The microwave-driven dynamics of the superconducting phase difference across a Josephson junction is now widely employed in superconducting qubits and quantum circuits. With their typical energy level separation frequency being several GHz, cooling these quantum devices to the ground state requires temperatures below 100 mK. Pushing the operation frequency of superconducting qubits up may allow for operation of superconducting qubits at 1 K and even higher temperatures. Here, we present measurements of the switching currents of niobium/aluminum–aluminum oxide/niobium Josephson junctions in the presence of millimeter-wave radiation at frequencies above 100 GHz. The observed switching current distributions display clear double-peak structures, which result from the resonant escape of the Josephson phase from a stationary state. We show that the data can be well explained by the strong-driving model including the irradiation-induced suppression of the potential barrier. While still being measured in the quasi-classical regime, our results point toward a feasibility of operating phase qubits around 100 GHz.The microwave-driven dynamics of the superconducting phase difference across a Josephson junction is now widely employed in superconducting qubits and quantum circuits. With their typical energy level separation frequency being several GHz, cooling these quantum devices to the ground state requires temperatures below 100 mK. Pushing the operation frequency of superconducting qubits up may allow for operation of superconducting qubits at 1 K and even higher temperatures. Here, we present measurements of the switching currents of niobium/aluminum–aluminum oxide/niobium Josephson junctions in the presence of millimeter-wave radiation at frequencies above 100 GHz. The observed switching current distributions display clear double-peak structures, which result from the resonant escape of the Josephson phase from a stationary state. We show that the data can be well explained by the strong-driving model including the irradiation-induced suppression of the potential barrier. While still being measured in the quasi-classical regime, our results point toward a feasibility of operating phase qubits around 100 GHz.

Applied Physics LettersApr 28, 20250 citations

Quantum and classical resonant escapes of a strongly driven Josephson junction

Hui Yu, X. B. Zhu, Zhihui Peng +9 more

The properties of phase escape in a dc superconducting quantum interference device (SQUID) at 25 mK, which is well below quantum-to-classical crossover temperature ${T}_{cr}$ , in the presence of strong resonant ac driving have been investigated. The SQUID contains two $\text{Nb}/{\text{Al-AlO}}_{x}/\text{Nb}$ tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power $W$ and at certain frequencies $\ensuremath{\nu}$ and $\ensuremath{\nu}/2$, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current $I$ and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As $W$ further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower $I$ . At certain $W$ , a second resonant peak appears, which can locate at very low $I$ depending on the value of $\ensuremath{\nu}$. Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at $T⪡{T}_{cr}$ , escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.The properties of phase escape in a dc superconducting quantum interference device (SQUID) at 25 mK, which is well below quantum-to-classical crossover temperature ${T}_{cr}$, in the presence of strong resonant ac driving have been investigated. The SQUID contains two $\text{Nb}/{\text{Al-AlO}}_{x}/\text{Nb}$ tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power $W$ and at certain frequencies $\ensuremath{\nu}$ and $\ensuremath{\nu}/2$, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current $I$ and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As $W$ further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower $I$. At certain $W$, a second resonant peak appears, which can locate at very low $I$ depending on the value of $\ensuremath{\nu}$. Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at $T⪡{T}_{cr}$, escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.

arXiv:1004.1863Physical Review BApr 28, 201029 citations

Quantum escape of the phase in a strongly driven Josephson junction

M. V. Fistul, Andreas J. Wallraff, Alexey Vladimirovich Ustinov

A quantum-mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e., when the frequency $\ensuremath{\omega}$ of the ac bias matches the Josephson-junction energy-level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current ${I}_{s}$ on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution ${P(I}_{s}).$ The developed theory is in a good accord with an experiment which we also report in this paper. The obtained features can be used to characterize certain aspects of the quantum-mechanical behavior of the Josephson phase, such as the energy level quantization, the Rabi frequency of coherent oscillations, and the effect of damping.A quantum-mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e., when the frequency $\ensuremath{\omega}$ of the ac bias matches the Josephson-junction energy-level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current ${I}_{s}$ on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution ${P(I}_{s}).$ The developed theory is in a good accord with an experiment which we also report in this paper. The obtained features can be used to characterize certain aspects of the quantum-mechanical behavior of the Josephson phase, such as the energy level quantization, the Rabi frequency of coherent oscillations, and the effect of damping.

arXiv:cond-mat/0307668Physical review. B, Condensed matterAug 19, 200329 citations

Study of microwave-induced phase switches from the finite voltage state in Bi2Sr2CaCu2Oyintrinsic Josephson junctions

Haruhisa Kitano, Ayami Yamaguchi, Yusaku Takahashi +2 more

We study the microwave-induced phase switches from the finite voltage state for the underdamped intrinsic Josephson junctions (IJJs) made of Bi 2 Sr 2 CaCu 2 O y (Bi2212). We observe the resonant double-peak structure in the switching current distribution at low temperatures. This feature is successfully explained by a quantum mechanical model where the strong microwave field effectively suppresses the potential barrier for the phase escape from a potential well and the macroscopic quantum tunneling (MQT) is resonantly enhanced. The detailed analyses considering the effects of multiple phase retrapping processes after the phase escape strongly suggest that the intense microwave field suppresses the energy-level spacing in the potential well, by effectively decreasing the fluctuation-free critical current and the Josephson plasma frequency. This effect also reduces the number of photons required for the multiphoton transition between the ground and the first excited states, making it possible to observe the energy level quantization in the MQT state. The temperature dependence of the resonance peak emerging in the switching rate clearly demonstrates that the quantized energy state can be survived up to ~10 K, which is much higher than a crossover temperature predicted by the conventional Caldeira-Leggett theory.We study the microwave-induced phase switches from the finite voltage state for the underdamped intrinsic Josephson junctions (IJJs) made of Bi 2 Sr 2 CaCu 2 O y (Bi2212). We observe the resonant double-peak structure in the switching current distribution at low temperatures. This feature is successfully explained by a quantum mechanical model where the strong microwave field effectively suppresses the potential barrier for the phase escape from a potential well and the macroscopic quantum tunneling (MQT) is resonantly enhanced. The detailed analyses considering the effects of multiple phase retrapping processes after the phase escape strongly suggest that the intense microwave field suppresses the energy-level spacing in the potential well, by effectively decreasing the fluctuation-free critical current and the Josephson plasma frequency. This effect also reduces the number of photons required for the multiphoton transition between the ground and the first excited states, making it possible to observe the energy level quantization in the MQT state. The temperature dependence of the resonance peak emerging in the switching rate clearly demonstrates that the quantized energy state can be survived up to ~10 K, which is much higher than a crossover temperature predicted by the conventional Caldeira-Leggett theory.

Journal of Physics Conference SeriesJul 1, 20173 citations

Resonant phase escape in Bi2Sr2CaCu2O8+δsurface intrinsic Josephson junctions

Haifeng Yu, Xiaobo Zhu, Jian-kun Ren +10 more

We present a study of phase escape in surface Bi 2 Sr 2 CaCu 2 O 8+ δ intrinsic Josephson junctions in the presence of microwave radiation. The measured switching current distributions display clear double-peak structures in the microwave field, which result from the single- and two-photon resonant escape processes accompanied by microwave-induced potential barrier suppression. We show that these results can be well explained by a quantum-mechanical model proposed by Fistul et al (2003 Phys. Rev. B 68 060504), from which the power and frequency dependences of the switching current distributions can be reproduced.We present a study of phase escape in surface Bi 2 Sr 2 CaCu 2 O 8+ δ intrinsic Josephson junctions in the presence of microwave radiation. The measured switching current distributions display clear double-peak structures in the microwave field, which result from the single- and two-photon resonant escape processes accompanied by microwave-induced potential barrier suppression. We show that these results can be well explained by a quantum-mechanical model proposed by Fistul et al (2003 Phys. Rev. B 68 060504), from which the power and frequency dependences of the switching current distributions can be reproduced.

New Journal of PhysicsSep 16, 20135 citations

Resonant Phase Escape from the First Resistive State of Bi2Sr2CaCu2Oy Intrinsic Josephson Junctions under Strong Microwave Irradiation

Yusaku Takahashi, Daiki Kakehi, Shuho Takekoshi +3 more

We report a study of the phase escape in Bi2Sr2CaCu2Oy intrinsic Josephson junctions under the strong microwave irradiation, focusing on the switch from the first resistive state (2nd SW). The resonant double-peak structure is clearly observed in the switching current distributions below 10 K and is successfully explained by a quantum-mechanical model on the quantum phase escape under the strong microwave field. These results provide the first evidence for the formation of the energy level quantization for the 2nd SW, supporting that the macroscopic quantum tunneling for the 2nd SW survives up to ∼10 K.We report a study of the phase escape in Bi2Sr2CaCu2Oy intrinsic Josephson junctions under the strong microwave irradiation, focusing on the switch from the first resistive state (2nd SW). The resonant double-peak structure is clearly observed in the switching current distributions below 10 K and is successfully explained by a quantum-mechanical model on the quantum phase escape under the strong microwave field. These results provide the first evidence for the formation of the energy level quantization for the 2nd SW, supporting that the macroscopic quantum tunneling for the 2nd SW survives up to ∼10 K.

Journal of the Physical Society of JapanJun 3, 20168 citations

The properties of phase escape in a dc superconducting quantum interference device (SQUID) at 25 mK, which is well below quantum-to-classical crossover temperature

{T}_{cr}

, in the presence of strong resonant ac driving have been investigated. The SQUID contains two

\text{Nb}/{\text{Al-AlO}}_{x}/\text{Nb}

tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power

W

and at certain frequencies $\ensuremath{\nu}$ and $\ensuremath{\nu}/2$, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current

I

and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As

W

further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower

I

. At certain

W

, a second resonant peak appears, which can locate at very low

I

depending on the value of $\ensuremath{\nu}$. Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at

T⪡{T}_{cr}

, escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.

{I}_{s}

on the power W of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution

{P(I}_{s}).

The developed theory is in a good accord with an experiment which we also report in this paper. The obtained features can be used to characterize certain aspects of the quantum-mechanical behavior of the Josephson phase, such as the energy level quantization, the Rabi frequency of coherent oscillations, and the effect of damping.