The Quantum Dot Memory Device · AI Generator #GEN-1CD0DA8C

Physics · quantum-mechanics

Problem

A quantum memory device uses an electron trapped in a three-dimensional cubic quantum dot with side length L=5.0×10−9  mL = 5.0 \times 10^{-9}\;\text{m}. The electron can be in various energy states, and information is stored by transitioning between specific levels. The device operates by applying a weak electric field E⃗=E0x^\vec{E} = E_0 \hat{x} in the xx-direction, where E0=1.2×107  V/mE_0 = 1.2 \times 10^7\;\text{V/m}. This field acts as a perturbation to the original cubic potential well. Initially, the electron is prepared in the first excited state of the unperturbed system where exactly one quantum number equals 2 and the others equal 1. Due to degeneracy, there are three such states: (nx,ny,nz)=(2,1,1)(n_x, n_y, n_z) = (2,1,1), (1,2,1)(1,2,1), and (1,1,2)(1,1,2). (a) Calculate the unperturbed energy of these degenerate first excited states. (b) Using first-order degenerate perturbation theory, find the energy shifts of these three states when the electric field is applied. (c) The device reads information by measuring photons emitted when the electron transitions from the perturbed excited states to the ground state. Calculate the wavelength of the photon emitted from the state with the largest energy shift. Given: Electron mass me=9.11×10−31  kgm_e = 9.11 \times 10^{-31}\;\text{kg}, Planck constant h=6.63×10−34  J⋅sh = 6.63 \times 10^{-34}\;\text{J⋅s}, speed of light c=3.00×108  m/sc = 3.00 \times 10^8\;\text{m/s}, elementary charge e=1.60×10−19  Ce = 1.60 \times 10^{-19}\;\text{C}.

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