Multiple Photon Assisted Tunneling in Two Quantum Dots

T. Fujisawa and S. Tarucha

  We describe  photon assisted tunneling (PAT)  between discrete
zero-dimensional (0D) levels in two weakly  coupled quantum dots.
Resonant tunneling current  with multiple  (up to three)  photon 
absorption is observed  when the two 0D levels are  separated by 
a multiple of the microwave photon energy. The PAT current shows 
a Bessel function dependence on the microwave power, which is in 
agreement  with time-dependent  tunneling theory.  The sharp PAT 
peaks can be well  resolved even  when the high  microwave power 
increases electron temperature in the reservoirs.

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Fig 1. Contour plot of the drain current vs. VGL and VGR through the two quantum dots coupled in series. Hexagonal regions shows the stable charging phase, in which (n, m) denotes n electrons in dot DL and m electrons in dot DR. The inset is a schematic diagram of the two coupled quantum dots.

Fig 2. (a) Schematic charging diagram of the coupled dot system. (n, m) represents a stable charged state, where n is the number of electrons in dot DL and m is that in dot DR. The resonant 0D-0D tunneling peaks are observed at vertices, M and M'. The thick lines, PA, PB, P'A, and P'B, indicate the conditions necessary for resonant 0D-0D PAT. (b) Energy diagram of PAT for the condition on line PA, and on line PB and of zero photon tunneling at the vertex M.

Fig. 3. Contour plot of the drain current in the vicinity of vertex M with and without microwave radiation. A part of the charging diagram is also illustrated.

Fig. 4. Contour plot of the drain current without a microwave field and when a relatively intense microwave is applied.

Fig. 5. Multiple PAT current peak against microwave power calibrated at a connector next to the sample. Circles, squares, and triangles represent the observed current peak with one, two, and three photon absorption, respectively. The solid, dashed, and dotted lines respectively are for the one, two, and three photon process.