m = 10

(blue-dashed) with

β 1 = 3 × 105

and

β 2 = 1.25 × 104

(same as Fig.3). The other parameters are

ω m = κ 1 = κ 2 = 104

Fig.7 The time delay

τ

vs. frequency detuning

x

for

κ 1 = κ 2 = 2 × 104

(red-solid) with

β 1 = 3 × 104

and

β 2 = 104

according to Eq. (9), and for

κ 1 = κ 2 = 8 × 103

(blue-dashed) with

β 1 = 3 × 104

and

β 2 = 160

according to Eq. (9). The other parameters are

ω m = 104

and

γ m = 1

Fig.8 The real part

Re [ε T]

vs. frequency detuning

x

for

κ 2 = 10

(blue-dashed) and

κ 2 = 1

(red-solid) with parameters

κ 1 = 4 × 103

ω m = 104

γ m = 1

β 1 = 105

and

β 2 = 100

Fig.9 The real part

Re [ε T]

vs. frequency detuning

x

for

β 2 = 5.91

(blue-dashed) and

β 2 = 105

(red-solid) with parameters

ω m = 104

κ 1 = 4 × 103

γ m = 1

β 1 = 105

and

κ 2 = 10

. The inset shows a zoom-in of the transparency window at

x ≃ − 5.55

1	Aspelmeyer M., J. Kippenberg T., Marquardt F.. Cavity optomechanics. Rev. Mod. Phys., 2014, 86(4): 1391 https://doi.org/10.1103/RevModPhys.86.1391
2	Gigan S., Böhm H., Paternostro M., Blaser F., Langer G., Hertzberg J., Schwab K., Bäuerle D., Aspelmeyer M., Zeilinger A.. Self-cooling of a micromirror by radiation pressure. Nature, 2006, 444(7115): 67 https://doi.org/10.1038/nature05273
3	Arcizet O., F. Cohadon P., Briant T., Pinard M., Heidmann A.. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature, 2006, 444(7115): 71 https://doi.org/10.1038/nature05244
4	J. Kippenberg T., Rokhsari H., Carmon T., Scherer A., J. Vahala K.. Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity. Phys. Rev. Lett., 2005, 95(3): 033901 https://doi.org/10.1103/PhysRevLett.95.033901
5	Tomes M., Carmon T.. Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates. Phys. Rev. Lett., 2009, 102(11): 113601 https://doi.org/10.1103/PhysRevLett.102.113601
6	Jiang X., Lin Q., Rosenberg J., Vahala K., Painter O.. High-Q double-disk microcavities for cavity optomechanics. Opt. Express, 2009, 17(23): 20911 https://doi.org/10.1364/OE.17.020911
7	A. Regal C., D. Teufel J., W. Lehnert K.. Measuring nanomechanical motion with a microwave cavity interferometer. Nat. Phys., 2008, 4(7): 555 https://doi.org/10.1038/nphys974
8	D. Teufel J., Li D., S. Allman M., Cicak K., J. Sirois A., D. Whittaker J., W. Simmonds R.. Circuit cavity electromechanics in the strong-coupling regime. Nature, 2011, 471(7337): 204 https://doi.org/10.1038/nature09898
9	D. Thompson J., M. Zwickl B., M. Jayich A., Marquardt F., M. Girvin S., G. E. Harris J.. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature, 2008, 452(7183): 72 https://doi.org/10.1038/nature06715
10	M. Jayich A., C. Sankey J., M. Zwickl B., Yang C., D. Thompson J., M. Girvin S., A. Clerk A., Marquardt F., G. E. Harris J.. Dispersive optomechanics: A membrane inside a cavity. New J. Phys., 2008, 10(9): 095008 https://doi.org/10.1088/1367-2630/10/9/095008
11	C. Sankey J., Yang C., M. Zwickl B., M. Jayich A., G. E. Harris J.. Strong and tunable nonlinear optomechanical coupling in a low-loss system. Nat. Phys., 2010, 6(9): 707 https://doi.org/10.1038/nphys1707
12	Karuza M., Biancofiore C., Bawaj M., Molinelli C., Galassi M., Natali R., Tombesi P., Di Giuseppe G., Vitali D.. Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature. Phys. Rev. A, 2013, 88(1): 013804 https://doi.org/10.1103/PhysRevA.88.013804
13	Marquardt F., P. Chen J., A. Clerk A., M. Girvin S.. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett., 2007, 99(9): 093902 https://doi.org/10.1103/PhysRevLett.99.093902
14	Wilson-Rae I., Nooshi N., Zwerger W., J. Kippenberg T.. Theory of ground state cooling of a mechanical oscillator using dynamical backaction. Phys. Rev. Lett., 2007, 99(9): 093901 https://doi.org/10.1103/PhysRevLett.99.093901
15	He B., Yang L., Lin Q., Xiao M.. Radiation pressure cooling as a quantum dynamical process. Phys. Rev. Lett., 2017, 118(23): 233604 https://doi.org/10.1103/PhysRevLett.118.233604
16	Y. Wang D., H. Bai C., Liu S., Zhang S., F. Wang H.. Optomechanical cooling beyond the quantum backaction limit with frequency modulation. Phys. Rev. A, 2018, 98(2): 023816 https://doi.org/10.1103/PhysRevA.98.023816
17	Y. Yang J., Y. Wang D., H. Bai C., Y. Guan S., Y. Gao X., D. Zhu A., F. Wang H.. Ground-state cooling of mechanical oscillator via quadratic optomechanical coupling with two coupled optical cavities. Opt. Express, 2019, 27(16): 22855 https://doi.org/10.1364/OE.27.022855
18	Wang J.. Ground-state cooling based on a three-cavity optomechanical system in the unresolved-sideband regime. Chin. Phys. B, 2021, 30(2): 024204 https://doi.org/10.1088/1674-1056/abc159
19	He Q., Badshah F., Song Y., Wang L., Liang E., L. Su S.. Force sensing and cooling for the mechanical membrane in a hybrid optomechanical system. Phys. Rev. A, 2022, 105(1): 013503 https://doi.org/10.1103/PhysRevA.105.013503
20	Yang J., Zhao C., Yang Z., Peng R., Chao S., Zhou L.. Nonreciprocal ground-state cooling of mechanical resonator in a spinning optomechanical system. Front. Phys., 2022, 17(5): 52507 https://doi.org/10.1007/s11467-022-1202-1
21	Li J., Li G., Zippilli S., Vitali D., Zhang T.. Enhanced entanglement of two different mechanical resonators via coherent feedback. Phys. Rev. A, 2017, 95(4): 043819 https://doi.org/10.1103/PhysRevA.95.043819
22	H. Bai C., Y. Wang D., F. Wang H., D. Zhu A., Zhang S.. Robust entanglement between a movable mirror and atomic ensemble and entanglement transfer in coupled optomechanical system. Sci. Rep., 2016, 6(1): 33404 https://doi.org/10.1038/srep33404
23	B. Yan X.. Enhanced output entanglement with reservoir engineering. Phys. Rev. A, 2017, 96(5): 053831 https://doi.org/10.1103/PhysRevA.96.053831
24	J. Deng Z., B. Yan X., D. Wang Y., W. Wu C.. Optimizing the output-photon entanglement in multimode optomechanical systems. Phys. Rev. A, 2016, 93(3): 033842 https://doi.org/10.1103/PhysRevA.93.033842
25	B. Yan X., J. Deng Z., D. Tian X., H. Wu J.. Entanglement optimization of filtered output fields in cavity optomechanics. Opt. Express, 2019, 27(17): 24393 https://doi.org/10.1364/OE.27.024393
26	T. Chen Y., Du L., Zhang Y., H. Wu J.. Perfect transfer of enhanced entanglement and asymmetric steering in a cavity-magnomechanical system. Phys. Rev. A, 2021, 103(5): 053712 https://doi.org/10.1103/PhysRevA.103.053712
27	Y. Guan S., F. Wang H., X. Yi X.. Cooperative-effect-induced one-way steering in open cavity magnonics. npj Quantum Inf., 2022, 8: 102 https://doi.org/10.1038/s41534-022-00619-y
28	Zeng Y., Xiong B., Li C.. Suppressing laser phase noise in an optomechanical system. Front. Phys., 2022, 17(1): 12503 https://doi.org/10.1007/s11467-021-1097-2
29	H. Bai C., Y. Wang D., Zhang S., Liu S., F. Wang H.. Engineering of strong mechanical squeezing via the joint effect between Duffing nonlinearity and parametric pump driving. Photon. Res., 2019, 7(11): 1229 https://doi.org/10.1364/PRJ.7.001229
30	J. Feng L., Yan L., Q. Gong S.. Unconventional photon blockade induced by the self-Kerr and cross-Kerr nonlinearities. Front. Phys., 2023, 18(1): 12304 https://doi.org/10.1007/s11467-022-1213-y
31	Qu K. and Agarwal G. S. , Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems, Phys. Rev. A 87, 031802(R) (2013)
32	S. Agarwal G., Huang S.. Nanomechanical inverse electromagnetically induced transparency and confinement of light in normal modes. New J. Phys., 2014, 16(3): 033023 https://doi.org/10.1088/1367-2630/16/3/033023
33	Wang J.. Optomechanically induced tunable ideal nonreciprocity in optomechanical system with Coulomb interaction. Quantum Inform. Process., 2022, 21(7): 238 https://doi.org/10.1007/s11128-022-03587-6
34	He B. , Yang L. , and Xiao M. , Dynamical phonon laser in coupled active-passive microresonators, Phys. Rev. A 94, 031802(R) (2016)
35	Du L., M. Liu Y., Jiang B., Zhang Y.. All-optical photon switching, router and amplifier using a passive-active optomechanical system. EPL, 2018, 122(2): 24001 https://doi.org/10.1209/0295-5075/122/24001
36	C. Xia C., B. Yan X., D. Tian X., Gao F.. Ideal optical isolator with a two-cavity optomechanical system. Opt. Commun., 2019, 451: 197 https://doi.org/10.1016/j.optcom.2019.06.059
37	B. Yan X., L. Cui C., H. Gu K., D. Tian X., B. Fu C., H. Wu J.. Coherent perfect absorption, transmission, and synthesis in a double-cavity optomechanical system. Opt. Express, 2014, 22(5): 4886 https://doi.org/10.1364/OE.22.004886
38	B. Yan X., L. Lu H., Gao F., Yang L.. Perfect optical nonreciprocity in a double-cavity optomechanical system. Front. Phys., 2019, 14(5): 52601 https://doi.org/10.1007/s11467-019-0922-3
39	T. Chen Y., Du L., M. Liu Y., Zhang Y.. Dual-gate transistor amplifier in a multimode optomechanical system. Opt. Express, 2020, 28(5): 7095 https://doi.org/10.1364/OE.385049
40	Wang T., H. Bai C., Y. Wang D., Liu S., Zhang S., F. Wang H.. Optomechanically induced Faraday and splitting effects in a double-cavity optomechanical system. Phys. Rev. A, 2021, 104(1): 013721 https://doi.org/10.1103/PhysRevA.104.013721
41	Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice. Front. Phys., 2021, 16(1): 12503 https://doi.org/10.1007/s11467-020-0983-3
42	R. Zhong Z., Chen L., Q. Sheng J., T. Shen L., B. Zheng S.. Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system. Front. Phys., 2022, 17(1): 12501 https://doi.org/10.1007/s11467-021-1092-7
43	Shahidani S., H. Naderi M., Soltanolkotabi M.. Control and manipulation of electromagnetically induced transparency in a nonlinear optomechanical system with two movable mirrors. Phys. Rev. A, 2013, 88(5): 053813 https://doi.org/10.1103/PhysRevA.88.053813
44	X. Liu Y., Davanco M., Aksyuk V., Srinivasan K.. Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators. Phys. Rev. Lett., 2013, 110(22): 223603 https://doi.org/10.1103/PhysRevLett.110.223603
45	Pan G., Xiao R., Chen H., Gao J.. Multicolor optomechanically induced transparency in a distant nano-electro-optomechanical system assisted by two-level atomic ensemble. Laser Phys., 2021, 31(6): 065202 https://doi.org/10.1088/1555-6611/abfe57
46	Xiong H., G. Si L., S. Zheng A., Yang X., Wu Y.. Higher-order sidebands in optomechanically induced transparency. Phys. Rev. A, 2012, 86(1): 013815 https://doi.org/10.1103/PhysRevA.86.013815
47	B. Yan X.. Optomechanically induced transparency and gain. Phys. Rev. A, 2020, 101(4): 043820 https://doi.org/10.1103/PhysRevA.101.043820
48	Agarwal G. S. and Huang S. , Electromagnetically induced transparency in mechanical effects of light, Phys. Rev. A 81, 041803(R) (2010)
49	Bodiya T., Sudhir V., Wipf C., Smith N., Buikema A., Kontos A., Yu H., Mavalvala N.. Sub-Hertz optomechanically induced transparency with a kilogram-scale mechanical oscillator. Phys. Rev. A, 2019, 100(1): 013853 https://doi.org/10.1103/PhysRevA.100.013853
50	Kronwald A., Marquardt F.. Optomechanically induced transparency in the nonlinear quantum regime. Phys. Rev. Lett., 2013, 111: 133601 https://doi.org/10.1103/PhysRevLett.111.133601
51	Jing H., K. Özdemir S., Geng Z., Zhang J., Y. Lü X., Peng B., Yang L., Nori F.. Optomechanically-induced transparency in parity−time-symmetric microresonators. Sci. Rep., 2015, 5(1): 9663 https://doi.org/10.1038/srep09663
52	Li W., Jiang Y., Li C., Song H.. Parity−time-symmetry enhanced optomechanically-induced-transparency. Sci. Rep., 2016, 6(1): 31095 https://doi.org/10.1038/srep31095
53	C. Liu Y., B. Li B., F. Xiao Y.. Electromagnetically induced transparency in optical microcavities. Nanophotonics, 2017, 6(5): 789 https://doi.org/10.1515/nanoph-2016-0168
54	Weis S., Rivie’re R., Deléglise S., Gavartin E., Arcizet O., Schliesser A., J. Kippenberg T.. Optomechanically induced transparency. Science, 2010, 330(6010): 1520 https://doi.org/10.1126/science.1195596
55	B. Yan X., H. Gu K., B. Fu C., L. Cui C., Wang R., H. Wu J.. Optical switching of optomechanically induced transparency and normal mode splitting in a double-cavity system. Eur. Phys. J. D, 2014, 68(5): 126 https://doi.org/10.1140/epjd/e2014-40760-0
56	H. Safavi-Naeini A., P. M. Alegre T., Chan J., Eichenfield M., Winger M., Lin Q., T. Hill J., E. Chang D., Painter O.. Electromagnetically induced transparency and slow light with optomechanics. Nature, 2011, 472(7341): 69 https://doi.org/10.1038/nature09933
57	B. Yan X.. Optomechanically induced optical responses with non-rotating wave approximation. J. Phys. At. Mol. Opt. Phys., 2021, 54(3): 035401 https://doi.org/10.1088/1361-6455/abd645
58	Chen B., Jiang C., D. Zhu K.. Slow light in a cavity optomechanical system with a Bose−Einstein condensate. Phys. Rev. A, 2011, 83(5): 055803 https://doi.org/10.1103/PhysRevA.83.055803
59	Tarhan D., Huang S., E. Müstecaplioğlu Ö.. Superluminal and ultraslow light propagation in optomechanical systems. Phys. Rev. A, 2013, 87(1): 013824 https://doi.org/10.1103/PhysRevA.87.013824
60	H. Gu K., B. Yan X., Zhang Y., B. Fu C., M. Liu Y., Wang X., H. Wu J.. Tunable slow and fast light in an atom-assisted optomechanical system. Opt. Commun., 2015, 338: 569 https://doi.org/10.1016/j.optcom.2014.11.036
61	E. Chang D., H. Safavi-Naeini A., Hafezi M., Painter O.. Slowing and stopping light using an optomechanical crystal array. New J. Phys., 2011, 13(2): 023003 https://doi.org/10.1088/1367-2630/13/2/023003
62	J. Akram M., M. Khan M., Saif F.. Tunable fast and slow light in a hybrid optomechanical system. Phys. Rev. A, 2015, 92(2): 023846 https://doi.org/10.1103/PhysRevA.92.023846
63	B. Yan X.. Optomechanically induced ultraslow and ultrafast light. Physica E, 2021, 131: 114759 https://doi.org/10.1016/j.physe.2021.114759
64	Wang L., T. Chen Y., Yin K., Zhang Y.. Nonreciprocal transmission and asymmetric fast–slow light effect in an optomechanical system with two PT-symmetric mechanical resonators. Laser Phys., 2020, 30(10): 105205 https://doi.org/10.1088/1555-6611/abb1be
65	N. Zhao Y., Wang T., Y. Wang D., Han X., Zhang S., F. Wang H.. Optical amplification and fast-slow light in a three-mode cavity optomechanical system without rotating wave approximation. Photonics, 2021, 8(9): 384 https://doi.org/10.3390/photonics8090384
66	W. Xu X., Li Y.. Optical nonreciprocity and optomechanical circulator in three-mode optomechanical systems. Phys. Rev. A, 2015, 91(5): 053854 https://doi.org/10.1103/PhysRevA.91.053854
67	R. Bernier N., D. Tóth L., Koottandavida A., A. Ioannou M., Malz D., Nunnenkamp A., K. Feofanov A., J. Kippenberg T.. Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun., 2017, 8(1): 604 https://doi.org/10.1038/s41467-017-00447-1
68	Ludwig M., H. Safavi-Naeini A., Painter O., Marquardt F.. Enhanced quantum nonlinearities in a two-mode optomechanical system. Phys. Rev. Lett., 2012, 109(6): 063601 https://doi.org/10.1103/PhysRevLett.109.063601
69	Y. Lü X., M. Zhang W., Ashhab S., Wu Y., Nori F.. Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems. Sci. Rep., 2013, 3(1): 2943 https://doi.org/10.1038/srep02943
70	Tian L.. Robust photon entanglement via quantum interference in optomechanical interfaces. Phys. Rev. Lett., 2013, 110(23): 233602 https://doi.org/10.1103/PhysRevLett.110.233602
71	Nunnenkamp A., Børkje K., M. Girvin S.. Single-photon optomechanics. Phys. Rev. Lett., 2011, 107(6): 063602 https://doi.org/10.1103/PhysRevLett.107.063602
72	Nunnenkamp A., Sudhir V., K. Feofanov A., Roulet A., J. Kippenberg T.. Quantum-limited amplification and parametric instability in the reversed dissipation regime of cavity optomechanics. Phys. Rev. Lett., 2014, 113(2): 023604 https://doi.org/10.1103/PhysRevLett.113.023604
73	Barzanjeh Sh., Abdi M., J. Milburn G., Tombesi P., Vitali D.. Reversible optical-to-microwave quantum interface. Phys. Rev. Lett., 2012, 109(13): 130503 https://doi.org/10.1103/PhysRevLett.109.130503
74	S. Bigelow M., N. Lepeshkin N., W. Boyd R.. Superluminal and slow light propagation in a room-temperature solid. Science, 2003, 301(5630): 200 https://doi.org/10.1126/science.1084429

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