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arXiv:0708.2652 · Physical Review B

Decoherence in a superconducting flux qubit with a π -junction

Takeo Kato, A. A. Golubov, Yasunobu Nakamura

Published Nov 15, 2007• 40 citations
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Abstract

We consider the use of a $\ensuremath{\pi}$ junction for flux qubits to realize degenerate quantum levels without external magnetic field. On the basis of the Caldeira-Leggett model, we derive an effective spin-Boson model and study decoherence of this type of qubits. We estimate the dephasing time by using parameters from recent experiments of superconductor-insulator-ferromagnet-superconductor junctions and show that high critical current and large subgap resistance are required for the $\ensuremath{\pi}$ junction to realize a long coherent time.

DOI
10.1103/physrevb.76.172502

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We consider the use of a \ensuremathπ\ensuremath{\pi}\ensuremathπ junction for flux qubits to realize degenerate quantum levels without external magnetic field. On the basis of the Caldeira-Leggett model, we derive an effective spin-Boson model and study decoherence of this type of qubits. We estimate the dephasing time by using parameters from recent experiments of superconductor-insulator-ferromagnet-superconductor junctions and show that high critical current and large subgap resistance are required for the \ensuremathπ\ensuremath{\pi}\ensuremathπ junction to realize a long coherent time.
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing. However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome. We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic pi junction which has a metallic contact and a normal Josephson junction with an insulating barrier. Thus, a quantum coherent two-level state is formed without an external magnetic field. This feature and the simple structure of the qubit make it possible to reduce its size leading to a long decoherence time.
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing.However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome.We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic junction which has a metallic contact and a normal Josephson junction with an insulating barrier.Thus, a quantum coherent two-level state is formed without an external magnetic field.This feature and the simple structure of the qubit make it possible to reduce its size leading to a long decoherence time.
Conventional superconducting flux qubits require the application of a precisely tuned magnetic field to set the operation point at half a flux quantum through the qubit loop, which complicates the on-chip integration of this type of device. It has been proposed that by inducing a π-phase shift in the superconducting order parameter using a precisely controlled nanoscale-thickness superconductor/ferromagnet/superconductor Josephson junction, commonly referred to as π-junction, it is possible to realize a flux qubit operating at zero magnetic flux. Here, we report the realization of a zero-flux-biased flux qubit based on three NbN/AlN/NbN Josephson junctions and a NbN/PdNi/NbN ferromagnetic π-junction. The qubit lifetime is in the microsecond range, which we argue is limited by quasiparticle excitations in the metallic ferromagnet layer. Our results pave the way for developing quantum coherent devices, including qubits and sensors, that utilize the interplay between ferromagnetism and superconductivity. Conventional superconducting flux qubits require a finely tuned magnetic field to operate, hindering their on-chip integration. Here, ferromagnetic Josephson junctions with a π-phase shift in the superconducting order parameter allow the realization of a flux qubit operating at zero magnetic field.
π-junction qubit based on superconducting quantum interference device ring has been already proposed. In this qubit, a quantum two-level system is spontaneously generated without any bias flux applied. Flux qubit with a single π-junction concerns the large inductance L of the loop, which makes the qubit vulnerable to decoherence caused by magnetic fluctuations in the environment. To overcome this difficulty one can use three-junction π-qubit, comprising three π-junctions in a loop with negligible small inductance or unharmonic two-junction interferometer exploiting non-sinusoidal current-phase relations of the junctions. In the paper we theoretically investigate the macroscopic quantum dynamics of proposed qubits. The measurement process in two types of qubits has been analyzed in the frame of Lindblad equation formalism. Different mechanisms giving a non-sinusoidal CPR in SFS structures are analyzed as well. It is shown, that the largest second harmonic can be obtained for the SFS junction in the "clean" limit with a thin ferromagnet layer at low temperature.
We propose a qubit consisting of a superconducting ring with two zero junctions and one ferromagnetic π junction. In the system, degenerate states appear in the phase space without an external magnetic field because of a competition between the zero and π states. Quantum tunneling between the degenerate states leads to a formation of bonding and antibonding states which are used as a bit. For manipulating the states, only a small magnetic field around zero is required. This feature leads to a large-scale integration and a construction of the smaller-sized qubit which is robust to the decoherence by external noises.
We present a multilevel quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multilevel dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e., transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation (T1){(T}_{1})(T1​) and decoherence (T2){(T}_{2})(T2​) times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.