Spinning microresonator-induced chiral optical transmission

doi:10.1007/s11467-022-1212-z

Front. Phys.

2023, Vol. 18

Issue (1) : 12305 https://doi.org/10.1007/s11467-022-1212-z

RESEARCH ARTICLE

Spinning microresonator-induced chiral optical transmission

Lu Bo¹, Xiao-Fei Liu¹(

), Chuan Wang², Tie-Jun Wang¹(

)

¹. State Key Laboratory of Information Photonics and Optical Communications and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
². School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China

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Abstract

Chiral quantum optics is a new research area in light-matter interaction that depends on the direction of light propagation and offers a new path for the quantum regulation of light-matter interactions. In this paper, we study a spinning Kerr-type microresonator coupled with Λ-type atom ensembles, which are driven in opposite directions to generate asymmetric photon statistics. We find that a photon blockade can only be generated by driving the spinning resonator on right side without driving the spinning microresonator from the left side, resulting in chirality. The coupling strength between system modes can be precisely controlled by adjusting the detuning amount of the atomic pump field. Because of the splitting of the resonant frequency generated by the Fizeau drag, the destructive quantum interference generated in right side drive prevents the nonresonant transition path of state |1,0⟩ to state |2,0⟩. This direction-dependent chiral quantum optics is expected to be applied to chiral optical devices, single-photon sources and nonreciprocal quantum communications.

Keywords chiral quantum optics spinning microresonator nonreciprocal photon blockade

Corresponding Author(s): Xiao-Fei Liu,Tie-Jun Wang

Issue Date: 30 November 2022

Cite this article:

Lu Bo,Xiao-Fei Liu,Chuan Wang, et al. Spinning microresonator-induced chiral optical transmission[J]. Front. Phys. , 2023, 18(1): 12305.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1212-z
https://academic.hep.com.cn/fop/EN/Y2023/V18/I1/12305

Fig.1 (a) Illustration of a spinning resonator coupled atom ensemble. The spinning resonator rotates counterclockwise at angular velocity

Ω

, and both CW and CCW modes are excited simultaneously in the microcavity. When a probe signal is input from port 1 (or port 2) or a transmission is detected from port 4 (or port 3), the intrinsic dissipation of the resonator is

κ 0

, and the dissipation of coupling with the fibers on both sides is

κ 1 e x t

and

κ 2 e x t

. (b) Fizeau drag

Δ F

versus angular velocity

Ω

of the resonator for the CCW (red line) and CW (blue line) cases. (c) The

Λ

-type energy level of the atom and its interaction with the cavity mode and external control field. The parameters are as follows: the optical wavelength is

λ

= 1550 nm, the radius of the resonator is

r = 100 μ m

, the coupling strength between cavity modes (CW and CCW) is J, and the linear refractive index of the resonator is

n

= 1.4.

Fig.2 Equal-time second-order correlation functions

g (2) (0)

as functions of the couple strength, detuning

Δ

, and rotation speed

Ω

. (a) The change in second-order coherence functions

g L (2) (0)

with coupling strength when the system is driven on the left. (b) The change in second-order correlation functions

g (2) (0)

with the effective detuning

Δ ′ / κ

under different driving directions. At

Δ / κ ≃ 0.085

, by driving the resonator on the left or right side, different properties will appear, with the right side driving for photon blockade and the left side for photon bunching. A nonspinning resonator is represented by a green line. (c) The second-order correlation functions

g (2) (0)

plotted as functions of the rotation speed

Ω

. The blue and red solid lines represent

g (2) (0)

of the system driven by the left and the right when

Ω = 5 k H z

, and the dotted line represents the case of

Ω = 10

kHz. The parameters are chosen as the coupling strength

g 12

and

g 21 = 3 κ

ε = 0.01 κ

n = 1.4

r = 100 μ

Q = 2.5 × 108

Ω = 5

kHz (

Δ F / κ = 0.3

κ = 5

MHz,

U = 0.05 κ

and

λ = 1550

nm.

Fig.3 (a) Dependence of parameter

Γ

on the effective detuning

Δ ′ / κ

and the spinning speed

Ω

. Other parameters, the nonlinear interaction strength

U / κ = 0.05

and the coupling strength

| g | = 3 κ

. (b) The equal-time second-order correlation functions

g (2) (0)

as functions of the spinning speed

Ω

. Other parameters are consistent with (a), and the amount of detuning increases from top to bottom. The red and blue lines are driven on the right side and left side, respectively.

Fig.4 The changes of the equal-time second-order correlation function

g L (2) 0

as the coupling strength

g

with the Kerr nonlinearity

U

. The marked line is the optical

U o p t

calculated from above. The detuning

Δ

is chosen as

0.105 κ

. The values of the other parameters are

ε = 0.01 κ

and

Δ F = 0.3 κ

Fig.5 The energy level diagram shows the zero-photon, single-photon and two-photon states and transition path leading to quantum interference responsible for the photon blockade (the solid green line with arrows is the transition path that is allowed to occur, the dashed red line is the transition path that is not allowed to occur, and the gray lines indicate quantum transition pathways with interference). (a) and (b) represent the photon blockade from the right drive and the photon bunching caused by the left drive, respectively.

1	R. Yennie D.. Integral quantum Hall effect for nonspecialists. Rev. Mod. Phys., 1987, 59(3): 781 https://doi.org/10.1103/RevModPhys.59.781
2	König M., Wiedmann S., Brüne C., Roth A., Buhmann H., W. Molenkamp L., L. Qi X., C. Zhang S.. Quantum spin Hall insulator state in HgTe quantum wells. Science, 2007, 318(5851): 766 https://doi.org/10.1126/science.1148047
3	X. Zhao Y.. Equivariant PT-symmetric real Chern insulators. Front. Phys., 2020, 15(1): 13603 https://doi.org/10.1007/s11467-019-0943-y
4	Serban I., Béri B., R. Akhmerov A., W. J. Beenakker C.. Domain wall in a chiral p-wave superconductor: A pathway for electrical current. Phys. Rev. Lett., 2010, 104(14): 147001 https://doi.org/10.1103/PhysRevLett.104.147001
5	Junge C., O’Shea D., Volz J., Rauschenbeutel A.. Strong coupling between single atoms and nontransversal photons. Phys. Rev. Lett., 2013, 110(21): 213604 https://doi.org/10.1103/PhysRevLett.110.213604
6	Shomroni I., Rosenblum S., Lovsky Y., Bechler O., Guendelman G., Dayan B.. All-optical routing of single photons by a one-atom switch controlled by a single photon. Science, 2014, 345(6199): 903 https://doi.org/10.1126/science.1254699
7	Mitsch R., Sayrin C., Albrecht B., Schneeweiss P., Rauschenbeutel A.. Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide. Nat. Commun., 2014, 5(1): 5713 https://doi.org/10.1038/ncomms6713
8	F. Liu X., J. Wang T., P. Gao Y., Cao C., Wang C.. Chiral microresonator assisted by Rydberg-atom ensembles. Phys. Rev. A, 2018, 98(3): 033824 https://doi.org/10.1103/PhysRevA.98.033824
9	J. Luxmoore I., A. Wasley N., J. Ramsay A., C. T. Thijssen A., Oulton R., Hugues M., Kasture S., G. Achanta V., M. Fox A., S. Skolnick M.. Interfacing spins in an InGaAs quantum dot to a semiconductor waveguide circuit using emitted photons. Phys. Rev. Lett., 2013, 110(3): 037402 https://doi.org/10.1103/PhysRevLett.110.037402
10	Holzmann D., Sonnleitner M., Ritsch H.. Self-ordering and collective dynamics of transversely illuminated pointscatterers in a 1D trap. Eur. Phys. J. D, 2014, 68(11): 352 https://doi.org/10.1140/epjd/e2014-50692-2
11	W. Shi Q., F. Wang Z., X. Li Q., L. Yang J.. Chiral selective tunneling induced graphene nanoribbon switch. Front. Phys. China, 2009, 4(3): 373 https://doi.org/10.1007/s11467-009-0027-5
12	Lodahl P., Mahmoodian S., Stobbe S., Rauschenbeutel A., Schneeweiss P., Volz J., Pichler H., Zoller P.. Chiral quantum optics. Nature, 2017, 541(7638): 473 https://doi.org/10.1038/nature21037
13	J. Kimble H.. Strong interactions of single atoms and photons in cavity QED. Phys. Scr., 1998, T76(1): 127 https://doi.org/10.1238/Physica.Topical.076a00127
14	W. Xu X., Q. Shi H., X. Chen A.. Nonreciprocal transition between two indirectly coupled energy levels. Front. Phys., 2022, 17(4): 42505 https://doi.org/10.1007/s11467-021-1138-x
15	Y. Bliokh K., J. Rodríguez-Fortuño F., Nori F., V. Zayats A.. Spin–orbit interactions of light. Nat. Photonics, 2015, 9(12): 796 https://doi.org/10.1038/nphoton.2015.201
16	Aiello A., Banzer P., Neugebauer M., Leuchs G.. From transverse angular momentum to photonic wheels. Nat. Photonics, 2015, 9(12): 789 https://doi.org/10.1038/nphoton.2015.203
17	Y. Bliokh K., Nori F.. Transverse and longitudinal angular momenta of light. Phys. Rep., 2015, 592: 1 https://doi.org/10.1016/j.physrep.2015.06.003
18	Lin Z., Ramezani H., Eichelkraut T., Kottos T., Cao H., N. Christodoulides D.. Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett., 2011, 106(21): 213901 https://doi.org/10.1103/PhysRevLett.106.213901
19	Chang L., Jiang X., Hua S., Yang C., Wen J., Jiang L., Li G., Wang G., Xiao M.. Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators. Nat. Photonics, 2014, 8(7): 524 https://doi.org/10.1038/nphoton.2014.133
20	Y. Fu Y., D. Xu Y., Y. Chen H.. Negative refraction based on purely imaginary metamaterials. Front. Phys., 2018, 13(4): 134206 https://doi.org/10.1007/s11467-018-0781-3
21	Imamoḡlu A., Schmidt H., Woods G., Deutsch M.. Strongly interacting photons in a nonlinear cavity. Phys. Rev. Lett., 1997, 79(8): 1467 https://doi.org/10.1103/PhysRevLett.79.1467
22	Q. Liao J., Law C.. Correlated two-photon transport in a one-dimensional waveguide side-coupled to a nonlinear cavity. Phys. Rev. A, 2010, 82(5): 053836 https://doi.org/10.1103/PhysRevA.82.053836
23	Miranowicz A., Paprzycka M., X. Liu Y., Bajer J., Nori F.. Two-photon and three-photon blockades in driven nonlinear systems. Phys. Rev. A, 2013, 87(2): 023809 https://doi.org/10.1103/PhysRevA.87.023809
24	P. Gao Y., F. Liu X., J. Wang T., Cao C., Wang C.. Photon excitation and photon-blockade effects in optomagnonic microcavities. Phys. Rev. A, 2019, 100(4): 043831 https://doi.org/10.1103/PhysRevA.100.043831
25	L. Xu W., P. Gao Y., J. Wang T., Wang C.. Magnon-induced optical high-order sideband generation in hybrid atom-cavity optomagnonical system. Opt. Express, 2020, 28(15): 22334 https://doi.org/10.1364/OE.394488
26	Wang K., P. Gao Y., Jiao R., Wang C.. Recent progress on optomagnetic coupling and optical manipulation based on cavity-optomagnonics. Front. Phys., 2022, 17(4): 42201 https://doi.org/10.1007/s11467-022-1165-2
27	P. Gao Y., Wang C.. Hybrid coupling optomechanical assisted nonreciprocal photon blockade. Opt. Express, 2021, 29(16): 25161 https://doi.org/10.1364/OE.431211
28	Rabl P.. Photon blockade effect in optomechanical systems. Phys. Rev. Lett., 2011, 107(6): 063601 https://doi.org/10.1103/PhysRevLett.107.063601
29	Nunnenkamp A., Børkje K., M. Girvin S.. Singlephoton optomechanics. Phys. Rev. Lett., 2011, 107(6): 063602 https://doi.org/10.1103/PhysRevLett.107.063602
30	B. Yan X., L. Lu H., Gao F., 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
31	Armani D., Kippenberg T., Spillane S., Vahala K.. Ultra-high-Q toroid microcavity on a chip. Nature, 2003, 421(6926): 925 https://doi.org/10.1038/nature01371
32	Dayan B.S. Parkins A.Aoki T.P. Ostby E.J. Vahala K.J. Kimble H., A photon turnstile dynamically regulated by one atom, Science 319(5866), 1062 (2008)
33	Braginsky V., Gorodetsky M., Ilchenko V.. Quality factor and nonlinear properties of optical whispering gallery modes. Phys. Lett. A, 1989, 137(7-8): 393 https://doi.org/10.1016/0375-9601(89)90912-2
34	Carmon T., Yang L., J. Vahala K.. Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express, 2004, 12(20): 4742 https://doi.org/10.1364/OPEX.12.004742
35	Totsuka K., Tomita M.. Optical microsphere amplification system. Opt. Lett., 2007, 32(21): 3197 https://doi.org/10.1364/OL.32.003197
36	S. Park Y., Wang H.. Resolved-sideband and cryogenic cooling of an optomechanical resonator. Nat. Phys., 2009, 5(7): 489 https://doi.org/10.1038/nphys1303
37	Weis S., Rivière 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
38	Carmon T., Rokhsari H., Yang L., J. Kippenberg T., J. Vahala K.. Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode. Phys. Rev. Lett., 2005, 94(22): 223902 https://doi.org/10.1103/PhysRevLett.94.223902
39	Monifi F., Zhang J., Ozdemir K., Peng B., Liu Y., Bo F., Nori F., Yang L.. Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nat. Photonics, 2016, 10(6): 399 https://doi.org/10.1038/nphoton.2016.73
40	P. Gao Y.Cao C.F. Lu P.Wang C., Phase-controlled photon blockade in optomechanical systems, Fundamental Research (2022) (in press)
41	W. Hu Y., F. Xiao Y., C. Liu Y., Gong Q.. Optomechanical sensing with on-chip microcavities. Front. Phys., 2013, 8(5): 475 https://doi.org/10.1007/s11467-013-0384-y
42	J. Kippenberg T., Holzwarth R., A. Diddams S.. Microresonator-based optical frequency combs. Science, 2011, 332(6029): 555 https://doi.org/10.1126/science.1193968
43	Bo F., Wang J., Cui J., K. Ozdemir S., Kong Y., Zhang G., Xu J., Yang L.. Lithium-niobate–silica hybrid whispering-gallery-mode resonators. Adv. Mater., 2015, 27(48): 8075 https://doi.org/10.1002/adma.201504722
44	T. Cao Q., Wang H., H. Dong C., Jing H., S. Liu R., Chen X., Ge L., Gong Q., F. Xiao Y.. Experimental demonstration of spontaneous chirality in a nonlinear microresonator. Phys. Rev. Lett., 2017, 118(3): 033901 https://doi.org/10.1103/PhysRevLett.118.033901
45	Peng B., K. Ozdemir S., Lei F., Monifi F., Gianfreda M., L. Long G., Fan S., Nori F., M. Bender C., Yang L.. Parity-time-symmetric whispering-gallery microcavities. Nat. Phys., 2014, 10(5): 394 https://doi.org/10.1038/nphys2927
46	Feng L., J. Wong Z., M. Ma R., Wang Y., Zhang X.. Single-mode laser by parity-time symmetry breaking. Science, 2014, 346(6212): 972 https://doi.org/10.1126/science.1258479
47	Hodaei H., A. Miri M., Heinrich M., N. Christodoulides D., Khajavikhan M.. Parity-time-symmetric microring lasers. Science, 2014, 346(6212): 975 https://doi.org/10.1126/science.1258480
48	M. Spillane S., J. Kippenberg T., J. Vahala K., W. Goh K., Wilcut E., J. Kimble H.. Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A, 2005, 71(1): 013817 https://doi.org/10.1103/PhysRevA.71.013817
49	Wang H.. Multi-peak solitons in PT-symmetric Bessel optical lattices with defects. Front. Phys., 2016, 11(5): 114204 https://doi.org/10.1007/s11467-016-0569-2
50	Zhu J., K. Ozdemir S., Xiao Y., Li L., He L., Chen D., Yang L.. On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator. Nat. Photonics, 2010, 30(2): 4,46
51	Zhi Y., C. Yu X., Gong Q., Yang L., F. Xiao Y.. Single nanoparticle detection using optical microcavities. Adv. Mater., 2017, 29(12): 1604920 https://doi.org/10.1002/adma.201604920
52	Reynolds T., Riesen N., Meldrum A., Fan X., M. M. Hall J., M. Monro T., François A.. Fluorescent and lasing whispering gallery mode microresonators for sensing applications. Laser Photonics Rev., 2017, 11(2): 1600265 https://doi.org/10.1002/lpor.201600265
53	X. Zhang L., Zhang R., Q. Li Z.. Study on a vapor sensor based on the optical properties of porous silicon microcavities. Front. Phys. China, 2007, 2(2): 166 https://doi.org/10.1007/s11467-007-0035-2
54	Maayani S., Dahan R., Kligerman Y., Moses E., U. Hassan A., Jing H., Nori F., N. Christodoulides D., Carmon T.. Flying couplers above spinning resonators generate irreversible refraction. Nature, 2018, 558(7711): 569 https://doi.org/10.1038/s41586-018-0245-5
55	Huang R., Miranowicz A., Q. Liao J., Nori F., Jing H.. Nonreciprocal photon blockade. Phys. Rev. Lett., 2018, 121(15): 153601 https://doi.org/10.1103/PhysRevLett.121.153601
56	Jiang Y., Maayani S., Carmon T., Nori F., Jing H.. Nonreciprocal phonon laser. Phys. Rev. Appl., 2018, 10(6): 064037 https://doi.org/10.1103/PhysRevApplied.10.064037
57	Jing H., Lü H., Özdemir S., Carmon T., Nori F.. Nanoparticle sensing with a spinning resonator. Optica, 2018, 5(11): 1424 https://doi.org/10.1364/OPTICA.5.001424
58	Li B., Huang R., Xu X., Miranowicz A., Jing H.. Nonreciprocal unconventional photon blockade in a spinning optomechanical system. Photon. Res., 2019, 7(6): 630 https://doi.org/10.1364/PRJ.7.000630
59	B. Malykin G.. The Sagnac effect: Correct and incorrect explanations. Phys. Uspekhi, 2000, 43(12): 1229 https://doi.org/10.1070/PU2000v043n12ABEH000830
60	C. H. Liew T., Savona V.. Single photons from coupled quantum modes. Phys. Rev. Lett., 2010, 104(18): 183601 https://doi.org/10.1103/PhysRevLett.104.183601
61	Bamba M., Imamoğlu A., Carusotto I., Ciuti C.. Origin of strong photon antibunching in weakly nonlinear photonic molecules. Phys. Rev. A, 2011, 83(2): 021802 https://doi.org/10.1103/PhysRevA.83.021802

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