Quantum Computing with a Cooper-Pair Box

Our group is studying quantum mechanical effects in superconducting circuits at very low temperatures (T~10 mK). The circuits that we are studying consist of a small superconducting island separated by a superconducting reservoir through two ultra-small tunnel junctions or Josephson junctions (see below figure). The number of Cooper pairs on the island of the device can be coherently controlled by modulating the voltage on a gate electrode that is capacitively coupled to the island of the device. Since charging effects in the devices that we are studying are relatively large with respect to both temperature and the Josephson energy these devices are called a superconducting charge qubit or Cooper-pair box.

SEM micrograph of typical Cooper-pair device

In our research, we are working to determine the limitations of a Cooper-pair box for quantum computing research. We have studied non-equilibrium quasiparticle effects (which prevent reliable initialization of the qubit) performed detailed spectroscopic measurements of the first excited state, and detailed lifetime measurements of the first excited state.

Non-equilibrium quasiparticles
In thermal equilibrium, the probability of observing a quasiparticle in Cooper-pair devices at T = 10 mK is on the order of 10‾³°(i.e. one part in nonillion). On the other hand, measurements of Cooper-pair electrometers and Cooper-pair boxes over the past decade have shown effects from quasiparticles which are called non-equilibrium or out of equilibrium quasiparticles. The tunneling of a quasiparticle on the island of the Cooper-pair box is important because it prevents reliable initialization of the quantum states of a Cooper-pair box.

We have performed steady-state measurements of non-equilibrium quasiparticles at different temperatures and have found surprisingly that when the temperature is raised from 10 mK up to 150 mK, that the probability of observing a quasiparticle can actually decrease. We have developed both a thermodynamic model (Palmer et al., Physical Review B 76, 054501 (2007)) and a tunneling rate model (Sanchez et al., submitted to Physical Review B) that model these measurements. Both measurements begin with the ansatz that a population of non-equilibrium quasiparticles exists in the leads.

We have performed detailed spectroscopic measurements of the first excited state of a Cooper-pair box from 15 GHz up to 50 GHz. In this frequency range, we have observed a handful of anomalous avoided level crossings (see the figure below for an example); note that similar avoided level crossings have been observed by other groups doing research on superconducting quantum devices. Avoided level crossings imply that the system is coupled to another quantum system. We have observed that:

  1. The avoided level crossings are coupled to the gate voltage (Vg). Specifically, if we consider the range: -1 < ng < 1, where ng = CgVg/e and Cg is the capacitance between the gate and the island of the box, the splitting for ng < 0 is at a different frequency than the one at ng > 0

  2. They have a periodicity with respect to ng of two; analogous to the energy levels of the Cooper-pair box.

  3. The size of the splittings decrease as the effective Josephson energy (EJ) is decreased.

Items one and three imply that the Cooper-pair box is coupled to another charge system while item two implies that the charge system resides in one of the two tunnel junctions of the Cooper-pair box. Note that the potential of the island also has a periodicity of two.  We have developed a model for these avoided level crossings which incorporates a point charge tunneling between two positions in the tunnel junction of the Cooper-pair box. Note that the displacement of a point charge in the Josephson junction effectively shifts the gate voltage of the Cooper-pair box. One of the interesting things about these results is that by modeling our data we are actually able to extract microscopic information of the charge fluctuator; namely the tunneling rate of the fluctuator between two positional sites of the fluctuator.


Lifetime measurements
We have also measured the lifetime of the first excited state. By decreasing the effective Josephson energy (EJ/kB) of the Cooper-pair box from 1.0 K to 0.1 K, we can increase the lifetime of the first excited state from less than 50 nanoseconds up to a few microseconds. These results are consistent with charge or voltage noise being the dominant noise source that controls the lifetime in the Cooper-pair box. We have also measured the lifetime at different energy level separations or different frequencies. In these measurements we have found that the lifetime decreases by nearly an order of magnitude at particular frequencies. The frequency where the lifetime decreases coincide with where we have found anomalous avoided level crossings in the Cooper-pair box spectrum. By using our lifetime measurements, we have actually found some avoided level crossings that were not initially visible in our spectroscopic measurements.

For further information please contact:
Benjamin S. Palmer
Laboratory for Physical Sciences
8050 Greenmead Road
College Park, MD 20740
Phone: 301-935-6727
bpalmer at lps.umd.edu