Spins in few-electron quantum dots

Abstract

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist's viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for ͑1͒ the rotation of an electron spin into a superposition of up and down, ͑2͒ the measurement of the quantum state of an individual spin, and ͑3͒ the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins ͑i.e., single spintronics͒.

Suppression of spin-bath dynamics for improved coherence of multi-spin-qubit systems

“…We find reasonable agreement between the measured and expected values for the NV/spin-bath coupling strength ∆ in all three NV-diamond samples, with ∆ scaling approximately linearly with the N concentration. As mentioned before, the measured and expected values for the spin-bath correlation time τ c agree well for the 12 C sample. However, we find a striking discrepancy between the measured and expected values of τ c for the two samples with 1.1% 13 C concentration (Apollo and HPHT): both samples have measured spin-bath correlation times that are more than an order of magnitude longer than that given by the simple electronic spin-bath model, although the relative values of τ c for these two samples scale inversely with N concentration, as expected.…”

“…NV multi-spin measurements (for samples 12 C and Apollo) were performed using a custom-built wide-field fluorescence microscope (Fig. 4a), which has previously been used for two-dimensional magnetic field imaging with thin-layer NV-diamond samples 13 .…”

“…Examples of such systems include nitrogen-vacancy (NV) colour centres in diamond 10 , phosphorous donors in silicon 11 and quantum dots 12 . In characterizing the potential usefulness of multi-qubit systems for quantum applications, the product of the qubit density (n qb ) and the qubit coherence lifetime (T 2 ) serves as a basic figure-of-merit (FOM), FOM = n qb T 2 .…”

The many aspects of quantum dots

“…It is also possible to make a quantum dot by trapping a single molecule or nanoparticle between two electrodes, by attaching electrodes to a nanotube or to graphene, or by modulating the level of doping in a single crystal of a semiconductor 4 . Moreover, further variety is possible because the nanoparticles trapped between the electrodes can, for example, be metallic, ferromagnetic or superconducting 5 Essential characteristics of quantum dots include the fact that the energy levels occupied by the charge carriers are quantized, as in atoms and molecules, and that the bandgap between the conduction and valence bands increases as the dot gets smaller, which decreases the wavelength at which they fluoresce. Electron-electron interactions also become stronger, single-electron effects such as the Coulomb blockade are observed, and chemical properties such as the redox potential change 6 .…”

Controlled high-fidelity navigation in the charge stability diagram of a double quantum dot

“…Particularly, the most used setup for semiconductor qubits consists of two coupled semiconductor quantum dots where the confinement potential and charge state can be controlled with high accuracy [7]. In principle, charge or spin qubits can be manipulated by both optical and electrical methods.…”