在超導電路中開發基於電磁誘發透明的微波量子記憶體

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：70

、訪客IP：18.117.172.189

姓名

朱凱翊(Kai-I Chu) 查詢紙本館藏

畢業系所

物理學系

論文名稱

在超導電路中開發基於電磁誘發透明的微波量子記憶體
(Developing Microwave Quantum Memory Based on Electromagnetically Induced Transparency in Superconducting Circuits)

相關論文

★ 單電子偵測器原理及製作與二維電子氣量子點電荷傳輸行為	★ 單電子系統中的電子穿隧事件
★ 石墨烯與超導金屬介面的電子穿隧行為	★ 實驗觀測混合式單電子箱中之共同穿隧事件
★ 石墨烯/超導體/石墨烯元件之古柏電子對分裂現象探討	★ 雙局部閘極石墨烯/超導體/石墨烯元件中古柏電子對分離現象觀測
★ 不連續鉛顆粒/單層二硫化鉬系統之超導鄰近效應觀測	★ 二維電子氣體中量子點接觸與量子點製作及量測
★ 二硫化鉬及二硫化鎢電晶體的低頻雜訊行為	★ 單一超導量子位元控制與狀態讀取
★ 超導量子干涉元件製作	★ 工程化超導電路上三維腔量子電動力學系統
★ Characterizing single-qubit gate fidelity on superconducting qubits	★ Virtual Potentials in Electric Circuit and Motion of Brownian Gyrator
★ 超導雙量子位元電路的實現	★ Developing Flux-Driven Josephson Parametric Amplifer

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

基於約瑟夫森結的超導電路的最新進展極大地推進量子資訊處理。為了要構建一個全面的基於超導的量子網絡，我們需要一個至關重要的元件：微波量子記憶體。然而，由於大多數超導人造原子缺乏亞穩態，超導電路平台上的光量子記憶體的發展受到阻礙。

在本論文中，我們從理論上研究並實驗實現了波導量子電動力學架構內的一種新型微波記憶體，由單個超導 Xmon 量子位元和耦合高品質諧振器組成，此諧振器可以被認為是電路的合適亞穩態。透過採用參數調變技術，調變量子位元躍遷頻率和以微波直接驅動量子位元躍遷的協同效應可以產生有效的三能階 Λ 型電磁誘發透明。在連續的參數調變下，伴隨的色散曲線被急劇修改，從而使通過此單個 Λ 型人造原子的探測脈衝的速度減慢到3.6 km/s。我們實驗證明透過電磁誘發透明的機制進行參數調變的動態控制，可以允許按需存取微波訊號，且儲存時間可延長至數百奈秒。這種簡單而多功能的裝置凸顯了在超導電路領域實現微波量子記憶體的潛力。

本論文詳細介紹了超導電路中第一個基於電磁誘發透明的微波量子記憶體的動機、理論背景、數值模擬、設計、實現和測量結果。

摘要(英)

Recent progress in Josephson-junction-based superconducting circuits has significantly advanced quantum information processing. To build a comprehensive superconducting-based quantum network, one requires a critical ingredient: microwave quantum memory. However, the development of photonic quantum memory on this platform is hindered by the absence of a metastable state in most superconducting artificial atoms.

In this thesis, we theoretically investigate and experimentally realize a novel type of microwave memory within the waveguide quantum electrodynamics architecture, consisting of a single superconducting Xmon qubit and a coupling high-quality resonator. This resonator can be considered a suitable metastable state for the circuit. By employing the parametric modulation technique, the synergy effect of modulating the qubit transition frequency and directly driving the qubit transition with a microwave can create an effective three-level Λ-type electromagnetically induced transparency. The accompanying dispersion profile is sharply modified under the continuous parametric modulation, resulting in the probe pulse passing through this single Λ-type artificial atom at a reduced group velocity of 3.6 km/s. We demonstrate that the dynamical control of such a parametric modulation allows for on-demand microwave storage and retrieval, with a memory time extending to several hundred nanoseconds via electromagnetically induced transparency. This simple yet versatile device highlights the potential of achieving microwave quantum memory within the superconducting circuits community.

This thesis details the motivation, theoretical background, numerical simulations, design, implementation, and measurement results of this first electromagnetically-induced-transparency-based microwave quantum memory device in superconducting circuits.

關鍵字(中)

★ 超導電路
★ 量子網絡
★ 人造原子
★ 微波量子記憶體
★ 波導量子電動力學
★ 參數調變
★ 電磁誘發透明

關鍵字(英)

★ Superconducting circuits
★ Quantum network
★ Artificial atoms
★ Microwave quantum memory
★ Waveguide quantum electrodynamics
★ Parametric modulation
★ Electromagnetically induced transparency

論文目次

摘要ix
Abstract xi
Contents xiii
1 Introduction and Motivation 1
1.1 Waveguide Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Photonic Quantum Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Electromagnetically Induced Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Microwave Memory in Superconducting Quantum Circuits. . . . . . . . . . . . . . . . . . 8
1.3.1 EIT in Superconducting Quantum Circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Thesis Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Circuit QED 13
2.1 Circuit Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Quantum LC Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Josephson Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Superconducting Artificial Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.4 Frequency Tunability - SQUID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Jaynes-Cummings Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Dispersive Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.2 Sideband Transition Induced by Parametric Modulation. . . . . . . . . . . . . 27
3 Waveguide QED in Superconducting Quantum Circuits 33
3.1 Wigner-Weisskopf Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Time Evolution of System Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Lindblad Master Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.2 Input-Output Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 Open Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Interaction between a Qubit and a 1D Open Transmission Line . . . . . 43
3.4 Light Scattering by a Qubit in a 1D Open Transmission Line. . . . . . . . . . . . . . . 45
4 Three-level Λ-type Atom Interacting with Lights 51
4.1 Dark State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Optical Response with Strong Coupling Lights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Electromagnetically Induced Transparency v.s. Autler-Townes Splitting
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 EIT-Based Quantum Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5 Investigation of Three-level Λ-type EIT-based Microwave Memory in
a Superconducting Quantum Circuit 63
5.1 Model: Detuend Quantum Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1.1 Λ-type Atom manipulated by Parametric Modulation . . . . . . . . . . . . . . . 65
5.2 EIT: Parametric Modulation Induced Transparency . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2.1 Observation of Dark State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Coherence Improvement via Purcell Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3.1 Description of the Purcell Filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3.2 Slow and Storing Microwaves with the Purcell Filter. . . . . . . . . . . . . . . . . 73
5.3.3 Storage Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Summary of the Theoretical Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.5 Theory Derivation for Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6 EIT-based Multimode Microwave Memory in a Superconducting Quantum
Circuit 79
6.1 Qubit Coupling to an Array of Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 EIT Spectroscopy with Multi-Metastable States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3 Storage of Multiple Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.4 Summary of the Multimode Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Experimental Realization of Slow and Stored Light via EIT Using A
Λ-type Superconducting Artificial Atom 87
7.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.2 Single-Tone Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.2.1 Power Dependent Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.2 Coupling Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.2.3 Flux Dependent Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.3 Observation of EIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 Slow Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.5 Stored Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.5.1 Light Shaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.6 Discussion: Improvement of Storage Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.7 Discussion: Sweet Spot Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.8 Summary of the Experimental Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8 Conclusion and Future Works 107
Bibliography 111

參考文獻

[1] A. Acín, I. Bloch, H. Buhrman, T. Calarco, C. Eichler, J. Eisert, D. Esteve, N. Gisin,
S. J. Glaser, F. Jelezko, S. Kuhr, M. Lewenstein, M. F. Riedel, P. O. Schmidt, R. Thew,
A. Wallraff, I. Walmsley, and F. K. Wilhelm, “The quantum technologies roadmap: A
european community view,” New Journal of Physics, vol. 20, no. 8, 2018, issn: 1367-2630.
doi: 10.1088/1367-2630/aad1ea.
[2] H. J. Kimble, “The quantum internet,” Nature, vol. 453, no. 7198, pp. 1023–30, 2008,
issn: 1476-4687 (Electronic) 0028-0836 (Linking). doi: 10.1038/nature07127. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/18563153.
[3] L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication
with atomic ensembles and linear optics,” Nature, vol. 414, no. 6862, pp. 413–8,
2001, issn: 0028-0836 (Print) 0028-0836 (Linking). doi: 10.1038/35106500. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/11719796.
[4] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S.
Boixo, F. G. Brandao, and D. A. Buell, “Quantum supremacy using a programmable
superconducting processor,” Nature, vol. 574, no. 7779, pp. 505–510, 2019, issn: 1476-
4687. doi: 10.1038/s41586-019-1666-5. [Online]. Available: https://www.ncbi.nlm.
nih.gov/pubmed/31645734.
[5] Y. Wu, W. S. Bao, S. Cao, F. Chen, M. C. Chen, X. Chen, T. H. Chung, H. Deng, Y.
Du, D. Fan, M. Gong, C. Guo, C. Guo, S. Guo, L. Han, L. Hong, H. L. Huang, Y. H.
Huo, L. Li, N. Li, S. Li, Y. Li, F. Liang, C. Lin, J. Lin, H. Qian, D. Qiao, H. Rong,
H. Su, L. Sun, L. Wang, S. Wang, D. Wu, Y. Xu, K. Yan, W. Yang, Y. Yang, Y. Ye,
J. Yin, C. Ying, J. Yu, C. Zha, C. Zhang, H. Zhang, K. Zhang, Y. Zhang, H. Zhao, Y.
Zhao, L. Zhou, Q. Zhu, C. Y. Lu, C. Z. Peng, X. Zhu, and J. W. Pan, “Strong quantum
computational advantage using a superconducting quantum processor,” Phys Rev Lett,
vol. 127, no. 18, p. 180 501, 2021, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi:
10.1103/PhysRevLett.127.180501. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/34767433.
[6] M. H. Devoret and R. J. Schoelkopf, “Superconducting circuits for quantum information:
An outlook,” Science, vol. 339, no. 6124, pp. 1169–74, 2013, issn: 1095-9203 (Electronic)
0036-8075 (Linking). doi: 10.1126/science.1231930. [Online]. Available: https://
www.ncbi.nlm.nih.gov/pubmed/23471399.
[7] G. Wendin, “Quantum information processing with superconducting circuits: A review,”
Rep Prog Phys, vol. 80, no. 10, p. 106 001, 2017, issn: 1361-6633 (Electronic) 0034-4885
(Linking). doi: 10.1088/1361-6633/aa7e1a. [Online]. Available: https://www.ncbi.
nlm.nih.gov/pubmed/28682303.
[8] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, “Circuit quantum electrodynamics,”
Reviews of Modern Physics, vol. 93, no. 2, 2021, issn: 0034-6861 1539-0756. doi:
10.1103/RevModPhys.93.025005.
[9] P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, “A
quantum engineer’s guide to superconducting qubits,” Applied Physics Reviews, vol. 6,
no. 2, 2019, issn: 1931-9401. doi: 10.1063/1.5089550.
[10] M. Caleffi, M. Amoretti, D. Ferrari, D. Cuomo, J. Illiano, A. Manzalini, and A. S. Cacciapuoti,
“Distributed quantum computing: A survey,” arXiv preprint arXiv:2212.10609,
2022.
[11] M. Mirhosseini, A. Sipahigil, M. Kalaee, and O. Painter, “Superconducting qubit to
optical photon transduction,” Nature, vol. 588, no. 7839, pp. 599–603, 2020, issn: 1476-
4687 (Electronic) 0028-0836 (Linking). doi: 10.1038/s41586- 020- 3038- 6. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/33361793.
[12] P. Magnard, S. Storz, P. Kurpiers, J. Schar, F. Marxer, J. Lutolf, T. Walter, J. C. Besse,
M. Gabureac, K. Reuer, A. Akin, B. Royer, A. Blais, and A. Wallraff, “Microwave quantum
link between superconducting circuits housed in spatially separated cryogenic systems,”
Phys Rev Lett, vol. 125, no. 26, p. 260 502, 2020, issn: 1079-7114 (Electronic)
0031-9007 (Linking). doi: 10 . 1103 / PhysRevLett . 125 . 260502. [Online]. Available:
https://www.ncbi.nlm.nih.gov/pubmed/33449744.
[13] K. Heshami, D. G. England, P. C. Humphreys, P. J. Bustard, V. M. Acosta, J. Nunn,
and B. J. Sussman, “Quantum memories: Emerging applications and recent advances,”
J Mod Opt, vol. 63, no. 20, pp. 2005–2028, 2016, issn: 0950-0340 (Print) 1362-3044
(Electronic) 0950-0340 (Linking). doi: 10 . 1080 / 09500340 . 2016 . 1148212. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/27695198.
[14] A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nature Photonics,
vol. 3, no. 12, pp. 706–714, 2009, issn: 1749-4885 1749-4893. doi: 10.1038/nphoton.
2009.231.
[15] L. Ma, O. Slattery, and X. Tang, “Optical quantum memory based on electromagnetically
induced transparency,” J Opt, vol. 19, no. 4, 2017, issn: 2040-8978 (Print) 2040-8986
(Electronic) 2040-8978 (Linking). doi: 10.1088/2040- 8986/19/4/043001. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/28828172.
[16] W. Tittel, M. Afzelius, T. Chaneliére, R. L. Cone, S. Kröll, S. A. Moiseev, and M.
Sellars, “Photon‐echo quantum memory in solid state systems,” Laser & Photonics Reviews,
vol. 4, no. 2, pp. 244–267, 2010, issn: 1863-8880 1863-8899. doi: 10.1002/lpor.
200810056.
[17] H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: Coherence in context,”
Science, vol. 298, no. 5597, pp. 1372–7, 2002, issn: 1095-9203 (Electronic) 0036-
8075 (Linking). doi: 10.1126/science.1078446. [Online]. Available: https://www.
ncbi.nlm.nih.gov/pubmed/12434052.
[18] A. Reiserer and G. Rempe, “Cavity-based quantum networks with single atoms and
optical photons,” Reviews of Modern Physics, vol. 87, no. 4, pp. 1379–1418, 2015, issn:
0034-6861 1539-0756. doi: 10.1103/RevModPhys.87.1379.
[19] A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. M.
Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting
qubit using circuit quantum electrodynamics,” Nature, vol. 431, no. 7005, pp. 162–7,
2004, issn: 1476-4687 (Electronic) 0028-0836 (Linking). doi: 10 . 1038 / nature02851.
[Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/15356625.
[20] A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum
electrodynamics for superconducting electrical circuits: An architecture for quantum
computation,” Physical Review A, vol. 69, no. 6, 2004, issn: 1050-2947 1094-1622. doi:
10.1103/PhysRevA.69.062320.
[21] X. Gu, A. F. Kockum, A. Miranowicz, Y.-x. Liu, and F. Nori, “Microwave photonics with
superconducting quantum circuits,” Physics Reports, vol. 718-719, pp. 1–102, 2017, issn:
03701573. doi: 10.1016/j.physrep.2017.10.002.
[22] B. Kannan, Waveguide Quantum Electrodynamics with Superconducting Qubits. Massachusetts
Institute of Technology, 2022. [Online]. Available: https://hdl.handle.net/
1721.1/144670.
[23] I. C. Hoi, T. Palomaki, J. Lindkvist, G. Johansson, P. Delsing, and C. M. Wilson,
“Generation of nonclassical microwave states using an artificial atom in 1d open space,”
Phys Rev Lett, vol. 108, no. 26, p. 263 601, 2012, issn: 1079-7114 (Electronic) 0031-
9007 (Linking). doi: 10.1103/PhysRevLett.108.263601. [Online]. Available: https:
//www.ncbi.nlm.nih.gov/pubmed/23004976.
[24] D. Roy, C. M. Wilson, and O. Firstenberg, “Colloquium : Strongly interacting photons
in one-dimensional continuum,” Reviews of Modern Physics, vol. 89, no. 2, 2017, issn:
0034-6861 1539-0756. doi: 10.1103/RevModPhys.89.021001.
[25] A. S. Sheremet, M. I. Petrov, I. V. Iorsh, A. V. Poshakinskiy, and A. N. Poddubny,
“Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations,”
Reviews of Modern Physics, vol. 95, no. 1, 2023, issn: 0034-6861 1539-0756. doi:
10.1103/RevModPhys.95.015002.
[26] O. Astafiev, A. M. Zagoskin, J. Abdumalikov A. A., Y. A. Pashkin, T. Yamamoto, K.
Inomata, Y. Nakamura, and J. S. Tsai, “Resonance fluorescence of a single artificial
atom,” Science, vol. 327, no. 5967, pp. 840–3, 2010, issn: 1095-9203 (Electronic) 0036-
8075 (Linking). doi: 10.1126/science.1181918. [Online]. Available: https://www.
ncbi.nlm.nih.gov/pubmed/20150495.
[27] I. C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing,
“Demonstration of a single-photon router in the microwave regime,” Phys Rev Lett,
vol. 107, no. 7, p. 073 601, 2011, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi:
10.1103/PhysRevLett.107.073601. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/21902392.
[28] K. Lalumière, B. C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraff, and A. Blais, “Inputoutput
theory for waveguide qed with an ensemble of inhomogeneous atoms,” Physical
Review A, vol. 88, no. 4, 2013, issn: 1050-2947 1094-1622. doi: 10.1103/PhysRevA.88.
043806.
[29] B. Kannan, A. Almanakly, Y. Sung, A. Di Paolo, D. A. Rower, J. Braumüller, A. Melville,
B. M. Niedzielski, A. Karamlou, K. Serniak, A. Vepsäläinen, M. E. Schwartz, J. L. Yoder,
R. Winik, J. I. J. Wang, T. P. Orlando, S. Gustavsson, J. A. Grover, and W. D. Oliver,
“On-demand directional microwave photon emission using waveguide quantum electrodynamics,”
Nature Physics, vol. 19, no. 3, pp. 394–400, 2023, issn: 1745-2473 1745-2481.
doi: 10.1038/s41567-022-01869-5.
[30] A. L. Grimsmo, B. Royer, J. M. Kreikebaum, Y. Ye, K. O’Brien, I. Siddiqi, and A. Blais,
“Quantum metamaterial for broadband detection of single microwave photons,” Physical
Review Applied, vol. 15, no. 3, 2021, issn: 2331-7019. doi: 10.1103/PhysRevApplied.
15.034074.
[31] K.-I. Chu, W.-T. Liao, and Y.-F. Chen, “Three-level λ-type microwave memory via
parametric-modulation-induced transparency in a superconducting quantum circuit,”
Physical Review Research, vol. 5, no. 3, p. 033 192, 2023.
[32] K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and
atomic ensembles,” Reviews of Modern Physics, vol. 82, no. 2, pp. 1041–1093, 2010, issn:
0034-6861 1539-0756. doi: 10.1103/RevModPhys.82.1041.
[33] M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,”
Reviews of Modern Physics, vol. 75, no. 2, pp. 457–472, 2003, issn: 0034-6861
1539-0756. doi: 10.1103/RevModPhys.75.457.
[34] G. Hetet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, “Multimodal
properties and dynamics of gradient echo quantum memory,” Phys Rev Lett, vol. 101,
no. 20, p. 203 601, 2008, issn: 0031-9007 (Print) 0031-9007 (Linking). doi: 10.1103/
PhysRevLett . 101 . 203601. [Online]. Available: https : / / www . ncbi . nlm . nih . gov /
pubmed/19113339.
[35] W. T. Liao, C. H. Keitel, and A. Palffy, “All-electromagnetic control of broadband quantum
excitations using gradient photon echoes,” Phys Rev Lett, vol. 113, no. 12, p. 123 602,
2014, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.
113.123602. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/25279629.
[36] B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll, and J. I. Cirac, “Quantum memory
for nonstationary light fields based on controlled reversible inhomogeneous broadening,”
Physical Review A, vol. 73, no. 2, 2006, issn: 1050-2947 1094-1622. doi: 10 . 1103 /
PhysRevA.73.020302.
[37] M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory
based on atomic frequency combs,” Physical Review A, vol. 79, no. 5, 2009, issn: 1050-
2947 1094-1622. doi: 10.1103/PhysRevA.79.052329.
[38] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency:
Optics in coherent media,” Reviews of Modern Physics, vol. 77, no. 2, pp. 633–
673, 2005, issn: 0034-6861 1539-0756. doi: 10.1103/RevModPhys.77.633.
[39] R. Finkelstein, S. Bali, O. Firstenberg, and I. Novikova, “A practical guide to electromagnetically
induced transparency in atomic vapor,” New Journal of Physics, vol. 25,
no. 3, 2023, issn: 1367-2630. doi: 10 . 1088 / 1367 - 2630 / acbc40. [Online]. Available:
https://iopscience.iop.org/article/10.1088/1367-2630/acbc40/pdf.
[40] M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced
transparency,” Phys Rev Lett, vol. 84, no. 22, pp. 5094–7, 2000, issn: 1079-7114 (Electronic)
0031-9007 (Linking). doi: 10.1103/PhysRevLett.84.5094. [Online]. Available:
https://www.ncbi.nlm.nih.gov/pubmed/10990875.
[41] L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17
metres per second in an ultracold atomic gas,” Nature, vol. 397, no. 6720, pp. 594–598,
1999, issn: 0028-0836 1476-4687. doi: 10.1038/17561.
[42] O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys
Rev Lett, vol. 86, no. 4, pp. 628–31, 2001, issn: 0031-9007 (Print) 0031-9007 (Linking).
doi: 10.1103/PhysRevLett.86.628. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/11177898.
[43] C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical
information storage in an atomic medium using halted light pulses,” Nature, vol. 409,
no. 6819, pp. 490–3, 2001, issn: 0028-0836 (Print) 0028-0836 (Linking). doi: 10.1038/
35054017. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/11206540.
[44] D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage
of light in atomic vapor,” Phys Rev Lett, vol. 86, no. 5, pp. 783–6, 2001, issn: 0031-9007
(Print) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.86.783. [Online]. Available:
https://www.ncbi.nlm.nih.gov/pubmed/11177939.
[45] Y. F. Hsiao, P. J. Tsai, H. S. Chen, S. X. Lin, C. C. Hung, C. H. Lee, Y. H. Chen, Y. F.
Chen, I. A. Yu, and Y. C. Chen, “Highly efficient coherent optical memory based on
electromagnetically induced transparency,” Phys Rev Lett, vol. 120, no. 18, p. 183 602,
2018, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.
120.183602. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/29775362.
[46] A. Imamoglu, “High efficiency photon counting using stored light,” Phys Rev Lett, vol. 89,
no. 16, p. 163 602, 2002, issn: 0031-9007 (Print) 0031-9007 (Linking). doi: 10.1103/
PhysRevLett . 89 . 163602. [Online]. Available: https : / / www . ncbi . nlm . nih . gov /
pubmed/12398723.
[47] W. Chen, K. M. Beck, R. Bucker, M. Gullans, M. D. Lukin, H. Tanji-Suzuki, and V.
Vuletic, “All-optical switch and transistor gated by one stored photon,” Science, vol. 341,
no. 6147, pp. 768–70, 2013, issn: 1095-9203 (Electronic) 0036-8075 (Linking). doi: 10.
1126/science.1238169. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/
23828886.
[48] Z. Y. Liu, Y. H. Chen, Y. C. Chen, H. Y. Lo, P. J. Tsai, I. A. Yu, Y. C. Chen, and
Y. F. Chen, “Large cross-phase modulations at the few-photon level,” Phys Rev Lett,
vol. 117, no. 20, p. 203 601, 2016, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi:
10.1103/PhysRevLett.117.203601. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/27886497.
[49] M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang,
J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J.
Schoelkopf, “Quantum memory with millisecond coherence in circuit qed,” Physical Review
B, vol. 94, no. 1, 2016, issn: 2469-9950 2469-9969. doi: 10.1103/PhysRevB.94.
014506.
[50] R. K. Naik, N. Leung, S. Chakram, P. Groszkowski, Y. Lu, N. Earnest, D. C. McKay,
J. Koch, and D. I. Schuster, “Random access quantum information processors using
multimode circuit quantum electrodynamics,” Nat Commun, vol. 8, no. 1, p. 1904, 2017,
issn: 2041-1723 (Electronic) 2041-1723 (Linking). doi: 10.1038/s41467-017-02046-6.
[Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/29199271.
[51] S. Chakram, A. E. Oriani, R. K. Naik, A. V. Dixit, K. He, A. Agrawal, H. Kwon,
and D. I. Schuster, “Seamless high-q microwave cavities for multimode circuit quantum
electrodynamics,” Phys Rev Lett, vol. 127, no. 10, p. 107 701, 2021, issn: 1079-7114
(Electronic) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.127.107701. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/34533363.
[52] A. Krasnok, P. Dhakal, A. Fedorov, P. Frigola, M. Kelly, and S. Kutsaev, “Advancements
in superconducting microwave cavities and qubits for quantum information systems,”
arXiv preprint arXiv:2304.09345, 2023.
[53] A. Megrant, C. Neill, R. Barends, B. Chiaro, Y. Chen, L. Feigl, J. Kelly, E. Lucero,
M. Mariantoni, P. J. J. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T. C. White,
Y. Yin, J. Zhao, C. J. Palmstrøm, J. M. Martinis, and A. N. Cleland, “Planar superconducting
resonators with internal quality factors above one million,” Applied Physics
Letters, vol. 100, no. 11, 2012, issn: 0003-6951 1077-3118. doi: 10.1063/1.3693409.
[54] M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk,
T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, “Reaching 10 ms
single photon lifetimes for superconducting aluminum cavities,” Applied Physics Letters,
vol. 102, no. 19, 2013, issn: 0003-6951 1077-3118. doi: 10.1063/1.4807015.
[55] E. Flurin, N. Roch, J. D. Pillet, F. Mallet, and B. Huard, “Superconducting quantum
node for entanglement and storage of microwave radiation,” Phys Rev Lett, vol. 114,
no. 9, p. 090 503, 2015, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi: 10.1103/
PhysRevLett . 114 . 090503. [Online]. Available: https : / / www . ncbi . nlm . nih . gov /
pubmed/25793790.
[56] J. Wenner, Y. Yin, Y. Chen, R. Barends, B. Chiaro, E. Jeffrey, J. Kelly, A. Megrant,
J. Y. Mutus, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, T. C.
White, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, “Catching time-reversed
microwave coherent state photons with 99.4% absorption efficiency,” Physical Review
Letters, vol. 112, no. 21, 2014, issn: 0031-9007 1079-7114. doi: 10.1103/PhysRevLett.
112.210501.
[57] Y. Yin, Y. Chen, D. Sank, P. J. O’Malley, T. C. White, R. Barends, J. Kelly, E. Lucero,
M. Mariantoni, A. Megrant, C. Neill, A. Vainsencher, J. Wenner, A. N. Korotkov, A. N.
Cleland, and J. M. Martinis, “Catch and release of microwave photon states,” Phys Rev
Lett, vol. 110, no. 10, p. 107 001, 2013, issn: 1079-7114 (Electronic) 0031-9007 (Linking).
doi: 10.1103/PhysRevLett.110.107001. [Online]. Available: https://www.ncbi.nlm.
nih.gov/pubmed/23521281.
[58] Z. Bao, Z. Wang, Y. Wu, Y. Li, C. Ma, Y. Song, H. Zhang, and L. Duan, “On-demand
storage and retrieval of microwave photons using a superconducting multiresonator quantum
memory,” Phys Rev Lett, vol. 127, no. 1, p. 010 503, 2021, issn: 1079-7114 (Electronic)
0031-9007 (Linking). doi: 10.1103/PhysRevLett.127.010503. [Online]. Available:
https://www.ncbi.nlm.nih.gov/pubmed/34270274.
[59] A. R. Matanin, K. I. Gerasimov, E. S. Moiseev, N. S. Smirnov, A. I. Ivanov, E. I. Malevannaya,
V. I. Polozov, E. V. Zikiy, A. A. Samoilov, I. A. Rodionov, and S. A. Moiseev,
“Toward highly efficient multimode superconducting quantum memory,” Physical Review
Applied, vol. 19, no. 3, 2023, issn: 2331-7019. doi: 10.1103/PhysRevApplied.19.034011.
[60] J. Abdumalikov A. A., O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and
J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys
Rev Lett, vol. 104, no. 19, p. 193 601, 2010, issn: 1079-7114 (Electronic) 0031-9007 (Linking).
doi: 10.1103/PhysRevLett.104.193601. [Online]. Available: https://www.ncbi.
nlm.nih.gov/pubmed/20866963.
[61] P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning autler-townes
splitting from electromagnetically induced transparency,” Phys Rev Lett, vol. 107, no. 16,
p. 163 604, 2011, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi: 10 . 1103 /
PhysRevLett . 107 . 163604. [Online]. Available: https : / / www . ncbi . nlm . nih . gov /
pubmed/22107383.
[62] S. Novikov, T. Sweeney, J. E. Robinson, S. P. Premaratne, B. Suri, F. C. Wellstood, and
B. S. Palmer, “Raman coherence in a circuit quantum electrodynamics lambda system,”
Nature Physics, vol. 12, no. 1, pp. 75–79, 2015, issn: 1745-2473 1745-2481. doi: 10.1038/
nphys3537.
[63] J. Long, H. S. Ku, X. Wu, X. Gu, R. E. Lake, M. Bal, Y. X. Liu, and D. P. Pappas,
“Electromagnetically induced transparency in circuit quantum electrodynamics with
nested polariton states,” Phys Rev Lett, vol. 120, no. 8, p. 083 602, 2018, issn: 1079-7114
(Electronic) 0031-9007 (Print) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.120.
083602. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/29543019.
[64] A. M. Vadiraj, A. Ask, T. G. McConkey, I. Nsanzineza, C. W. S. Chang, A. F. Kockum,
and C. M. Wilson, “Engineering the level structure of a giant artificial atom in waveguide
quantum electrodynamics,” Physical Review A, vol. 103, no. 2, 2021, issn: 2469-9926
2469-9934. doi: 10.1103/PhysRevA.103.023710.
[65] A. Wallraff, D. I. Schuster, A. Blais, J. M. Gambetta, J. Schreier, L. Frunzio, M. H.
Devoret, S. M. Girvin, and R. J. Schoelkopf, “Sideband transitions and two-tone spectroscopy
of a superconducting qubit strongly coupled to an on-chip cavity,” Phys Rev
Lett, vol. 99, no. 5, p. 050 501, 2007, issn: 1079-7114 (Electronic) 0031-9007 (Linking).
doi: 10.1103/PhysRevLett.99.050501. [Online]. Available: https://www.ncbi.nlm.
nih.gov/pubmed/17930736.
[66] B.-m. Ann and G. A. Steele, “Tunable and weakly invasive probing of a superconducting
resonator based on electromagnetically induced transparency,” Physical Review A,
vol. 102, no. 5, 2020, issn: 2469-9926 2469-9934. doi: 10.1103/PhysRevA.102.053721.
[67] J. D. Brehm, A. N. Poddubny, A. Stehli, T. Wolz, H. Rotzinger, and A. V. Ustinov,
“Waveguide bandgap engineering with an array of superconducting qubits,” npj Quantum
Materials, vol. 6, no. 1, 2021, issn: 2397-4648. doi: 10.1038/s41535-021-00310-z.
[68] J. D. Brehm, R. Gebauer, A. Stehli, A. N. Poddubny, O. Sander, H. Rotzinger, and A. V.
Ustinov, “Slowing down light in a qubit metamaterial,” Applied Physics Letters, vol. 121,
no. 20, 2022, issn: 0003-6951 1077-3118. doi: 10.1063/5.0122003.
[69] P. M. Leung and B. C. Sanders, “Coherent control of microwave pulse storage in superconducting
circuits,” Phys Rev Lett, vol. 109, no. 25, p. 253 603, 2012, issn: 1079-7114
(Electronic) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.109.253603. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/23368461.
[70] K.-H. Chiang and Y.-F. Chen, “Tunable λ -type system made of a superconducting
qubit pair,” Physical Review A, vol. 106, no. 2, 2022, issn: 2469-9926 2469-9934. doi:
10.1103/PhysRevA.106.023707.
[71] Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, “Coherent control of macroscopic quantum
states in a single-cooper-pair box,” Nature, vol. 398, no. 6730, pp. 786–788, 1999, issn:
0028-0836 1476-4687. doi: 10.1038/19718.
[72] J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H.
Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived
from the cooper pair box,” Physical Review A, vol. 76, no. 4, 2007, issn: 1050-2947
1094-1622. doi: 10.1103/PhysRevA.76.042319.
[73] R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J.
Mutus, C. Neill, P. O’Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, and
J. M. Martinis, “Coherent josephson qubit suitable for scalable quantum integrated circuits,”
Phys Rev Lett, vol. 111, no. 8, p. 080 502, 2013, issn: 1079-7114 (Electronic) 0031-
9007 (Linking). doi: 10.1103/PhysRevLett.111.080502. [Online]. Available: https:
//www.ncbi.nlm.nih.gov/pubmed/24010421.
[74] A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow,
L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Generating
single microwave photons in a circuit,” Nature, vol. 449, no. 7160, pp. 328–31, 2007,
issn: 1476-4687 (Electronic) 0028-0836 (Linking). doi: 10.1038/nature06126. [Online].
Available: https://www.ncbi.nlm.nih.gov/pubmed/17882217.
[75] F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. Lancaster, T. Deuschle, C.
Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the cirac-zoller controllednot
quantum gate,” Nature, vol. 422, no. 6930, pp. 408–11, 2003, issn: 0028-0836 (Print)
0028-0836 (Linking). doi: 10.1038/nature01494. [Online]. Available: https://www.
ncbi.nlm.nih.gov/pubmed/12660777.
[76] A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J.
Schoelkopf, “Quantum-information processing with circuit quantum electrodynamics,”
Physical Review A, vol. 75, no. 3, 2007, issn: 1050-2947 1094-1622. doi: 10 . 1103 /
PhysRevA.75.032329.
[77] J. D. Strand, M. Ware, F. Beaudoin, T. A. Ohki, B. R. Johnson, A. Blais, and B. L. T.
Plourde, “First-order sideband transitions with flux-driven asymmetric transmon qubits,”
Physical Review B, vol. 87, no. 22, 2013, issn: 1098-0121 1550-235X. doi: 10 . 1103 /
PhysRevB.87.220505.
[78] F. Beaudoin, M. P. da Silva, Z. Dutton, and A. Blais, “First-order sidebands in circuit
qed using qubit frequency modulation,” Physical Review A, vol. 86, no. 2, 2012, issn:
1050-2947 1094-1622. doi: 10.1103/PhysRevA.86.022305.
[79] S. A. Caldwell, N. Didier, C. A. Ryan, E. A. Sete, A. Hudson, P. Karalekas, R. Manenti,
M. P. da Silva, R. Sinclair, E. Acala, N. Alidoust, J. Angeles, A. Bestwick, M. Block,
B. Bloom, A. Bradley, C. Bui, L. Capelluto, R. Chilcott, J. Cordova, G. Crossman, M.
Curtis, S. Deshpande, T. E. Bouayadi, D. Girshovich, S. Hong, K. Kuang, M. Lenihan, T.
Manning, A. Marchenkov, J. Marshall, R. Maydra, Y. Mohan, W. O’Brien, C. Osborn,
J. Otterbach, A. Papageorge, J. P. Paquette, M. Pelstring, A. Polloreno, G. Prawiroatmodjo,
V. Rawat, M. Reagor, R. Renzas, N. Rubin, D. Russell, M. Rust, D. Scarabelli,
M. Scheer, M. Selvanayagam, R. Smith, A. Staley, M. Suska, N. Tezak, D. C. Thompson,
T. W. To, M. Vahidpour, N. Vodrahalli, T. Whyland, K. Yadav, W. Zeng, and C. Rigetti,
“Parametrically activated entangling gates using transmon qubits,” Physical Review Applied,
vol. 10, no. 3, 2018, issn: 2331-7019. doi: 10.1103/PhysRevApplied.10.034050.
[80] N. Didier, E. A. Sete, M. P. da Silva, and C. Rigetti, “Analytical modeling of parametrically
modulated transmon qubits,” Physical Review A, vol. 97, no. 2, 2018, issn:
2469-9926 2469-9934. doi: 10.1103/PhysRevA.97.022330.
[81] X. Li, Y. Ma, J. Han, T. Chen, Y. Xu, W. Cai, H. Wang, Y. P. Song, Z.-Y. Xue, Z.-q.
Yin, and L. Sun, “Perfect quantum state transfer in a superconducting qubit chain with
parametrically tunable couplings,” Physical Review Applied, vol. 10, no. 5, 2018, issn:
2331-7019. doi: 10.1103/PhysRevApplied.10.054009.
[82] Y. Lu, S. Chakram, N. Leung, N. Earnest, R. K. Naik, Z. Huang, P. Groszkowski, E.
Kapit, J. Koch, and D. I. Schuster, “Universal stabilization of a parametrically coupled
qubit,” Phys Rev Lett, vol. 119, no. 15, p. 150 502, 2017, issn: 1079-7114 (Electronic) 0031-
9007 (Linking). doi: 10.1103/PhysRevLett.119.150502. [Online]. Available: https:
//www.ncbi.nlm.nih.gov/pubmed/29077454.
[83] Y. Zhou, Z. Zhang, Z. Yin, S. Huai, X. Gu, X. Xu, J. Allcock, F. Liu, G. Xi, Q. Yu,
H. Zhang, M. Zhang, H. Li, X. Song, Z. Wang, D. Zheng, S. An, Y. Zheng, and S.
Zhang, “Rapid and unconditional parametric reset protocol for tunable superconducting
qubits,” Nat Commun, vol. 12, no. 1, p. 5924, 2021, issn: 2041-1723 (Electronic) 2041-
1723 (Linking). doi: 10.1038/s41467-021-26205-y. [Online]. Available: https://www.
ncbi.nlm.nih.gov/pubmed/34635663.
[84] C. A. Brasil, F. F. Fanchini, and R. d. J. Napolitano, “A simple derivation of the lindblad
equation,” Revista Brasileira de Ensino de Física, vol. 35, pp. 01–09, 2013, issn: 1806-
1117.
[85] C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems:
Quantum stochastic differential equations and the master equation,” Phys Rev A Gen
Phys, vol. 31, no. 6, pp. 3761–3774, 1985, issn: 0556-2791 (Print) 0556-2791 (Linking).
doi: 10.1103/physreva.31.3761. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/9895956.
[86] I. C. Hoi, A. F. Kockum, L. Tornberg, A. Pourkabirian, G. Johansson, P. Delsing, and
C. M. Wilson, “Probing the quantum vacuum with an artificial atom in front of a mirror,”
Nature Physics, vol. 11, no. 12, pp. 1045–1049, 2015, issn: 1745-2473 1745-2481. doi:
10.1038/nphys3484.
[87] Y. Lu, A. Bengtsson, J. J. Burnett, E. Wiegand, B. Suri, P. Krantz, A. F. Roudsari,
A. F. Kockum, S. Gasparinetti, G. Johansson, and P. Delsing, “Characterizing decoherence
rates of a superconducting qubit by direct microwave scattering,” npj Quantum
Information, vol. 7, no. 1, 2021, issn: 2056-6387. doi: 10.1038/s41534-021-00367-5.
[88] I.-C. Hoi, Quantum optics with propagating microwaves in superconducting circuits.
Chalmers University of Technology, 2013, isbn: 9173858781.
[89] P. Anisimov and O. Kocharovskaya, “Decaying-dressed-state analysis of a coherently
driven three-level λ system,” Journal of Modern Optics, vol. 55, no. 19-20, pp. 3159–
3171, 2008, issn: 0950-0340 1362-3044. doi: 10.1080/09500340802302378.
[90] Q.-C. Liu, T.-F. Li, X.-Q. Luo, H. Zhao, W. Xiong, Y.-S. Zhang, Z. Chen, J. S. Liu,
W. Chen, F. Nori, J. S. Tsai, and J. Q. You, “Method for identifying electromagnetically
induced transparency in a tunable circuit quantum electrodynamics system,” Physical
Review A, vol. 93, no. 5, 2016, issn: 2469-9926 2469-9934. doi: 10.1103/PhysRevA.93.
053838.
[91] M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: Dark-state polaritons,”
Physical Review A, vol. 65, no. 2, 2002, issn: 1050-2947 1094-1622. doi: 10.1103/
PhysRevA.65.022314.
[92] J. Li, M. P. Silveri, K. S. Kumar, J. M. Pirkkalainen, A. Vepsalainen, W. C. Chien, J.
Tuorila, M. A. Sillanpaa, P. J. Hakonen, E. V. Thuneberg, and G. S. Paraoanu, “Motional
averaging in a superconducting qubit,” Nat Commun, vol. 4, p. 1420, 2013, issn: 2041-
1723 (Electronic) 2041-1723 (Linking). doi: 10.1038/ncomms2383. [Online]. Available:
https://www.ncbi.nlm.nih.gov/pubmed/23361011.
[93] J. R. Johansson, P. D. Nation, and F. Nori, “Qutip: An open-source python framework for
the dynamics of open quantum systems,” Computer Physics Communications, vol. 183,
no. 8, pp. 1760–1772, 2012, issn: 00104655. doi: 10.1016/j.cpc.2012.02.021.
[94] T. Y. Abi-Salloum, “Electromagnetically induced transparency and autler-townes splitting:
Two similar but distinct phenomena in two categories of three-level atomic systems,”
Physical Review A, vol. 81, no. 5, 2010, issn: 1050-2947 1094-1622. doi: 10.1103/
PhysRevA.81.053836.
[95] P. Alsing, D. Guo, and H. J. Carmichael, “Dynamic stark effect for the jaynes-cummings
system,” Phys Rev A, vol. 45, no. 7, pp. 5135–5143, 1992, issn: 1050-2947 (Print) 1050-
2947 (Linking). doi: 10.1103/physreva.45.5135. [Online]. Available: https://www.
ncbi.nlm.nih.gov/pubmed/9907600.
[96] X. Wang, H.-r. Li, D.-x. Chen, W.-x. Liu, and F.-l. Li, “Tunable electromagnetically
induced transparency in a composite superconducting system,” Optics Communications,
vol. 366, pp. 321–327, 2016, issn: 00304018. doi: 10.1016/j.optcom.2016.01.024.
[97] X. Wang, A. Miranowicz, H.-R. Li, F.-L. Li, and F. Nori, “Two-color electromagnetically
induced transparency via modulated coupling between a mechanical resonator and a
qubit,” Physical Review A, vol. 98, no. 2, 2018, issn: 2469-9926 2469-9934. doi: 10 .
1103/PhysRevA.98.023821.
[98] E. A. Sete, J. M. Martinis, and A. N. Korotkov, “Quantum theory of a bandpass purcell
filter for qubit readout,” Physical Review A, vol. 92, no. 1, 2015, issn: 1050-2947 1094-
1622. doi: 10.1103/PhysRevA.92.012325.
[99] P. R. Rice and R. J. Brecha, “Cavity induced transparency,” Optics Communications,
vol. 126, no. 4-6, pp. 230–235, 1996, issn: 00304018. doi: 10 . 1016 / 0030 - 4018(96 )
00102-2.
[100] M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light
fields produced in parametric amplification,” Physical Review A, vol. 30, no. 3, pp. 1386–
1391, 1984, issn: 0556-2791. doi: 10.1103/PhysRevA.30.1386.
[101] W. J. Lin, Y. Lu, P. Y. Wen, Y. T. Cheng, C. P. Lee, K. T. Lin, K. H. Chiang, M. C.
Hsieh, C. Y. Chen, C. H. Chien, J. J. Lin, J. C. Chen, Y. H. Lin, C. S. Chuu, F.
Nori, A. Frisk Kockum, G. D. Lin, P. Delsing, and I. C. Hoi, “Deterministic loading of
microwaves onto an artificial atom using a time-reversed waveform,” Nano Lett, vol. 22,
no. 20, pp. 8137–8142, 2022, issn: 1530-6992 (Electronic) 1530-6984 (Print) 1530-6984
(Linking). doi: 10.1021/acs.nanolett.2c02578. [Online]. Available: https://www.
ncbi.nlm.nih.gov/pubmed/36200986.
[102] I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sorensen, M. D. Lukin, and R. L.
Walsworth, “Optimal control of light pulse storage and retrieval,” Phys Rev Lett, vol. 98,
no. 24, p. 243 602, 2007, issn: 0031-9007 (Print) 0031-9007 (Linking). doi: 10.1103/
PhysRevLett . 98 . 243602. [Online]. Available: https : / / www . ncbi . nlm . nih . gov /
pubmed/17677964.
[103] A. V. Gorshkov, A. Andre, M. Fleischhauer, A. S. Sorensen, and M. D. Lukin, “Universal
approach to optimal photon storage in atomic media,” Phys Rev Lett, vol. 98, no. 12,
p. 123 601, 2007, issn: 0031-9007 (Print) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.
98.123601. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/17501121.
[104] M. Kervinen, J. E. Ramirez-Munoz, A. Valimaa, and M. A. Sillanpaa, “Landau-zenerstuckelberg
interference in a multimode electromechanical system in the quantum regime,”
Phys Rev Lett, vol. 123, no. 24, p. 240 401, 2019, issn: 1079-7114 (Electronic) 0031-
9007 (Linking). doi: 10.1103/PhysRevLett.123.240401. [Online]. Available: https:
//www.ncbi.nlm.nih.gov/pubmed/31922814.
[105] D. C. McKay, R. Naik, P. Reinhold, L. S. Bishop, and D. I. Schuster, “High-contrast
qubit interactions using multimode cavity qed,” Phys Rev Lett, vol. 114, no. 8, p. 080 501,
2015, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi: 10.1103/PhysRevLett.
114.080501. [Online]. Available: https://www.ncbi.nlm.nih.gov/pubmed/25768741.
[106] K.-I. Chu, X.-C. Lu, K.-H. Chiang, Y.-H. Lin, C.-D. Chen, I. A. Yu, W.-T. Liao, and
Y.-F. Chen, “Slow and stored light via electromagnetically induced transparency using
a Λ-type superconducting artificial atom,” arXiv preprint arXiv:2406.05007, 2024. doi:
10.48550/arXiv.2406.05007. [Online]. Available: https://ui.adsabs.harvard.edu/
abs/2024arXiv240605007C.
[107] S. Probst, F. B. Song, P. A. Bushev, A. V. Ustinov, and M. Weides, “Efficient and
robust analysis of complex scattering data under noise in microwave resonators,” Rev
Sci Instrum, vol. 86, no. 2, p. 024 706, 2015, issn: 1089-7623 (Electronic) 0034-6748
(Linking). doi: 10.1063/1.4907935. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/25725869.
[108] Y.-F. Chen, S.-H. Wang, C.-Y. Wang, and I. A. Yu, “Manipulating the retrieved width of
stored light pulses,” Physical Review A, vol. 72, no. 5, 2005, issn: 1050-2947 1094-1622.
doi: 10.1103/PhysRevA.72.053803.
[109] Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, and I. A. Yu, “Coherent
optical memory with high storage efficiency and large fractional delay,” Phys Rev Lett,
vol. 110, no. 8, p. 083 601, 2013, issn: 1079-7114 (Electronic) 0031-9007 (Linking). doi:
10.1103/PhysRevLett.110.083601. [Online]. Available: https://www.ncbi.nlm.nih.
gov/pubmed/23473142.
[110] B. Kannan, M. J. Ruckriegel, D. L. Campbell, A. Frisk Kockum, J. Braumuller, D. K.
Kim, M. Kjaergaard, P. Krantz, A. Melville, B. M. Niedzielski, A. Vepsalainen, R. Winik,
J. L. Yoder, F. Nori, T. P. Orlando, S. Gustavsson, and W. D. Oliver, “Waveguide
quantum electrodynamics with superconducting artificial giant atoms,” Nature, vol. 583,
no. 7818, pp. 775–779, 2020, issn: 1476-4687 (Electronic) 0028-0836 (Linking). doi: 10.
1038/s41586- 020- 2529- 9. [Online]. Available: https://www.ncbi.nlm.nih.gov/
pubmed/32728243.
[111] K. F. Reim, J. Nunn, V. O. Lorenz, B. J. Sussman, K. C. Lee, N. K. Langford, D.
Jaksch, and I. A. Walmsley, “Towards high-speed optical quantum memories,” Nature
Photonics, vol. 4, no. 4, pp. 218–221, 2010, issn: 1749-4885 1749-4893. doi: 10.1038/
nphoton.2010.30.
[112] E. Saglamyurek, T. Hrushevskyi, A. Rastogi, K. Heshami, and L. J. LeBlanc, “Coherent
storage and manipulation of broadband photons via dynamically controlled autler–townes
splitting,” Nature Photonics, vol. 12, no. 12, pp. 774–782, 2018, issn: 1749-4885 1749-
4893. doi: 10.1038/s41566-018-0279-0.

指導教授

陳永富(Yung-Fu Chen)

審核日期

2024-8-9

推文