Phase Qubit - Quantized Energy Levels

Quantized Energy Levels

The phase qubit is operated in the zero-voltage state, with . At very low temperatures, much less than 1 K (achievable using a cryogenic system known as a dilution refrigerator), with a sufficiently high resistance and small capacitance Josephson junction, quantum energy levels become detectable in the local minima of the washboard potential. These were first detected using microwave spectroscopy, where a weak microwave signal is added to the current biasing the junction. Transitions from the zero voltage state to the voltage state were measured by monitoring the voltage across the junction. Clear resonances at certain frequencies were observed, which corresponded well with the quantum transition energies obtained by solving the Schrödinger equation for the local minimum in the washboard potential. Classically only a single resonance is expected, centered at the plasma frequency . Quantum mechanically, the potential minimum in the washboard potential can accommodate several quantized energy levels, with the lowest (ground to first excited state) transition at an energy, but the higher energy transitions (first to second excited state, second to third excited state) shifted somewhat below this due to the non-harmonic nature of the trapping potential minimum, whose resonance frequency falls as the energy increases in the minimum. Observing multiple, discrete levels in this fashion is extremely strong evidence that the superconducting device is behaving quantum mechanically, rather than classically.

The phase qubit uses the lowest two energy levels in the local minimum; the ground state is the zero state of the qubit, and the first excited state is the one state. The slope in the washboard potential is set by the bias current, and changes in this current change the washboard potential, changing the shape of the local minimum (equivalently, changing the value of the nonlinear inductance, as discussed above). This changes the energy difference between the ground and first excited states. Hence the phase qubit has a tunable energy splitting.