Quantum Dots
Quantum dots are artificially fabricated solid-state objects with sizes in the nanometers range (2-10 nm or 10-50 atoms wide). They confine the motion of charge carriers in all three spatial dimensions in the conduction band by creating a potential of the order of 0.1 eV to 1 eV.
Some notable applications of quantum dots include:
- Displays: Quantum dots enable the creation of displays with enhanced image quality, sharper details, and wider color gamuts.
- Solar cells: Quantum dots can be utilized in solar cells to improve their efficiency in converting sunlight into electricity.
- Biosensors: Quantum dots find application in biosensors, allowing for the detection of specific molecules in biological samples.
To create quantum dots, a semiconductor material like gallium arsenide or cadmium selenide is initially heated to a high temperature until it melts. The molten material is then rapidly cooled, causing it to solidify into tiny particles—these particles are the quantum dots.
The size of quantum dots plays a crucial role in determining their properties. Smaller quantum dots emit blue light, while larger ones emit red light. This property enables the creation of quantum dots that can emit a wide range of colors.
Quantum dots represent a highly promising technology with numerous potential applications. Ongoing research in this field continues to unveil new and innovative uses for these minuscule particles.
- Quantum dots are so small that they can only be observed using an electron microscope.
- The size and shape of quantum dots directly influence their properties.
- Quantum dots can be fabricated from various semiconductor materials, including gallium arsenide, cadmium selenide, and indium phosphide.
- Quantum dots are often combined with other materials like polymers and organic molecules to enhance their functionalities.
- The field of quantum dots is rapidly advancing, with continuous exploration leading to the discovery of novel applications.
Quantum Computation Through Quantum Dots
The reason for using quantum dots as qubits is that the energy spectrum of a quantum dot is quantized due to the separation of energy levels of the order of a few meV by the created potential. The size of the quantum dot is very important because smaller quantum dots have larger energy differences between the ground and first excited states.
Therefore, the electronic properties of quantum dots can be changed by applying an external electromagnetic field. This makes them promising candidates for use as qubits in future quantum computers.
Lateral quantum dots are formed at different locations during the growth of two crystals from different substances due to the mismatch of lattice between the dot and substrate material. This creates structures layer by layer with different bandgaps. For example, GaAs3 is a lateral quantum dot that is fabricated from crystals of different substances of GaAs and AlGaAs during their growth.
A thin sheet of free charge carriers with a size of nearly 10 nanometers can be introduced. These free charge carriers can move and accumulate along the GaAs/AlGaAs interface, which is nearly 50-100 nanometers below the surface. This can be done through different techniques, such as current injection or doping. This creates a 2D electron or hole gas.
Surface gates can be introduced on top of the heterostructure to deplete locally small regions of the 2D electron or hole gas with the help of an electric field. This controls the number of electrons in quantum dots and the tunnel coupling of electrons between quantum dots and reservoirs. This gives the isolating properties of blocking layers.
The tunneling of electrons between quantum dots and reservoirs can be suppressed at low temperatures. This is known as Coulomb blockade (CB). This allows access to the quantum regime and avoids thermal excitations. In Coulomb blockade, the tunneling of electrons onto or off the quantum dot is suppressed at very low temperatures, which is about 20 millikelvins. This means that the charge in the quantum dot is conserved.
Qubits in quantum dots can be stored in the spin degree of freedom of single confined electrons. The two spin states are |↑> ≡ |0> and |↓> ≡ |1>, which are first-order insensitive to voltage fluctuations.
When a magnetic field is applied along the z-axis, the Zeeman splitting occurs, and the two spin states split according to the equation:
ωz = gµBB
where:
- g is the splitting factor, also known as the Landé g-factor
- µB is the Bohr magneton
- B is the magnetic field strength
The value of g for a quantum dot is typically around -0.44.
It is difficult to measure the spin directly in a quantum dot. Instead, it is typically measured through spin-to-charge conversion. This involves applying a voltage to the quantum dot that depends on the spin state of the electron.
Spin-to-charge conversion is a technique used to read out the spin state of an electron in a quantum dot. It works by exploiting the difference in tunneling rates between electrons with different spin states.
When the Zeeman splitting, ωZ, exceeds the thermal energy, kBT, the energy difference between the two spin states can be used to make the tunneling rate of electrons from a point to convert spin-state information into charge.
An electron with spin state |↓> can tunnel off the dot to a reservoir whose potential is µres, by changing the occupation number. This means that the number of electrons in the dot will decrease by one. An electron with spin state |↑> is trapped into the quantum dot, due to which the occupation number remains unchanged.
In this way, we can read-out the spin states of qubits to perform quantum computation. This is a promising technique for quantum computing, as it allows us to measure the spin state of an electron without destroying it.