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We present measurements of hyperfine structure (HFS) of the $nP_J$ Rydberg states for large principal quantum number $n$ range ($n=41-55$) employing the microwave spectroscopy in an ultra-cold cesium Rydberg ensemble. A microwave field with 30-$\mu$s duration couples the $ nS \to nP $ transition, yielding a narrow linewidth spectroscopy that approaches the Fourier limit, which allows us to resolve the hyperfine structure of $ nP_J $ states. By analyzing the hyperfine splittings of $nP_J$ states, we determine the magnetic-dipole HFS coupling constant $\bar{A}_{HFS,P_{1/2}}=3.760(26) ~$GHz for $P_{1/2}$ state, $\bar{A}_{HFS,P_{3/2}}= 0.718(27)~$GHz, and $ \bar{B}_{HFS,P_{3/2}}= -0.084(102)~$GHz for $P_{3/2}$ state, respectively. Systematic uncertainties caused by stray electromagnetic field, microwave field power and Rydberg interaction are analyzed. This measurement is significant for the investigation of Rydberg electrometry and quantum simulation with dipole interaction involving $nP_J$ state.

Long-range $(n+2)D_{5/2} \, nF_J$ Rydberg macro-dimers are observed in an ultracold cesium Rydberg gas for $39\leq n\leq48$. Strong dipolar "flip" ($\langle D_{5/2} F_{5/2} \vert \hat{V}_{dd} \vert F_{5/2} D_{5/2} \rangle$, $\langle D_{5/2} F_{7/2} \vert \hat{V}_{dd} \vert F_{7/2} D_{5/2} \rangle$) and "cross" ($\langle D_{5/2} F_{7/2} \vert \hat{V}_{dd} \vert F_{5/2} D_{5/2} \rangle$) couplings lead to bound, fine-structure-mixed $(n+2)D_{5/2}nF_J$ macro-dimers at energies between the $F_J$ fine-structure levels. The $DF$ macro-dimers are measured by microwave photo-association from optically prepared $[(n+2)D_{5/2}]_2$ Rydberg pair states. Calculated adiabatic potential curves are used to elucidate the underlying physics and to model the $DF$ macro-dimer spectra, with good overall agreement. Microwave photo-association allows Franck-Condon tuning, which we have studied by varying the detuning of a Rydberg-atom excitation laser. Further, in Stark spectroscopy we have measured molecular DC electric polarizabilities that are considerably larger than those of the atomic states. The large molecular polarizabilities may be caused by high-$\ell$ mixing. The observed linewidths of the Stark-shifted molecular lines provide initial evidence for intra-molecular induced-dipole-dipole interaction.

We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2)D_{5/2}\rightarrow nF_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the $D$ Rydberg state using a two-photon laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier side-band spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\gtrsim 3 \pi$. Furthermore, we investigate the Zeeman effect of the clearly resolved $nF_J$ fine-structure levels in fields up to 120~mG, where the transition into $nF_{7/2}$ displays a thee-peak Zeeman pattern, while $nF_{5/2}$ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of DC magnetic fields in experimental chambers for cold atoms.

We present precise measurements of the quantum defects of cesium $n$F$_J$ Rydberg levels. We employ high-precision microwave spectroscopy of $(n+2)\mathrm{D}_{5/2}\rightarrow n\mathrm{F}_{5/2,7/2}$ transitions for $n=45$ to 50 in a cold-atom setup. Cold cesium $(n+2)$D$_{5/2}$ atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the $n\mathrm{F}_{5/2,7/2}$ resonances. Transition spectra are acquired using state-selective electric-field ionization and time-gated ion detection. Transition-frequency intervals are obtained by Lorentzian fits to the measured spectral lines, which have linewidths ranging between 70~kHz and 190~kHz, corresponding to about one to three times the Fourier limit. A comprehensive analysis of relevant line-shift uncertainties and line-broadening effects is conducted. We find quantum defect parameters $\delta_{0}(\mathrm{F}_{5/2})=0.03341537(70)$ and $\delta_{2}(\mathrm{F}_{5/2})=-0.2014(16)$, as well as $\delta_{0}(\mathrm{F}_{7/2})=0.0335646(13)$ and $\delta_{2}(\mathrm{F}_{7/2})=-0.2052(29)$, for $J=5/2$ and $J=7/2$, respectively. Fine structure parameters $A_{FS}$ and $B_{FS}$ for Cs $n{\rm{F}}_J$ are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

We demonstrate a continuous frequency electric field measurement based on the far off-resonant AC stark effect in a Rydberg atomic vapor cell. In this configuration, a strong far off-resonant field, denoted as a local oscillator (LO) field, acts as a gain shifting the Rydberg level to a high sensitivity region. An incident weak signal field with a few hundreds of kHz difference from the LO field is mixed with the LO field in Rydberg system to generate an intermediate frequency (IF) signal, which is read out by the Rydberg electromagnetically induced transparency (Rydberg-EIT) spectroscopy. Not like resonant EIT-AT spectra, we realize the electric field measurement of the signal frequency from 2 GHz to 5 GHz using a single Rydberg state. A minimum detectable filed strength is down to 2.31~$\mu$V/cm and a linear dynamic range is over 65~dB. The minimum detectable filed is comparable with a resonant microwave-dressed Rydberg heterodyne receiver using the same system, which is 1.45~$\mu$V/cm. We also show the system has an inherent polarization selectivity feature. Our method can provide a high sensitivity of electric field measurement and be extended to arbitrary frequency measurements., Comment: 5 pages, 4 figures

Music generation is always interesting in a sense that there is no formalized recipe. In this work, we propose a novel dual-track architecture for generating classical piano music, which is able to model the inter-dependency of left-hand and right-hand piano music. Particularly, we experimented with a lot of different models of neural network as well as different representations of music, and the results show that our proposed model outperforms all other tested methods. Besides, we deployed some special policies for model training and generation, which contributed to the model performance remarkably. Finally, under two evaluation methods, we compared our models with the MuseGAN project and true music., Comment: 8 pages, 7 figures