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arXiv:cond-mat/0304383 · Journal of Experimental and Theoretical Physics Letters

Decoherence due to nodal quasiparticles in d-wave qubits

Ya. V. Fominov, A. A. Golubov, M. Yu. Kupriyanov

Published May 1, 2003• 54 citations
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Abstract

We study the Josephson junction between two d -wave superconductors, which is discussed as an implementation of a qubit. We propose an approach to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles, which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.

DOI
10.1134/1.1595702

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We study the Josephson junction between two d -wave superconductors, which is discussed as an implementation of a qubit. We propose an approach to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles, which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.
We have theoretically investigated macroscopic quantum tunneling (MQT) and the influence of nodal quasiparticles and zero energy bound states (ZES) on MQT in s-wave/d-wave hybrid Josephson junctions. In contrast to d-wave/d-wave junctions, the low-energy quasiparticle dissipation resulting from nodal quasiparticles and ZES is suppressed due to a quasiparticle-tunneling blockade effect in an isotropic s-wave superconductor. Therefore, the inherent dissipation in these junctions is found to be weak. This result suggests high potential of s-wave/d-wave hybrid junctions for applications in quantum information devices.
It is important to know the decoherence mechanism of a qubit based on Josephson junctions. At low temperatures, as quasiparticle concentration becomes exponentially small, one needs to consider energy transfer from tunneling electrons to other degrees of freedom to find dissipation in Josephson junctions and decoherence in qubits. Here we discuss the energy transfer to two-level systems, i.e., the transitions between two different configurations of ions inside an insulating layer separated by a potential barrier. We derive a general equation of motion for the phase difference between two superconducting electrodes and we find a retarded dissipation term due to electromagnetic mechanism and also contribution due to electron tunneling mechanism. Using the equation of motion we calculate the decay of Rabi oscillations and frequency shift in qubits due to the presence of the two-level systems. In the long-time limit our results coincide with those obtained by Martinis et al. [Martinis et al., Phys. Rev. Lett. 95, 210503 (2005)] within the Fermi's Golden Rule approach up to a numerical factor.
We have theoretically investigated macroscopic quantum tunneling (MQT) and the influence of nodal quasiparticles and zero energy bound states (ZESs) on MQT in sss-wave/ddd-wave hybrid Josephson junctions. In contrast to ddd-wave/ddd-wave junctions, the low-energy quasiparticle dissipation resulting from nodal quasiparticles and ZESs is suppressed due to a quasiparticle-tunneling blockade effect in an isotropic sss-wave superconductor. Therefore, the inherent dissipation in these junctions is found to be weak. We have also investigated MQT in a realistic sss-wave/ddd-wave (Nb∕Au∕YBCO)(\mathrm{Nb}∕\mathrm{Au}∕\mathrm{YBCO})(Nb∕Au∕YBCO) junction in which Ohmic dissipation in a shunt resistance is stronger than the inherent dissipation and find that MQT is observable within the current experimental technology. This result suggests the high potential of sss-wave/ddd-wave hybrid junctions for applications in quantum information devices.
It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response nonequilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a d-wave junction with appropriate parameters.
While Josephson-junction-like structures intrinsic to the layered cuprate high temperature superconductors offer an attractive stage for exploiting possible applications to new quantum technologies, the low energy quasiparticle excitations characteristically present in these d-wave superconductors may easily destroy the coherence required. Here we demonstrate for the first time the feasibility of macroscopic quantum tunneling in the intrinsic Josephson junctions of a high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8 + delta), and find it to be characterized by a high classic-to-quantum crossover temperature and a relatively weak quasiparticle dissipation.