Detection of geometric phases in superconducting nanocircuits

by Giuseppe Falci, Rosario Fazio, G. Massimo Palma, Jens Siewert and Vlatko Vedral

Journal club talk by Nakyeon Hwang
Summary by Patrick Morales



This week's talk, given by Nakyeon, was on a proposed experimental setup to detect geometrical phases in a superconducting device. The proposed device is an asymmetric SQUID where the thickness of the tunneling barrier is different in the two arms of the SQUID. The quantum interference due to the geometrical phases could be detected by measuring the charge state of the asymmetric SQUID as the Hamiltonian is adiabatically evolved by varying the offset charge and the flux through the SQUID in a cyclical fashion. Quantum interferometery based on these geometric phases can be used to develop a new design of gates for quantum computation using charge qubits.

When a quantum mechanical system, is evolved adiabatically such that the phase and the amplitude of the wave function describing the system is varied in a cyclical manner, the resulting wave function may differ from the original wave function by a phase factor. This geometrical phase, or Berry phase, results from the geometrical properties of the parameter space of the Hamiltonian. One example of this is the Aharonov-Bohm phase picked up from a charged particle encircling a magnetic field. The Aharonov-Bohm effect results in a periodic modulation of the critical current of a conventional SQUID as a function of magnetic field and provides evidence of macroscopic phase coherence of the superconducting condensate.

The Hamiltonian of an asymmetric SQUID operating in the charging regime, where the temperature is lower than the Josephson coupling energies of the junctions which in turn is much smaller than the charging energy of the SQUID contains two terms: one related to the charge of the SQUID and the other to the flux through it. The Hamiltonian can be swept through its phase space by applying a voltage across the SQUID, varying the charge of the SQUID, and by applying a perpendicular magnetic field to vary the flux through the SQUID. A non-trivial loop in phase space produces a Berry phase due to the asymmetry of the SQUID. The dynamical component of the phase can be subtracted by inverting the state of the SQUID and retracing the same path in phase space in the reverse direction. The resulting phase difference is due only to the geometrical component of the phase.

Ultimately, the geometric phase in an asymmetric SQUID could be used in the design of gates for quantum computation. Two capacitively coupled asymmetric SQUIDS could be used to create a universal two qubit gate. The gate voltages and the magnetic fluxes of each SQUID could be set independently. The effective charging of the target qubit would depend on the state of the control qubit, resulting in a controllable phase shift of the target qubit.