The ac Stark effect was used to induce resonant energy transfer between translationally cold Rydberg atoms. The Rb Rydberg atoms were obtained by laser excitation of cold atoms from a magneto-optical trap. Using two-photon microwave spectroscopy of the 49s_{1/2}-50s_{1/2} transition, the field strength of a 28.5 GHz dressing field was calibrated. When this dressing field was set at specific field strengths, the two-atom dipole-dipole process 43d_{5/2} + 43d_{5/2} -> 45p_{3/2} + 41f was dramatically enhanced, due to induced degeneracy of the initial and final states. A series of observed resonant field strengths correspond to different magnetic sublevel possibilities for the initial and final states. These agree well with calculated resonance fields based on a perturbative ac Stark shift formula. This method for enhancing interactions is complementary to dc electric-field-induced resonant energy transfer, but has more flexibility due to the possibility of varying the applied frequency.
Precision measurements of transitions between singlet ($S=0$) Rydberg states of H$_2$ belonging to series converging on the $\mathrm{X}^+\,^2Σ_g^+(v^+=0,N^+=0)$ state of H$_2^+$ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number $\ell$ and leads to quadratic Stark shifts of low-$\ell$ states and to linear Stark shifts of the nearly degenerate manifold of high-$\ell$ states. Transitions to the Stark manifold were ob…
We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to princip…
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…
Experimental and theoretical studies of the effects of weak radio-frequency electric fields on Rydberg-Stark states with electric dipole moments as large as 10000 D are reported. High-resolution laser spectroscopic studies of Rydberg states with principal quantum number $n=52$ and $53$ were performed in pulsed supersonic beams of metastable helium with the excited atoms detected by pulsed electric field ionisation. Experiments were carried out in the presence of sinusoidally oscillating electric fields with frequencies of 20~MHz, amplitudes of up to 120~mV/cm, and dc offsets of up to 4.4~V/cm.…
Precision spectroscopy of the fine and hyperfine structures of high molecular Rydberg-Stark states: Metrology of molecular hydrogen ions
ETH Zürich（苏黎世联邦理工学院）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Université Paris-Saclay（巴黎萨克雷大学）；Centre National de la Recherche Scientifique（法国国家科学研究中心）
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…
Dipole-dipole interactions between helium atoms in Rydberg-Stark states with principal quantum number $n=53$ and approximately linear Stark energy shifts, resulting from induced electric dipole moments of approximately 7900 D, have been investigated experimentally. The experiments were performed in pulsed supersonic metastable helium beams, with particle number densities of up to $\sim10^9$ cm$^{-3}$. In the presence of amplitude-modulated, radio-frequency electric fields, changes in the spectral intensity distributions associated with the transitions to these states that are attributed to dip…
The spatial evolution of the Rydberg blockade is studied taking into account Stark-split energy levels across several manifolds. We find that the unexpected restoration of a blockaded Rydberg excitation at small interatomic distances, e.g., experimentally observed by P.Schauss, et al. [Nature 491, 87 (2012)], can be explained by the perturbed energy levels from neighboring manifolds that enter the energy window of excitation defined by the bandwidth of the exciting laser. The same mechanism can also explain why the pair correlation function of Rydberg atoms remains nonzero in the entire region…
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）
We demonstrate the single-photon Rydberg excitation of cesium atoms in a magneto-optical trap (MOT). We excite atoms directly from ${{6S}_{1/2}}$ ground state to ${{nP}_{3/2}}(n=70-100)$ Rydberg state with a narrow-linewidth 319 nm ultra-violet laser. The detection of Rydberg states is performed by monitoring the reduction of fluorescence signal of the MOT as partial population on ${{6S}_{1/2}} (F = 4)$ ground state are transferred to Rydberg state. We clearly observe Autler-Townes doublet in the trap-loss spectra due to the cooling lights. Utilizing the large electric polarizibility of Rydber…
The large electric dipole moments associated with highly excited Rydberg states of atoms and molecules make gas-phase samples in these states very well suited to deceleration and trapping using inhomogeneous electric fields. The methods of Rydberg-Stark deceleration with which this can be achieved are reviewed here. Using these techniques, the longitudinal motion of beams of atoms and molecules moving at speeds as high as 2500~m/s have been manipulated, with changes in kinetic energy of up to $|ΔE_{\mathrm{kin}}|=1.3\times10^{-20}$~J ($|ΔE_{\mathrm{kin}}|/e=80$~meV or $|ΔE_{\mathrm{kin}}|/hc=6…
We report on Rydberg spectroscopy of ultracold atoms in an atom-ion hybrid trap for probing the electric fields in a mixture of atoms and ions. We obtain spectra which exhibit excitation gaps corresponding to avoided level crossings in the Stark map. From these measurements we can conclude that the ground state atoms experience electrical fields of up to 250 V/cm. There is, however, a difficulty in interpreting the results, because some data indicate that the electrical fields are produced by the ions while other data indicate that they stem from the Paul trap. We discuss possible scenarios fo…
Trapping a Rydberg atom close to a surface is an important step towards the realisation of many proposals of quantum information or hybrid quantum systems. One of the challenges in these experiments is to overcome the electric field emanating from contaminations on the surface. Here we report on measurements of an electric field created by $^{87}$Rb atoms absorbed on a 25$\,$nm thick layer of SiO$_2$, covering a 90$\,$nm layer of Au. The electric field is measured using a two-photon transition to the 23$D_{5/2}$ and 25$S_{1/2}$ state. The electric field value that we measure is higher than typ…
Three-dimensional three-photon Stark spectroscopy of a single Rb Rydberg atom in an ultrahigh-vacuum glass cell with eight electrodes
Rzhanov Institute of Semiconductor Physics SB RAS（列扎诺夫半导体物理研究所西伯利亚分院）；Novosibirsk State University（新西伯利亚国立大学）；Institute of Laser Physics SB RAS（激光物理研究所西伯利亚分院）
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 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…
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）
On-resonance Rydberg atom-based radio-frequency (RF) electric field sensing methods remain limited by the narrow frequency signal detection bands available by resonant transitions. The use of an additional RF tuner field to dress or shift a target Rydberg state can be used to return a detuned signal field to resonance and thus dramatically extend the frequency range available for resonant sensing. Here we investigate three distinct tuning level schemes based on adjacent Rydberg transitions, which are shown to have distinct characteristics and can be controlled with mechanisms based on the tuni…
Nitric oxide (NO) molecules initially traveling at 795 m/s in pulsed supersonic beams have been photoexcited to long-lived hydrogenic Rydberg-Stark states, decelerated and electrostatically trapped in a cryogenically cooled, chip-based transmission-line Rydberg-Stark decelerator. The decelerated and trapped molecules were detected $in$ $situ$ by pulsed electric field ionization. The operation of the decelerator was validated by comparison of the experimental data with the results of numerical calculations of particle trajectories. Studies of the decay of the trapped molecules on timescales up …
Splitting the energy levels of a hydrogen-like atom by the electric field nonuniform at the atomic scale is studied. This situation is important for the multi-level treatment of the phenomenon of Rydberg blockade [Yu.V. Dumin, J. Phys. B, v.47, p.175502 (2014)]. An explicit formula for the energy levels is derived. A typical value of the energy shift by the electric field gradient turns out to be proportional to the 4th power of the principal quantum number (i.e., the square of atomic size), as would be expected from a qualitative consideration. Finally, the fine spatial structure of the Rydbe…
Electric-field induced dipole blockade with Rydberg atoms
高分辨激光斯塔克激发超冷铯原子的np（60 < n < 85）里德堡态，有效地阻断了长程偶极-偶极相互作用的激发.偶极阻断效应被观察为里德伯激发的淬灭，取决于由外部电场诱导的偶极矩的值。最终的离子，可以匹配偶极封锁效应的影响进行了详细讨论，但排除了我们的实验条件。相互作用的里德伯原子的激发的解析和蒙特卡罗模拟与实验一致，表明最近邻的里德伯原子的主要作用。
We report on the appearance of a structure at low energies in the photo-electron momentum distribution of the hydrogen atom exposed to two-color counter-rotating bi-circular laser fields. These structures, which arise due to AC-Stark shifted resonances, break the three-fold symmetry, typical for the $ω-2ω$ bi-circular fields. We discuss the physical origin of this structure in terms of partial-wave interference between direct ionization channels and a resonant pathway, that passes through the AC-Stark shifted state and show how the underlying Rydberg state population depend on the field streng…
The electron signals from the field ionization of two closely-spaced Rydberg states of \mbox{rubidium-85} are separated using quantum control. In selective field ionization, the state distribution of a collection of Rydberg atoms is measured by ionizing the atoms with a ramped electric field. Generally, atoms in higher energy states ionize at lower fields, so ionized electrons which are detected earlier in time can be correlated with higher energy Rydberg states. However, the resolution of this technique is limited by the Stark effect. As the electric field is increased, the electron encounter…
Rydberg states of atomic helium with principal quantum numbers ranging from n=20 to n=100 have been prepared by non-resonance-enhanced single-color two-photon excitation from the metastable 2 {^3}S{_1} state. Photoexcitation was carried out using linearly and circularly polarized pulsed laser radiation. In the case of excitation with circularly polarized radiation, Rydberg states with azimuthal quantum number |m_{\ell}|=2 were prepared in zero electric field, and in homogeneous electric fields oriented parallel to the propagation axis of the laser radiation. In sufficiently strong electric fie…
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 …
Metastable (1s)(2s) $^3{\rm S}_1$ helium atoms produced in a supersonic beam were excited to Rydberg-Stark states (with $n$ in the $27-30$ range) in a cryogenic environment and subsequently decelerated by, and trapped above, a surface-electrode decelerator. In the trapping experiments, the Rydberg atoms were brought to rest in 75~$μ$s and over a distance of 33~mm and kept stationary for times $t_{\mathrm{trap}}$ in the $0-525$~$μ$s range, before being re-accelerated for detection by pulsed field ionization. The use of a home-built valve producing short gas pulses with a duration of about 20~$μ…
We demonstrate the use of multiple atomic-level Rydberg-atom schemes for continuous frequency detection of radio frequency (RF) fields. Resonant detection of RF fields by electromagnetically-induced transparency and Autler-Townes (AT) in Rydberg atoms is typically limited to frequencies within the narrow bandwidth of a Rydberg transition. By applying a second field resonant with an adjacent Rydberg transition, far-detuned fields can be detected through a two-photon resonance AT splitting. This two-photon AT splitting method is several orders of magnitude more sensitive than off-resonant detect…
High-fidelity entangled Bell states are of great interest in quantum physics. Entanglement of ultracold neutral atoms in two spatially separated optical dipole traps is promising for implementation of quantum computing and quantum simulation and for investigation of Bell states of material objects. We propose a new method to entangle two atoms via long-range Rydberg-Rydberg interaction. Alternatively to previous approaches, based on Rydberg blockade, we consider radiofrequency-assisted Stark-tuned Förster resonances in Rb Rydberg atoms. To reduce the sensitivity of the fidelity of Bell states …
We measure strong radio-frequency (RF) electric fields using rubidium Rydberg atoms prepared in a room-temperature vapor cell as field sensors. Electromagnetically induced transparency is employed as an optical readout. We RF-modulate the 60$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 demonstrate improved sensitivity of Rydberg electrometry based on electromagnetically induced transparency (EIT) with a ground state repumping laser. Though there are many factors that limit the sensitivity of radio frequency field measurements, we show that repumping can enhance the interaction strength while avoiding additional Doppler or power broadening. Through this method, we nearly double the EIT amplitude without an increase in the width of the peak. A similar increase in amplitude without the repumping field is not possible through simple optimization.We also establish that one of …
