動力學解耦(DD) 是一種源於核磁共振(NMR) 的技術。通過快速地控制量子系統， DD可以把不需要的耦合抑制。它可以用來保護處於噪音環境中的量于系統或者用來測量環境噪音譜，甚至它可以用來測量單分子的核磁共振信號。 / 在論文的第一部分，我們主要研究和設計DD技術來保護量子系統。(i)我們提出最套DD來保護量子算符，例如嵌套Uhrig DD (NUDD)。NUDD保護一個相互正交算符集(MOOS); 通過保護這個MOOS算符集， NUDD可以保護所有由MOOS生成的算符。對於量子比特系統，任何一個物理量都可以由NUDD保護;而且，NUDD可以通過單量子比特的操作實現。由於對於單量子比特系統， NUDD 剛好是內層含有偶數階UDD 的quadratic DD (QDD). 所以我們證明了內層含有偶數階UDD 的QDD可以達到設計上所期待的效能。隨著解耦階數的增長， NUDD 只需要多項式增長的脈衝數目，而以前的最套DD(CDD)則要指數增長的脈衝數目。基於保護MOOS 的DD可以用一種通用的有限寬度的服衝代替理想的瞬時脈衝，這種非瞬時的脈衝只會引起正比於脈衝寬度的二階小量的誤差。(ii) 我們也證明了，如果一個動態操控方法能夠以一定的控制精度O(TN +1 )控制一個與不依賴於時間的通屬量子庫耦合的量子系統，那麼它也能夠以同樣階數的精度控制含時的這類系統。這裡T是很短的控制時間。這個結果拓展了各種普適量子控制方法的應用範圍，使它們也可以用於含時系統。(iii) 一個量子系統如果和一個無限大的環境耦合，它會受到馬科夫噪音的影響。這種噪音的關聯函數對於時間的級數展開會有奇數項。我們證明，對於這種噪音， DD不會特別有效，因為退相干只能被DD抑制到一定的階數(以時間的級數展開的階數計算)。在這種噪音下，我們做了DD 的脈衝優化。我們發現，當脈衝比較少的時候，它和UDD序列一樣，但當脈衝比較多的時候，它接近於Carr-Purcell-Meiboom-Gill(CPMG)序列 。對於關聯函數對時間的級數展開含有線性項的情況， CPMG序列在時間很短的情況下是最優的。我們也得到了外加約束條件的做衝序列優化方程組，通過解這方程組，我們得到了一些DD序列，它們可以完全消去由非均勻展寬導致的退相干。(iv) 我們通過一個例子演示了，如果我們不能解析地優化量子控制方案，遺傳算法是很有用的。遺傳算法可以有效地得到優化的控制方案。對比以前的控制方案，我們通過遺傳算法得到的控制方案在性能上好很多。 / 在論文的第二部分，我們提出用原子干涉技術和動力學解捐助〈衝技術來選擇性地測量隨時間變化的引力場。通過惆整脈衝序列的時間，我們可以提取特定頻率下的信號或者噪音譜。我們得到了通用的相移公式。這些公式對於任意的π 脈衝序列都適用。當引力場的漲落對於光子的頻率的變化可以忽略的時候，由引力場引起的相位差和序列時間T的二次方成正比，或者對於某個測量頻率，相位差和脈衝數N成正比。對於引力波探測，這個相位差和自永衝數N的平方成正比，所以，對比於以前的π/2一π一π/2序列，我們的方法提供了額外的N²倍信號放大。 / Dynamical decoupling (DD) is a technique originated from the spin echo techniques in nuclear magnetic resonance (NMR). DD can average out unwanted couplings through fast control on the quantum systems. It has applications in protection of quantum systems from noisy environments, measurements of environmental noise spectra, and even NMR of single molecule. / In the first part of this thesis, we study and design DD techniques for quantum system preservation. (i) We propose nested DD, such as nested Uhrig DD (NUDD), for protection of system operators. NUDD protects a set of mutually orthogonal operators (a MOOS) and hence all system operators generated by the MOOS. For multiqubit systems, any physical quantities can be protected, and NUDD can be implemented by single-qubit operations. For single-qubit systems NUDD reduces to quadratic DD (QDD) with even-order UDD on the inner level. Thus we have proved the validity of QDD with even-order DD on the inner level. NUDD achieves a desired decoupling order with only a polynomial increase in the number of pulses, with exponential saving of the number of pulses as compared with concatenated DD (CDD) of the same decoupling order. DD based on protection of a MOOS can be implemented with pulses of finite amplitude, up to an error in the second order of the pulse durations. (ii) We also establish that if a scheme can control a time-independent system arbitrarily coupled to a generic finite bath over a short period oftime T with control precision O(T[superscript N]⁺¹), it can also realize the control with the same order of precision on smoothly time-dependent systems. This result extends the validity of various universal dynamical control schemes to arbitrary analytically time-dependent systems. (iii) A quantum systems coupled to infinite baths feels a Markovian noise. The short-time correlation function expansion of this noise has odd-order expansion terms. We proof that in this case DD is not very efficient and the decoherence can be suppressed only to some order in short-time T. In the optimization of pulse sequence for a qubit under dephasing due to Markovian noise, the optimal sequences coincide the Uhrig DD sequence when the number N of pulses is small, and they resemble Carr-Purcell-Meiboom-Gill (CPMG) sequences when N is large. For a special case, if the short-time correlation function expansion has a linear term in time, the CPMG sequences are optimal in short-time limit. We have also derived the optimizing equations for suppressing decoherence with arbitrary constraints, and have obtained optimized sequences that can also perfectly eliminate the decoherence due to inhomogeneous broadening. (iv) When analytic results is not possible, we demonstrate that genetic algorithm may be useful by showing an optimized quantum control which has much better performance than the previous results. / In the second part, we combine atom interferometry and dynamical decoupling pulse sequences to selectively measure time-dependent gravitational fields. Using the pulse sequences, we can extract signals or noise with certain frequencies by tuning the timing of the sequences. We obtain the general phase-shift formulas for arbitrary π pulse sequences. When the effect of gravity fluctuations on the light is not considered in the interferometers, the phase shift due to gravitational fields scales quadratically with the duration time T of pulse sequences or linearly with the number N of pulses for a given detection frequency. For gravitational wave detection, the phase shift due to the spacetime fluctuations scales quadratic ally with the number N of pulses, N²-fold enhancement over the traditional π/2-π-π/2 sequences. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Zhenyu = 信息處理和頻譜測定中的量子相干動態操控 / 王振宇. / "December 2011." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 100-112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Wang, Zhenyu = Xin xi chu li he pin pu ce ding zhong de liang zi xiang gan dong tai cao kong / Wang Zhenyu. / Abstract --- p.iii / Acknowledgment --- p.vii / List of Figures --- p.xiii / List of Appendices --- p.xiv / Chapter 1 --- Introduction and Outline --- p.1 / Chapter I --- Dynamical Control of Quantum Coherence / Chapter 2 --- Introduction --- p.5 / Chapter 3 --- Decoherence and Dynamical Control --- p.11 / Chapter 3.1 --- Quantum decoherence --- p.11 / Chapter 3.1.1 --- Semiclassical picture of decoherence --- p.12 / Chapter 3.1.2 --- Quantum picture of decoherence --- p.13 / Chapter 3.2 --- Dynamical control of open quantum systems --- p.14 / Chapter 3.3 --- Protection of system operators --- p.15 / Chapter 4 --- Dynamical Oecoupling for Quantum Systems --- p.19 / Chapter 4.1 --- Dynamical decoupling for a qubit --- p.19 / Chapter 4.1.1 --- A semiclassical model --- p.19 / Chapter 4.1.1.1 --- Filter functions --- p.21 / Chapter 4.1.2 --- Geometrical view of decoherence and control --- p.22 / Chapter 4.1.3 --- Uhrig dynamical decoupling (UDD) --- p.25 / Chapter 4.2 --- Nested dynamical decoupling for quantum systems --- p.26 / Chapter 4.2.1 --- Mutually orthogonal operation set --- p.26 / Chapter 4.2.2 --- Lowest-order protection of system operators --- p.29 / Chapter 4.2.3 --- Higher-order protection by nesting and concatenation --- p.31 / Chapter 4.2.4 --- Higher-order protection by nested UDD (NUDD) --- p.33 / Chapter 4.2.4.1 --- A theorem on UDD control of time-dependent systerns --- p.34 / Chapter 4.2.4.2 --- Nested Uhrig dynamical decoupling (NUDD) --- p.37 / Chapter 4.2.5 --- Pulses of finite amplitude --- p.39 / Chapter 5 --- Dynamical Control for Time-Dependent Hamiltonians --- p.43 / Chapter 5.1 --- Universal control of time-independent systems --- p.44 / Chapter 5.2 --- Time-dependence in interaction frames --- p.44 / Chapter 5.3 --- Generalization to time-dependent systems --- p.45 / Chapter 6 --- Dynamical Decoupling for Noise Spectra with Soft Cutoff --- p.49 / Chapter 6.1 --- Decoherence functions in frequency domain --- p.50 / Chapter 6.2 --- Performance of dynamical decoupling against noise with soft highfrequency cutoff --- p.53 / Chapter 6.3 --- Relation between noise correlation and high-frequency cutoff --- p.54 / Chapter 6.4 --- Sequence optimization --- p.57 / Chapter 6.4.1 --- Short-time optimization --- p.57 / Chapter 6.4.2 --- Optimization with constraints --- p.59 / Chapter 7 --- Design of Optimal Control by Genetic Algorithm --- p.64 / Chapter 8 --- Summary and Discussions --- p.69 / Chapter II --- Dynamical Decoupling for Gravitational Spectrometry / Chapter 9 --- Introduction --- p.73 / Chapter 10 --- Selective Detection of Gravitational Field by Dynamical Decoupling --- p.75 / Chapter 10.1 --- Atom interferometry --- p.75 / Chapter 10.2 --- Phase shift calculation --- p.76 / Chapter 10.2.1 --- Path phase Δφ[subscript path] --- p.79 / Chapter 10.2.2 --- Laser phase Δφ[subscript laser] --- p.80 / Chapter 10.3 --- Spectroscopy by dynamical decoupling --- p.82 / Chapter 10.4 --- Effects due to gravity gradient --- p.85 / Chapter 11 --- Gravitational Wave Antenna by Dynamical Decoupling --- p.89 / Chapter 11.1 --- Configuration and simple understanding --- p.89 / Chapter 11.1.1 --- Path phase --- p.93 / Chapter 11.1.2 --- Laser phase --- p.95 / Chapter 11.2 --- Gravitational wave signal --- p.96 / Chapter 12 --- Summary and Discussions --- p.99 / Bibliography --- p.100
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328151 |
| Date | January 2012 |
| Contributors | Wang, Zhenyu, Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xiv, 143 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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