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Physical Review A

Quantum interference in half-cycle microwave multiphoton transitions

C. W. S. Conover, Julia H. Rentz

Published May 1, 1997• 7 citations
Publisher

Abstract

We observe microwave multiphoton transitions in Rydberg states of Na using intense subnanosecond half-cycle electric field pulses in a microwave transmission line. Transition probabilities from ns and nd states, ranging in principal quantum number from 18 to 40, to nearby nl (l\ensuremath{\geqslant}2) states are measured both as a function of pulse amplitude and the delay between two identical temporally spaced pulses. The transition rate depends strongly on both the pulse amplitude and the temporal delay between the two pulses. Nearly 100% of the population can be transferred for certain amplitudes of the half-cycle pulse. Transition probabilities are successfully described both with a dynamic Stark model and direct numerical integration of the time-dependent Schr\"odinger equation. Ramsey interference between two delayed pulses is observed that shows strong-field behavior. The two-pulse experiment is a technique for high-order multiphoton spectroscopy without concern for ac Stark shifts.

DOI
10.1103/physreva.55.3787

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We observe microwave multiphoton transitions in Rydberg states of Na using intense subnanosecond half-cycle electric field pulses in a microwave transmission line. Transition probabilities from ns and nd states, ranging in principal quantum number from 18 to 40, to nearby nl (l\ensuremath{\geqslant}2) states are measured both as a function of pulse amplitude and the delay between two identical temporally spaced pulses. The transition rate depends strongly on both the pulse amplitude and the temporal delay between the two pulses. Nearly 100% of the population can be transferred for certain amplitudes of the half-cycle pulse. Transition probabilities are successfully described both with a dynamic Stark model and direct numerical integration of the time-dependent Schr"odinger equation. Ramsey interference between two delayed pulses is observed that shows strong-field behavior. The two-pulse experiment is a technique for high-order multiphoton spectroscopy without concern for ac Stark shifts.
We observe interference in the resonant microwave multiphoton transition probability between the 21s state and the 19,3 Stark state of K in a static field as a function of the duration and intensity of a microwave pulse at 9 GHz. The 19,3 state adiabatically connects to the 19f state in zero field. The ac Stark effect shifts the 21s state through a multiphoton resonance with the 19,3 Stark state during both the rising and falling edges of the microwave pulse. The transitions that occur during each traversal of the resonance lead to an interference in the net transition probability as a function of the relative phase accumulated by each state during the pulse. We measure both the frequency of the interference oscillations for different detunings from resonance and the amplitude of the fringes for different degrees of pulse asymmetry. The latter results are in complete agreement with the predictions of a Landau-Zener model for the resonance transitions.
A method for quantum interferometry and phase control of degenerate Rydberg states has been proposed and realized experimentally. Phase control was carried out by a pulse of a weak dc electric field which caused a Stark splitting of degenerate Rydberg sublevels for a short time. A strong interference dependence of the probability of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ in sodium Rydberg atoms on a phase difference between the Stark sublevels of the 37P3/2{37P}_{3/2}37P3/2​ state has been detected. Changes in the probability were measured directly by a pulsed resonant microwave radiation applied after the electric-field pulse. Records of the quantum interference signals and Stark spectra of the microwave transition are presented and discussed. An influence of the laboratory magnetic field has been analyzed.
Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.
Ionization of Rydberg atoms by short, half-cycle electrical pulses is investigated experimentally in the intermediate-pulse duration regime where the ionization threshold fields are determined both by the slew rate of the ionizing pulse and its duration. Electrical pulses with durations ranging from 140 ps to 9 ns and amplitudes up to are applied to rubidium and lithium atoms prepared in high Rydberg states by laser excitation (n ranges from 42 to 82). The amplitude of the 140 ps pulse required for ionization of the Rb and Li Rydberg population is found to be a factor of two higher than the expected amplitude based on diabatic field ionization and recent theoretical calculations by Reinhold et al (1993 26 L659). Using the longer pulses we studied the transition from the diabatic/adabatic ionization towards ionization in the impulse-kick regime.
We conduct a systematic investigation of the oscillations of the Rydberg-state populations as a function of intensity arising from strong-field multiphoton excitation of Rydberg atoms. By numerically solving the time-dependent Schrödinger equation and by constructing a quantum model based on Freeman resonances, we elucidate the underlying physical mechanisms governing the intensity-dependent oscillatory behavior of the Rydberg-state population dynamics. Our analysis shows that these oscillations originate from the synergistic interplay of three distinct quantum-interference mechanisms: (1) interference between excitation pathways at the rising and falling edges of the laser pulse (long-time interference), (2) interference between different optical cycles within the same side of the laser pulse (short-time interference), and (3) interference within individual optical cycles (intracycle interference). Additionally, we find that ground-state depletion has varying degrees of influence on the oscillation patterns formed by the three interference mechanisms under different laser-intensity conditions.