Capacitively Coupled Charge Qubits: Difference between revisions

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Capacitively Coupled Charge Qubits (view source)

Revision as of 01:19, 28 October 2014

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which to second order in <math>\epsilon_1</math> are:
 
[[Image:Second order.png|thumb|Energy gap between 01 and 10 states as a function of both detunings. Here, <math>\Delta_1 = 2</math>,<math>\Delta_2 = 1</math>, and <math>g = 1</math>, so the gap is invariant to second-order fluctuations in <math>\epsilon_1</math>.|300px]]
 
<math>
 
Unfortunately, none of the other transitions can be made to be invariant to second order fluctuations in <math>\epsilon_1</math>. Also, If we wish to make this transition invariant to all second order detuning fluctuations, we must set <math>\Delta_1 = \Delta_2</math>, making <math>g = 0</math>.
 
[[File:Second order.png]]
 
===Tunnel Coupling and Capacitive Coupling Noise===
[[Image:equal_deltas.png|thumb|Energy gap between 01 and 10 states as a function of both detunings. Here, <math>\Delta_1= \Delta_2 = 1</math>. Although the second order effects of the detunings are non-zero, they are relatively small.|300px]]
Assuming that we sit at the sweet spot <math>\epsilon_1 = \epsilon_2 = 0</math>, the energies are relatively simple, so we can easily see the effect of noise on the other parameters.
 
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Note that if we want any of the transitions to be invariant to first-order fluctuations in tunnel coupling, we would need to set either <math>\Delta_1 = \Delta_2</math> or set either <math>\Delta_1Delta_2</math> to zero or set <math>\Delta_1 = \Delta_2</math> to zero. AnyThe offirst these changes howeverchange would make the energy levels degenerate, which must be avoided. TheIf conclusionwe thereforeset isthe thattunnel wecouplings cannotto be equal, it would be impossible to make any of the transitions invariant to first-second order fluctuationseffects in tunnelthe couplingdetuning.
 
Similarly, thereThere is nothing we can do short of making the energy levels degenerate to make the transitions invariant with respect to first-order fluctuations in capacitive coupling. We could, however, make the coupling itself as stable as possible through manipulating the geometry of the system.
 
==Rotations==
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