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

电子除了带电荷外，还有自旋，这是一种量子力学性质。多年来，一直有人提议设计通过操纵电子自旋而不是电荷来操作的电子设备。最终的极限是探测和操纵单个电子自旋。单个自旋可以存在于自旋态的任意叠加中，自旋向上和自旋向下，并且可以在纠缠态中存在不止一个自旋，这些特性在密码学和计算中具有潜在的巨大好处。然而，显然，操纵只有一个自旋的脆弱量子态是极具挑战性的。这一提议试图通过首先在量子点-纳米结构半导体中捕获单个电子，然后使用高度相干的激光进行操纵来实现这一点。我们的目标不仅是开发将单个自旋初始化为所选择的量子态的基本能力，而且还要了解电子自旋与其复杂的宿主环境相互作用的基本方式。这些相互作用包括与移动电子自旋的隧道相互作用，高度依赖于点和磁场的声子过程，以及与宿主材料的核自旋的相互作用，而且可能还有其他相互作用。第一个挑战是只解决单个电子。这可以通过利用两个电子的库仑斥力来实现。在所谓的库仑阻挡机制中，只有一个电子占据量子点；第二个电子被两个电子之间的大库仑排斥力阻止进入量子点。在纳米尺寸的量子点中，例如由自组装的砷化镓制成的量子点，库仑阻塞非常明显，并在4.2K完全建立起来，这是一个很低但很容易获得的温度。第二个挑战是操纵旋转。这是一项非常重要的任务。这一提议旨在通过利用跨越半导体基本禁带的强烈光学跃迁来实现这一点。光学转换将使用激光的高度相干输出来驱动，激光的频率被调谐到量子点的共振。至关重要的是，半导体量子点有明确的选择规则。自旋向上的电子与具有右旋圆极化的激光光子相互作用，而不与具有左旋圆极化的光子相互作用，反之亦然。这使得人们能够设想这样的方案，即在磁场中，电子自旋通过用激光泵浦自旋而投射到自旋向上或向下的状态；而在没有磁场的情况下，很有可能只通过控制激光偏振就可以将自旋投射到任意叠加。事实上，用激光连续泵浦应该可以防止自旋松弛，从而有可能在较长时间内保持自旋状态。自旋共振，即电子自旋的磁偶极跃迁，是一种成熟的探测自旋的技术。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。关键的想法是利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学光子的吸收-也提供了空间分辨率的大幅降低-探测体积由小的光学波长决定，而不是由大的微波波长决定。最后，该方案解决了如何通过监测共振荧光来测量单电子的自旋态的问题，共振荧光是由共振激光产生的自发辐射。

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.