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

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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.