Laser cooling and spin resonance of a single spin in a quantum dot

一个电子除了它的电荷之外还有自旋，这是一种量子力学性质。多年来，已经提出了设计通过操纵电子自旋而不是电荷来操作的电子器件的建议。最终的极限是探测和操纵单个电子的自旋。单个自旋可以存在于自旋状态的任意叠加中，自旋向上和自旋向下，并且在纠缠态中可以存在不止一个自旋，这些特性在密码学和计算中可能具有巨大的益处。不过很明显，操纵单自旋的脆弱量子态是极具挑战性的。该提案试图通过首先在量子点（纳米结构半导体）中捕获单个电子，然后用高度相干的激光进行操纵来实现这一目标。其目标不仅是开发将单个自旋初始化为所选量子态的基本能力，而且还要了解电子自旋与其复杂宿主环境相互作用的基本方式。这些相互作用包括与移动的电子自旋的隧穿相互作用、高度依赖于点和磁场的声子过程以及与主体材料的核自旋的相互作用，可能还有其他的。第一个挑战是只处理单个电子。这可以通过利用两个电子的库仑排斥来实现。在所谓的库仑阻塞机制中，只有一个电子占据量子点;第二个电子被两个电子之间的巨大库仑排斥所禁止。在纳米尺寸的量子点中，例如由GaAs制成的具有自组装的量子点，库仑阻塞非常明显，并且在4.2 K下完全建立，这是一个低但容易达到的温度。第二个挑战是操纵旋转。这是一项非常重要的任务。该提案旨在通过利用跨越半导体的基本间隙的强光学跃迁来实现这一点。光学跃迁将使用激光器的高度相干输出来驱动，该激光器的频率被调谐到量子点的共振。至关重要的是，半导体量子点具有明确定义的选择规则。自旋向上的电子与右旋圆偏振的激光光子相互作用，但不与左旋圆偏振的光子相互作用，反之亦然。这使得在磁场中，通过用激光泵浦自旋，电子自旋被投射到自旋向上或自旋向下的状态;而在没有磁场的情况下，通过控制激光偏振，自旋可以被投射到任意叠加态的可能性很大。事实上，用激光器连续泵浦应该防止自旋松弛，使得自旋状态可以潜在地保持长时间。自旋共振，即电子自旋的磁偶极跃迁，是一种用于探测自旋的成熟技术。它总是在大量的电子上进行，以增强信号。这里的建议是只对一个电子进行自旋共振。关键的想法是使用量子点的光学响应作为自旋共振的探测器，因为这既提供了巨大的放大-微波光子的吸收导致光子的吸收-又大大降低了空间分辨率-探测体积由小的光波长而不是由大的微波波长确定。最后，该提案解决了如何通过监测共振荧光（共振激光产生的自发辐射）来测量单个电子的自旋状态的问题。

An electron has in addition to its charge a spin, a quantum mechanical property. For some years, proposals have been made to design electronic devices which operate by manipulating electronic spin rather than charge. The ultimate limit is to probe and manipulate individual electron spins. A single spin can exist in an arbitrary superposition of spin states, spin-up and spin-down, and more than one spin can exist in entangled states, properties that are potentially of enormous benefit in cryptography and computing. Clearly though, it is extremely challenging to manipulate the fragile quantum states of just a single spin. This proposal attempts to achieve this by first trapping a single electron in a quantum dot, a nano-structured semiconductor, and second, performing the manipulation with a highly coherent laser. The goal is not only to develop basic capabilities in initializing a single spin into a quantum state of choice but also to understand the fundamental way an electron spin interacts with its complex host environment. These interactions include tunneling interactions with mobile electron spins, highly dot and magnetic field dependent phonon processes, and interactions with the nuclear spins of the host material, and there may be others.The first challenge is to address just a single electron. This can be achieved by exploiting the Coulomb repulsion of two electrons. In the so-called Coulomb blockade regime, just one electron occupies the quantum dot; a second electron is prohibited from entering the dot by the large Coulomb repulsion between the two electrons. In a nano-sized quantum dot, for instance one made in GaAs with self-assembly, the Coulomb blockade is very pronounced and is completely established at 4.2 K, a low but easily-accessed temperature. The second challenge is to manipulate the spin. This is a highly non-trivial task. This proposal aims to achieve this by exploiting the strong optical transition across the fundamental gap of a semiconductor. The optical transition will be driven using the highly coherent output of a laser whose frequency is tuned to the resonance of the quantum dot. Crucially, a semiconductor quantum dot has well-defined selection rules. A spin up electron interacts with a laser photon with right-handed circular polarization but not with a photon with left-handed circular polarization, and vice versa. This enables schemes to be dreamt up whereby in a magnetic field, an electron spin is projected into either the spin up or spin down states by pumping the spin with the laser; and without a magnetic field, there is a strong possibility that the spin can be projected into an arbitrary superposition simply by controlling the laser polarization. In fact, continuous pumping with the laser should prevent the spin from relaxing such that a spin state can be potentially maintained for long periods of time. Spin resonance, the magnetic dipole transition of an electron spin, is a well established technique for probing spins. It is invariably carried out on a huge number of electrons in order to boost the signal. The proposal here is to perform spin resonance on just one electron. The crucial idea is to use the optical response of the quantum dot as a detector for spin resonance as this offers both a huge amplification - the absorption of a microwave photon results in the absorption of an optical photon - and a massive reduction in spatial resolution - the probing volume is determined by the small optical wavelength and not by the large microwave wavelength. Finally, the proposal addresses the question how to measure the spin state of a single electron by monitoring the resonance fluorescence, the spontaneous emission generated by the resonant laser.