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This "accordion lattice" was able to vary the lattice periodicity from 1.30 to 9.3 μm. More recently, a different method of real-time control of the lattice periodicity was demonstrated, [9] in which the center fringe moved less than 2.7 μm while the lattice periodicity was changed from 0.96 to 11.2 μm. Keeping atoms (or other particles ...
Bloch oscillations were predicted by Nobel laureate Felix Bloch in 1929. [1] However, they were not experimentally observed for a long time, because in natural solid-state bodies, is (even with very high electric field strengths) not large enough to allow for full oscillations of the charge carriers within the diffraction and tunneling times, due to relatively small lattice periods.
In 2013 optical lattice clocks (OLCs) were shown to be as good as or better than caesium fountain clocks. Two optical lattice clocks containing about 10 000 atoms of strontium-87 were able to stay in synchrony with each other at a precision of at least 1.5 × 10 −16, which is as accurate as the experiment could measure. [21]
The difference is in the length and energy scales. Lattice constants of atomic crystals are of the order of 1Å while those of superlattices (a) are several hundreds or thousands larger as dictated by technological limits (e.g. electron-beam lithography used for the patterning of the heterostructure surface). Energies are correspondingly ...
The phase modulation of the Bloch state = is the same as that of a free particle with momentum , i.e. gives the state's periodicity, which is not the same as that of the lattice. This modulation contributes to the kinetic energy of the particle (whereas the modulation is entirely responsible for the kinetic energy of a free particle).
After the rotation by +2π/n, A is moved to the lattice point C and after the rotation by -2π/n, B is moved to the lattice point D. Due to the assumed periodicity of the lattice, the two lattice points C and D will be also in a line directly below the initial row; moreover C and D will be separated by r = ma, with m an integer. But by ...
where k is a vector (called the wavevector), n is a discrete index (called the band index), and u n,k is a function with the same periodicity as the crystal lattice. For any given n, the associated states are called a band. In each band, there will be a relation between the wavevector k and the energy of the state E n,k, called the band dispersion.
This is based on the fact that a reciprocal lattice vector (the vector indicating a reciprocal lattice point from the reciprocal lattice origin) is the wavevector of a plane wave in the Fourier series of a spatial function (e.g., electronic density function) which periodicity follows the original Bravais lattice, so wavefronts of the plane wave ...