We propose a combination of Electromagnetically Induced Transparency (EIT)/Raman and pulsed spectroscopy techniques to accurately cancel frequency shifts arising from EIT fields in forbidden optical lattice clock transitions of alkaline earth atoms. Time-separated laser pulses are designed to trap atoms in coherent superpositions while eliminating off-resonance ac Stark contributions at particular laser detunings from the intermediate excited state. The scheme achieves efficient population transfer up to 60% with potential inaccuracy $<$ $10^{-17}$. Cancellation of external light shifts determined by a density matrix approach is confirmed by a complex wave-function formalism, sufficient at the mHz accuracy, under low field strengths or short interaction times.
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.…
We make use of an inhomogeneous electrostatic dipole field to impart a quantum-state-dependent deflection to a pulsed beam of OCS molecules, and show that those molecules residing in the absolute ground state, $X ^1Σ^+$, $\ket{00^00}$, J=0, can be separated out by selecting the most deflected part of the molecular beam. Past the deflector, we irradiate the molecular beam by a linearly polarized pulsed nonresonant laser beam that impulsively aligns the OCS molecules. Their alignment, monitored via velocity-map imaging, is measured as a function of time, and the time dependence of the alignment …
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 feedback control optimization for the Stark deceleration and trapping of neutral polar molecules using evolutionary strategies. In a Stark-decelerator beamline pulsed electric fields are used to decelerate OH radicals and subsequently store them in an electrostatic trap. The efficiency of the deceleration and trapping process is determined by the exact timings of the applied electric field pulses. Automated optimization of these timings yields an increase of 40 % of the number of trapped OH radicals.
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 …
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 have developed a quite stringent method in selectivity to ionize the low angular- momentum ($\ell$) states which lie below and above the adjacent manifold in highly excited Rb Rydberg atoms. The method fully exploits the pulsed field-ionization characteristics of the manifold states in high slew-rate regime: Specifically the low $\ell$ state below (above) the adjacent manifold is firstly transferred to the lowest (highest) state in the manifold via the adiabatic transition at the first avoided crossing in low slew-rate regime, and then the atoms are driven to a high electric field for ioniz…
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…
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…
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）
Single-photon sources are at the heart of quantum-optical networks, with their uniquely quantum emission and phenomenon of two-photon interference allowing for the generation and transfer of nonclassical states. Although a few analytical methods have been briefly investigated for describing pulsed single-photon sources, these methods apply only to either perfectly ideal or at least extremely idealized sources. Here, we present the first complete picture of pulsed single-photon sources by elaborating how to numerically and fully characterize non-ideal single-photon sources operating in a pulsed…
The burgeoning fields of quantum computing and quantum key distribution have created a demand for a quantum memory. The gradient echo memory scheme is a quantum memory candidate for light storage that can boast efficiencies approaching unity, as well as the flexibility to work with either two or three level atoms. The key to this scheme is the frequency gradient that is placed across the memory. Currently the three level implementation uses a Zeeman gradient and warm atoms. In this paper we model a new gradient creation mechanism - the ac Stark effect - to provide an improvement in the flexibi…
The Jaynes--Cummings system is one of the most fundamental models of how light and matter interact. When driving the system with a coherent state (e.g. laser light), it is often assumed that whether the light couples through the cavity or atom plays an important role in determining the dynamics of the system and its emitted field. Here, we prove that the dynamics are identical in either case except for the offset of a trivial coherent state. In particular, our formalism allows for both steady-state and the treatment of any arbitrary multimode coherent state driving the system. Finally, the off…
Based on numerical solutions of the time-dependent Schrödinger equation for either one or two active electrons, we propose a method for observing instantaneous level shifts in an oscillating strong infrared (IR) field in time, using a single tunable attosecond pulse to probe excited states of the perturbed atom. The ionization probability in the combined fields depends on both, the frequency of the attosecond pulse and the time delay between both pulses, since the IR field shifts excited energy levels into and out of resonance with the attosecond probe pulse. We show that this method (i) allow…
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…
The ac Stark shift (or light shift) of the 6$^{2}$S$_{1/2}$ (F $=$ 3 $\leftrightarrow $ 4) transition in $^{133}$Cs, as observed through coherent population trapping under pulsed excitation, is measured using a $^{133}$Cs gas cell and the $D_1$-line vertical-cavity surface-emitting laser. This light shift can be calculated using density-matrix analysis. We derive an expression for this shift as a function of light intensity, showing that it varies linearly with respect to light intensity only with intensities higher than 1.0~mW/cm$^2$. For pulsed excitation of high laser intensity, the variati…
We propose a compact atomic clock based on ultracold Rb atoms that are magnetically trapped near the surface of an atom microchip. An interrogation scheme that combines electromagnetically-induced transparency (EIT) with Ramsey's method of separated oscillatory fields can achieve atomic shot-noise level performance of 10^{-13}/sqrt(tau) for 10^6 atoms. The EIT signal can be detected with a heterodyne technique that provides noiseless gain; with this technique the optical phase shift of a 100 pW probe beam can be detected at the photon shot-noise level. Numerical calculations of the density mat…
We develop a generalized principle of EIT vector magnetometry based on high-contrast EIT-resonances and the symmetry of atom-light interaction in the linearly polarized bichromatic fields. Operation of such vector magnetometer on the D1 line of 87Rb has been demonstrated. The proposed compass-magnetometer has an increased immunity to shifts produced by quadratic Zeeman and ac-Stark effects, as well as by atom-buffer gas and atom-atom collisions. In our proof-of-principle experiment the detected sensitivity to magnetic field orientation is 10^{-3} deg/Hz^{1/2}, which is limited by laser intensi…
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 …
Inhomogeneous electric fields generated above two-dimensional electrode structures have been used to transversely split beams of helium Rydberg atoms into pairs of spatially separated components. The atomic beams had initial longitudinal speeds of between 1700 and 2000 m/s and were prepared in Rydberg states with principle quantum number $n=52$ and electric dipole moments of up to 8700 D by resonance-enhanced two-color two-photon laser excitation from the metastable 1s2s $^3$S$_1$ level. Upon exiting the beam splitter the ensembles of Rydberg atoms were separated by up to 15.6 mm and were dete…
The response of a SERF atomic magnetometer to a repetitive short-pulsed pump was investigated. Quantum sub-resonances at a repetition rate of $1/n$ of the Larmor frequency of the magnetic field inside the shield are experimentally observed and theoretically explained. This is a type of synchronization phenomenon. Investigations in single alkali atoms cells as well as mixed alkali atoms of K and Rb are presented. In the later, one species is pumped while the probe is on the other specie polarized by spin exchange. The effect of spin destruction, spin exchange and collisions are studied in order…
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…
We characterized the pulsed Rydberg-positronium production inside the AEgIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) apparatus in view of antihydrogen formation by means of a charge exchange reaction between cold antiprotons and slow Rydberg-positronium atoms. Velocity measurements on positronium along two axes in a cryogenic environment (10K) and in 1T magnetic field were performed. The velocimetry was done by MCP-imaging of photoionized positronium previously excited to the $n=3$ state. One direction of velocity was measured via Doppler-scan of this $n=3$-line, another …
The ability to characterize static and time-dependent electric fields in situ is an important prerequisite for quantum-optics experiments with atoms close to surfaces. Especially in experiments which aim at coupling Rydberg atoms to the near field of superconducting circuits, the identification and subsequent elimination of sources of stray fields is crucial. We present a technique that allows the determination of stray-electric-field distributions $(F^\text{str}_\text{x}(\vec{r}),F^\text{str}_\text{y}(\vec{r}),F^\text{str}_\text{z}(\vec{r}))$ at distances of less than $2~\text{mm}$ from (cryo…
Helium atoms have been prepared in the circular $|n=55,\ell=54,m_{\ell}=+54\rangle$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially travelling in pulsed supersonic beams, were photoexcited from the metastable $1s2s\,^3S_1$ level to the outermost, $m_{\ell}=0$ Rydberg-Stark state with $n=55$ in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with $m_{\ell}=+54$ defined with respect to the magnetic fie…
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.
Sideband cooling is a popular method for cooling atoms to the ground state of an optical trap. Applying the same method to molecules requires a number of challenges to be overcome. Strong tensor Stark shifts in molecules cause the optical trapping potential, and corresponding trap frequency, to depend strongly on rotational, hyperfine and Zeeman state. Consequently, transition frequencies depend on the motional quantum number and there are additional heating mechanisms, either of which can be fatal for an effective sideband cooling scheme. We develop the theory of sideband cooling in state-dep…
We present ionization probability and line shape calculations for the two-step 3-photon ionization process, $1S \stackrel{2\hbar ω}{\longrightarrow}2S \stackrel{\hbar ω}{\longrightarrow}εP $, of the ground state of hydrogenic atoms in a non-monochromatic laser field with a time--dependent amplitude. Within the framework of a three--level model, the {\it AC Stark} shifts and non-zero ionization rates of all states involved were taken into account together with spatial and temporal inhomogeneities of the laser signal. In contrast with the usual perturbative technique, the time evolution of the a…
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced transparency (EIT). For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective uniform force in momentum space. The quantum lattice dynamics, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be…
Metal atoms in solid and liquid helium-4 have attracted some interest either as a way to keep the atoms in a weakly perturbing matrix, or using them as a probe for the helium host medium. Laser sputtering with nanosecond pulsed lasers is the most often used method for atom production, resulting however in a substantial perturbation of the matrix. We show that a much weaker perturbation can be obtained by using femtosecond laser pulses with energy as low as 10 $μ$J. As an unexpected benefit, the atomic density produced is much higher.
