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Physical Review A

Experimental study of Rabi oscillations induced by a phase-jump field

R. Boscaino, Rosario N. Mantegna

Published Aug 1, 1989• 2 citations
Publisher

Abstract

The nutational regime induced by a stochastic field with phase telegraph noise is experimentally investigated in a two-level system at microwave frequency. Regular oscillations are observed in the average transient response of the system with an effective Rabi frequency whose value depends both on the jump amplitude and on the mean dwell time of the phase noise. Motional-narrowing, weak-damping, and strong-damping regimes are observed on varying the dwell time and the jump amplitude. The experimental results are in fair agreement with theoretical predictions.

DOI
10.1103/physreva.40.2217

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The nutational regime induced by a stochastic field with phase telegraph noise is experimentally investigated in a two-level system at microwave frequency. Regular oscillations are observed in the average transient response of the system with an effective Rabi frequency whose value depends both on the jump amplitude and on the mean dwell time of the phase noise. Motional-narrowing, weak-damping, and strong-damping regimes are observed on varying the dwell time and the jump amplitude. The experimental results are in fair agreement with theoretical predictions.
We report on an experimental study of strong radiation–matter interactions between a phase-telegraph field and an inhomogeneous S = 1/2 two-level system. The phase-telegraph field is obtained by performing a stochastic phase modulation to control the statistical properties of the radiation field. We detect the average time evolution of the system, and we study the dependence of the effective Rabi frequency on the parameters characterizing the stochastic evolution of the radiation field. Experimental results are in good agreement with a theoretical picture of this process given by Eberly et al. [ Phys. Rev. A30, 2381 ( 1984)].
Stochastic fields with non-Gaussian Markovian phase or frequency jumplike noise are produced at microwave frequency and used to induce two-photon (TP) processes in a S=(1/2 spin system. The influence of the field statistics on the TP-induced second-order response is experimentally investigated in a system with very short relaxation times, in its stationary state and in the weak-field limit. In the case of frequency-telegraph noise the experimental spectra of the nonlinear response are found to reproduce roughly the spectral profiles of the corresponding driving fields but with a larger width. When the telegraph noise modulates the phase of the field, the relationship between input and output spectra depends on the phase-jump amplitude ${\ensuremath{\varphi}}_{0}$. For ${\ensuremath{\varphi}}_{0}$=\ensuremath{\pi}/4 the spectrum of the response is much broader than the input one, whereas it is much narrower for ${\ensuremath{\varphi}}_{0}$=\ensuremath{\pi}/2. The experimental results are interpreted using the calculation of the TP-induced second-order response worked out in the preceding paper [Boscaino and Mantegna, Phys. Rev. A 40, 5 (1989)].
Recent theoretical investigations have shown that when atoms resonantly interact with strong, phase-fluctuating fields of fairly arbitrary character there is an underlying simplicity in their temporal response to the field. Specifically, theory predicts that the atom's response can be divided into two distinct temporal components: an adiabatic component manifesting itself in the instantaneous frame of field-atom interactions as a Bloch-vector trajectory figure-eight pattern, and a nonadiabatic component manifesting itself as population variations oscillating at the Rabi frequency. Here, we experimentally verify theoretical expectations regarding the nonadiabatic component of the field's temporal response. In the presence of a resonant field suffering broadband phase noise we show that atomic population fluctuations display a resonant enhancement at Fourier frequencies corresponding to the Rabi frequency, and that the characteristics of this resonance are similar to those of a damped, driven harmonic oscillator.
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field ω rf is close to the Rabi frequency ω 1 in a microwave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency ɛ are accompanied by higher-frequency oscillations at frequencies n ω rf and n ω rf ± ɛ, where n = 1, 2,.... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency ɛ on the sign of the detuning ω 1 − ω rf from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency ω rf + ɛ increases, while the amplitude at the difference frequency ω rf − ɛ decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of E ′ 1 centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.
We present a classical analysis of the transient response of Josephson junctions perturbed by microwaves and thermal fluctuations. The results include a specific low-frequency modulation in phase and amplitude behavior of a junction in its zero-voltage state. This transient modulation frequency is linked directly to an observed variation in the probability for the system to switch to its nonzero voltage state. Complementing previous work on linking classical analysis to the experimental observations of Rabi oscillations, this expanded perturbation method also provides closed-form analytical results for attenuation of the modulations and the Rabi-type oscillation frequency. Results of perturbation analysis are compared directly (and quantitatively) to numerical simulations of the classical model as well as published experimental data, suggesting that transients to phase-locking are closely related to the observed oscillations.
Superconducting qubits often show signatures of coherent coupling to microscopic two-level fluctuators (TLFs), which manifest themselves as avoided level crossings in spectroscopic data. In this work we study a phase qubit, in which we induce Rabi oscillations by resonant microwave driving. When the qubit is tuned close to the resonance with an individual TLF and the Rabi driving is strong enough (Rabi frequency of order of the qubit-TLF coupling), interesting four-level dynamics are observed. The experimental data show a clear asymmetry between biasing the qubit above or below the fluctuator's level splitting. Theoretical analysis indicates that this asymmetry is due to an effective coupling of the TLF to the external microwave field induced by the higher qubit levels.