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Physical Review A

Dynamical effects at avoided level crossings: A study of the Landau-Zener effect using Rydberg atoms

Jan R. Rubbmark, Michael M. Kash, Michael G. Littman, Daniel Kleppner

Published Jun 1, 1981• 280 citations
Publisher

Abstract

We present a study of the dynamics of traversing an avoided energy level crossing. A pair of Stark levels of Rydberg states of lithium are used as a test system for measuring the diabatic transition probability. The experimental conditions are close to those assumed by the Landau-Zener theory. Possible corrections to the Landau-Zener theory are analyzed, and applications of the results to pulsed-field ionization are discussed.

DOI
10.1103/physreva.23.3107

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Physical Review A•Jul 1, 1997•38 citations
We present a study of the dynamics of traversing an avoided energy level crossing. A pair of Stark levels of Rydberg states of lithium are used as a test system for measuring the diabatic transition probability. The experimental conditions are close to those assumed by the Landau-Zener theory. Possible corrections to the Landau-Zener theory are analyzed, and applications of the results to pulsed-field ionization are discussed.
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 present a direct comparison between calculated and measured ionization in Li and Rb when an initially bound Rydberg electron is stripped from the atom by ramping an electric field [0.415 V/(cm ns)]. We describe the method used to calculate the field dependence of the ionization; the method can be used to evolve the population from field strengths where three or more n manifolds cross to the fields where the electron is stripped from the atom. The essential feature of the method is the repeated application of the Landau-Zener approximation for all of the level crossings as the field is ramped. We also give a description of the dynamics of Li and Rb in the ramping field. We observe that the Li selective field ionization is sensitive to the Stark levels within an n manifold, while for Rb only an n dependence is observed.
The time evolution groups of parallel energy levels (m, m{prime} = 0, 1, 2,...) is considered as a model of dynamic state mixing of interacting Rydberg manifolds by ramped electric fields used in selective field ionization (SFI). Each intersection [m, m{prime}] of the triangular grid of level crossings is treated as an isolated 2-level Landau-Zener anticrossing with amplitudes d and a for diabatic and adiabatic transitions, respectively ({vert_bar}d{vert_bar}{sup 2} + {vert_bar}a{vert_bar}{sup 2} = 1). Beginning on the uppermost upward-going level (m = 0) and following successive time steps {tau}{sup (N)} (N = 0,1,2,...), a path analysis leads to complex interference patterns among the many paths arriving at an intersection [m, m{prime}] after passing through N = m + m{prime} previous ones. The relative phase between any two paths is a multiple of the unit of action {var_phi} defined by the two pairs of adiabatic levels connecting four neighboring anticrossings. Compared to results from an analysis neglecting interference effects, there occurs here a general {open_quotes}emptying out{close_quotes} of population at the center of the interaction region (where the majority of paths lead). Most striking are resonances at high ramp rates (d {yields} 1), which with high probability enhance upward-going levels whose indexmore » m is an integral multiple of 27{pi}/{var_phi}. Though {var_phi} is sensitive to ramp rate, it is nevertheless expected that observed diabatic SFI signals should exhibit sequences of secondary peaks traceable to such resonances, which should not be assigned to extraneous initial states.« less
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.
Theoretical investigation of the dynamics of adiabatic quantum mechanics in two different, highly polar systems has been made. The systems were chosen for their fundamental scientific interest, as they represent atoms and molecules with exagger-ated properties, as well as ease of experimental study as such highly polar systems are easier to manipulate using readily-available electric fields. A model two-level system is used to derive one approach for maximizing the probability of adiabatic passage through an avoided crossing and this is compared with the classic Landau-Zener re-sult, and the commonly encountered spin-flip problem of a particle with spin located in a rotating magnetic field. This approach is applied to the avoided crossing between the n = 13, n1 − n2 = 11 (dipole moment of 532 D) and the n = 14, n1 − n2 = −12 (dipole moment of-657 D) highly polar Stark states of the lithium atom at 447 kV/m. Ion-pair formation from two neutral lithium atoms, one in the 2s ground state and the other in an excited state, is also investigated. The cross section σ(v) for free ion-pairs is calculated for the initial colliding pairs of atomic states located below
A model of the time evolution of two interacting Rydberg manifolds of energy levels subject to a linearly ramped electric field is solved exactly in the Landau-Zener (LZ) approximation. Each manifold's levels are treated as linear in time, parallel, equally spaced, and infinite in number. Their pairwise interactions produce a regular two-dimensional grid of isolated anticrossings. The time development of an initially populated state is then governed by two-level LZ transitions at avoided crossings and adiabatic evolution between them, parametrized by the LZ transition probability DDD and a dynamical phase unit \ensuremath{\varphi}. The resulting probability distributions of levels are given analytically in the form of recursion relations, generating functions, integral representations involving DDD and \ensuremath{\varphi}, and in certain limits by Bessel or Whittaker functions. Level populations are mapped out versus location on the grid for a range of cases. Interference effects lead to two principal types of probability distributions: a braiding adiabatic pattern with revivals for small DDD and a diabatic pattern for $D\ensuremath{\rightarrow}1$ in which only certain levels parallel to the initial one are appreciably populated. The sensitivity of the coherent evolution to \ensuremath{\varphi} is discussed, along with the relation of this model to others and to selective-field ionization.