A giant atom with modulated transition frequency

doi:10.1007/s11467-022-1215-9

Front. Phys.

2023, Vol. 18

Issue (1) : 12301 https://doi.org/10.1007/s11467-022-1215-9

RESEARCH ARTICLE

A giant atom with modulated transition frequency

Lei Du^1,², Yan Zhang³(

), Yong Li^1,⁴(

)

¹. Center for Theoretical Physics and School of Science, Hainan University, Haikou 570228, China
². Beijing Computational Science Research Center, Beijing 100193, China
³. Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
⁴. Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China

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Abstract

Giant atoms are known for the frequency-dependent spontaneous emission and associated interference effects. In this paper, we study the spontaneous emission dynamics of a two-level giant atom with dynamically modulated transition frequency. It is shown that the retarded feedback effect of the giant-atom system is greatly modified by a dynamical phase arising from the frequency modulation and the retardation effect itself. Interestingly, such a modification can in turn suppress the retarded feedback such that the giant atom behaves like a small one. By introducing an additional phase difference between the two atom-waveguide coupling paths, we also demonstrate the possibility of realizing chiral and tunable temporal profiles of the output fields. The results in this paper have potential applications in quantum information processing and quantum network engineering.

Keywords giant atoms frequency modulation spontaneous emission dynamics non-Markovian retardation effect

Corresponding Author(s): Yan Zhang,Yong Li

Issue Date: 23 November 2022

Cite this article:

Lei Du,Yan Zhang,Yong Li. A giant atom with modulated transition frequency[J]. Front. Phys. , 2023, 18(1): 12301.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1215-9
https://academic.hep.com.cn/fop/EN/Y2023/V18/I1/12301

Fig.1 Dynamic evolutions of atomic population probability

P e (t)

with (a)

ϕ 0 = (2 m + 1) π

and (b)

ϕ 0 = 2 m π

. Panels (a) and (b) share the same legend. The vertical dotted lines correspond to the moment

t = τ

that the atom feels the retarded feedback. Other parameters are

χ = 1

θ = 0

φ = 0

, and

τ Γ = 0.2

(except for indicated).

Fig.2 (a, b) Dynamic evolutions of atomic population probability

P e (t)

with different values of

χ

and

ϕ 0

. Panels (a) and (b) share the same legend. (c)

P e (t = 2 / Γ)

as a function of

χ

for

ϕ 0 = 2 m π

. (d) Dynamic evolutions of atomic population probability

P e (t)

with different values of

θ

and

ϕ 0 = 2 m π

. We assume

θ = 0

in panels (a−c) and

χ = 1

in panel (d). The vertical dotted lines in (a), (b), and (d) correspond to

t = τ

as those in Fig.1. Other parameters are

τ Γ = 0.2

Ω / Γ = 5 π

, and

φ = 0

Fig.3 (a, c) Dynamic evolutions of atomic population probability

P e (t)

with (a) different values of modulation depth

χ

and (c) different values of modulation frequency

Ω

. The inset in panel (c) depicts

P e (t = 11 / Γ)

versus

Ω

for fixed

χ

. (b, d) Dynamic evolutions of the real part of the dynamical phase factor

Re (F)

with (b) different values of modulation depth

χ

and (d) different values of modulation frequency

Ω

. We assume

Ω / Γ = 0.5 π

in panels (a) and (b) and

χ = 0.5

in panels (c) and (d). Panels (a) and (b) [(c) and (d)] share the same legend. Other parameters are

ϕ 0 = 2 m π

τ Γ = 10

θ = 0

, and

φ = 0

Fig.4 Dynamic evolutions of the left and right output intensities (in units of

Γ / (2 v g)

) versus

t ~ − τ

with different values of modulation parameters (cosine-type modulation). We assume

χ = 1

in panels (a−c) and

φ = π / 2

in panels (d−f). Other parameters are

ϕ 0 = (2 m + 1) π

ϕ 0 ′ = (2 n + 1 / 2) π

τ Γ = 0.2

Ω / Γ = 5 π

, and

θ = 0

Fig.5 Dynamic evolutions of the left (a) and right (b) output intensities (in units of

Γ / (2 v g)

) versus

t ~ − τ

with different values of

β

(linear modulation). Other parameters are

ϕ 0 = (2 m + 1) π

ϕ 0 ′ = (2 n + 1 / 2) π

φ = π / 2

, and

τ Γ = 1

1	S. Agarwal G., Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approaches, Springer, Berlin, 1974
2	J. Carmichael H., An Open Systems Approach to Quantum Optics, Springer-Verlag, Berlin, 1993
3	W. Gardiner C.Zoller P., Quantum Noise, 2nd Ed., Springer, Berlin, 2000
4	T. Shen J., Fan S.. Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits. Phys. Rev. Lett., 2005, 95(21): 213001 https://doi.org/10.1103/PhysRevLett.95.213001
5	Zhou L., R. Gong Z., X. Liu Y., P. Sun C., Nori F.. Controllable scattering of a single photon inside a one-dimensional resonator waveguide. Phys. Rev. Lett., 2008, 101(10): 100501 https://doi.org/10.1103/PhysRevLett.101.100501
6	Zhou L., P. Yang L., Li Y., P. Sun C.. Quantum routing of single photons with a cyclic three-level system. Phys. Rev. Lett., 2013, 111(10): 103604 https://doi.org/10.1103/PhysRevLett.111.103604
7	Zheng H., J. Gauthier D., U. Baranger H.. Waveguide-QED-based photonic quantum computation. Phys. Rev. Lett., 2013, 111(9): 090502 https://doi.org/10.1103/PhysRevLett.111.090502
8	Gonzalez-Ballestero C., Moreno E., J. Garcia-Vidal F., Gonzalez-Tudela A.. Nonreciprocal few-photon routing schemes based on chiral waveguide-emitter couplings. Phys. Rev. A, 2016, 94(6): 063817 https://doi.org/10.1103/PhysRevA.94.063817
9	Mirhosseini M., Kim E., Zhang X., Sipahigil A., B. Dieterle P., J. Keller A., Asenjo-Garcia A., E. Chang D., Painter O.. Cavity quantum electrodynamics with atom-like mirrors. Nature, 2019, 569(7758): 692 https://doi.org/10.1038/s41586-019-1196-1
10	W. Adams B., Buth C., Cavaletto S., Evers J., Harman Z., H. Keitel C., Palffy A., Picon A., Röhlsberger R., Rostovtsev Y., Tamasaku K.. X-ray quantum optics. J. Mod. Opt., 2013, 60(1): 2 https://doi.org/10.1080/09500340.2012.752113
11	Cavaletto S., Harman Z., Ott C., Buth C., Pfeifer T., H. Keitel C.. Broadband high-resolution X-ray frequency combs. Nat. Photon., 2014, 8: 520 https://doi.org/10.1038/nphoton.2014.113
12	Z. Qin X., H. Huang J., H. Zhong H., Lee C.. Clock frequency estimation under spontaneous emission. Front. Phys., 2018, 13(1): 130302 https://doi.org/10.1007/s11467-017-0706-6
13	Söllner I., Mahmoodian S., L. Hansen S., Midolo L., Javadi A., Kiršanskė G., Pregnolato T., El-Ella H., H. Lee E., D. Song J., Stobbe S., Lodahl P.. Deterministic photon-emitter coupling in chiral photonic circuits. Nat. Nanotechnol., 2015, 10(9): 775 https://doi.org/10.1038/nnano.2015.159
14	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
15	Kleppner D.. Inhibited spontaneous emission. Phys. Rev. Lett., 1981, 47(4): 233 https://doi.org/10.1103/PhysRevLett.47.233
16	Jhe W., Anderson A., A. Hinds E., Meschede D., Moi L., Haroche S.. Suppression of spontaneous decay at optical frequencies: Test of vacuum-field anisotropy in confined space. Phys. Rev. Lett., 1987, 58(14): 1497 https://doi.org/10.1103/PhysRevLett.58.1497.2
17	J. Heinzen D., J. Childs J., E. Thomas J., S. Feld M.. Enhanced and inhibited visible spontaneous emission by atoms in a confocal resonator. Phys. Rev. Lett., 1987, 58(13): 1320 https://doi.org/10.1103/PhysRevLett.58.1320
18	Yablonovitch E.. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett., 1987, 58(20): 2059 https://doi.org/10.1103/PhysRevLett.58.2059
19	Lambropoulos P., M. Nikolopoulos G., R. Nielsen T., Bay S.. Fundamental quantum optics in structured reservoirs. Rep. Prog. Phys., 2000, 63(4): 455 https://doi.org/10.1088/0034-4885/63/4/201
20	Lodahl P., Floris van Driel A., S. Nikolaev I., Irman A., Overgaag K., Vanmaekelbergh D., L. Vos W.. Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals. Nature, 2004, 430(7000): 654 https://doi.org/10.1038/nature02772
21	Noda S., Fujita M., Asano T.. Spontaneous emission control by photonic crystals and nanocavities. Nat. Photonics, 2007, 1(8): 449 https://doi.org/10.1038/nphoton.2007.141
22	G. Kofman A., Kurizki G.. Universal dynamical control of quantum mechanical decay: Modulation of the coupling to the continuum. Phys. Rev. Lett., 2001, 87(27): 270405 https://doi.org/10.1103/PhysRevLett.87.270405
23	Dorner U., Zoller P.. Laser-driven atoms in half cavities. Phys. Rev. A, 2002, 66(2): 023816 https://doi.org/10.1103/PhysRevA.66.023816
24	Kiffner M., Macovei M., Evers J., H. Keitel C.. Vacuum-induced processes in multilevel atoms. Prog. Opt., 2010, 55: 85 https://doi.org/10.1016/B978-0-444-53705-8.00003-5
25	Viola L., Lloyd S.. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A, 1998, 58(4): 2733 https://doi.org/10.1103/PhysRevA.58.2733
26	G. Kofman A., Kurizki G.. Acceleration of quantum decay processes by frequent observations. Nature, 2000, 405(6786): 546 https://doi.org/10.1038/35014537
27	Dhar D., K. Grover L., M. Roy S.. Preserving quantum states using inverting pulses: A super-Zeno effect. Phys. Rev. Lett., 2006, 96(10): 100405 https://doi.org/10.1103/PhysRevLett.96.100405
28	Evers J., H. Keitel C.. Spontaneous-emission suppression on arbitrary atomic transitions. Phys. Rev. Lett., 2002, 89(16): 163601 https://doi.org/10.1103/PhysRevLett.89.163601
29	Akram U., Evers J., H. Keitel C.. Multiphoton quantum interference on a dipole-forbidden transition. J. Phys. At. Mol. Opt. Phys., 2005, 38(4): L69 https://doi.org/10.1088/0953-4075/38/4/L01
30	F. Kockum A., Delsing P., Johansson G.. Designing frequency-dependent relaxation rates and Lamb shifts for a giant artificial atom. Phys. Rev. A, 2014, 90(1): 013837 https://doi.org/10.1103/PhysRevA.90.013837
31	F. Kockum A., Quantum Optics with Giant Atoms the First Five Years, in: Mathematics for Industry, Springer, Singapore, 2021, pp 125−146
32	Dong H., R. Gong Z., Ian H., Zhou L., P. Sun C.. Intrinsic cavity QED and emergent quasinormal modes for a single photon. Phys. Rev. A, 2009, 79(6): 063847 https://doi.org/10.1103/PhysRevA.79.063847
33	Bradford M., T. Shen J.. Spontaneous emission in cavity QED with a terminated waveguide. Phys. Rev. A, 2013, 87(6): 063830 https://doi.org/10.1103/PhysRevA.87.063830
34	Tufarelli T., Ciccarello F., S. Kim M.. Dynamics of spontaneous emission in a single-end photonic waveguide. Phys. Rev. A, 2013, 87(1): 013820 https://doi.org/10.1103/PhysRevA.87.013820
35	Tufarelli T., S. Kim M., Ciccarello F.. Non-Markovianity of a quantum emitter in front of a mirror. Phys. Rev. A, 2014, 90(1): 012113 https://doi.org/10.1103/PhysRevA.90.012113
36	Calajó G., L. L. Fang Y., U. Baranger H., Ciccarello F.. Exciting a bound state in the continuum through multiphoton scattering plus delayed quantum feedback. Phys. Rev. Lett., 2019, 122(7): 073601 https://doi.org/10.1103/PhysRevLett.122.073601
37	F. Kockum A., Johansson G., Nori F.. Decoherence-free interaction between giant atoms in waveguide quantum electrodynamics. Phys. Rev. Lett., 2018, 120(14): 140404 https://doi.org/10.1103/PhysRevLett.120.140404
38	Kannan B., J. Ruckriegel M., L. Campbell D., Frisk Kockum A., Braumüller J., K. Kim D., Kjaergaard M., Krantz P., Melville A., M. Niedzielski B., Vepsäläinen A., Winik R., L. Yoder J., Nori F., P. Orlando T., Gustavsson S., D. Oliver W.. Waveguide quantum electrodynamics with superconducting artificial giant atoms. Nature, 2020, 583(7818): 775 https://doi.org/10.1038/s41586-020-2529-9
39	Carollo A., Cilluffo D., Ciccarello F.. Mechanism of decoherence-free coupling between giant atoms. Phys. Rev. Res., 2020, 2(4): 043184 https://doi.org/10.1103/PhysRevResearch.2.043184
40	Guo L., F. Kockum A., Marquardt F., Johansson G.. Oscillating bound states for a giant atom. Phys. Rev. Res., 2020, 2(4): 043014 https://doi.org/10.1103/PhysRevResearch.2.043014
41	Guo S., Wang Y., Purdy T., Taylor J.. Beyond spontaneous emission: Giant atom bounded in the continuum. Phys. Rev. A, 2020, 102(3): 033706 https://doi.org/10.1103/PhysRevA.102.033706
42	Wang X., Liu T., F. Kockum A., R. Li H., Nori F.. Tunable chiral bound states with giant atoms. Phys. Rev. Lett., 2021, 126(4): 043602 https://doi.org/10.1103/PhysRevLett.126.043602
43	Zhao W., Wang Z.. Single-photon scattering and bound states in an atom-waveguide system with two or multiple coupling points. Phys. Rev. A, 2020, 101(5): 053855 https://doi.org/10.1103/PhysRevA.101.053855
44	Vega C., Bello M., Porras D., González-Tudela A.. Qubit-photon bound states in topological waveguides with long-range hoppings. Phys. Rev. A, 2021, 104(5): 053522 https://doi.org/10.1103/PhysRevA.104.053522
45	Soro A., F. Kockum A.. Chiral quantum optics with giant atoms. Phys. Rev. A, 2022, 105(2): 023712 https://doi.org/10.1103/PhysRevA.105.023712
46	Wang X., R. Li H.. Chiral quantum network with giant atoms. Quantum Sci. Technol., 2022, 7(3): 035007 https://doi.org/10.1088/2058-9565/ac6a04
47	Du L., Zhang Y., H. Wu J., F. Kockum A., Li Y.. Giant atoms in synthetic frequency dimensions. Phys. Rev. Lett., 2022, 128(22): 223602 https://doi.org/10.1103/PhysRevLett.128.223602
48	Du L., Li Y.. Single-photon frequency conversion via a giant Λ-type atom. Phys. Rev. A, 2021, 104(2): 023712 https://doi.org/10.1103/PhysRevA.104.023712
49	Du L., T. Chen Y., Li Y.. Nonreciprocal frequency conversion with chiral Λ-type atoms. Phys. Rev. Res., 2021, 3(4): 043226 https://doi.org/10.1103/PhysRevResearch.3.043226
50	Y. Cai Q., Z. Jia W.. Coherent single-photon scattering spectra for a giant-atom waveguide-QED system beyond the dipole approximation. Phys. Rev. A, 2021, 104(3): 033710 https://doi.org/10.1103/PhysRevA.104.033710
51	L. Feng S., Z. Jia W.. Manipulating single-photon transport in a waveguide-QED structure containing two giant atoms. Phys. Rev. A, 2021, 104(6): 063712 https://doi.org/10.1103/PhysRevA.104.063712
52	Zhao W., Zhang Y., Wang Z.. Phase-modulated Autler−Townes splitting in a giant-atom system within waveguide QED. Front. Phys., 2022, 17(4): 42506 https://doi.org/10.1007/s11467-021-1135-0
53	L. Yin X., H. Liu Y., F. Huang J., Q. Liao J.. Single photon scattering in a giant-molecule waveguide-QED system. Phys. Rev. A, 2022, 106(1): 013715 https://doi.org/10.1103/PhysRevA.106.013715
54	T. Chen Y., Du L., Guo L., Wang Z., Zhang Y., Li Y., H. Wu J.. Nonreciprocal and chiral single-photon scattering for giant atoms. Commun. Phys., 2022, 5(1): 215 https://doi.org/10.1038/s42005-022-00991-3
55	Xiao H., Wang L., Li Z.-H., Chen X., Yuan L.. Bound state in a giant atom-modulated resonators system. npj Quantum Infom., 2022, 8: 80 https://doi.org/10.1038/s41534-022-00591-7
56	D. Oliver W., Yu Y., C. Lee J., K. Berggren K., S. Levitov L., P. Orlando T.. Mach−Zehnder interferometry in a strongly driven superconducting qubit. Science, 2005, 310(5754): 1653 https://doi.org/10.1126/science.1119678
57	M. Wilson C., Duty T., Persson F., Sandberg M., Johansson G., Delsing P.. Coherence times of dressed states of a superconducting qubit under extreme driving. Phys. Rev. Lett., 2007, 98(25): 257003 https://doi.org/10.1103/PhysRevLett.98.257003
58	Metcalfe M., M. Carr S., Muller A., S. Solomon G., Lawall J.. Resolved sideband emission of InAs/GaAs quantum dots strained by surface acoustic waves. Phys. Rev. Lett., 2010, 105(3): 037401 https://doi.org/10.1103/PhysRevLett.105.037401
59	Schmidt M., Kessler S., Peano V., Painter O., Marquardt F.. Optomechanical creation of magnetic fields for photons on a lattice. Optica, 2015, 2(7): 635 https://doi.org/10.1364/OPTICA.2.000635
60	Roushan P., Neill C., Megrant A., Chen Y., Babbush R., Barends R., Campbell B., Chen Z., Chiaro B., Dunsworth A., Fowler A., Jeffrey E., Kelly J., Lucero E., Mutus J., J. J. O’Malley P., Neeley M., Quintana C., Sank D., Vainsencher A., Wenner J., White T., Kapit E., Neven H., Martinis J.. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys., 2017, 13(2): 146 https://doi.org/10.1038/nphys3930
61	Fang K., Luo J., Metelmann A., H. Matheny M., Marquardt F., A. Clerk A., Painter O.. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering. Nat. Phys., 2017, 13(5): 465 https://doi.org/10.1038/nphys4009
62	Jin L., Wang P., Song Z.. One-way light transport controlled by synthetic magnetic fluxes and PT-symmetric resonators. New J. Phys., 2017, 19(1): 015010 https://doi.org/10.1088/1367-2630/aa57ba
63	Jin L., Song Z.. Incident direction independent wave propagation and unidirectional lasing. Phys. Rev. Lett., 2018, 121(7): 073901 https://doi.org/10.1103/PhysRevLett.121.073901
64	Ramos T., Vermersch B., Hauke P., Pichler H., Zoller P.. Non-Markovian dynamics in chiral quantum networks with spins and photons. Phys. Rev. A, 2016, 93(6): 062104 https://doi.org/10.1103/PhysRevA.93.062104
65	T. Shen J., Fan S.. Theory of single-photon transport in a single-mode waveguide (I): Coupling to a cavity containing a two-level atom. Phys. Rev. A, 2009, 79(2): 023837 https://doi.org/10.1103/PhysRevA.79.023837
66	Longhi S.. Photonic simulation of giant atom decay. Opt. Lett., 2020, 45(11): 3017 https://doi.org/10.1364/OL.393578
67	Guo L., Grimsmo A., F. Kockum A., Pletyukhov M., Johansson G.. Giant acoustic atom: A single quantum system with a deterministic time delay. Phys. Rev. A, 2017, 95(5): 053821 https://doi.org/10.1103/PhysRevA.95.053821
68	H. Dicke R.. Coherence in spontaneous radiation processes. Phys. Rev., 1954, 93(1): 99 https://doi.org/10.1103/PhysRev.93.99
69	Lalumière K., C. Sanders B., F. van Loo A., Fedorov A., Wallraff A., Blais A.. Input−output theory for waveguide QED with an ensemble of inhomogeneous atoms. Phys. Rev. A, 2013, 88(4): 043806 https://doi.org/10.1103/PhysRevA.88.043806
70	Macovei M., H. Keitel C.. Quantum dynamics of a two-level emitter with a modulated transition frequency. Phys. Rev. A, 2014, 90(4): 043838 https://doi.org/10.1103/PhysRevA.90.043838
71	Du L., T. Chen Y., Zhang Y., Li Y.. Giant atoms with time-dependent couplings. Phys. Rev. Res., 2022, 4(2): 023198 https://doi.org/10.1103/PhysRevResearch.4.023198
72	Janowicz M.. Non-Markovian decay of an atom coupled to a reservoir: Modification by frequency modulation. Phys. Rev. A, 2000, 61(2): 025802 https://doi.org/10.1103/PhysRevA.61.025802
73	Andersson G., Suri B., Guo L., Aref T., Delsing P.. Non-exponential decay of a giant artificial atom. Nat. Phys., 2019, 15(11): 1123 https://doi.org/10.1038/s41567-019-0605-6
74	Lorenzo S., Plastina F., Paternostro M.. Geometrical characterization of non-Markovianity. Phys. Rev. A, 2013, 88: 020102(R) https://doi.org/10.1103/PhysRevA.88.020102
75	Koshino K., Terai H., Inomata K., Yamamoto T., Qiu W., Wang Z., Nakamura Y.. Observation of the three-state dressed states in circuit quantum electrodynamics. Phys. Rev. Lett., 2013, 110(26): 263601 https://doi.org/10.1103/PhysRevLett.110.263601
76	Liu Y., A. Houck A.. Quantum electrodynamics near a photonic bandgap. Nat. Phys., 2017, 13(1): 48 https://doi.org/10.1038/nphys3834
77	Mirhosseini M., Kim E., S. Ferreira V., Kalaee M., Sipahigil A., J. Keller A., Painter O.. Superconducting metamaterials for waveguide quantum electrodynamics. Nat. Commun., 2018, 9(1): 3706 https://doi.org/10.1038/s41467-018-06142-z
78	Bello M., Platero G., I. Cirac J., González-Tudela A.. Unconventional quantum optics in topological waveguide QED. Sci. Adv., 2019, 5(7): eaaw0297 https://doi.org/10.1126/sciadv.aaw0297
79	Sánchez-Burillo E., Wan C., Zueco D., González-Tudela A.. Chiral quantum optics in photonic sawtooth lattices. Phys. Rev. Res., 2020, 2(2): 023003 https://doi.org/10.1103/PhysRevResearch.2.023003
80	Guimond P.-O., Vermersch B., L. Juan M., Sharafiev A., Kirchmair G., Zoller P.. A unidirectional onchip photonic interface for superconducting circuits. npj Quantum Infom., 2020, 6: 32 https://doi.org/10.1038/s41534-020-0261-9
81	Du L., R. Cai M., H. Wu J., Wang Z., Li Y.. Single-photon nonreciprocal excitation transfer with non-Markovian retarded effects. Phys. Rev. A, 2021, 103(5): 053701 https://doi.org/10.1103/PhysRevA.103.053701
82	Y. Qiu Q.Wu Y.Y. Lü X., Collective radiance of giant atoms in non-Markovian regime, arXiv: 2205.10982 (2022)
83	Soro A.S. Muñoz C.F. Kockum A., Interaction between giant atoms in a one-dimensional structured environment, arXiv: 2208.04102 (2022)
84	Jin Z., L. Su S., D. Zhu A., F. Wang H., Zhang S.. Engineering multipartite steady entanglement of distant atoms via dissipation. Front. Phys., 2018, 13(5): 134209 https://doi.org/10.1007/s11467-018-0826-7
85	A. Clerk A., Introduction to quantum non-reciprocal interactions: From non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes, arXiv: 2201.00894 (2022)
86	P. Silveri M., A. Tuorila J., V. Thuneberg E., S. Paraoanu G.. Quantum systems under frequency modulation. Rep. Prog. Phys., 2017, 80(5): 056002 https://doi.org/10.1088/1361-6633/aa5170

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