Stark Effect and Generalized Bloch-Siegert Shift in a Strongly Driven Two-Level System

Tuorila, Jani; Silveri, Matti; Sillanpää, Mika; Thuneberg, E. V.; Makhlin, Yuriy; Hakonen, Pertti

doi:10.1103/physrevlett.105.257003

Cited by 100 publications

(104 citation statements)

References 37 publications

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“…Resolved sidebands appear at o ¼ o 0 ± kO (k ¼ 0,1,2,y), and are amplitude-modulated with Bessel functions J k (d/O), where d and O denote the modulation amplitude and frequency, respectively. The HamiltonianĤ þĤ drive (equations (1) and (4)) can be transformed to a non-uniformly rotating frame 18,19 (see Methods). The theoretical prediction for the steady-state occupation probability on the resolved sidebands ( O4g4G 2 ) is…”

Section: Resultsmentioning

confidence: 99%

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Motional averaging in a superconducting qubit

et al. 2013

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Superconducting circuits with Josephson junctions are promising candidates for developing future quantum technologies. Of particular interest is to use these circuits to study effects that typically occur in complex condensed-matter systems. Here we employ a superconducting quantum bit-a transmon-to perform an analogue simulation of motional averaging, a phenomenon initially observed in nuclear magnetic resonance spectroscopy. By modulating the flux bias of a transmon with controllable pseudo-random telegraph noise we create a stochastic jump of its energy level separation between two discrete values. When the jumping is faster than a dynamical threshold set by the frequency displacement of the levels, the initially separate spectral lines merge into a single, narrow, motional-averaged line. With sinusoidal modulation a complex pattern of additional sidebands is observed. We show that the modulated system remains quantum coherent, with modified transition frequencies, Rabi couplings, and dephasing rates. These results represent the first steps towards more advanced quantum simulations using artificial atoms.

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Section: Resultsmentioning

confidence: 99%

“…We show below how to eliminate the time-dependence from the longitudinal drive. After moving to a non-uniformly rotating frame with the unitary transformation 18,19 …”

Section: Methodsmentioning

confidence: 99%

Motional averaging in a superconducting qubit

et al. 2013

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“…The first-order correction to the position of the resonances is the so-called Bloch-Siegert shift [1]; it was demonstrated for the superconducting qubits in Ref. [115]. Thus, in general, the position of the multiphoton resonances is amplitude-dependent.…”

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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“…For a driven two-level system, drastic effects on the tunneling rate arise from quasi-energy crossing and anticrossing 15,16 . At certain amplitudes of the driving field, dynamical localization and trapping of the system into a non-linear resonance can take place [17][18][19][20][21][22][23][24][25] . As the parameters are changed when the level-approaching and level-crossing take place, the effects of band-to-band tunneling (Landau-Zener transitions) can occur.…”

Section: Introductionmentioning

confidence: 99%

Amplitude spectroscopy of two coupled qubits

2012

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We study the effect of a time-dependent driving field with a large amplitude on a system composed of two coupled qubits (two-level systems). Using the rotating wave approximation (RWA) makes it possible to find simple conditions for resonant excitation of the four-level system. We find that the resonance conditions include the coupling strength between the qubits. Numerical simulations confirm the qualitative conclusions following from the RWA. To reveal the peculiarities of resonant transitions caused by the quasi-level motion and crossing in a periodic driving field, we use Floquet states, which determine the precise intermediate states of the system. Calculating the quasi-energy states of the multi-level system makes it possible to find the transition probabilities and build interference patterns for the transition probabilities. The interference patterns demonstrate the possibility of obtaining various pieces of information about the qubits, since the positions of transition-probability maxima depend on various system parameters, including the coupling strength between the qubits.

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Stark Effect and Generalized Bloch-Siegert Shift in a Strongly Driven Two-Level System

Cited by 100 publications

References 37 publications

Motional averaging in a superconducting qubit

Motional averaging in a superconducting qubit

Multiphoton transitions in Josephson-junction qubits (Review Article)

Amplitude spectroscopy of two coupled qubits

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