M. A. Baranov,†,‡,§ M. Dalmonte,†,⊥ G. Pupillo,†,‡,∇ and P. Zoller*,†,‡ †Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria ‡Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria RRC “Kurchatov Institute”, Kurchatov Square 1, 123182, Moscow, Russia Dipartimento di Fisica dell’Universita di Bologna, via Irnerio 46, 40126 Bologna, Italy ISIS (UMR 7006) and IPCMS (UMR 7504), Universite de Strasbourg and CNRS, Strasbourg, France

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Condensed matter theory of dipolar quantum gases.

Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized.

Condensed Matter Theory of Dipolar Quantum Gases

State-selected rubidium-87 molecules were created at rest in a dilute Bose-Einstein condensate of rubidium-87 atoms with coherent free-bound stimulated Raman transitions. The transition rate exhibited a resonance line shape with an extremely narrow width as small as 1.5 kilohertz. The precise shape and position of the resonance are sensitive to the mean-field interactions between the molecules and the atomic condensate. As a result, we were able to measure the molecule-condensate interactions. This method allows molecular binding energies to be determined with unprecedented accuracy and is of interest as a mechanism for the generation of a molecular Bose-Einstein condensate.

Molecules in a Bose-Einstein condensate

A study was conducted to demonstrate the manipulation of molecular beams with electric and magnetic fields. Seeded pulsed supersonic expansions were employed to conduct the investigations. The conservative forces exerted further downstream by the electric and magnetic fields enabled the researchers to manipulate and control the shape and the position of the distribution in the six-dimensional phase-space. All of the original experimental geometries were devised to create strong magnetic or electric field gradients to efficiently deflect particles from the beam axis. It was demonstrated that a detailed understanding of the influence of the external field on the energy level structure of the molecules was required for the manipulation of molecules with electric or magnetic fields.

Manipulation and control of molecular beams.

Ion imaging methods are making ever greater impact on studies of gas phase molecular reaction dynamics. This article traces the evolution of the technique, highlights some of the more important breakthroughs with regards to improving image resolution and in image processing and analysis methods, and then proceeds to illustrate some of the many applications to which the technique is now being applied—most notably in studies of molecular photodissociation and of bimolecular reaction dynamics.

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Imaging the dynamics of gas phase reactions

Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17–18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 μs after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.

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Deflection and deceleration of hydrogen Rydberg molecules in inhomogeneous electric fields.

The controlled deflection of Rydberg atoms in an inhomogeneous electric field is demonstrated and shown to be in agreement with predictions based on a well-defined Stark map. Krypton atoms in a supersonic beam are excited in a two-colour multiphoton process to selected Stark states with n = 16-19 and undergo deflections in the field of an electrostatic dipole. The spatial distribution of the deflected atoms is monitored by ion imaging. The atoms travelling ~10 cm in the beam direction after excitation are deflected from the beam axis by distances of up to 3 mm, the interaction with the field taking place over 40 µs. Simulations of the trajectories agree well with the experimental results, demonstrating that the detected Rydberg atoms are those which have not undergone decay processes in the 40 µs applied field.

https://iopscience.iop.org/article/10.1088/0953-4075/34/3/319/pdf

Deflection of krypton Rydberg atoms in the field of an electric dipole

The Stark effect in autoionizing Rydberg states of NO, n=10–20,v+=1, is studied by a combination of experimental and theoretical methods. Double resonant excitation via selected intermediate rotation levels of the A 2Σ+, v′=1 state is carried out in the presence of fields 0–1000 V/cm. The spectra are simulated using both matrix diagonalization and full multichannel quantum defeat theory (MQDT) approaches, providing a test of quantum defect parameters and transition dipoles for Rydberg series from l=0 to l=4. The use of the same input parameters in these two types of calculation allows comparison of the validity and utility of these methods.

The Stark effect in the v + =1 autoionizing Rydberg states of NO

A novel theoretical study of the control of translational motion of atomic and molecular Rydberg states in inhomogeneous static electric fields is presented. Simulations have been carried out demonstrating that, under realistic conditions, the deflection and focusing of Rydberg atoms and molecules should be achievable. Advantage is taken of the high susceptibility of the Rydberg states to external electric fields, allowing the use of much smaller fields than would be necessary for ground state neutrals. The simulations presented are for trajectories of Rydberg states with n = 18-20 in the fields of an electric dipole, quadrupole and hexapole. A deflection of 7 mm is predicted for n = 18 Rydberg states travelling parallel to the dipole after 100 µs time of flight. In the hexapole n = 20 Rydberg states are refocused to a spot size of the order of the laser beam waist (10 µm) after 20 µs. It is demonstrated that the hexapole can also act as a cylindrical lens if its axis is perpendicular to the Rydberg beam direction. Spontaneous emission and black-body decay rates are also calculated, and their variation with the applied field is investigated. The potential applications of this work might include the use of focusing and deflection for controlled low-energy collisions of Rydberg molecules with surfaces.

Control of atomic and molecular motion via the Stark effect in Rydberg states

A spectroscopic study of the Stark effect in the predissociating v + = 0 Rydberg states of nitric oxide, (n = 13–16) is reported. The states are excited by two-colour excitation via the A2Σ+, v = 0, N = 0 state in the presence of a field in the range 0–1125 V cm−1, and the excitation is observed by using (2 + 1) REMPI detection of nitrogen (2 D) atoms formed by predissociation. The spectra recorded over a range of fields are compared with, and show excellent agreement with, multichannel quantum defect theory (MQDT) simulations of the absorption spectra applied in the bound state formalism of Sakimoto [J. Phys. B. 22, 2727 (1989)]. The spectroscopy demonstrates the possibility of producing N(2 D) or O(3 P) atoms with very narrow centre-of-mass frame speed distributions and arbitrarily selected speed.

A L Goodgame

Papers

Deflection and deceleration of hydrogen Rydberg molecules in inhomogeneous electric fields.

Deflection of krypton Rydberg atoms in the field of an electric dipole

The Stark effect in the v + =1 autoionizing Rydberg states of NO

Control of atomic and molecular motion via the Stark effect in Rydberg states

The Stark effect in the predissociating Rydberg states of NO