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:1110.3588 · Physical Review B

Inverse Landau-Zener-Stückelberg problem for qubit-resonator systems

Sergey N Shevchenko, Sahel Ashhab, Franco Nori

Published Mar 2, 2012• 42 citations
arXivHTMLPDF

Abstract

We consider theoretically a superconducting qubit--nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature (London) 459, 960 (2009)]. First, we study the problem where the state of the strongly driven qubit is probed through a frequency shift of the low-frequency NR. In the case where the coupling is capacitive, the measured quantity can be related to the so-called quantum capacitance. Our theoretical results agree with the experimentally observed result that, under resonant driving, the frequency shift repeatedly changes sign. We then formulate and solve the inverse Landau-Zener-St\"uckelberg problem, where we assume the driven qubit's state to be known (i.e., measured by some other device) and aim to find the parameters of the qubit's Hamiltonian. In particular, for our system the qubit's bias is defined by the NR's displacement. This may provide a tool for monitoring of the NR's position.

DOI
10.1103/physrevb.85.094502

Related papers

Coupled Dynamics of a Nanomechanical Resonator and Superconducting Quantum Circuits

Junho Suh

The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.

•May 17, 2011•1 citation

Landau-Zener-Stückelberg interferometry in dissipative circuit quantum electrodynamics

Mariano Bonifacio, Daniel Domı́nguez, María José Sánchez

We study Landau-Zener-St\"uckelberg (LZS) interferometry in a cQED architecture under the effects of dissipation. To be specific, we consider a superconducting qubit driven by a $\mathrm{dc}+\mathrm{ac}$ signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an Ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for an arbitrary amplitude of the drive and different timescales. We unveil important differences in the resonant patterns between the strong coupling and ultrastrong coupling regimes in the qubit-resonator interaction, which are mainly due to the magnitude of photonic gaps in the energy spectrum of the system. We identify in the LZS patterns the contribution of the qubit gap and the photonic gaps, showing that for large driving amplitudes the patterns present a weaving structure due to the combined intercrossing of the different gaps contributions.

arXiv:2002.10827•Physical review. B./Physical review. B•Jun 15, 2020•17 citations

Probing the quantum coherence of a nanomechanical resonator using a superconducting qubit: I. Echo scheme

Andrew D. Armour, M. P. Blencowe

We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonator's interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system we show that it should be possible to carry out this scheme with existing device technology.

arXiv:0804.2194•New Journal of Physics•Sep 30, 2008•45 citations

Multiphoton transitions in Josephson-junction qubits (Review Article)

Sergey N Shevchenko, A. N. Omelyanchouk, E. V. Il’ichev

Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic \nscale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the \ndistance between the qubit energy levels and their populations and to read out the resonator's state, as well as the \nunavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum \nphenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent \nresults for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC \ncircuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a \nqubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. \nApplication of this theory allows to describe many phenomena for the single and two coupled superconducting \nqubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping \nand amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type \ncharacter, and creation of the inverse population for lasing.

•Jan 1, 2012•41 citations

Multiphoton transitions in Josephson-junction qubits (Review Article)

S. N. Shevchenko, A. N. Omelyanchouk, E. Il’ichev

Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator’s state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing.

arXiv:1205.0696•Low Temperature Physics•Apr 1, 2012•41 citations

Landau-Zener-Stuckelberg interferometry in multilevel superconducting flux qubit

Xueda Wen, Yiwen Wang, Shanhua Cong +7 more

Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.

arXiv:1003.2025•Mar 10, 2010•2 citations
We consider theoretically a superconducting qubit--nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature (London) 459, 960 (2009)]. First, we study the problem where the state of the strongly driven qubit is probed through a frequency shift of the low-frequency NR. In the case where the coupling is capacitive, the measured quantity can be related to the so-called quantum capacitance. Our theoretical results agree with the experimentally observed result that, under resonant driving, the frequency shift repeatedly changes sign. We then formulate and solve the inverse Landau-Zener-St"uckelberg problem, where we assume the driven qubit's state to be known (i.e., measured by some other device) and aim to find the parameters of the qubit's Hamiltonian. In particular, for our system the qubit's bias is defined by the NR's displacement. This may provide a tool for monitoring of the NR's position.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.
We study Landau-Zener-St\"uckelberg (LZS) interferometry in a cQED architecture under the effects of dissipation. To be specific, we consider a superconducting qubit driven by a dc+ac\mathrm{dc}+\mathrm{ac}dc+ac signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an Ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for an arbitrary amplitude of the drive and different timescales. We unveil important differences in the resonant patterns between the strong coupling and ultrastrong coupling regimes in the qubit-resonator interaction, which are mainly due to the magnitude of photonic gaps in the energy spectrum of the system. We identify in the LZS patterns the contribution of the qubit gap and the photonic gaps, showing that for large driving amplitudes the patterns present a weaving structure due to the combined intercrossing of the different gaps contributions.
We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonator's interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system we show that it should be possible to carry out this scheme with existing device technology.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic \nscale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the \ndistance between the qubit energy levels and their populations and to read out the resonator's state, as well as the \nunavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum \nphenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent \nresults for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC \ncircuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a \nqubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. \nApplication of this theory allows to describe many phenomena for the single and two coupled superconducting \nqubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping \nand amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type \ncharacter, and creation of the inverse population for lasing.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator’s state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing.
Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.