Microwave coupled Zeeman splitting spectroscopy of a cesium nPJ Rydberg atom.

We perform measurements of microwave spectra of cesium Rydberg 51S1/2 → 51PJ transitions with the linewidth approaching the Fourier limit. A two-photon scheme excites the ground-state atoms to the Rydberg 51S1/2 state, and a weak microwave photon couples the Rydberg transition of 51S1/2 → 51PJ. The hyperfine structure of 51P1/2 can be clearly resolved with a narrow linewidth microwave spectra by using the method of ion detection. Furthermore, we investigate the Zeeman effect of the 51P1/2,3/2 state. The theoretical calculations reproduce the measurement well. Our experimental measurements provide a reliable technical solution for the investigation of high angular momentum Rydberg states, which is conducive to further realizing the coherent manipulation of Rydberg energy levels and improving the sensitivity of electromagnetic field measurement.

Quantum sensing of microwave electric fields based on Rydberg atoms.

Microwave electric field (MW E-field) sensing is important for a wide range of applications in the areas of remote sensing, radar astronomy and communications. Over the past decade, Rydberg atoms have been used in ultrasensitive, wide broadband, traceable, stealthy MW E-field sensing because of their exaggerated response to MW E-fields, plentiful optional energy levels and integratable preparation methods. This review first introduces the basic concepts of quantum sensing, the properties of Rydberg atoms and the principles of quantum sensing of MW E-fields with Rydberg atoms. An overview of this very active research direction is gradually expanding, covering the progress of sensitivity and bandwidth in Rydberg atom-based microwave sensing, superheterodyne quantum sensing with microwave-dressed Rydberg atoms, quantum-enhanced sensing of MW E-field and recent advanced quantum measurement systems and approaches to further improve the performance of MW E-field sensing. Finally, a brief outlook on future development directions is provided.

Robust Ramsey interferometer based on a single Rydberg polariton.

We demonstrate a robust single-photon Ramsey interferometer based on a single Rydberg excitation, where the photon is stored as a Rydberg polariton in an ensemble of atoms. This coherent conversion of the photon to Rydberg polariton enables to split an incoming photon into a superposition state of two Rydberg states by applying microwave fields, which constructs two paths of interferometer. Ramsey interference fringes are demonstrated when we scan either the detuning of the microwave or the free evolution time, from which we can obtain the resonant transition frequency of two Rydberg states. We use the Ramsey-like sequence to demonstrate coherent manipulation of the stored single-photon to construct different interference patterns. In addition, the robustness of the Ramsey interferometer to the fluctuation of incoming photon numbers and optical depth (OD) of the atomic ensemble is tested, showing that the coherent of Ramsey interferometer is preserved for input photon number in a range of Rin < 15 and for OD varying from 1.0 to 4.0. The robust interferometer will find its applications in quantum precision measurement.

Dephasing of ultracold cesium 80D5/2-Rydberg electromagnetically induced transparency.

We study Rydberg electromagnetically induced transparency (EIT) of a cascade three-level atom involving 80D5/2 state in a strong interaction regime employing a cesium ultracold cloud. In our experiment, a strong coupling laser couples 6P3/2 to 80D5/2 transition, while a weak probe, driving 6S1/2 to 6P3/2 transition, probes the coupling induced EIT signal. At the two-photon resonance, we observe that the EIT transmission decreases slowly with time, which is a signature of interaction induced metastability. The dephasing rate γOD is extracted with optical depth OD = γODt. We find that the optical depth linearly increases with time at onset for a fixed probe incident photon number Rin before saturation. The dephasing rate shows a nonlinear dependence on Rin. The dephasing mechanism is mainly attributed to the strong dipole-dipole interactions, which leads to state transfer from nD5/2 to other Rydberg states. We demonstrate that the typical transfer time τ0(80D) obtained by the state selective field ionization technique is comparable with the decay time of EIT transmission τ0(EIT). The presented experiment provides a useful tool for investigating the strong nonlinear optical effects and metastable state in Rydberg many-body systems.

Manipulation of single stored-photon with microwave field based on Rydberg polariton.

We demonstrate a coherent microwave manipulation of a single optical photon based on a single Rydberg excitation in an atomic ensemble. Due to the strong nonlinearities in a Rydberg blockade region, a single photon can be stored in the formation of Rydberg polariton using electromagnetically induced transparency (EIT). The manipulation of the stored single photon is performed by applying a microwave field that resonantly couples the nS1/2 and nP3/2, while the coherent readout is performed by mapping the excitation into a single photon. We achieve a single photon source with g(2)(0) = 0.29 ± 0.08 at 80S1/2 without applying microwave fields. By implementing the microwave field during the storage time and retrieval process, we show the Rabi oscillation and modulation of stored photons that can be controlled to retrieve early or late. Rapid modulation frequencies up to 50 MHz can be obtained. Our experimental observations can be well explained via numerical simulations based on an improved superatom model accounting for the dipole-dipole interactions in a Rydberg EIT medium. Our work provides a way to manipulate the stored photons by employing the microwave field, which is significant for developing quantum technologies.

Super low-frequency electric field measurement based on Rydberg atoms.

We demonstrate the measurement of super low-frequency electric field using Rydberg atoms in an atomic vapor cell with inside parallel electrodes, thus overcoming the low-frequency electric-field-screening effect at frequencies below a few kHz. Rydberg electromagnetically induced transparency (EIT) spectra involving 52D5/2 state is employed to measure the signal electric field. An auxiliary DC field is applied to improve the sensitivity. A DC Stark map is demonstrated, where the utilized 52D5/2 exhibits mj = 1/2, 3/2, 5/2 Stark shifts and splittings. The mj = 1/2 state is employed to detect the signal field because of its larger polarizability than that of mj = 3/2, 5/2. Also, we show that the strength of the spectrum is dependent on the angle between the laser polarizations and the electric field. With optimization of the applied DC field to shift the mj = 1/2 Rydberg energy level to a high sensitivity region and the laser polarizations to obtain the maximum mj = 1/2 signal, we achieve the detection of the signal electric field with a frequency of 100 Hz down to 214.8 µV/cm with a sensitivity of 67.9 µV cm-1Hz-1/2, and the linear dynamic range is over 37 dB. Our work extends the measurement frequency of Rydberg sensors to super low frequency with high sensitivity, which has the advantages of high sensitivity and miniaturization for receiving super low frequency.

Dissociation of ultracold cesium Rydberg-ground molecules.

We report the experimental measurements of the decay rate of polar cesium nD5/2 - 6S1/2 Rydberg-ground molecules with a large principal quantum number range of 35 ≤ n ≤ 40. Rydberg molecules are prepared employing the method of two-photon photoassociation and the molecular (atomic) ions, due to autoionization (blackbody photoionization), are detected with a microchannel plate detector. The decay rate Γ of the vibrational ground state of the deep and shadow bound molecules for triplet (TΣ) and mixed singlet-triplet (S,TΣ) are measured by fitting the molecular population with the exponential function. Comparing with the parent atom, the decay rate of the polar Rydberg-ground molecule shows an obvious increase with a magnitude of a few µs. The possible dissociation mechanism of polar Rydberg-ground molecules including a collisional decay, blackbody induced decay, and coupling of adjacent Rydberg states and tunneling decay are discussed in detail. The theoretical model is induced to simulate the measurements, showing agreement.

Vibronic and Cationic Features of 2-Fluorobenzonitrile and 3-Fluorobenzonitrile Studied by REMPI and MATI Spectroscopy and Franck-Condon Simulations.

Fluorinated organic compounds have superior physicochemical properties than general organic compounds due to the strong C-F single bond; they are widely used in medicine, biology, pesticides, and materials science. In order to gain a deeper understanding of the physicochemical properties of fluorinated organic compounds, fluorinated aromatic compounds have been investigated by various spectroscopic techniques. 2-fluorobenzonitrile and 3-fluorobenzonitrile are important fine chemical intermediates and their excited state S1 and cationic ground state D0 vibrational features remain unknown. In this paper, we used two-color resonance two photon ionization (2-color REMPI) and mass analyzed threshold ionization (MATI) spectroscopy to study S1 and D0 state vibrational features of 2-fluorobenzonitrile and 3-fluorobenzonitrile. The precise excitation energy (band origin) and adiabatic ionization energy were determined to be 36,028 ± 2 cm-1 and 78,650 ± 5 cm-1 for 2-fluorobenzonitrile and 35,989 ± 2 cm-1 and 78,873 ± 5 cm-1 for 3-fluorobenzonitrile, respectively. The density functional theory (DFT) at the levels of RB3LYP/aug-cc-pvtz, TD-B3LYP/aug-cc-pvtz, and UB3LYP/aug-cc-pvtz were used to calculate the stable structures and vibrational frequencies for the ground state S0, excited state S1, and cationic ground state D0, respectively. Franck-Condon spectral simulations for transitions of S1 ← S0 and D0 ← S1 were performed based on the above DFT calculations. The theoretical and experimental results were in good agreement. The observed vibrational features in S1 and D0 states were assigned according to the simulated spectra and the comparison with structurally similar molecules. Several experimental findings and molecular features were discussed in detail.

Autler-Townes splitting of three-photon excitation of cesium cold Rydberg gases.

We demonstrate the three-photon Autler-Townes (AT) spectroscopy in a cold cesium Rydberg four-level atom by detecting the field ionized Rydberg population. The ground state |6S1/2〉, two intermediate states |6P3/2〉 and |7S1/2〉 and Rydberg state |60P3/2〉 form a cascade four-level atomic system. The three-photon AT spectra and AT splittings are characterized by the Rabi frequency Ω852 and Ω1470 and detuning δ852 of the coupling lasers. Due to the interaction of two coupling lasers with the atoms, the AT spectrum has three peaks denoted with the letters A, B and C. Positions of the peaks and relative AT splittings, γAB and γBC, strongly depend on two coupling lasers. The dependence of the AT splitting, γAB and γBC, on the coupling laser detuning, δ852, and Rabi frequency, Ω852 and Ω1470 are investigated. It is found that the AT splitting γAB mainly comes from the first photon coupling, whereas the γBC mainly comes from the second photon coupling with the atom. The three-photon AT spectra and relevant AT splittings are simulated with the four-level density matrix equation and show good agreement with the theoretical simulations considering the spectral line broadening. Our work is of great significance both for further understanding the interaction between the laser and the atom, and for the application of the Rydberg atom based field measurement.

Rydberg atom-based AM receiver with a weak continuous frequency carrier.

We demonstrate an atom-based amplitude-modulation (AM) receiver for digital communication with a weak continuous frequency carrier using a Rydberg AC Stark effect in a vapor cell and achieve the operating carrier frequency continuously from 0.1 GHz to 5 GHz at a single Rydberg state. A strong local oscillator (LO) field ELO acts as a gain to shift the Rydberg level to a high sensitivity region, and a weak carrier field ECarr keeps the same frequency with the LO field. The digital baseband signals are encoded onto the ECarr using the amplitude modulation technique with the different modulation frequency. The response of Rydberg atom to the baseband signal is probed via a Rydberg electromagnetically induced transparency (EIT). The measured instantaneous bandwidth of the system is about 230 kHz. To demonstrate the performance of our system for an actual communication, we consider a color image as an example, the received image displays that the bit error rate (BER) is less than 5% when the maximum data transfer rate is about 238 kbps. Meanwhile, our system shows the weak carrier field of ECarr ≥ 13.52 µV/cm can be used for the practical communication with BER less than 5%. Our works break the limitation that EIT-AT based atomic receivers only operate at the near resonant frequencies of the Rydberg transitions, making this emerging of quantum technology close to the practical application with high sensitivity and broad bandwidth.

Pole analysis of EIT-AT spectrum with Rydberg atoms.

We investigate the electromagnetically induced transparency (EIT) and Autler Townes (AT) splitting spectrum with a four-level Rydberg atom by pole analysis of the probe coherence. A pair of poles corresponding to the two peaks of the spectral splitting is observed. The spectral split or the pole positions are affected by the microwave intensity (MW) and the detuning between the probe and the coupling laser. In the absence of any detuning, the two poles coincide and separate again on the imaginary axis of the complex detuning plane at weak MW field. The two poles do not coincide when the probe (coupling) laser is detuned for scanning the coupling (probe) laser frequency. However, under finite detuning, the two poles approach the nearest distance in the absence of any splitting and are separated again in the direction parallel to the imaginary axis. The spectral analysis of the poles provides an alternate way to establish the relationship between the splitting and the intensity of MW, which may play a role in the application of atomic-based MW measurements.

Distinction of electromagnetically induced transparency and Autler-Towners splitting in a Rydberg-involved ladder-type cold atom system.

Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two similar quantum coherent phenomena but have different mechanisms and applications. Akaike information criteria (AIC), an objective method to discriminate EIT and ATS from an experimental viewpoint, has been employed in a variety of systems. Here we use AIC method to quantitively discriminate a series of spectra of cold atoms in a Rydberg-involved upper-driving ladder-type. The derived weights of EIT and ATS reflect that our spectra change from EIT-ATS intermediate region to ATS-dominated region along Rabi frequency of coupling field increases. We find that there are two factors affecting EIT-ATS weights in a Rydberg-involved three-level system: dephasing rate, induced by the interactions among Rydberg atoms, makes the EIT-ATS crossover move to the direction of low Rabi frequency of coupling field and the experimental noise makes the difference between EIT and ATS weights reduce at elsewhere. Our investigation could provide a meaningful reference for the observations and applications of Rydberg-involved quantum coherent spectroscopy.

Collectively Encoded Rydberg Qubit.

We demonstrate a collectively encoded qubit based on a single Rydberg excitation stored in an ensemble of N entangled atoms. Qubit rotations are performed by applying microwave fields that drive excitations between Rydberg states. Coherent readout is performed by mapping the excitation into a single photon. Ramsey interferometry is used to probe the coherence of the qubit, as well as to test the robustness to external perturbations. We show that qubit coherence is preserved even as we lose atoms from the polariton mode, preserving Ramsey fringe visibility. We show that dephasing due to electric field noise scales as the fourth power of field amplitude. These results show that robust quantum information processing can be achieved via collective encoding using Rydberg polaritons, and hence this system could provide an attractive alternative coding strategy for quantum computation and networking.

Single-photon stored-light Ramsey interferometry using Rydberg polaritons.

We demonstrate a single-photon stored-light interferometer, where a photon is stored in a laser-cooled atomic ensemble in the form of a Rydberg polariton with a spatial extent of 10×1×1µm3. The photon is subject to a Ramsey sequence, i.e., "split" into a superposition of two paths. After a delay of up to 450 ns, the two paths are recombined to give an output dependent on their relative phase. The superposition time of 450 ns is equivalent to a free-space propagation distance of 135 m. We show that the interferometer fringes are sensitive to external fields and suggest that stored-light interferometry could be useful for localized sensing applications.

Observation of photoassociation spectroscopy of ultralong 37D5/2 + 6S1/2Cs2 Rydberg molecules.

We present an experimental observation of 37D5/2 + 6S1/2Cs2 Rydberg-ground molecules by employing a two-photon photoassociation method. Two distinct Rydberg-ground molecular signals, deep and shallow bound molecules, are observed at the red detuning of atomic line. In theory, the model of scattering interaction between the Rydberg electron and ground-state atom is used to simulate the experiments. Two potential energy curves with energy minimum, deep pure triplet 3Σ and shallow hyperfine-mixed singlet-triplet 1,3Σ potentials, refer to the attained Rydberg-ground molecular signals, respectively. Calculations of the binding energy of triplet 3Σ and mixed 1,3Σv = 0 states are compared with the measurements. The agreement between the calculated and measured values of the binding energy yields zero-energy scattering lengths as T(0) = -19.2a0 and as S(0) = -1.3a0, respectively.

Zeeman-tunable modulation transfer spectroscopy.

Active frequency stabilization of a laser to an atomic or molecular resonance underpins many modern-day AMO physics experiments. With a flat background and high signal-to-noise ratio, modulation transfer spectroscopy (MTS) offers an accurate and stable method for laser locking. However, despite its benefits, the four-wave mixing process that is inherent to the MTS technique entails that the strongest modulation transfer signals are only observed for closed transitions, excluding MTS from numerous applications. Here we report for the first time, to the best of our knowledge, the observation of a magnetically tunable MTS error signal. Using a simple two-magnet arrangement, we show that the error signal for the Rb87F=2→F'=3 cooling transition can be Zeeman-shifted over a range of >15 GHzto any arbitrary point on the rubidium D2 spectrum. Modulation transfer signals for locking to the Rb87F=1→F'=2 repumping transition, as well as 1 GHz red-detuned to the cooling transition, are presented to demonstrate the versatility of this technique, which can readily be extended to the locking of Raman and lattice lasers.