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arXiv:0705.0095 · Physical Review Letters

Temperature Dependence of Coherent Oscillations in Josephson Phase Qubits

Jürgen Lisenfeld, Alexander V. Lukashenko, M. Ansmann, John M. Martinis, Alexey Vladimirovich Ustinov

Published Oct 26, 2007• 56 citations
arXivHTMLPDF

Abstract

We experimentally investigate the temperature dependence of Rabi oscillations and Ramsey fringes in superconducting phase qubits. In a wide range of temperatures, we find that both the decay time and the amplitude of these coherent oscillations remain nearly unaffected by thermal fluctuations. In the two-level limit, coherent qubit response rapidly vanishes as soon as the energy of thermal fluctuations k(B)T becomes larger than the energy level spacing variant Planck's over h omega of the qubit. In contrast, a sample of much shorter coherence times displayed semiclassical oscillations very similar to Rabi oscillation, but showing a qualitatively different temperature dependence. Our observations shed new light on the origin of decoherence in superconducting qubits. The experimental data suggest that, without degrading already achieved coherence times, phase qubits can be operated at temperatures much higher than those reported till now.

DOI
10.1103/physrevlett.99.170504

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We experimentally investigate the temperature dependence of Rabi oscillations and Ramsey fringes in superconducting phase qubits. In a wide range of temperatures, we find that both the decay time and the amplitude of these coherent oscillations remain nearly unaffected by thermal fluctuations. In the two-level limit, coherent qubit response rapidly vanishes as soon as the energy of thermal fluctuations k(B)T becomes larger than the energy level spacing variant Planck's over h omega of the qubit. In contrast, a sample of much shorter coherence times displayed semiclassical oscillations very similar to Rabi oscillation, but showing a qualitatively different temperature dependence. Our observations shed new light on the origin of decoherence in superconducting qubits. The experimental data suggest that, without degrading already achieved coherence times, phase qubits can be operated at temperatures much higher than those reported till now.
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Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop induce the voltage oscillations across the coil of a high quality resonant tank circuit, inductively coupled to the phase qubit. It is the presence of these voltage oscillations in the detected signal which reveals the existence of Rabi oscillations in the qubit. A detailed calculation for zero and nonzero temperatures are made for the case of persistent current qubit. According to the estimates for decoherence and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in the MHz range.
Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose "coherence amplitude" is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.
We study decoherence effects in qubits coupled to environments that exhibit resonant frequencies in their spectral function. We model the coupling of the qubit to its environment via the Caldeira-Leggett formulation of quantum dissipation/coherence, and study the simplest example of decoherence effects in circuits with resonances such as a dc superconducting quantum interference device (SQUID) phase qubit in the presence of an isolation circuit. Using the dc SQUID phase qubit as an example, we obtain two quite general results. First, when the frequency of the qubit is at least two times larger than the resonance frequency of the environmental spectral density (the isolation circuit in the case of a dc SQUID phase qubit), we find that the decoherence time of the qubit is a few orders of magnitude larger than that of the typical Ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the spectral density. Second, we show that, when the qubit frequency is nearly the same as the resonant frequency of the environmental spectral density, an oscillatory non-Markovian decay emerges, as the qubit and its environment self-generate Rabi oscillations of characteristic time scales shorter than the decoherence time.
Decoherence is a quantum-mechanical phenomenon severely limiting quantum information processing and storage capability in quantum computers. Decoherence refers to mechanisms that cause transfer of information from a quantum system to its bath. Typically, in theoretical and experimental considerations of different systems containing superconducting qubits, the coupling strength between a qubit and its bath has been assumed to be constant in time. In this case, many standard results in the dynamics of two-level systems follow. For example, due to decoherence, driven Rabi oscillations in a qubit have a characteristic decay time. In addition, the oscillations may take place at any phase. However, by considering time-dependent coupling to the bath, these phenomena may be absent. In this thesis, we demonstrate with numerical simulations of a time-dependent Lindblad master equation persistent Rabi oscillations in a qubit driven by a coherent drive tone. The persistent Rabi oscillations are induced by modulating the coupling of the qubit to the bath with a sinusoidal temporal shape. We observe that the temporal modulation enforces a limit cycle on the evolution of the dressed qubit state with a fixed phase relative to the phase of the sinusoidal modulation regardless of the initial state of the system. Through a synchronization-like phenomenon, the frequency of the Rabi oscillation adapts to match the frequency of the modulation. We determine the effect of different system parameters on the limit cycle and study how the amplitude of the persistent oscillation depends on the coupling modulation parameters. We also observe a similar effect in the freely evolving qubit precession. In addition, the qubit acts as a non-linear mixer, resulting in different linear combinations of the original modulation waveform appearing in the bath-induced Rabi oscillations. We also introduce a design for a physical system where our simulations can be verified experimentally.
Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and 1∕f1∕f1∕f noise in the Josephson junction critical current I0{I}_{0}I0​. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.