Cold and ultracold Rydberg atoms in strong magnetic fields

Cold Rydberg atoms exposed to strong magnetic fields possess unique properties which open the pathway for an intriguing many-body dynamics taking place in Rydberg gases, consisting of either matter or anti-matter systems. We review both the foundations and recent developments of the field in the cold and ultracold regime where trapping and cooling of Rydberg atoms have become possible. Exotic states of moving Rydberg atoms, such as giant dipole states, are discussed in detail, including their formation mechanisms in a strongly magnetized cold plasma. Inhomogeneous field configurations influence the electronic structure of Rydberg atoms, and we describe the utility of corresponding effects for achieving tightly trapped ultracold Rydberg atoms. We review recent work on large, extended cold Rydberg gases in magnetic fields and their formation in strongly magnetized ultracold plasmas through collisional recombination. Implications of these results for current antihydrogen production experiments are pointed out, and techniques for the trapping and cooling of such atoms are investigated.     

Coherent excitation of Rydberg atoms in an ultracold gas

We demonstrate two schemes for the coherent excitation of Rydberg atoms in an ultracold gas of rubidium atoms employing the three-level ladder system 5S_1/2-5P_3/2-n?_j. In the first approach rapid adiabatic passage with pulsed laser fields yields Rydberg excitation probabilities of 90% in the center of the laser focus. In a second experiment two-photon Rydberg excitation with continuous-wave fields is applied which results in Rabi oscillations between the ground and Rydberg state. The experiments represent a prerequisite for the control of interactions in ultracold Rydberg gases and the application of ultracold Rydberg gases for quantum information processing.     

Fast Rydberg gates without dipole blockade via quantum control

We propose a scheme for controlling interactions between Rydberg-excited neutral atoms in order to perform a fast high-fidelity quantum gate. Unlike dipole-blockade mechanisms already found in the literature, we drive resonantly the atoms with a state-dependent excitation to Rydberg levels, and we exploit the resulting dipole-dipole interaction to induce a controlled atomic motion in the trap, in a similar way as discussed in recent ion-trap quantum computing proposals. This leads atoms to gain the required gate phase, which turns out to be a combination of a dynamic and a geometrical contribution. The fidelity of this scheme is studied including small anharmonicity and temperature effects, with promising results for reasonably achievable experimental parameters.     

Experimental Research of Spontaneous Evolution from Ultracold Rydberg Atoms to Plasma

The spontaneous evolution from ultracold Rydberg atoms to plasma is investigated in a caesium MOT by using the method of field ionization. The plasma transferred from atoms in different Rydberg states （n = 22-32） are obtained experimentally. Dependence of the threshold time of evolving to plasma and the threshold number of initial Rydberg atoms on the principal quantum number of initial Rydberg states is studied. The experimental results are in agreement with hot-cold Rydberg-Rydberg atom collision ionization theory.     

Polyatomic molecules formed with a Rydberg atom in an ultracold environment

We investigate properties of ultralong-range polyatomic molecules formed with a Rb Rydberg atom and several ground-state atoms whose distance from the Rydberg atom is of the order of n²a₀, where n is the principle quantum number of the Rydberg electron. In particular, we put emphasis on the splitting of the energy levels, and elucidate the nature of the splitting via the construction of symmetry-adapted orbitals.     

Dynamics of resonant energy transfer in a cold Rydberg gas

We investigate excitation transfer and migration processes in a cold gas of rubidium Rydberg atoms. Density-dependent measurements of the resonant population exchange for atoms initially excited into the 32P_3/2(|m_J|=3/2) state are compared with a Monte Carlo model for coherent energy transfer. The model is based on simulations of small atom subensembles involving up to ten atoms interacting via coherent pair processes. The role of interatomic mechanical forces due to the resonant dipole-dipole interaction is investigated. Good agreement is found between the experimental data and the predictions of the model, from which we infer that atomic motion has negligible influence on the energy transfer up to Rydberg densities of 10⁸ cm^-3, that the system has to be described in terms of many-body dynamics, and that the energy transfer preserves coherence on microsecond timescales.     

Magnetic trapping of strongly-magnetized Rydberg atoms

Effective magnetic moments of drift Rydberg atoms in strong magnetic fields are obtained for different energy and angular-momentum states. Classical two-body trajectory calculations and quantum-mechanical one-body calculations are employed. For heavy atoms such as rubidium, the trapping dynamics can largely be explained by the net magnetic moment due to the cyclotron and the magnetron motion of the Rydberg electron. In light Rydberg atoms such as hydrogen, the intrinsic two-body nature of the dynamics becomes manifest in that the ionic motion significantly contributes to the effective magnetic moment. Also, light drift Rydberg atoms exhibit an anisotropic response to field-inhomogeneities parallel and transverse to the magnetic-field lines. The results are relevant to magnetic trapping of Rydberg atoms in strong-magnetic-field atom traps.     

Relativistic Multichannel Treatment of Ionic Rydberg States of Lanthanum

Ionic Rydberg energy levels of lanthanum are calculated from first principles by relativistic multichannel theory within the framework of multichannel quantum defect theory. The present calculated results are in better agreement with the experimental measurements than the previous calculations [J. Phys. B 34 （2001）369] due to the consideration of dynamical polarizations. Moreover, in the experimental spectra achieved by a five-laser resonance excitation via the intermediate state 5d6d^3 F2, a series of weak ionic Rydberg states and some of perturbing states are found and assigned in this work.     

Simultaneous position and state measurement of Rydberg atoms

We present a technique for state-selective position detection of cold Rydberg atoms. Ground state Rb atoms in a magneto-optical trap are excited to a Rydberg state and are subsequently ionized with a tailored electric field pulse. This pulse selectively ionizes only atoms in e.g. the 54d state and not in the 53d state. The released electrons are detected after a slow flight towards a micro channel plate. From the time of flight of the electrons the position of the atoms is deduced. The state selectivity is about 20:1 when comparing 54d with 53d and the one-dimensional position resolution ranges from 6 to 40 μm over a range of 300 μm. This state selectivity and position resolution are sufficient to allow for the observation of coherent quantum excitation transport.     

Isotope shifts and hyperfine structure in calcium 4snp and 4snf F Rydberg states

Isotope shifts and hyperfine structure have been measured in 4snp ¹ P₁ and Rydberg states for all stable calcium isotopes and the radioisotope ⁴¹Ca using high-resolution laser spectroscopy. Triple-resonance excitation via Rydberg state was followed by photoionization with a CO₂ laser and mass selective ion detection. Isotope shifts for the even-mass isotopes have been analyzed to derive specific mass shift and field shift factors. The apparent isotope shifts for ⁴¹Ca and ⁴³Ca exhibit anomalous values that are n-dependent. This is interpreted in terms of hyperfine-induced fine-structure mixing, which becomes very pronounced when singlet-triplet fine-structure splitting is comparable to the hyperfine interaction energy. Measurements of fine-structure splittings for the predominant isotope ⁴⁰Ca have been used as input parameters for theoretical calculation of the perturbed hyperfine structure. Results obtained by diagonalizing the second-order hyperfine interaction matrices agree very well with experimentally observed spectra. These measurements allow the evaluation of highly selective and sensitive methods for the detection of the rare ⁴¹Ca isotope. Received 17 December 1999 and Received in final form 29 March 2000     

里德堡钠原子抗磁谱的模型势计算

用B样条基组展开方法结合模型势计算了里德堡钠原子抗磁谱和相应的振子强度谱.径向和角向均采用高阶B样条基组.计算结果与已有的R-矩阵和多通道量子亏损理论相结合(R-matrix MQDT)法及其他理论计算结果作了比较,几种理论结果在我们所研究的能区内符合得非常好.本文方法较R-ma-trix MQDT法简单,易于推广到交叉电磁场中里德堡原子的精确谱的计算中.     

Analysis of a teleportation scheme involving cavity field states in a linear superposition of Fock states

We analyse a teleportation scheme of cavity field states. The experimental sketch discussed makes use of cavity quantum electrodynamics involving the interaction of Rydberg atoms with superconducting (micromaser) cavities as well as with classical microwave (Ramsey) cavities. In our scheme the Ramsey cavities and the atoms play the role of auxiliary systems used to teleport a field state, which is formed by a linear superposition of vacuum |∅〉 and the one-photon state |1〉, from a micromaser cavity to another.     

Possible excitation of a fast sodium beam by laser irradiation

We present results of model calculations concerning the fraction of excited atoms obtained by laser irradiation of a fast sodium atom beam (100–400 eV kinetic energy). We calculated relative absorption probabilities as a function of the intersection angle between the two beams, the atom-beam energy, the atom-beam energy spread and the atom-beam divergence. The fraction of excited atoms that can be obtained at 300 eV is at least a factor of 5 smaller than in the case of a thermal beam, due to the divergence and energy spread of the fast atom beam giving rise to a large Doppler broadening.     

囚禁于巴基球内的原子的里德堡特性

通过非线性变换和特殊设计结点的B样条函数研究计算了囚禁于巴基球内的氢原子里德堡能级结构和振子强度 .结果表明 ,巴基球等效势阱深度可以有选择的影响和改变里德堡原子的特性 ;囚禁原子拥有很多自由原子所没有的奇特性质. Rydberg energy levels and oscillator strength of endohedrally confined H atom have been calculated by using a nonlinear algebraic mapping technique and B-spline method.The boundary conditions are conveniently satisfied with a specially designing knot sequence.Our results show that endohedral can selectively alter the properties and energy levels of Rydberg atoms, and such atoms possess some properties and behaviours which are not previously met or studied in free systems.     

Matter-wave interferometry with atoms in high Rydberg states

Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ～320?nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.     

Observation of the Dipole Blockade Effect in Detecting Rydberg Atoms by the Selective Field Ionization Method

The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1–5 atoms when they are detected by the selective field ionization method. We have investigated the spectra of the three-photon laser excitation 5S1/2 → 5P3/2 → 6S1/2 → nP3/2 of cold Rydberg Rb atoms in a magneto-optical trap. We have found that for mesoscopic ensembles this method allows only a partial dipole blockage to be observed. This is most likely related to the presence of parasitic electric fields reducing the interaction energy of Rydberg atoms, the decrease in the probability of detecting high states, and the strong angular dependence of the interaction energy of Rydberg atoms in a single interaction volume.     

一种高分辨里德堡原子外场光谱实验方法

介绍一种用于里德堡原子外场效应研究的实验方法，用该方法获得了Ｓｅ原子里德堡态各种外场效应研究的初步结果，显示了此方法用于外场效应的研究的有效性。     

氢原子Rydberg态抗磁谱的高阶B-spline基组计算

在球坐标下采用基组展开方法计算了均匀磁场中的氢原子高Rydberg态能谱和振子强度谱.径向和角向均采用高阶B样条基组. 径向采用B样条基组能很好地描述束缚态与连续态的耦合；角向采用B样条基组有效地减少了基组维数，计算效率得到大幅度提高. 用上述方法计算了磁场中氢原子Rydberg态-40cm^-1到零场电离阈的高精度抗磁谱并与已有理论和实验结果作了比较. 该方法适用于低于离化阈的所有能区的精确谱计算并易于推广到非氢原子、交叉场中的原子以及高于离化阈的正能区光谱的计算. 关键词： 氢原子 B样条基组 能谱 振子强度谱     

Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap

We present an investigation of sub-Doppler effects in a cesium magneto-optical trap. First, a simple one-dimensional theoretical model of the trap is developed for aJ _g = 1 J _e = 2 transition. This model predicts the size of the trapped atom cloud and temperature as a function of laser intensity and detuning. In the limit of small magnetic field gradients, the trap temperature is found to be equal to the molasses temperature and a minimum size for the trap is calculated. We then describe several experiments performed in a three-dimensional cesium trap to measure the trap parameters, spring constant, friction coefficient, temperature and density. Whilst the temperature of the trapped atoms is found to be equal to the molasses temperature, in agreement with theory, the trap spring constant is found to be two orders of magnitude smaller than the one-dimensional prediction, a value close to that predicted by Doppler models. The maximum density is found to be on the order of 10¹² atoms/cm³ or one atom per optical wavelength on average. When the number of trapped atoms becomes large, the temperature begins to increase dramatically. This excess temperature depends in a very simple way on the atom number, laser intensity and detuning, suggesting that its origin lies in multiple photon scattering within the trap.     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999