Quantum physics

Swift control of a single spin

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For now, quantum information processing systems remain a dream. Step by step, however, progress towards that goal is being made, with one promising route involving a novel means of manipulating electron spin.

The basic quantity of magnetic recording — the working principle of a computer's hard disk — is an electron's spin. Although the technology for magnetic recording is reaching recording densities as high as 1 terabit per square inch (ref. 1), storing a single bit of information still involves around 105 electron spins. Future quantum information processing systems that use the electron's spin as a unit of quantum information2,3 — a quantum bit or qubit — will require the qubit to be stored in a single spin and manipulated on a timescale in which the coherence of the spin is preserved. Press et al.4 (page 218 of this issue) report that, using ultrafast laser pulses, they have controlled and observed the spin of a single electron in a semiconductor during the spin's coherence time.

The quantum state of a qubit that is based on an electron's spin can be described by a vector, known as a Bloch vector, in a sphere (a Bloch sphere), as shown in Figure 1. An arbitrary single-qubit gate operation is expressed in terms of the rotation of the Bloch vector. In general, the process is split into three rotation steps, called Euler rotations — for example, two rotations about the x axis and one about the z axis. But how can spin-state rotations with arbitrary angles about the two axes be achieved? The rotation about the z axis is implemented by applying a static magnetic field along this axis. This field induces the energy separation between the spin-up and spin-down states, known as Zeeman splitting, and the spin state precesses about the z axis with an angular frequency that is proportional to the amplitude of the field — a phenomenon known as Larmor precession. The rotation about the x axis is achieved by applying an oscillating (microwave) driving field that is resonant with the energy separation between the spin-up and spin-down states. This technique is called electron spin resonance (ESR). The coherent interaction between the spin state and the oscillating field results in the periodic rotation of the spin state about the x axis, and is called Rabi oscillation.

Figure 1: Bloch sphere of an electron's spin.
figure1

A semiconductor quantum dot containing an extra electron acquires a net spin. The quantum state of the electron's spin is represented by a vector (bold arrow) from the origin of the Bloch sphere to a point on its surface: the spin-up and spin-down states are at the north and south poles, respectively; and the spins that correspond to equal superpositions of the spin-up and spin-down states are in the equatorial plane. The spin rotation about the z axis is achieved by applying a static magnetic field (B) along the z axis; the spin rotation about the x axis is produced by a circularly polarized optical pulse injected along the x axis. Press et al.4 demonstrate that arbitrary Euler rotations of the spin state can be accomplished by combining these two processes.

Although the rotation of a single electron spin has been successfully demonstrated using ESR5,6, the time required to achieve rotation with this technique is rather long — typically longer than a few nanoseconds. For quantum information processing to remain effective, rotation must be performed within a timescale that is much shorter than the spin's decoherence time.

One way of increasing the spin-state rotation is to use ultrafast laser pulses. In place of the microwave field used in ESR, a circularly polarized laser pulse is applied along the x axis (Fig. 1). The laser induces transitions between the two spin states through intermediate excited states in a process called stimulated Raman adiabatic passage (STIRAP)7,8. The effect of STIRAP is to rotate the spin about the x axis, as in ESR.

Another challenge for spin-based quantum information processing is to establish a technique for observing the spin state of a single electron. Until now, optical5,9,10 and electrical6,11 methods have done the job. Optical pumping5,10 in particular, which is a standard technique in atomic systems12, can be a sensitive tool for single-spin detection. In this method, one observes the emission (or absorption) of a photon following spin-selective optical excitation by a pumping laser. A further advantage of this technique is that the same laser can be used to initialize the spin state.

Press et al.4 have exploited ultrafast laser control and optical pumping to manipulate a single electron spin in a semiconductor using charged quantum dots. Quantum dots are nanometre-sized, artificially fabricated semiconductor structures in which electrons are confined in all three dimensions. The ground state of a neutral quantum dot has no net spin because it forms a singlet state with equal numbers of spin-up and spin-down electrons. When an extra electron, or an electron 'hole', is added to a neutral quantum dot, it will acquire a net charge and a spin. This can be achieved, for instance, by introducing impurities in the semiconductor, a method known as doping.

The above techniques can be used in combination with an optical microscope to optically control and observe the spin state in a single quantum dot. In Press and colleagues' experiment4, the spin state was initialized to the spin-up state by optical pumping. The spin state was then rotated about the x axis by a laser pulse through STIRAP. By changing the intensity of the rotating laser pulse, the authors obtained a remarkable result: they observed up to six and a half rotations (periodic Rabi oscillations) of a single spin state.

In a second experiment, the authors observed an effect known as Ramsey interference. The initialized spin-up state was first rotated by 90° about the x axis, and then rotated by an arbitrary angle about the z axis using Larmor precession. After a certain period, it was rotated back by −90° about the x axis. In terms of Euler rotations, the total process corresponds to performing a rotation about the y axis. The spin state projected onto the z axis was then observed using optical pumping and photon detection. The result was the observation of Ramsey fringes of interference with amplitudes that decay within about 200 picoseconds. This experiment is the first clear proof-of-principle demonstration of complete control of the single-spin state using an ultrafast laser.

There is no experiment that doesn't have a few 'buts'. First, the measurement of the spin state was obtained from a large, time-averaged ensemble of events, not from a single-shot measurement, a feat that has already been achieved using an electrical method11. Second, the amplitude of the Rabi oscillation fell with increasing number of rotations because of incoherent processes induced by the laser rotating the spin. Decoherence in the Ramsey fringes also seems to occur quite rapidly; the short coherence time is attributed mainly to the continuous optical pumping, and could be made longer in future experiments. If the spin coherence time in quantum dots is extended to a few microseconds13, 105 single-qubit gate operations could occur within this time4.

We have reached a stage at which we can manipulate and observe a single electron spin: albeit not perfectly, we have obtained arbitrary single-qubit gates of spins. The next step will be to realize scalable two-qubit gates, which, together with the single-qubit gates, can form a universal set for quantum computing2,14. Another challenge is to interface electron-spin-based qubits with other qubits, such as photons or nuclear spins, so that we can use appropriate qubits for different tasks, such as processing, communicating and storing quantum information.

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Edamatsu, K. Swift control of a single spin. Nature 456, 182–183 (2008) doi:10.1038/456182a

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