本文利用高对比度 Rydberg EIT 光谱研究热蒸气低频电场测量中的表面吸附效应，实现 10 Hz–1 MHz 电场检测，并提出基于 Zeeman 峰锁定和参考池频标的精密 Stark 频移测量方法。
摘要：
采用热蒸气的 Rydberg 辅助原子电学测量为检测外部电场提供了一种有前景的方法。然而，由于吸附在真空室内表面的金属-碱金属原子所产生的影响，该技术在测量低频时面临重大挑战。在本工作中，我们应用高对比度 Rydberg 电磁诱导透明（EIT）光谱来系统研究这些效应，包括激光功率和电场强度的影响。我们展示了测量频率范围为 10 Hz 至 1 MHz 的电场的能力。此外，本研究确定了此类测量中数据容量的一个基本限制。而且，我们提出了一种通过将耦合激光锁定到 Zeeman 分裂的 Rydberg EIT 峰来精确测量 Stark 频移的方法。利用参考池中 Zeeman 频移作为稳定的频率基准，我们追踪科学池中由 Stark 诱导的频移，并证实其与理论预测高度吻合。这些结果为未来基于 Rydberg 原子系统的精密测量技术和场传感应用提供了有价值的见解。
英文摘要：
Rydberg-assisted atomic electrometry with thermal vapors offers a promising approach for detecting external electric fields. However, this technique presents significant challenges for measuring low frequencies due to the effects of metal-alkali atoms adsorbed on the interior surface of the vacuum chamber. In this work, we apply high-contrast Rydberg electromagnetically induced transparency (EIT) spectroscopy to systematically investigate these effects, including the influence of laser power and electric field strength. We demonstrate the ability to measure electric field frequencies ranging from 10 Hz to 1 MHz. Additionally, this study identifies a fundamental limit for data capacity in such measurements. Furthermore, we propose a method for precise Stark shift measurements by locking the coupling laser to Zeeman-split Rydberg EIT peaks. Using the Zeeman shift in a reference cell as a stable frequency reference, we track Stark-induced shifts in a science cell and confirm excellent agreement with theoretical predictions. These results provide valuable insights for future precision measurement techniques and field sensing applications based on Rydberg atom systems.
We perform Zeeman spectroscopy on a Rydberg electromagnetically induced transparency (EIT) system in a room-temperature Cs vapor cell, in magnetic fields up to 50~Gauss and for several polarization configurations. The magnetic interactions of the $\vert 6S_{1/2}, F_g=4 \rangle$ ground, $\vert 6P_{3/2}, F_e=5 \rangle$ intermediate, and $\vert 33S_{1/2} \rangle$ Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the deep hyperfine Paschen-Back regimes, respectively. Starting in magnetic fields of about 5~Gauss, the spectra develop an asymmetry tha…
We study $Λ$-type Electromagnetically Induced Transparency (EIT) on the Rb D2 transition in a buffer-gas-free thermal vapor cell without anti-relaxation coating. Experimental data show distinguished features of velocity-selective optical pumping and one EIT resonance. The Zeeman splitting of the EIT line in magnetic fields up to 12 Gauss is investigated. One Zeeman component is free of the first-order shift and its second-order shift agrees well with theory. The full width at half maximum (FWHM) of this magnetic-field-insensitive EIT resonance is reduced due to Doppler narrowing, scales linear…
We present results of a study of four-wave mixing in Rb vapour with highly nonlinear susceptibility, using both homodyne and heterodyne detection. We demonstrate that the spectra have different appearances for media possessing electromagnetically induced transparency and electromagnetically induced absorption, and for different relative polarizations of the drive and probe fields. We show that these differences allow the contributions of different processes responsible for the enhanced Kerr nonlinearity of the media to be distinguished.
We demonstrate electromagnetically induced transparency (EIT) in a four-level cascade system where the upper level is a Rydberg state. The observed spectral features are sub-Doppler and can be enhanced due to the compensation of Doppler shifts with AC Stark shifts. A theoretical description of the system is developed which agrees well with the experimental results and an expression for the optimum parameters is derived.
Cavity linewidth narrowing via double-dark resonances has been experimentally observed using the 87Rb Zeeman splitting sublevels. With the steep dispersion led by the interacting dark resonances in the tripodtype electromagnetically induced transparency system, we narrow the cavity linewidth to 250 KHz at room temperature. Furthermore, the position of this ultranarrow cavity linewidth could be tuned in a 60 MHz coupling field detuning range.
Previously, we had proposed an optically-pumped five-level Gain EIT (GEIT) system, which has a transparency dip superimposed on a gain profile and exhibits a negative dispersion suitable for the white-light-cavity signal-recycling (WLC-SR) scheme of the interferometeric gravitational wave detector [Phys. Rev. D. 92, 082002 (2015)]. Using this system as the negative dispersion medium (NDM) in the WLC-SR, we get an enhancement in the quantum noise (QN) limited sensitivity-bandwidth product by a factor of ~18. Here, we show how to realize this GEIT system in a realistic platform, using non-degene…
Rotational levels of molecular free radicals can be tuned to degeneracy using laboratory-scale magnetic fields. Because of their intrinsically narrow width, these level crossings of opposite-parity states have been proposed for use in the study of parity-violating interactions and other applications. We experimentally study a typical manifestation of this system using $^{138}$BaF. Using a Stark-mixing method for detection, we demonstrate level-crossing signals with spectral width as small as 6 kHz. We use our data to verify the predicted lineshapes, transition dipole moments, and Stark shifts,…
We report on the observation of the motional Stark effect of highly excited $^{87}$Rb Rydberg atoms moving in the presence of a weak homogeneous magnetic field in a vapor cell. Employing electromagnetically induced transparency for spectroscopy of an atomic vapor, we observe the velocity-, quantum state- and magnetic field-dependent transition frequencies between the ground and Rydberg excited states. For atoms moving at velocities around $400\,\mathrm{m/s}$, the principal quantum number $n=100$ of the valence electron, and a magnetic field of $B=100\,\mathrm{G}$, we measure a motional Stark s…
Synthetic Gauge Phase in Rydberg Electromagnetically Induced Transparency
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学中国科学院量子信息与量子物理卓越创新中心）
We discuss a Λ-like model of atomic levels involving two autoionizing (AI) states of the same energy. The system is irradiated by two external electromagnetic fields (strong -- driving and weak -- probing ones). For such a system containing degenerate AI levels we derive the analytical formula describing the medium susceptibility. We show that the presence of the second AI level lead to the additional electromagnetically induced transparency (EIT) window appearance. We show that the characteristic of this window can be manipulated by changes of the parameters describing the interactions of AI …
We experimentally investigate the transient dynamics of an optical cavity field interacting with large ion Coulomb crystals in a situation of electromagnetically induced transparency (EIT). EIT is achieved by injecting a probe field at the single photon level and a more intense control field with opposite circular polarization into the same mode of an optical cavity to couple Zeeman substates of a metastable level in 40Ca+ ions. The EIT interaction dynamics are investigated both in the frequency-domain - by measuring the probe field steady state reflectivity spectrum - and in the time-domain -…
We report on the measurement of Stark shifted energy levels of $^{87}$Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500V/cm, ranging beyond the classical ionisation threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers $n=35$ and $n=70$ have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in [M. L. Zimmerman et al., Phys. Rev. A 20, 2251 (1979)], which…
Floquet Interpretation of Avoided Crossings in AC Stark-Shifted Rydberg-EIT Spectra
National Institute of Standards and Technology（美国国家标准与技术研究院）；Department of Electrical, Computer, and Engineering, University of Colorado, Boulder（科罗拉多大学博尔德分校电气、计算机与工程学院）
We demonstrate that the differential ac-Stark shift of a ground-state hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the |2S1/2,F=2,mF=-2> to the |2S1/2,F=1,mF=-1> state of 7Li to observe 0.59+-0.02 Hz linewidth with interrogation time of 2 s and 0.82+-0.06 s coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision…
We report on experimental and theoretical study of the nonlinear Faraday effect under conditions of electromagnetically induced transparency at the 5$S_{1/2} \to 5P_{3/2} \to 5D_{5/2}$ two-photon transition in rubidium vapors. These transitions realize the inverted Y model which combines the $Λ$ and ladder systems. Strong nonlinearity allowing for large rotation angles of a probe beam tuned to the $S\to P$ transition was obtained by creation of quantum superpositions of magnetic sublevels (Zeeman coherences) in the rubidium ground state ($Λ$ scheme). Additionally, electromagnetically induced t…
We have studied the phenomenon of electromagnetically induced transparency (EIT) of 87Rb vapor with a buffer gas in a magnetic field at room temperature. It is found that the spectral lines caused by the velocity selective optical pump effects get much weaker and wider when the sample cell mixed with a 5-Torr N2 gas while the EIT signal kept almost unchanged. A weighted least-square fit is also developed to remove the Doppler broadening completely. This spectral method provides a way to measure the Zeeman splitting with high resolution, for example, the Λ-type EIT resonance splits into four pe…
We report on a method for measuring ac Stark shifts observed in stored light experiments while simultaneously determining the energetic splitting between the electronic ground states involved in the two-photon transition. To this end we make use of the frequency matching effect in light storage spectroscopy. We find a linear dependence on the intensity of the control field applied during the retrieval phase of the experiment. At the same time, we observe that the light shift is insensitive to the intensity of the signal field which is in contrast to continuously operated schemes using electrom…
We report the first observation of electromagnetically induced transparency (EIT) in an isotopically purified Nd$^{3+}$:YLiF$_4$ crystal. This crystal demonstrates inhomogeneous broadening of optical transitions of about 35 MHz. EIT is observed in a symmetrical $Λ$-like system formed by two hyperfine sublevels of the ground state corresponding to a zero first order Zeeman (ZEFOZ) transition and a hyperfine sublevel of the excited state, which is not coupled to other ground-state sublevels. It is found that transmission of the probe field as a function of the two-photon detuning demonstrates a …
Electrometry is performed using Rydberg states to evaluate the quadratic Stark shift of the $5s^2$ $^1\textrm{S}_0-5s5p$ $^3\textrm{P}_0$ clock transition in strontium. By measuring the Stark shift of the highly excited $5s75d\;^1\textrm{D}_2$ state using electromagnetically induced transparency, we characterize the electric field with sufficient precision to provide tight constraints on the systematic shift to the clock transition. Using the theoretically derived, and experimentally verified, polarizability for this Rydberg state we can measure the residual field with an uncertainty well belo…
We present experimental results on the influence of magnetic fields and laser polarization on electromagnetically induced transparency (EIT) using Rydberg levels of $^{87}$Rb atoms. The measurements are performed in a room temperature vapor cell with two counter-propagating laser beams at 480nm and 780nm in a ladder-type energy level scheme. We measure the EIT spectrum of a range of $ns_{1/2}$ Rydberg states for $n=19-27$, where the hyperfine structure can still be resolved. Our measurements span the range of magnetic fields from the low field linear Zeeman regime to the high field Paschen-Bac…
We report on measurements of the differential polarizability between the nearly degenerate, opposite parity states in atomic dysprosium at 19797.96 cm$^{-1}$. The differential scalar and tensor polarizabilities due to additional states were measured for the $|M| = 7,...,10$ sublevels in $^{164}$Dy and $^{162}$Dy and determined to be $\bar{\boldsymbolα}_{\scriptscriptstyle BA}^{(0)} = 180\,(45)_\text{stat}\,(8)_\text{sys}$ $\text{mHz}/(\mathrm{V}/\mathrm{cm})^2$ and $\bar{\boldsymbolα}_{\scriptscriptstyle BA}^{(2)} = -163\,(65)_\text{stat}\,(5)_\text{sys}$ $\text{mHz}/(\mathrm{V}/\mathrm{cm})^2…
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are similar,but different quantum optical phenomena: EIT results from a Fano interference, whereas ATS is described by the AC-Stark effect. Likewise, despite their close resemblance, light-storage techniques based on the EIT memory protocol and the recently-proposed ATS memory protocol (E. Saglamyurek et al. Nature Photonics 12, 2018) are distinct: the EIT protocol relies on adiabatic elimination of absorption, whereas the ATS protocol is based on absorption. In this article, we elaborate on the distinction betwee…
People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four state system with double-V linkage pattern for…
An Accurate Vector Magnetometer via Zeeman Rabi Oscillations
JILA, National Institute of Standards and Technology and University of Colorado（美国国家标准与技术研究院与科罗拉多大学JILA联合研究所）；Department of Physics, University of Colorado（科罗拉多大学物理系）；ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究所光子科学研究所）；Paul M. Rady Department of Mechanical Engineering, University of Colorado（科罗拉多大学保罗·M·雷迪机械工程系）；FieldLine Medical（FieldLine医疗公司）
We investigate the effect of band-limited white Gaussian noise (BLWGN) on electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, when performing atom-based continuous-wave (CW) radio-frequency (RF) electric (E) field strength measurements with Rydberg atoms in an atomic vapor. This EIT/AT-based E-field measurement approach is currently being investigated by several groups around the world as a means to develop a new SI traceable RF E-field measurement technique. For this to be a useful technique, it is important to understand the influence of BLWGN. We perform EIT/AT …
Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear $\perp$ linear ($lin \perp lin$) polarization of the probe and the pump beams in $^{87}Rb$ - $D_2$ transition. The dependence of the EIT on the direction of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the $σ$ and $π$ EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the $σ$ and $π$ EIT peaks, the strength…
Angle-of-Arrival Determination of Radio-Frequency Fields Using Stark-Shifted Rydberg-EIT Spectra
National Institute of Standards and Technology（美国国家标准与技术研究院）；Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder（科罗拉多大学博尔德分校电气、计算机与能源工程系）
A method for performing a precision measurement of the Rydberg constant, $R_{\infty}$, using cold circular Rydberg atoms is proposed. These states have long lifetimes, as well as negligible quantum-electrodynamics (QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle" [Bernauer, Pohl, Sci. Am. 310, 32 (2014)]. The atoms are trapped using a Rydberg-atom optical lattice, and transitions are driven using a recently-demonstrated lattice-modulation technique to perform Doppler-free spectroscopy. The circular-state transition freq…
We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have $I=J=F=0$, where $I$, $J$, and $F$ are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation…
The precise measurement of molecular vibrational transition frequencies is useful in the search for variation in the proton-to-electron mass ratio μ. Homonuclear diatomic molecules are particularly advantageous for precise measurement because of the small Stark shift. This paper discusses the Stark and Zeeman shifts in the 16O2+ vibrational transition frequencies.To search for the variation μ(<10-17/yr), the X2Π1/2(v,J)=(0,1/2)-(v',1/2)(v'>1)in transition frequencies are much more advantageous than the transition frequencies between the X2Π1/2 v=21 and a4Π1/2 v=0 states, whose sensitivity to t…
The magnetic force is retained in the Lorentz Oscillator Model and a perturbation solution is derived beyond the dipole approximation. Perturbation series for the electric dipole, magnetic dipole, and electric quadrupole moments in addition to their macroscopic, spatially-averaged counterparts are also obtained. These expressions are shown to describe many optical phenomena: the normal, linear Zeeman, Faraday, and magneto-optic Kerr effects, the linear Stark, Pockels, and Kerr effects (when the restoring force is anharmonic), the momentum and angular momentum of a photon in matter (contributin…
The nonlinear Zeeman effect can induce splittings and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. We demonstrate a scheme to suppress the nonlinear Zeeman effect all optically based on spin locking. Spin locking is achieved with an effective oscillating magnetic field provided by the AC Stark-shift of an intensity-modulated and polarization-modulated laser beam. This results in the collapse of the multi-component asymmetric magnetic-resonance line with about 100 Hz width in the Earth-field range into a peak with a central component width of 25Hz. The techni…
The electric-field-dependent $g$ factor and the electron electric dipole moment (eEDM)-induced Stark splittings for the lowest rotational levels of $^{207,208}$PbF are calculated. Observed and calculated Zeeman shifts for $^{207}$PbF are found to be in very good agreement. It is shown that the $^{207}$PbF hyperfine sublevels provide a promising system for the eEDM search and related experiments.
Arrays of trapped ultracold molecules represent a promising platform for implementing a universal quantum computer. DeMille has detailed a prototype design based on Stark states of polar $^1Σ$ molecules as qubits. Herein, we consider an array of polar $^2Σ$ molecules which are, in addition, inherently paramagnetic and whose Hund's case (b) free-rotor states are Bell states. We show that by subjecting the array to combinations of concurrent homogeneous and inhomogeneous electric and magnetic fields, the entanglement of the array's Stark and Zeeman states can be tuned and the qubit sites address…
We investigate the probe field induced shift for atomic lattice-based and ion-trap clocks, which can be considered as a near resonant ac-Stark shift, connected to the Zeeman structure of atomic levels and their splitting in a dc magnetic field. This shift arises from possible residual ellipticity in the polarization of the probe field and uncertainty in the magnetic field orientation. Such a shift can have an arbitrary sign and, for some experimental conditions, can reach the fractional value of the order of 10$^{-18}$-10$^{-19}$, i.e., it is not negligible. Thus, it should be taken into accou…
We measure strong radio-frequency (RF) electric fields using rubidium Rydberg atoms prepared in a room-temperature vapor cell as field sensors. Electromagnetically induced transparency is employed as an optical readout. We RF-modulate the 60$S_{1/2}$ and 58$D_{5/2}$ Rydberg states with 50~MHz and 100~MHz fields, respectively. For weak to moderate RF fields, the Rydberg levels become Stark-shifted, and sidebands appear at even multiples of the driving frequency. In high fields, the adjacent hydrogenic manifold begins to intersect the shifted levels, providing rich spectroscopic structure suitab…
We have extended Ramsey spectroscopy by stepping the probe frequency during the two Ramsey excitation pulses to compensate frequency shifts induced by the excitation itself. This makes precision Ramsey spectroscopy applicable even for transitions that have Stark and Zeeman shifts comparable to the spectroscopic resolution. The method enables a new way to evaluate and compensate key frequency shifts, which benefits in particular, optical clocks based on magnetic field-induced, spectroscopy, two-photon transitions, or heavily forbidden transitions.
A spectroscopic study of Rydberg states of helium ($n$ = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ($n$ = 30, $B \leq$ 120 mT and $F$ = 0 - 78 V/cm ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ($n$ = 45, $B$ = 277 mT and $F$ = 0 - 8 V/cm). Both cases correspond to regimes where the interactions induced by the electric and …
We demonstrate the use of multiple atomic-level Rydberg-atom schemes for continuous frequency detection of radio frequency (RF) fields. Resonant detection of RF fields by electromagnetically-induced transparency and Autler-Townes (AT) in Rydberg atoms is typically limited to frequencies within the narrow bandwidth of a Rydberg transition. By applying a second field resonant with an adjacent Rydberg transition, far-detuned fields can be detected through a two-photon resonance AT splitting. This two-photon AT splitting method is several orders of magnitude more sensitive than off-resonant detect…
In this paper, two-photon absorption resonance has been investigated . We studied this phenomenon in three-level system with common upper level, two lower long-life levels and two quasi-resonant laser fields with different frequency spectrum. It has been shown that, the absorption coefficient in the far distance from absorption line at the frequency of two-photon resonance has considerable amplitude and narrow width. Frequency difference between two lower levels is transition frequency for optical clocks. This resonance is much less sensitive to the effects of noise components and probing fiel…
We present direct measurements of the hyperfine splitting of Rydberg states in rubidium 87 using Electromagnetically Induced Transparency (EIT) spectroscopy in a room-temperature vapour cell. With this method, and in spite of Doppler-broadening, line-widths of 3.7 MHz FWHM, i.e. significantly below the intermediate state natural linewidth are reached. This allows resolving hyperfine splittings for Rydberg s-states with n=20...24. With this method we are able to determine Rydberg state hyperfine splittings with an accuracy of approximately 100 kHz. Ultimately our method allows accuracies of ord…
