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Physical Review Letters

Landau-Zener Transitions in Frozen Pairs of Rydberg Atoms

Nicolas Saquet, Anne Cournol, J. Beugnon, Jacques Robert, P. Pillet, Nicolas Vanhaecke

Published Apr 2, 2010• 29 citations
Publisher

Abstract

We have induced adiabatic transitions in pairs of frozen Rydberg sodium atoms of a supersonic beam. The diatomic ns+ns-->np+(n-1)p transition takes place in a time-dependent electric field and originates from the adiabatic change of the internal state of the pair induced by the dipole-dipole interaction. This is experimentally achieved by sweeping an electric field across the energy degeneracy ns ns-np(n-1)p. Our results fully agree with a two-level Landau-Zener model in the diatom system.

DOI
10.1103/physrevlett.104.133003

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We have induced adiabatic transitions in pairs of frozen Rydberg sodium atoms of a supersonic beam. The diatomic ns+ns-->np+(n-1)p transition takes place in a time-dependent electric field and originates from the adiabatic change of the internal state of the pair induced by the dipole-dipole interaction. This is experimentally achieved by sweeping an electric field across the energy degeneracy ns ns-np(n-1)p. Our results fully agree with a two-level Landau-Zener model in the diatom system.
We report the observation of a controlled Landau-Zener transition (LZT) in Rydberg atoms by breaking the symmetry of the underlying Hamiltonian. For a nonhydrogenic Rydberg atom inside a changing electric (F) field, a LZT occurs between the avoided crossing energy levels of neighboring Rydberg states only for a sufficiently high changing rate. If a transverse magnetic (B) field is applied as we implement, the atomic level symmetry is broken, which causes the Stark manifolds denoted by a different |m| (m is the magnetic quantum number) to interact with each other. The mixed state levels end up pushing the adiabatically repelled target states closer and additionally they serve as stepping stones for the sequential LZTs between the neighboring sublevels. Such a feature significantly decreases the changing rate required for an efficient LZT inside a pure electric field. We report experimental observations that support the above scenario. It opens a versatile approach for engineering a controlled LZT in more general systems.
We have observed a significant yield of (n + 2)P atoms after the excitation of nD Rydberg atoms in a Rb MOT, where 27 < n < 41, which can be attributed to binary collisions between Rydberg atoms. We have measured its dependence on principle quantum number as well as DC electric field. These results are compared to a model which uses the Landau-Zener method to calculate transition probabilities at avoided crossings in the two-atom potential energy curves, taking into account the effects of the DC Stark effect due to the background electric field.
We study the Landau-Zener (LZ) dynamics in a setup of two Rydberg atoms with time-dependent detuning, both linear and periodic, using both the exact numerical calculations as well as the method of adiabatic impulse approximation (AIA). By varying the Rydberg-Rydberg interaction strengths, the system can emulate different three-level LZ models, for instance, bow-tie and triangular LZ models. The LZ dynamics exhibits nontrivial dependence on the initial state, the quench rate, and the interaction strengths. For large interaction strengths, the dynamics is well captured by AIA. In the end, we analyze the periodically driven case, and AIA reveals a rich phase structure involved in the dynamics. The latter may find applications in quantum state preparation, quantum phase gates, and atom interferometry.
The mixing of substates of an isolated Rydberg manifold (constant n,m) is studied using time-evolution matrices U(t,t0). Coherent mixing is effected by a linearly ramped electric field, F(t)=F\ifmmode \dot{}\else \.{}\fi{}t. The spherical l basis, diabatic (hydrogenic) p basis, and adiabatic (nonhydrogenic) q basis are considered. In the linear Stark regime, the diabatic levels are coupled by F(t) through the atomic core, parametrized by quantum defects. The resulting adiabatic levels EqF in this model group into a submanifold degenerate at F=0 plus shifted levels split off from the adiabatic manifold. Analytical expressions for the q levels Eq\ensuremath{\tau} and their coupling \ensuremath{\Gamma}qq\ensuremath{'}\ensuremath{\tau} are derived as a function of rescaled field or time \ensuremath{\tau}. The time evolution of the levels' populations is studied first for the two-level case---the usual Landau-Zener effect (LZE)---which is generalized to a multilevel Landau-Zener effect (MLZE) for any n manifold. The matrices U(t,t0) are constructed in the Riemann product representation, including Magnus corrections up to fourth order. The probability Pq\ensuremath{\rightarrow}q\ensuremath{'}(Vl) of making a transition from state q to q\ensuremath{'} upon a one-way pass across the manifold depends on a single parameter Vl=[2\ensuremath{\mu}l2/(3F\ifmmode \dot{}\else \.{}\fi{}n9)]1/2 (when one \ensuremath{\mu}l\ensuremath{\ne}0). Numerical results for l=m=0 indicate that either diabatic (p\ensuremath{\rightarrow}p\ensuremath{'}=p) or adiabatic (q\ensuremath{\rightarrow}q\ensuremath{'}=q) transitions always predominate, no matter what the ramp rate F\ifmmode \dot{}\else \.{}\fi{}. Strong evidence supports the conjecture that outer diabatic transitions between edge states of a manifold obey Pndiab(V)=exp(-\ensuremath{\beta}n\ensuremath{\pi}V2) for l=m=0, with \ensuremath{\beta}n=1 for n=2 (the LZE) and \ensuremath{\beta}n\ensuremath{\approx}lnn for n\ensuremath{\gg}2 (the MLZE), and that a similar analytical result holds for arbitrary {\ensuremath{\mu}l} and m.
We develop the distorted-wave and adiabatic theories of the ion-pair formation in collisions of a Rydberg atom A∗∗{\mathit{A}}^{\mathrm{*}\mathrm{*}}A∗∗ with a ground-state atom B at thermal collision velocities. The e-B interaction is modeled by a zero-range potential. Both theories give results that are in qualitative agreement with the standard Landau-Zener model, although their prediction for m-changing transitions is different, where m is the projection of the angular momentum. To incorporate these transitions into the adiabatic theory, we take into account the rotation of the internuclear axis before and after a nonadiabatic transition. The m-averaged cross sections are substantially higher than those following from the standard Landau-Zener model, and the distorted-wave results are slightly higher than the adiabatic results with the internuclear-axis rotation taken into account. We apply our results to a description of the McLaughlin and Duquette experiment on Ca+{\mathrm{Ca}}^{+}Ca+-${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ pair formation. The calculated n dependence of the rate for the ion-pair formation is too flat as compared to the experimental observations and does not agree with known values of the electron affinity of Ca. We discuss other possible mechanisms responsible for the ion-pair formation in this process. \textcopyright{} 1996 The American Physical Society.