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

Journal of Physics Conference Series

Pure dephasing in a superconducting three-level system

Jian Li, Mika A. Sillanpää, Gheorghe Sorin Paraoanu, Pertti Juhani Hakonen

Published Dec 17, 2012• 11 citations
Publisher

Abstract

The mathematical description of pure dephasing in a three-level system is not as straightforward as it is in a two-level system. Here we provide a detailed derivation of the Liouvillean for pure dephasing for a ladder three-level system, based on [J Li et al ., Phys. Rev. B 84 , 104527 (2011)]. Numerical calculations based on this model give good fittings to the spectral line and Autler-Townes splitting observed in a superconducting phase qubit.

DOI
10.1088/1742-6596/400/4/042039

Related papers

Decoherence, Autler-Townes effect, and dark states in two-tone driving of a three-level superconducting system

Jian Li, Gheorghe Sorin Paraoanu, Katarina Cicak +5 more

We present a detailed theoretical analysis of a multilevel quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanp\"a\"a et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.

arXiv:1103.2223•Physical Review B•Sep 30, 2011•56 citations

Autler-Townes Effect in a Superconducting Three-Level System

Mika A. Sillanpää, Jian Li, Katarina Cicak +5 more

When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross coupling) provides excellent agreement with all of the experimental data.

arXiv:0904.2553•Physical Review Letters•Nov 2, 2009•161 citations

Electromagnetically induced transparency in a superconducting three-level system

Mika A. Sillanpää, Jian Li, Katarina Cicak +5 more

When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an artificial atom with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross-coupling) provides excellent agreement with all the experimental data.

•Apr 16, 2009•1 citation

Quantum coherence between cavity and artificial atom in a superconducting circuit QED ladder system

Qichun Liu, Han Cai, Yingshan Zhang +2 more

We have created a quantum three-level ladder system with the cavity dispersive energy level in a superconducting circuit quantum electrodynamics system consisting of a transmon qubit and a cavity, and have directly observed the Autler-Townes splitting effect instead of representing it by the probability of the qubit being at each level. A coupler tone is applied on the transition between the second excited state of transmon and cavity dispersive level, while the cavity spectrum is probed. A doublet transmission and anormalous dispersion spectrum of the cavity level is clearly shown. The inverse Fourier transform of cavity spectrum indicates that there is a quantum coherence Rabi oscillation of the populations between cavity and qubit.

arXiv:1604.03663•Apr 13, 2016•0 citations

Qubit dephasing by spectrally diffusing quantum two-level systems

Shlomi Matityahu, Alexander Shnirman, Moshe Schechter

We investigate the pure dephasing of a Josephson qubit due to the spectral diffusion of two-level systems that are close to resonance with the qubit. We identify the parameter regime in which this pure dephasing rate can be of the order of the energy relaxation rate and, thus, the relation ${T}_{2}=2{T}_{1}$ is violated for the qubit. This regime is reached if the dynamics of the thermal TLSs responsible for the spectral diffusion is sufficiently slower than the energy relaxation of the qubit. By adding periodic bias modulating the qubit frequency or TLS excitation energies we show that this pure dephasing mechanism can be mitigated, allowing enhancement of superconducting qubits' coherence time. Mitigating pure dephasing, even if it is subdominant, is of special significance in view of recent suggestions for converting the dominant relaxation process (${T}_{1}$) into erasure errors, leaving pure dephasing as the bottleneck for efficient quantum computation.

arXiv:2306.15264•Physical Review Applied•Apr 30, 2024•2 citations

Autler—Townes Splitting in a Δ-Type Quantum Three-Level System

Qichun Liu, Han Cai, Yingshan Zhang +2 more

We observe the Autler—Townes splitting effect in a Δ-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A control tone at different strengths is applied in resonance with the transition between the first and second excited states, while the spectra between each of them and the ground state are probed by another microwave tone. The experimental result shows the difference between the two spectra, and fits well with the Lindblad master equation model.

Chinese Physics Letters•Jul 1, 2016•1 citation
The mathematical description of pure dephasing in a three-level system is not as straightforward as it is in a two-level system. Here we provide a detailed derivation of the Liouvillean for pure dephasing for a ladder three-level system, based on [J Li et al ., Phys. Rev. B 84 , 104527 (2011)]. Numerical calculations based on this model give good fittings to the spectral line and Autler-Townes splitting observed in a superconducting phase qubit.
We present a detailed theoretical analysis of a multilevel quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanp\"a\"a et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.
When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an "artificial atom" with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross coupling) provides excellent agreement with all of the experimental data.
When a three-level quantum system is irradiated by an intense coupling field resonant with one of the three possible transitions, the absorption peak of an additional probe field involving the remaining level is split. This process is known in quantum optics as the Autler-Townes effect. We observe these phenomena in a superconducting Josephson phase qubit, which can be considered an artificial atom with a multilevel quantum structure. The spectroscopy peaks can be explained reasonably well by a simple three-level Hamiltonian model. Simulation of a more complete model (including dissipation, higher levels, and cross-coupling) provides excellent agreement with all the experimental data.
We have created a quantum three-level ladder system with the cavity dispersive energy level in a superconducting circuit quantum electrodynamics system consisting of a transmon qubit and a cavity, and have directly observed the Autler-Townes splitting effect instead of representing it by the probability of the qubit being at each level. A coupler tone is applied on the transition between the second excited state of transmon and cavity dispersive level, while the cavity spectrum is probed. A doublet transmission and anormalous dispersion spectrum of the cavity level is clearly shown. The inverse Fourier transform of cavity spectrum indicates that there is a quantum coherence Rabi oscillation of the populations between cavity and qubit.
We investigate the pure dephasing of a Josephson qubit due to the spectral diffusion of two-level systems that are close to resonance with the qubit. We identify the parameter regime in which this pure dephasing rate can be of the order of the energy relaxation rate and, thus, the relation T2=2T1{T}_{2}=2{T}_{1}T2​=2T1​ is violated for the qubit. This regime is reached if the dynamics of the thermal TLSs responsible for the spectral diffusion is sufficiently slower than the energy relaxation of the qubit. By adding periodic bias modulating the qubit frequency or TLS excitation energies we show that this pure dephasing mechanism can be mitigated, allowing enhancement of superconducting qubits' coherence time. Mitigating pure dephasing, even if it is subdominant, is of special significance in view of recent suggestions for converting the dominant relaxation process (T1{T}_{1}T1​) into erasure errors, leaving pure dephasing as the bottleneck for efficient quantum computation.
We observe the Autler—Townes splitting effect in a Δ-type quantum three-level system, using the lowest three levels of a SQUID-type Al/AlOx/Al transmon qubit embedded in a three-dimensional copper microwave cavity. A control tone at different strengths is applied in resonance with the transition between the first and second excited states, while the spectra between each of them and the ground state are probed by another microwave tone. The experimental result shows the difference between the two spectra, and fits well with the Lindblad master equation model.