Rydberg States Of Atoms Research Articles

Symmetry and coherent control of the quantum dynamics of Rydberg atoms

Transitions probabilities for highly excited Rydberg states of atoms in electromagnetic traps under the influence of an external electromagnetic fields are calculated. We used the method of groups of dynamical symmetry for hydrogenlike atoms and the technique of relevant coherent states. This allows us to calculate the transition probabilities between atomic levels outside the framework of perturbation theory. The problem of coherent controlling the quantum dynamics of atoms in cavities and some possible applications for quantum information theory are briefly discussed.

Excitation of strongly interacting moving Rydberg atoms by photon recoil momentum

Based on the fact that an ensemble of moving Rydberg atoms in two counterpropagating laser beams in the limit of complete dipole blocking is isomorphic to a Jaynes–Cummings model, a scheme for robust and efficient excitation of atomic Rydberg states is proposed. It is shown that the Doppler frequency shifts play an important role in atomic population transfer processes. The suggested method can be employed to detect the symmetric entangled states and paves the way to preparing entangled states with a single excited atom in a Rydberg state. It is shown that this process is robust with respect to parameter fluctuations, such as the laser pulse area, the relative spatial offset (the delay) of the laser beams and the number of atoms.

Polarizabilities of Rydberg states of Rb atoms with n up to 140

Polarizabilities of Rydberg states of Rb atoms with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> up to 140

A photon–photon quantum gate based on Rydberg interactions

The interaction between Rydberg states of neutral atoms is strong and long-range, making it appealing to put it to use in the context of quantum technologies. Recently, first applications of this idea have been reported in the fields of quantum computation and quantum simulation. Furthermore, electromagnetically induced transparency allows to map these Rydberg interactions to light. Here we exploit this mapping and the resulting interaction between photons to realize a photon-photon quantum gate, demonstrating the potential of Rydberg systems as a platform also for quantum communication and quantum networking. We measure a controlled-NOT truth table with a fidelity of 70(8)% and an entangling-gate fidelity of 63.7(4.5)%, both post-selected upon detection of a control and a target photon. The level of control reached here is an encouraging step towards exploring novel many-body states of photons or for future applications in quantum communication and quantum networking.

Effective spin-spin interactions in bilayers of Rydberg atoms and polar molecules

We show that indirect spin-spin interactions between effective spin-1/2 systems can be realized in two parallel 1D optical lattices loaded with polar molecules and/or Rydberg atoms. The effective spin can be encoded into low-energy rotational states of polar molecules or long-lived states of Rydberg atoms, tightly trapped in a deep optical lattice. The spin-spin interactions can be mediated by Rydberg atoms, placed in a parallel shallow optical lattice, interacting with the effective spins by charge-dipole (for polar molecules) or dipole-dipole (for Rydberg atoms) interaction. Indirect XX, Ising and XXZ interactions with interaction coefficients $J^{\bot}$ and $J^{zz}$ sign varying with interspin distance can be realized, in particular, the $J_{1}-J_{2}$ XXZ model with frustrated ferro-(antiferro-)magnetic nearest (next-nearest) neighbor interactions.

A vapor-cell atomic sensor for radio-frequency field detection using a polarization-selective field enhancement resonator

We present a hybrid atomic sensor that realizes radio-frequency electric field detection with intrinsic field enhancement and polarization selectivity for robust high-sensitivity field measurement. The sensor incorporates a passive resonator element integrated with an atomic vapor cell that provides enhancement and polarization selectivity of incident radio-frequency fields. The enhanced intra-cavity radio-frequency field is measured by atoms using a quantum-optical readout of AC level shifts of field-sensitive atomic Rydberg states. In our demonstration, we employ a split field-enhancement resonator embedded in a rubidium vapor cell to enhance and detect C-band radio-frequency fields. We observe a field enhancement equivalent to a 24 dB gain in intensity sensitivity. The spatial profile of the resonant field mode inside the field-enhancement cavity is characterized and robust polarization measurement of the incident field is demonstrated. The measured performance metrics of the sensor are in good agreement with simulations. Applications of such atomic sensors in ultra-weak radio-frequency detection and advanced measurement capabilities are discussed.

Nonlinear quantum optics for spinor slow light

We investigate quantum nonlinear effects at a level of individual quanta in a double tripod atom-light coupling scheme involving two atomic Rydberg states. In such a scheme the slow light coherently coupled to strongly interacting Rydberg states represents a two-component or spinor light. The scheme provides additional possibilities for the control and manipulation of light quanta. A distinctive feature of the proposed setup is that it combines the spin-orbit coupling for the spinor slow light with an interaction between the photons, enabling generation of the second probe beam even when two-photon detuning is zero. Furthermore, the interaction between the photons can become repulsive if the one-photon detunings have opposite signs. This is different from a single ladder atom-light coupling scheme, in which the interaction between the photons is attractive for both positive and negative detunings, as long as the Rabi frequency of the control beam is not too large.

Highly sensitive atomic based MW interferometry

We theoretically study a scheme to develop an atomic based micro-wave (MW) interferometry using the Rydberg states in Rb. Unlike the traditional MW interferometry, this scheme is not based upon the electrical circuits, hence the sensitivity of the phase and the amplitude/strength of the MW field is not limited by the Nyquist thermal noise. Further, this system has great advantage due to its much higher frequency range in comparision to the electrical circuit, ranging from radio frequency (RF), MW to terahertz regime. In addition, this is two orders of magnitude more sensitive to field strength as compared to the prior demonstrations on the MW electrometry using the Rydberg atomic states. Further, previously studied atomic systems are only sensitive to the field strength but not to the phase and hence this scheme provides a great opportunity to characterize the MW completely including the propagation direction and the wavefront. The atomic based MW interferometry is based upon a six-level loopy ladder system involving the Rydberg states in which two sub-systems interfere constructively or destructively depending upon the phase between the MW electric fields closing the loop. This work opens up a new field i.e. atomic based MW interferometry replacing the conventional electrical circuit in much superior fashion.

Radio-over-fiber using an optical antenna based on Rydberg states of atoms

We provide an experimental demonstration of a direct fiber-optic link for RF transmission (“radio-over-fiber”) using a sensitive optical antenna based on a rubidium vapor cell. The scheme relies on measuring the transmission of laser light at an electromagnetically induced transparency resonance that involves highly excited Rydberg states. By dressing pairs of Rydberg states using microwave fields that act as local oscillators, we encoded RF signals in the optical frequency domain. The light carrying the information is linked via a virtually lossless optical fiber to a photodetector where the signal is retrieved. We demonstrate a signal bandwidth in excess of 1 MHz limited by the available coupling laser power and atomic optical density. Our sensitive, non-metallic and readily scalable optical antenna for microwaves allows extremely low-levels of optical power (∼1 μW) throughput in the fiber-optic link. It offers a promising future platform for emerging wireless network infrastructures.

Van-der-Waals interaction of atoms in dipolar Rydberg states

An asymptotic expression for the van-der-Waals constant C6(n) ≈ –0.03n12K p (x) is derived for the long-range interaction between two highly excited hydrogen atoms A and B in their extreme Stark states of equal principal quantum numbers n A = n B = n ≫ 1 and parabolic quantum numbers n1(2) = n - 1, n2(1) = m = 0 in the case of collinear orientation of the Stark-state dipolar electric moments and the interatomic axis. The cubic polynomial K3(x) in powers of reciprocal values of the principal quantum number x = 1/n and quadratic polynomial K2(y) in powers of reciprocal values of the principal quantum number squared y = 1/n2 were determined on the basis of the standard curve fitting polynomial procedure from the calculated data for C6(n). The transformation of attractive van-der-Waals force (C6 > 0) for low-energy states n < 23 into repulsive force (C6 < 0) for all higher-energy states of n ≥ 23, is observed from the results of numerical calculations based on the second-order perturbation theory for the operator of the long-range interaction between neutral atoms. This transformation is taken into account in the asymptotic formulas (in both cases of p = 2, 3) by polynomials K p tending to unity at n → ∞ (K p (0) = 1). The transformation from low-n attractive van-der-Waals force into high-n repulsive force demonstrates the gradual increase of the negative contribution to C6(n) from the lower-energy two-atomic states, of the A(B)-atom principal quantum numbers n′A(B) = n-Δn (where Δn = 1, 2, … is significantly smaller than n for the terms providing major contribution to the second-order series), which together with the states of n″B(A) = n+Δn make the joint contribution proportional to n12. So, the hydrogen-like manifold structure of the energy spectrum is responsible for the transformation of the power-11 asymptotic dependence C6(n) ∝ n11of the low-angular-momenta Rydberg states in many-electron atoms into the power-12 dependence C6(n) ∝ n12 for the dipolar states of the Rydberg manifold.

The Excitation of Rydberg Atoms of Thallium in an Electric Field

The spectrum of excitation of Rydberg states of thallium atoms has been investigated using a collimated atomic beam in a two-step isotope selective laser scheme 62P1/2 → 62D3/2 → Tl** in the presence of an electric field with a strength of up to 1.5 kV/cm near the level 16F5/2. The optical transitions 6D3/2 → 18D3/2 and 6D3/2 → 16G7/2, which were induced by an external electric field and dipole-forbidden, have been studied experimentally. The values for the scalar polarizabilities (in units сm–1/(kV/сm)2) α0(16F5/2) = 3.71 ± 0.3, α0(18D3/2) = 11.70 ± 0.25, and α0(16G7/2) = 44.1 ± 0.9, which are compared with the calculated one, have been obtained. The new values of energy parameters for the states 18D3/2 and 16G7/2 have been determined.

Long-term frequency stabilized and linewidth-narrowed cw-laser system for excitation of lithium Rydberg states

We transfer the frequency stability from a diode laser, which was locked to Doppler-free saturation absorption resonance in lithium vapor cell, to a tunable Ti-sapphire laser. We get the laser linewidth < 100 kHz/100 ms and absolute frequency stability ±0.5 MHz. The uv laser system which included the stabilized Ti-sapphire laser and frequency doubler has output optical beam with power near 100 mW and wavelength 350 nm. This uv laser system will be used for excitation and study of Rydberg states in lithium atoms.

Rydberg Atoms: From Determinism to Chaos

R.F. Stebbings and F.B. Dunning were the editors of Rydberg States of Atoms and Molecules. Issued in 1983, this book actually reflected the emergence of a new field in atomic and molecular physics, which subsequently resulted in a number of applications in academic sciences and technology. In this paper, we analyze the results obtained in recent years for ionization processes in collisions of heavy particles with the participation of Rydberg atoms in a wide energy range. These results have been actively used in modern applications of atomic physics. In addition, we consider the influence of nonlinear resonant interaction of Rydberg complexes with electromagnetic waves on the rate of propagation of satellite signals in the atmosphere.

Optical frequency synthesizer for precision spectroscopy of Rydberg states of Rb atoms

We have developed an optical frequency synthesizer for the precision spectroscopy of highly excited Rydberg states of Rb atoms. This synthesizer can generate a widely tunable 480 nm laser light with an optical power of 150 mW and an absolute frequency uncertainty of less than 100 kHz using a high-repetition-rate (325 MHz) Er fiber-based optical frequency comb and a tunable frequency-doubled diode laser at 960 nm. We demonstrate the precision two-photon spectroscopy of the Rydberg states of 87Rb atoms by observing the electromagnetically induced transparency in a vapor cell, and measure the absolute transition frequencies of 87Rb to nD (n = 53–92) and nS (n = 60–90) Rydberg states with an uncertainty of less than 250 kHz. It is the first direct frequency measurements of these transitions using an optical frequency comb.

Coherent laser-millimeter-wave interactions en route to coherent population transfer.

We demonstrate coherent two-photon population transfer to Rydberg states of barium atoms using a combination of a pulsed dye laser and a chirped-pulse millimeter-wave spectrometer. Numerical calculations, using a density matrix formalism, reproduce our experimental results and explain the factors responsible for the observed fractional population transferred, optimal experimental conditions, and possibilities for future improvements. The long coherence times associated with the millimeter-wave radiation aid in creating coherence between the ground state and Rydberg states, but higher-coherence laser sources are required to achieve stimulated Raman adiabatic passage and for applications to molecules.

Comment on “Entropy and complexity analysis of hydrogenic Rydberg atoms” [J. Math. Phys. 54, 052109 (2013)

In a recent paper [S. López-Rosa et al., J. Math. Phys. 54, 052109 (2013)], the authors made detailed investigations on the information-theoretic quantities for hydrogenic atoms in Rydberg states. Asymptotic forms of different types of complexity measures (Crámer-Rao, Fisher-Shannon, and LMC types) in both position and momentum spaces were obtained for hydrogenic states (n,l,m) with fixed l and increasingly large n. However, the expressions for the Crámer-Rao complexity are incorrect due to the wrong definition of variance. The correct form of this complexity in position space is presented exactly in this work. In momentum space, two different definitions of variance are provided and corresponding Crámer-Rao complexities are discussed separately. In either case, the momentum complexity increases much faster than that in position space when increasing principal quantum number n.

Energy of van der Waals and dipole-dipole interactions between atoms in Rydberg states

The van der Waals coefficient ${C}_{6}(\ensuremath{\theta};nlJM)$ of two like Rydberg atoms in their identical Rydberg states $|nlJM\ensuremath{\rangle}$ is resolved into four irreducible components called scalar ${R}_{ss}$, axial (vector) ${R}_{aa}$, scalar-tensor ${R}_{sT}={R}_{Ts}$, and tensor-tensor ${R}_{TT}$ parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of ${C}_{6}(\ensuremath{\theta};nlJM)$ on the angle $\ensuremath{\theta}$ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components ${R}_{\ensuremath{\alpha}\ensuremath{\beta}}$ of atoms in their Rydberg series of doublet states of the low angular momenta ($^{2}S, ^{2}P, ^{2}D, ^{2}F$). The polynomial presentations in powers of the Rydberg-state principal quantum number $n$ taking into account the asymptotic dependence ${C}_{6}(\ensuremath{\theta};nlJM)\ensuremath{\propto}{n}^{11}$ are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{S}_{1/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{P}_{1/2,3/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{D}_{3/2,5/2}$, and $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{F}_{5/2,7/2}$ Rydberg states of arbitrary high $n$. The transformation of the van der Waals interaction law $\ensuremath{-}{C}_{6}/{R}^{6}$ into the dipole-dipole law ${C}_{3}/{R}^{3}$ in the case of close dipole-connected two-atomic states (the F\orster resonance) is considered and the dependencies on the magnetic quantum numbers $M$ and on the angle $\ensuremath{\theta}$ of the constant ${C}_{3}(\ensuremath{\theta};nlJM)$ are determined together with the ranges of interatomic distances $R$, where the transformation appears.

Enhanced spectral profile in the study of Doppler-broadened Rydberg ensembles

Combination of the electromagnetically-induced-transparency (EIT) effect and Rydberg-state atoms has attracted great attention recently due to its potential application in the photon-photon interaction or qubit operation. In this work, we studied the Rydberg-EIT spectra with room-temperature 87Rb atoms. Spectroscopic data under various experimental parameters all showed that the contrast of EIT transparency as a function of the probe field intensity is initially enhanced, reaches a maximum value and then decays gradually. The contrast of spectral profile at the optimum probe field intensity is enhanced by 2–4 times as compared with that at weakest intensity. Moreover, the signal-to-noise ratio of the spectrum can potentially be improved by 1 to 2 orders of magnitude. We provided a theoretical model to explain this behavior and clarified its underlying mechanism. Our work overcomes the obstacle of weak signal in the Rydberg-EIT spectrum caused by an apparent relaxation rate of the Rydberg polariton and weak coupling transition strength, and provides the useful knowledge for the Rydberg-EIT study.

ARC: An open-source library for calculating properties of alkali Rydberg atoms

We present an object-oriented Python library for the computation of properties of highly-excited Rydberg states of alkali atoms. These include single-body effects such as dipole matrix elements, excited-state lifetimes (radiative and black-body limited) and Stark maps of atoms in external electric fields, as well as two-atom interaction potentials accounting for dipole and quadrupole coupling effects valid at both long and short range for arbitrary placement of the atomic dipoles. The package is cross-referenced to precise measurements of atomic energy levels and features extensive documentation to facilitate rapid upgrade or expansion by users. This library has direct application in the field of quantum information and quantum optics which exploit the strong Rydberg dipolar interactions for two-qubit gates, robust atom-light interfaces and simulating quantum many-body physics, as well as the field of metrology using Rydberg atoms as precise microwave electrometers. Program summaryProgram Title: ARC: Alkali Rydberg CalculatorProgram Files doi:http://dx.doi.org/10.17632/hm5n8w628c.1Licensing provisions: BSD-3-ClauseProgramming language: Python 2.7 or 3.5, with C extensionExternal Routines: NumPy [1], SciPy [1], Matplotlib [2]Nature of problem: Calculating atomic properties of alkali atoms including lifetimes, energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated from radial wavefunctions.Solution method: Numerical integration of radial Schrödinger equation to obtain atomic wavefunctions, which are then used to evaluate dipole matrix elements. Properties are calculated using second order perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation.Restrictions: External electric field fixed to be parallel to quantisation axis.Supplementary material: Detailed documentation (.html), and Jupyter notebook with examples and benchmarking runs (.html and .ipynb).[1] T.E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/.[2] J.D. Hunter, Comput. Sci. Eng. 9, 90 (2007). http://matplotlib.org/.

Focusing of a Rydberg Positronium Beam with an Ellipsoidal Electrostatic Mirror.

Slow atoms in Rydberg states can exhibit specular reflection from a cylindrical surface upon which an azimuthally periodic potential is imposed. We have constructed a concave mirror of this type, in the shape of a truncated oblate ellipsoid of revolution, which has a focal length of (1.50±0.01) m measured optically. When placed near the center of a long vacuum pipe, this structure brings a beam of n=32 positronium (Ps) atoms to a focus on a position sensitive detector at a distance of (6.03±0.03) m from the Ps source. The intensity at the focus implies an overall reflection efficiency of ∼30%. The focal spot diameter (32±1) mm full width at half maximum is independent of the atoms' flight times from 20 to 60 μs, thus indicating that the mirror is achromatic to a good approximation. Mirrors based on this principle would be of use in a variety of experiments, allowing for improved collection efficiency and tailored transport or imaging of beams of slow Rydberg atoms and molecules.