Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.
Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.
We study a hitherto unexplored regime of the Rydberg excitation blockade using highly Stark-shifted, yet long-living, states of Rb atoms subject to electric fields above the classical ionization limit. Such states allow tuning the dipole-dipole interaction strength while their ionization rate can be changed over 2 orders of magnitude by small variations of the electric field. We demonstrate laser excitation of the interacting Rydberg states followed by their detection using controlled ionization and magnified imaging with high spatial and temporal resolution. Our work reveals new possibilities to engineer the interaction strength and dynamically control the ionization and detection of Rydberg atoms, which can be useful for realizing and assessing quantum simulators that vary in space and time.
In this work, numerical calculations were implemented based on the diagonalisation of a matrix representation of the Stark Hamiltonian on a subset of the basis given by the zero-field Hamiltonian. Dipole matrix elements between the involved states were calculated, which allow for the prediction of transition strengths to Stark shifted Rydberg states. The applicability of the numerical methods were confirmed experimentally by precision spectroscopy in a rubidium vapour cell with electrodes using electromagnetically induced transparency (EIT). The numerical methods were then extended to predict ionisation rates of Rydberg states in the highly Stark shifted regime beyond the classical ionisation threshold. For this purpose, a complex absorbing potential (CAP) was specifically adjusted to the Stark Hamiltonian. An experiment was conducted, in which cold atoms from a magneto-optical trap (MOT) were excited to Stark shifted Rydberg states and the arising ions were detected. The obtained ionisation spectra agree well with the results from the numerical calculations. Another extension of the numerical methods was implemented for crossed electric and magnetic fields. This was used for approximate calculations of the motional Stark effect (MSE), which acts on atoms moving through static magnetic fields and thereby experiencing a Lorentz electric field. In a precision spectroscopy, once more using EIT in a vapour cell, the MSE was observed in low magnetic fields for the first time in rubidium. The spectral shift, which is caused by the MSE, matches the prediction from the numerical calculations. In a final experiment, the practical use of the knowledge of several properties of Stark shifted Rydberg states was illustrated. The numerical methods including the CAP were used to specifically select states for their optical accessibility, permanent electric dipole moments and ionisation rates. In the experiment, atoms from a MOT were excited to these states to observe different characteristics of the dipole blockade effect. The detection scheme for this experiment was realised by controlled ionisation using only small changes in the external electric field.
The large electric dipole moments associated with transitions between Rydberg states of atoms or molecules, make them ideal model systems with which to study Förster resonance energy transfer in collisions with other Rydberg atoms or molecules, or with polar ground-state molecules [1,2]. The sensitivity of high Rydberg states to electric fields allows these energy transfer processes to be tuned thorough resonance by exploiting the Stark effect. In this talk, I will describe recent experiments in which we have observed the resonant transfer of energy from the ground-state inversion sublevels in ammonia, to helium atoms in triplet Rydberg states with principal quantum numbers between 38 and 43. The experiments were performed at translational temperatures below 1 K in seeded, pulsed supersonic beams [3]. Electric fields up to ~10 V/cm were used to tune transitions between selected Rydberg states into resonance with the transitions between the inversion sublevels. Resonant energy transfer was identified by Rydberg-state-selective electric-field ionisation. The experimental data exhibit quantum-state-dependent resonance widths that range from 200 to 700 MHz and, in general, reduce as the value of the principal quantum number is increased. Comparison with the results of numerical calculations of the Rydberg energy-level structure and transition moments, shows a dependence of the measured widths on the electric dipole transition moments of the Rydberg-Rydberg transitions. These results are of particular interest, e.g., for applications in coherent control and quantum sensing [4-6], and in the study of low-temperature ion-molecule reactions performed within the orbit of a Rydberg electron [7]. [1] T. F. Gallagher, Phys. Rep. 210, 319 (1992) [2] F. B. Dunning, S. Buathong, Int. Rev. Phys. Chem. 37, 287 (2018) [3] K. Gawlas and S. D. Hogan, J. Phys. Chem. Lett. 11, 83 (2020) [4] M. Zeppenfeld, Euro. Phys. Lett. 118, 13002 (2017). [5] E. Kuznetsova, S. T. Rittenhouse, H. R. Sadeghpour, and S. F. Yelin, Phys. Rev. A 94, 032325 (2016). [6] E. Kuznetsova, S. T. Rittenhouse, H. R. Sadeghpour, and S. F. Yelin, Phys. Chem. Chem. Phys. 13, 17115 (2011). [7] K. Höveler, J. Deiglmayr, J. A. Agner, H. Schmutz and F. Merkt, Phys. Chem. Chem. Phys. 23, 2676 (2021).
Systems of cold, interacting Rydberg atoms are of interest because they exhibit a wide range of collective quantum phenomena. This thesis describes experimental and theoretical work related to these systems with an emphasis on two phenomena: Rydberg excitation blockades and quantum-state-changing collisions. I begin by presenting a detailed calculation of the interaction energies of two Rydberg atoms for a variety of orientations, quantum states, and applied electric fields. The calculated energies are used to interpret the experimental results that follow. I then describe measurements showing that the widths of the distributions of Rydberg excitation number are related to the effectiveness of a Rydberg excitation blockade. These distributions are investigated as a function of principal quantum number, n, and applied electric field. In the presence of a Forster resonant field, sub-Poissonian distributions are measured. I next present a spectroscopic measurement of the energy level shift of a system of atoms which collectively shares two Rydberg excitations. The qualitative nature of the shift depends sensitively on the type of interactions between the atoms (van der Waals or dipole-dipole) and may be changed by changing the quantum state or applied electric field. This measurement provides the first spectroscopic proof that Rydberg excitation blockades are operative. Finally, I describe measurements of the probability for quantum state-changing and Penning-ionizing collisions to provide evidence for intrinsic, electric field-free-interaction resonances and complex many-body interactions in systems of cold Rydberg atoms.
We demonstrated a tuned dipole interaction between Rydberg atoms by employing a controllable electric field in a cold cesium ensemble. The | n P 3/2 ⟩ ( n = 38–40) Rydberg pairs are prepared with a three-photon scheme and detected via the state-selective field ionization technique. A weak DC electric field is used to tune the Rydberg pair interaction from the van der Waals interaction regime to the dipole–dipole interaction regime. The Förster resonant interaction and an adiabatic resonance energy transfer between the n P and n S Rydberg states are attained by precisely tuning the electric field. Rydberg excitation blockade with and without the electric field is investigated by changing the excitation pulse duration, which demonstrates that the dipole interaction–induced blockade effect is stronger than the van der Waals interaction–induced blockade effect. The precise control of the Rydberg interaction is of great significance to the coherent interaction in many-body systems and non-radiative collision processes.
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 principal quantum numbers of 43 and 70 at various electric fields. The emerging ions are detected using an ion optics. We find good agreement between the numerically and experimentally obtained spectra.