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研究生:林冠廷
研究生(外文):Kuan-Ting Lin
論文名稱:鏡前一維超導量子位元陣列之可擴充的集體蘭姆位移
論文名稱(外文):Scalable collective Lamb shift of a 1D superconducting qubit array in front of a mirror
指導教授:林俊達林俊達引用關係
指導教授(外文):Guin-Dar Lin
口試委員:陳應誠管希聖許耀銓郭華丞
口試委員(外文):Ying-Cheng ChenHsi-Sheng GoanIo-Chun HoiWatson Kuo
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:應用物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:英文
論文頁數:63
中文關鍵詞:偶極-偶極交互作用集體蘭姆位移超輻射亞輻射量子壓縮
外文關鍵詞:Dipole-dipole interactionCollective Lamb shiftSuperradianceSubradianceQuantum squeezing
DOI:10.6342/NTU202000176
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本論文主要探究一維人造原子陣列間的偶極-偶極交互作用,如同原子間的偶極-偶及交互作用,由於原子間會互相交換虛光子,藉此,原子能級會產生位移,其被稱為集體蘭姆位移。為了測量此位移,我們考慮真實實驗架構:將一維傳輸線的一端斷路並與一維超導量子位元陣列相互耦合,此架構可被等效為一維超導量子位元陣列被置於鏡前,藉此,量子位元感受到電場不再是行進波,而是駐波。我們透過理論計算反射頻譜發現當我們將一個位元放置在波腹上而另一個位元放在波節上,其反射頻譜會有兩個分裂的低谷,這個巨大的分裂可以間接地反映出此雙位元系統具有巨大的集體蘭姆位移。此外,我們更進一步的考慮兩個不同的量子位元系統、引進去同調化效應,並且推導其主方程式。我們也計算其他多體協同性效應,如:超輻射及亞輻射,並且探究集體蘭姆位移與多量子位元系統的關聯性。不僅如此,我們還探究由偶極-偶極交互作用媒介的量子壓縮,我們發現當此一維量子位元陣列為超輻射組態時,多位元的量子壓縮態無法辦法被產生。
We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line. Similar to the atomic cases, RDDI comes from exchange of virtual photons of the continuous modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located at an antinode. This directly implies the interplay of virtual photon processes and explicitly signals the CLS. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved. Meanwhile, the RDDI mediated quantum squeezing of the resonance mode of radiation fields from the multiple qubits is also addressed. In the superradiant regime, when more than 10 qubits are involved, the squeezing is vanishing and the single mode coherent state is observed.
致謝i
摘要ii
Abstract iii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Resonant dipole-dipole interaction in a 3D space . . . . . . . . . . . . . . . 3
1.3 Quantum squeezing of output fields . . . . . . . . . . . . . . . . . . . . . . 5
1.4 A transmon qubit as a two-level atom . . . . . . . . . . . . . . . . . . . . . 7
1.5 Open quantum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.2 Born-Markov approximation . . . . . . . . . . . . . . . . . . . . . . 11
1.5.3 Lindblad form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5.4 The numerical method . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Model 17
2.1 Dipole-dipole interaction and master equation . . . . . . . . . . . . . . . . . 17
2.2 Scattering and reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Input-output formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Squeezing spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Superradiance and collective Lamb shift for two-atom cases 26
3.1 Reflection spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Dephasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Power broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Multi-atom cases 35
5 Squeezing for the output field 39
5.1 Single atom case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Many-atom case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Conclusion 43
A Derivation of dipole-dipole interaction 46
B Multi-level system 48
C Correlation function of variance operators 50
D Squeezing spectrum for a single atom 52
Bibliography 55
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