Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1305.6159 · Journal of the Physical Society of Japan

Observation of Higher-Order Sideband Transitions and First-Order Sideband Rabi Oscillations in a Superconducting Flux Qubit Coupled to a SQUID Plasma Mode

Yoshihiro Shimazu, Masaki Takahashi, Natsuki Okamura

Published Jun 14, 2013• 3 citations
arXivHTMLPDF

Abstract

We report results of spectroscopic measurements and time-domain measurements of a superconducting flux qubit. The dc superconducting quantum interference device (SQUID), used for readout of the qubit, and a shunt capacitor formed an LC resonator generating a SQUID plasma mode. Higher-order red and blue sidebands were observed in a simple measurement scheme because the resonant energy of the resonator, 600 MHz, was comparable to the thermal energy. We also observed Rabi oscillations on the carrier transition and the first-order sideband transitions. Because the qubit was coupled to a single arm of the dc SQUID, the qubit-SQUID coupling was significant at zero bias current, where these phenomena were observed. The ratios between the Rabi periods for the carrier transition and the sideband transitions are compared with those estimated from the coupling constant, which was separately determined. The result may be explained by assuming initial excitation of the resonator.

DOI
10.7566/jpsj.82.074710

Related papers

Observation and calculation of higher-order sideband transitions in a flux qubit coupled to a SQUID-based resonator

Yoshihiro Shimazu, Ryōen Shirasaki, S Toda +1 more

Qubit-resonator coupled systems have been intensively studied because of their potential usefulness in quantum information processing. We investigated a superconducting flux qubit coupled to a resonator mode (SQUID plasma mode) associated with a dc SQUID used to read out the qubit state. Higher-order red and blue sideband transitions with | M | = 1, 2, and 3, where M represents the change in the quantum number of the resonator state, were clearly observed away from the symmetry point. We calculated the transition matrix elements between the dressed states and examined their dependence on both the coupling strength and the flux bias for the qubit. The observation of the sidebands up to | M | = 3 is consistent with the calculation results.

Journal of Physics Conference Series•Dec 8, 2014•0 citations

Spectroscopy and coherent manipulation of single and coupled flux qubits

Yulin Wu, Hui Deng, Keqiang Huang +7 more

Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device (dc-SQUID) for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time T Rabi = 78 ns and energy relaxation time T 1 = 315 ns. We found that the value of T Rabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.

Chinese Physics B•Sep 1, 2013•3 citations

DC SQUID Phase Qubit Coupled to an On-Chip LC Resonator

Rangga P. Budoyo, Benjamin K. Cooper, V. Zaretskey +4 more

We have fabricated and tested an Al/AlOx/Al dc SQUID phase qubit on a sapphire substrate with a qubit junction area 0.17 μm2and critical current I0,J1= 1.4 μA. The qubit is shunted by an interdigitated capacitor and isolated from the bias leads by an inductive isolation network using a larger Josephson junction with area 2 μm2and critical current I0,J2= 29 μA. Additional high-frequency filtering is provided by an on-chip LC filter, which consists of square spiral inductors and parallel plate SiNxcapacitors. From detuned Rabi oscillation measurements, we estimate a relaxation time T1≈ 400 ns and dephasing time TΦ1700 ns. Additionally, we observe that the qubit transition spectrum has multiple equally spaced subpeaks. These subpeaks are caused by coupling between the phase qubit and the LC filter, forming a Jaynes-Cummings system. Each individual subpeak corresponds to transitions with different photon numbers in the LC filter.

IEEE Transactions on Applied Superconductivity•Jan 4, 2013•0 citations

Phase coherent dynamics of a superconducting flux qubit with capacitive bias readout

Frank Deppe, M. Mariantoni, E. P. Menzel +7 more

We present a systematic study of the phase coherent dynamics of a superconducting three-Josephson-junction flux qubit. The qubit state is detected with the integrated-pulse method, which is a variant of the pulsed switching-dc-superconducting quantum interference device (SQUID) method. In this scheme, the dc SQUID bias current pulse is applied via a capacitor instead of a resistor, giving rise to a narrow bandpass instead of a pure low-pass filter configuration of the electromagnetic environment. Measuring one and the same qubit with both setups allows a direct comparison. With the capacitive method about four times faster switching pulses and an increased visibility are achieved. Furthermore, the deliberate engineering of the electromagnetic environment, which minimizes the noise due to the bias circuit, is facilitated. Right at the degeneracy point, the qubit coherence is limited by energy relaxation. We find two main noise contributions. White noise limits the energy relaxation and contributes to the dephasing far from the degeneracy point. $1∕f$ noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of $1∕f$ noise is also supported by nonrandom beatings in the Ramsey and spin echo decay traces. Numeric simulations of a coupled qubit-oscillator system indicate that these beatings are due to the resonant interaction of the qubit with at least one pointlike fluctuator, coupled especially strongly to the qubit.

arXiv:0710.4455•Physical Review B•Dec 4, 2007•38 citations

rf-SQUID-Mediated Coherent Tunable Coupling between a Superconducting Phase Qubit and a Lumped-Element Resonator

Michael S. Allman, Fabio Altomare, Jed D. Whittaker +6 more

We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. The coupling strength is mediated by a flux-biased rf SQUID operated in the nonhysteretic regime. By tuning the applied flux bias to the rf SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator. We verify the modulation of coupling strength from 0 to 100 MHz by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillation frequency when on resonance. The measured spectroscopic splittings and vacuum Rabi oscillations agree well with theoretical predictions.

arXiv:1001.0816•Physical Review Letters•Apr 29, 2010•89 citations

Decoherence in dc SQUID phase qubits

Hanhee Paik, S. K. Dutta, Rupert Lewis +8 more

We report measurements of Rabi oscillations and spectroscopic coherence times in an $\text{Al}/{\text{AlO}}_{x}/\text{Al}$ and three $\text{Nb}/{\text{AlO}}_{x}/\text{Nb}$ dc SQUID phase qubits. One junction of the SQUID acts as a phase qubit and the other junction acts as a current-controlled nonlinear isolating inductor, allowing us to change the coupling to the current bias leads in situ by an order of magnitude. We found that for the Al qubit, a spectroscopic coherence time ${T}_{2}^{\ensuremath{\ast}}$ varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant ${T}^{\ensuremath{'}}=25\phantom{\rule{0.3em}{0ex}}\text{ns}$ on average at 80 mK. The three Nb devices also showed ${T}_{2}^{\ensuremath{\ast}}$ in the range of 3--8 ns, but ${T}^{\ensuremath{'}}$ was 9--15 ns, just about 1/2 the value we found in the Al device. For all the devices, the time constants were roughly independent of the isolation from the bias lines, implying that noise and dissipation from the bias leads were not the principal sources of dephasing and inhomogeneous broadening.

arXiv:0804.4430•Physical Review B•Jun 13, 2008•18 citations
We report results of spectroscopic measurements and time-domain measurements of a superconducting flux qubit. The dc superconducting quantum interference device (SQUID), used for readout of the qubit, and a shunt capacitor formed an LC resonator generating a SQUID plasma mode. Higher-order red and blue sidebands were observed in a simple measurement scheme because the resonant energy of the resonator, 600 MHz, was comparable to the thermal energy. We also observed Rabi oscillations on the carrier transition and the first-order sideband transitions. Because the qubit was coupled to a single arm of the dc SQUID, the qubit-SQUID coupling was significant at zero bias current, where these phenomena were observed. The ratios between the Rabi periods for the carrier transition and the sideband transitions are compared with those estimated from the coupling constant, which was separately determined. The result may be explained by assuming initial excitation of the resonator.
Qubit-resonator coupled systems have been intensively studied because of their potential usefulness in quantum information processing. We investigated a superconducting flux qubit coupled to a resonator mode (SQUID plasma mode) associated with a dc SQUID used to read out the qubit state. Higher-order red and blue sideband transitions with | M | = 1, 2, and 3, where M represents the change in the quantum number of the resonator state, were clearly observed away from the symmetry point. We calculated the transition matrix elements between the dressed states and examined their dependence on both the coupling strength and the flux bias for the qubit. The observation of the sidebands up to | M | = 3 is consistent with the calculation results.
Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device (dc-SQUID) for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time T Rabi = 78 ns and energy relaxation time T 1 = 315 ns. We found that the value of T Rabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.
We have fabricated and tested an Al/AlOx/Al dc SQUID phase qubit on a sapphire substrate with a qubit junction area 0.17 μm2and critical current I0,J1= 1.4 μA. The qubit is shunted by an interdigitated capacitor and isolated from the bias leads by an inductive isolation network using a larger Josephson junction with area 2 μm2and critical current I0,J2= 29 μA. Additional high-frequency filtering is provided by an on-chip LC filter, which consists of square spiral inductors and parallel plate SiNxcapacitors. From detuned Rabi oscillation measurements, we estimate a relaxation time T1≈ 400 ns and dephasing time TΦ1700 ns. Additionally, we observe that the qubit transition spectrum has multiple equally spaced subpeaks. These subpeaks are caused by coupling between the phase qubit and the LC filter, forming a Jaynes-Cummings system. Each individual subpeak corresponds to transitions with different photon numbers in the LC filter.
We present a systematic study of the phase coherent dynamics of a superconducting three-Josephson-junction flux qubit. The qubit state is detected with the integrated-pulse method, which is a variant of the pulsed switching-dc-superconducting quantum interference device (SQUID) method. In this scheme, the dc SQUID bias current pulse is applied via a capacitor instead of a resistor, giving rise to a narrow bandpass instead of a pure low-pass filter configuration of the electromagnetic environment. Measuring one and the same qubit with both setups allows a direct comparison. With the capacitive method about four times faster switching pulses and an increased visibility are achieved. Furthermore, the deliberate engineering of the electromagnetic environment, which minimizes the noise due to the bias circuit, is facilitated. Right at the degeneracy point, the qubit coherence is limited by energy relaxation. We find two main noise contributions. White noise limits the energy relaxation and contributes to the dephasing far from the degeneracy point. 1∕f1∕f1∕f noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of 1∕f1∕f1∕f noise is also supported by nonrandom beatings in the Ramsey and spin echo decay traces. Numeric simulations of a coupled qubit-oscillator system indicate that these beatings are due to the resonant interaction of the qubit with at least one pointlike fluctuator, coupled especially strongly to the qubit.
We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. The coupling strength is mediated by a flux-biased rf SQUID operated in the nonhysteretic regime. By tuning the applied flux bias to the rf SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator. We verify the modulation of coupling strength from 0 to 100 MHz by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillation frequency when on resonance. The measured spectroscopic splittings and vacuum Rabi oscillations agree well with theoretical predictions.
We report measurements of Rabi oscillations and spectroscopic coherence times in an Al/AlOx/Al\text{Al}/{\text{AlO}}_{x}/\text{Al}Al/AlOx​/Al and three Nb/AlOx/Nb\text{Nb}/{\text{AlO}}_{x}/\text{Nb}Nb/AlOx​/Nb dc SQUID phase qubits. One junction of the SQUID acts as a phase qubit and the other junction acts as a current-controlled nonlinear isolating inductor, allowing us to change the coupling to the current bias leads in situ by an order of magnitude. We found that for the Al qubit, a spectroscopic coherence time ${T}_{2}^{\ensuremath{\ast}}$ varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant ${T}^{\ensuremath{'}}=25\phantom{\rule{0.3em}{0ex}}\text{ns}$ on average at 80 mK. The three Nb devices also showed ${T}_{2}^{\ensuremath{\ast}}$ in the range of 3--8 ns, but ${T}^{\ensuremath{'}}$ was 9--15 ns, just about 1/2 the value we found in the Al device. For all the devices, the time constants were roughly independent of the isolation from the bias lines, implying that noise and dissipation from the bias leads were not the principal sources of dephasing and inhomogeneous broadening.