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.     

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.     

Trapping and focusing ground state atoms with static fields

Possibilities of trapping ground state atoms in static fields are studied. It is shown that it is impossible to trap ground state particles at rest using arbitrary combinations of electric, magnetic, and gravitational fields, a result which is a considerable generalization of Wing's theorem. Similarly, it is impossible to make a thin lens for ground state atoms using static fields. Confinement of ground state particles in dynamic equilibrium can be achieved. Axially symmetric storage rings with electric or magnetic fields are possible and should be experimentally feasible. Such storage rings have the important advantage that ground state particles can be confined, hence loss of atoms by two-body collisions is avoided.     

Magnetic trapping of long-lived cold Rydberg atoms

We report on the trapping of long-lived strongly magnetized Rydberg atoms. 85Rb atoms are laser cooled and collected in a superconducting magnetic trap with a strong bias field (2.9 T) and laser excited to Rydberg states. Collisions scatter a small fraction of the Rydberg atoms into long-lived high-angular momentum "guiding-center" Rydberg states, which are magnetically trapped. The Rydberg atomic cloud is examined using a time-delayed, position-sensitive probe. We observe magnetic trapping of these Rydberg atoms for times up to 200 ms. Oscillations of the Rydberg-atom cloud in the trap reveal an average magnetic moment of the trapped Rydberg atoms of approximately -8microB. These results provide guidance for other Rydberg-atom trapping schemes and illuminate a possible route for trapping antihydrogen.     

Autoionization of an ultracold Rydberg gas through resonant dipole coupling

We investigate a possible mechanism for the autoionization of ultracold Rydberg gases, based on the resonant coupling of Rydberg pair states to the ionization continuum. Unlike an atomic collision where the wave functions begin to overlap, the mechanism considered here involves only the long-range dipole interaction and is in principle possible in a static system. It is related to the process of intermolecular Coulombic decay (ICD). In addition, we include the interaction-induced motion of the atoms and the effect of multi-particle systems in this work. We find that the probability for this ionization mechanism can be increased in many-particle systems featuring attractive or repulsive van der Waals interactions. However, the rates for ionization through resonant dipole coupling are very low. It is thus unlikely that this process contributes to the autoionization of Rydberg gases in the form presented here, but it may still act as a trigger for secondary ionization processes. As our picture involves only binary interactions, it remains to be investigated if collective effects of an ensemble of atoms can significantly influence the ionization probability. Nevertheless our calculations may serve as a starting point for the investigation of more complex systems, such as the coupling of many pair states proposed in [P.J. Tanner et al., Phys. Rev. Lett. 100, 043002 (2008)].     

Laser cooling force in noisy quadrature of squeezed light

The laser cooling of atoms is a result of the combined effect of Doppler shift, light shift and polarization gradient. These are the phenomena which generally introduce frequency shift and uncertainty. However, they combine gainfully in realizing laser cooling and trapping of the atoms. In this paper we discuss the laser cooling of atoms in the presence of the squeezed light with the decay of atomic dipole moment into noisy quadrature. We show that the higher decay rate of the atomic dipole moment into the noisy quadrature, which leads to decrease in the signal to noise ratio, may contribute in realizing larger cooling force vis-à-vis with coherent laser light.     

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.     

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.     

Ionization of fast rydberg atoms in longitudinal and transverse electric fields

The main properties of longitudinal and transverse electric field ionizers for fast Rydberg atoms n=21–40 have been investigated. The dispersion and the background due to collisional processes between fast atoms and residual gas molecules have been measured and calculated. The kinetic energy spread of ions formed by field ionization of Rydberg atoms and their trajectories have been calculated. The potassium beam energy was 3.9 keV.     

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.     

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.     

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.     

A Time-Dependent Approach to High-Resolution Photoabsorption Spectrum of Rydberg Atoms in Magnetic Fields

A robust time-dependent approach to the high-resolution photoabsorption spectrum of Rydberg atoms in magnetic fields is presented. Traditionally we have to numerically diagonalize a huge matrix to solve the eigen-problem and then to obtain the spectral information. This matrix operation requires high-speed computers with large memories. Alternatively we present a unitary but very easily parallelized time-evolution method in an inexpensive way, which is very accurate and stable even in long-time scaie evolution. With this method, we perform the spectral caiculation of hydrogen atom in magnetic field, which agrees well with the experimentai observation. It can be extended to study the dynamics of Rydberg atoms in more complicated cases such as in combined electric and magnetic fields.     

Capture into rydberg states and momentum distributions of ionized electrons

The yield of neutral excited atoms and low-energy photoelectrons generated by the electron dynamics in the combined Coulomb and laser field after tunneling is investigated. We present results of Monte-Carlo simulations built on the two-step semiclassical model, as well as analytic estimates and scaling relations for the population trapping into the Rydberg states. It is shown that mainly those electrons are captured into bound states of the neutral atom that due to their initial conditions (i) have moderate drift momentum imparted by the laser field and (ii) avoid strong interaction (“hard” collision) with the ion. In addition, it is demonstrated that the channel of capture, when accounted for in semiclassical calculations, has a pronounced effect on the momentum distribution of electrons with small positive energy. For the parameters that we investigated its presence leads to a dip at zero momentum in the longitudinal momentum distribution of the ionized electrons.     

Realization of a single-beam mini magneto-optical trap: A candidate for compact CPT cold atom-clocks

We have demonstrated the experimental realization of a single-beam mini magneto-optical trap of ⁸⁷Rb atoms, originally designed for a cold atom-clock with coherent population trapping (CPT). Only one beam is used as cooling, trapping and repumping beams rather than the three pairs of orthogonal beams of the standard magneto-optical trap. The core optics, which consists of a modified pyramidal funnel type mirror, a quarter-wave plate and a retroreflect mirror, is installed inside a mini titanium cubic chamber. The vacuum system, rubidium source, magnetic field coils and beam expander are designed in a compact geometry. As many as 1.1 × 10⁷ rubidium atoms are cooled and trapped, and thus the mini trap is ready for the implementation of a novel compact coherent population trapping cold atom-clock.     

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.     

Magnetic trapping of ultracold Rydberg atoms

We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-n-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.     

Ionization and plasma formation in high n cold Rydberg samples

The experiments reported here show that the dipole-dipole interaction, the fundamental interaction between the cold Rydberg atoms, is the dominant initial ionization mechanism for evolution from a frozen Rydberg gas into a plasma. The study also indicates that plasma formation follows a path of initial ionization, redistribution of Rydberg population to higher angular momentum states, and rapid avalanche ionization due to electron-Rydberg collisions.     

Towards a test of string theory using Rydberg atoms

The current controversy over the need for an experimental test of String Theory is considered. We report recent experiments on quasi-bound electrons in crossed electric and magnetic fields, in which states of very large electric dipole moment are excited. The excited electron is confined to one side of the atomic nucleus in the outer well of a controllable double-well potential. These states are discussed in relation to a recent theoretical proposal to test the spatial non-commutativity underpinning String Theory by studying Penning orbits of Rydberg atoms in crossed electric and magnetic fields.