Berry's phase of bloch oscillation

In summary, Berry's phase of Bloch oscillation is a geometric phase acquired by a quantum particle moving in a crystal lattice under the influence of a time-dependent external force. It is intimately related to Bloch oscillation and has important physical implications, including affecting the particle's energy spectrum and transport properties. It can be experimentally observed by measuring the interference pattern of the particle and can be controlled by tuning the parameters of the external force or modifying the crystal lattice. This presents potential applications in quantum information processing and control.
  • #1
wdlang
307
0
we know in bloch oscillation, the wavefunction of an electron returns to its initial state after a period, but up to a phase.

my question is, can this phase be nontrivial?
 
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  • #2
wdlang said:
we know in bloch oscillation, the wavefunction of an electron returns to its initial state after a period, but up to a phase.

my question is, can this phase be nontrivial?


I don't think a periodic potential by itself leads to berry phase--berry phase arises when the Hamiltonian depends on parameters which are taken around a closed path in the parameter space.
 
  • #3


Yes, the phase in Bloch oscillation can indeed be nontrivial, and this is known as Berry's phase. This phase arises due to the geometric nature of the electron's motion in a crystal lattice, and it can have significant consequences in the behavior of electronic systems. In fact, Berry's phase has been observed in various experiments, such as in the quantum Hall effect and topological insulators. It is an important concept in the field of condensed matter physics and has implications for the understanding of electronic properties in materials.
 

Related to Berry's phase of bloch oscillation

1. What is Berry's phase of Bloch oscillation?

Berry's phase of Bloch oscillation refers to the geometric phase that is acquired by a quantum particle moving in a crystal lattice under the influence of a time-dependent external force. It is a manifestation of the adiabatic theorem in quantum mechanics.

2. How is Berry's phase related to Bloch oscillation?

Berry's phase is intimately related to Bloch oscillation as it describes the additional phase that is accumulated by the particle during its motion in the crystal lattice. This phase is crucial in understanding the dynamics of quantum particles in periodic structures.

3. What is the significance of Berry's phase in Bloch oscillation?

Berry's phase in Bloch oscillation has important physical implications, such as affecting the energy spectrum of the particle and influencing its transport properties. It has also been used to demonstrate topological effects in condensed matter systems.

4. How is Berry's phase experimentally observed in Bloch oscillation?

Berry's phase in Bloch oscillation can be observed experimentally by measuring the interference pattern of the particle after it completes a full oscillation. The accumulated phase can be extracted by comparing the measured interference pattern with the expected pattern in the absence of Berry's phase.

5. Can Berry's phase be controlled in Bloch oscillation?

Yes, Berry's phase in Bloch oscillation can be controlled by tuning the parameters of the external force, such as its frequency and amplitude, or by modifying the properties of the crystal lattice. This offers potential applications in quantum information processing and quantum control.

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