以磁共振力顯微鏡量測單一自旋之理論研究

Abstract

從單一分子結構的成像到量子電腦的實現，單一電子自旋以及單一核子自旋的量測一直都是科學家們所感興趣的。「磁共振力顯微鏡（Magnetic Resonance Force Microscopy）MRFM」被認為是最有可能實現單一自旋量測的技術之一。磁共振力顯微鏡結合了「原子力顯微鏡（Atomic Force Microscopy）」以及「核磁共振（Nuclear Magnetic Resonance）」的原理，能夠觀測極小的磁矩。最近的實驗結果顯示MRFM能夠達到單一電子自旋的解析度，但是訊雜比仍然十分微弱，以至於需費時數小時才能累積足夠的訊號以平均雜訊的干擾。在本論文中，我們研究以MRFM量測單一自旋的理論分析，並且探討一個稱為「震盪探針驅動極緩翻轉（Oscillating Cantilever driven Adiabatic Reversal）OSCAR」的MRFM量測方案。我們使用兩種不同的回饋控制以實現OSCAR方案，並且進一步執行此系統的數值模擬以驗證理論分析的結果。我們更進一步研究另一個以MRFM量測單一核子自旋態的方案，在此方案中，探針的震盪頻率與自旋的拉摩（Larmor）頻率是相同的，使得我們可以以純機械方式實現核磁共振的原理。在本論文的最後，我們估計量測單一電子自旋以及單一核子自旋的訊雜比，並且討論以MRFM量測單一的可行性。

The problem of measuring a single electron spin or a single nuclear spin is of great interest for a variety of purposes, from imaging the structure of a single molecule to spin-based quantum information processing. Magnetic resonance force microscopy (MRFM) has been proposed as one of the most promising techniques for direct single-spin detection. This MRFM technique combines ultra-sensitive force detection with principles of magnetic resonance. As a result, it could be regarded as a combination of the technologies of atomic force microscopy and nuclear magnetic resonance (NMR). Recently, MRFM has been demonstrated experimentally to achieve a detection sensitivity of a single electron spin. But the signal-to noise ratio is still very weak, so the required averaging time of several hours is still too long to achieve the real-time readout of the single electron spin quantum state. In this thesis, we study theoretically to detect a single spin using MFRM and discuss in particular a detection protocol called the OScillating Cantilever driven Adiabatic Reversal (OSCAR) protocol. Two different feedback schemes are investigated to achieve the OSCAR protocol, and numerical simulations are performed to verify it. We furthermore investigate to use a cantilever with a frequency equal to the Larmor frequency of a single nuclear spin to achieve the purely mechanical NMR detection of the single nuclear spin. Finally, an estimate of the signal-to-noise ratio of measuring a single electron and a single proton spin is presented and the feasibility to detect a single nuclear spin is discussed.