Knowing a quantum system's environment is critical for its practical use as a quantum device. Qubit sensors can reconstruct the noise spectral density of a classical bath, provided long enough coherence time. Here we present a protocol that can unravel the characteristics of a more complex environment, comprising both unknown coherently coupled quantum systems, and a larger quantum bath that can be modeled as a classical stochastic field. We exploit the rich environment of a Nitrogen-Vacancy center in diamond, tuning the environment behavior with a bias magnetic field, to experimentally demonstrate our method. We show how to reconstruct the noise spectral density even when limited by relatively short coherence times, and identify the local spin environment. Importantly, we demonstrate that the reconstructed model can have predictive power, describing the spin qubit dynamics under control sequences not used for noise spectroscopy, a feature critical for building robust quantum devices. At lower bias fields, where the effects of the quantum nature of the bath are more pronounced, we find that more than a single classical noise model are needed to properly describe the spin coherence under different controls, due to the back action of the qubit onto the bath.
Doppler-free optical double-resonance spectroscopy is used to study the s p p 5 5 6 1 2 3 2 3 2 excitation sequence in room-temperature rubidium atoms. This involves a s p 5 5 F or ±2 electric quadrupole transitions.
The experimental verification of quantum fluctuation relations for driven open quantum system is currently a challenge, due to the conceptual and operative difficulty of distinguishing work and heat. The Nitrogen-Vacancy center in diamond has been recently proposed as a controlled test bed to study fluctuation relations in the presence of an engineered dissipative channel, in absence of work [Hernández-Gómez et al, Phys. Rev. Research 2, 023327 (2020)]. Here, we extend those studies to exploring the validity of quantum fluctuation relations in a driven-dissipative scenario, where the spin exchanges energy both with its surroundings because of a thermal gradient, and with an external work source. We experimentally prove the validity of the quantum fluctuation relations in the presence of cyclic driving in two cases, when the spin exchanges energy with an effective infinite-temperature reservoir, and when the total work vanishes at stroboscopic times -although the power delivered to the NV center is non-null. Our results represent the first experimental study of quantum fluctuation relation in driven open quantum systems.
Direct evidence of excitation of the 5p 3/2 → 6p 3/2 electric dipole forbidden transition in atomic rubidium is presented. The experiments were performed in a room temperature rubidium cell with continuous wave extended cavity diode lasers. Optical-optical double resonance spectroscopy with counterpropagating beams allows the detection of the non-dipole transition free of Doppler broadening. The 5p 3/2 state is prepared by excitation with a laser locked to the maximum F cyclic transition of the D2 line, and the forbidden transition is produced by excitation with a 911 nm laser. Production of the forbidden transition is monitored by detection of the 420 nm fluorescence that results from decay of the 6p 3/2 state. Spectra with three narrow lines (≈ 13 MHz FWHM) with the characteristic F − 1, F and F + 1 splitting of the 6p 3/2 hyperfine structure in both rubidium isotopes were obtained. The results are in very good agreement with a direct calculation that takes into account the 5s → 5p 3/2 preparation dynamics, the 5p 3/2 → 6p 3/2 non-dipole excitation geometry and the 6p 3/2 → 5s 1/2 decay. The comparison also shows that the electric dipole forbidden transition is a very sensitive probe of the preparation dynamics.PACS numbers: 32.70. Cs,32.70.Fw While the electric dipole approximation is a cornerstone in the study of the interaction between optical radiation fields and atoms, transitions induced by optical fields beyond this approximation have also become important tools in basic and applied studies of atoms. These so called "forbidden transitions" have been traditionally used in astrophysical and plasma studies [1]. They now play a fundamental role in metrology [2] and have also been used in experiments testing parity nonconserving interactions in atoms [3].In early studies of forbidden transitions, Sayer et al. [4] determined transition probabilities of electric quadrupole (E2) transitions using a tungsten lamp. The first direct observation of electric quadrupole effects in multiphoton ionization dates back to the work of Lambropoulos et al.[5]. Electric-dipole-forbidden transitions were exploited in three-wave-mixing experiments for optical sum and difference frequency generation in [6].The use of intense continuous-wave or pulsed laser sources has facilitated the observation of weak absorption lines. For instance, Tojo et al.[7] reported a determination of the oscillator strength of a E2 transition with a temperature-controlled cell and an extended cavity diode laser. Also, the study of strongly forbidden J = 0 → J = 0 transitions via single-photon excitation is presented in [8]. Excitation of forbidden transitions involving states with nonzero angular momentum in alkali atoms have also been studied over the last few years [9][10][11][12][13]. The coherent mixing of waves is theoretically studied in [9] for n 1 2 P − n 2 2 P transitions. The excitation of the 5p → 8p forbidden transition in thermal rubidium atoms was produced with a pulsed laser in [10] and using cold atoms in [12]. The experiment with co...
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