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arXiv:cond-mat/0311289 · Physical Review Letters

Energy Relaxation Time between Macroscopic Quantum Levels in a Superconducting Persistent-Current Qubit

Yang Yu, D. Nakada, Janice C. Lee, Bhuwan Singh, Donald S. Crankshaw, Terry P. Orlando, Karl K. Berggren, William D. Oliver

Published Mar 18, 2004• 42 citations
arXivHTMLPDF

Abstract

We measured the intrawell energy relaxation time tau(d) approximately 24 micros between macroscopic quantum levels in the double well potential of a Nb persistent-current qubit. Interwell population transitions were generated by irradiating the qubit with microwaves. Zero population in the initial well was then observed due to a multilevel decay process in which the initial population relaxed to lower energy levels during the driven transitions. The decoherence time, estimated from tau(d) within the spin-boson model, is about 20 micros for this configuration with a Nb superconducting qubit.

DOI
10.1103/physrevlett.92.117904

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 26, 2001•1 citation
We measured the intrawell energy relaxation time tau(d) approximately 24 micros between macroscopic quantum levels in the double well potential of a Nb persistent-current qubit. Interwell population transitions were generated by irradiating the qubit with microwaves. Zero population in the initial well was then observed due to a multilevel decay process in which the initial population relaxed to lower energy levels during the driven transitions. The decoherence time, estimated from tau(d) within the spin-boson model, is about 20 micros for this configuration with a Nb superconducting qubit.
Single-, two-, and three-photon transitions were driven amongst five quantum states of a niobium persistent-current qubit. A multi-level energy-band diagram was extracted using microwave spectroscopy, and avoided crossings were directly measured between the third and fourth excited states. The energy relaxation times between states connected by single-photon and multi-photon transitions were approximately 30 - 100 microseconds. Three-photon coherent oscillations were observed between the qubit ground and fourth excited states with a decoherence time of approximately 50 nanoseconds.
dc measurements are made in a superconducting, persistent current qubit structure with a time-ordered meter. The persistent-current qubit has a double-well potential, with the two minima corresponding to magnetization states of opposite sign. Macroscopic resonant tunneling between the two wells is observed at values of energy bias that correspond to the positions of the calculated quantum levels. The magnetometer, a superconducting quantum interference device, detects the state of the qubit in a time-ordered fashion, measuring one state before the other. This results in a different meter output depending on the initial state, providing different signatures of the energy levels for each tunneling direction.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2T_1, T_2 \propto J_{q,τ}^{-2}T1​,T2​∝Jq,τ−2​ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.
We determined the dissipation-induced decoherence time (DIDT) of a superconducting Josephson tunnel junction by time-resolved measurements of its escape dynamics. Double-exponential behavior of the time-dependent escape probability was observed, suggesting the occurrence of a two-level decay-tunneling process in which energy relaxation from the excited to the ground level significantly affects the escape dynamics of the system. The observation of temporal double-exponential dependence enables direct measurements of the DIDT, a property critical to the study of quantum dynamics and the realization of macroscopic quantum coherence and quantum computing. We found that the DIDT was tau(d) > 11 micros at T = 0.55 K, demonstrating good prospects for implementing quantum computing with Josephson devices.
This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.