Interband transitions and interference effects in superconducting qubits

Paila, Antti; Tuorila, Jani; Sillanpää, Mika; Gunnarsson, David; Sarkar, Jayanta; Makhlin, Yuriy; Thuneberg, E. V.; Hakonen, Pertti

doi:10.1007/s11128-009-0102-4

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…The charge can then be related to the charge-qubit occupation, the derivative of which (under resonant driving) exhibits sign changes. Similar sign-changing response under strong driving was recently studied for qubits probed by an LC (tank) circuit for capacitive coupling 14,15 as well as for inductive coupling 16,17 . Thus, in the first part of this work (Section II) we study the situation where the strong-driving qubit's state is probed by the NR.…”

supporting

confidence: 57%

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

Shevchenko

Nori

2012

Phys. Rev. B

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We consider theoretically a superconducting qubit -nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)]. First, we study the problem where the state of the strongly driven qubit is probed through the 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-Stückelberg 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.

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supporting

confidence: 57%

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

Shevchenko

Nori

2012

Phys. Rev. B

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“…Alternatively, the qubit was probed via an inductive coupling to the resonant circuit (Tuorila et al, 2013). Two types of multi-photon transitions in this system were further studied by (Paila et al, 2009). A similar aluminum Cooper pair box was probed via the reflection coefficient in a coupled electric resonator in Refs.…”

Section: A Superconducting Circuitsmentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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H. Comparison of different methods IV. Interferometry A. Superconducting circuits B. Semiconductor quantum dots C. Donors and impurities (atomic qubits) D. Graphene E. Microscopic systems F. Other systems G. Multilevel systems V. Quantum control A. Coherent control of microscopic and mesoscopic structures B. Universal single-and two-qubit control C. Shortcuts to adiabaticity D. Adiabatic quantum computation VI. Related classical coherent phenomena VII. Conclusion 1. With near-adiabatic limit (Landau) 2. With parabolic cylinder functions (Zener) 3. With contour integrals (Majorana) 4. With WKB approximation and phase integral method (Stückelberg) 5. Duration of the LZSM transition B. Description of a periodically driven two-level system 1. Adiabatic-impulse model a. Adiabatic evolution b. Multiple-passage evolution 2. Rotating-wave approximation (RWA) 3. Floquet theory 4. Rate equation and white noise approach a. Transition rate b. Rate equation c. From Bessel to Airy d. Double-passage regime ReferencesAbbreviations and most-often-used symbols Because this review article is quite long, for the readers' convenience, we present the main abbreviations used. This list also includes some of the topics covered.

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“…Such transitions were studied both in microscopic systems [2,125], and in the Josephson-junction qubits [126][127][128]. Also for the case of a flux qubit it was demonstrated that the persistence of Rabi oscillations can be supported by either the low-frequency signal [129] or induced by noise [130].…”

Section: Dynamical Behavior Of a Two-level Systemmentioning

confidence: 99%

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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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. Contents

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Interband transitions and interference effects in superconducting qubits

Cited by 7 publications

References 31 publications

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

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

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Multiphoton transitions in Josephson-junction qubits (Review Article)

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