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Journal of Physics B Atomic Molecular and Optical Physics

On the validity of an approximation method for two-colour photodetachment

Edward J. Robinson

Published Oct 14, 1995• 3 citations
Publisher

Abstract

The validity of an approximation method used by Bivona et al. (1984) for two-colour photodetachment is investigated. It is found that while their approach may be valid for some S-matrix elements, in others, contributions neglected in the scheme are much larger than the terms that are retained. In addition, an explanation is suggested for the linear dependence found for the transition probability on final-state energy.

DOI
10.1088/0953-4075/28/19/001

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The validity of an approximation method used by Bivona et al. (1984) for two-colour photodetachment is investigated. It is found that while their approach may be valid for some S-matrix elements, in others, contributions neglected in the scheme are much larger than the terms that are retained. In addition, an explanation is suggested for the linear dependence found for the transition probability on final-state energy.
We show that by using the approximation method of Bivona et al , two-colour photodetachment cross sections are obtained that behave according to the Wigner threshold law even if the dressing effect of the low-frequency radiation field on the bound state is ignored. Within the range of the low frequency and intensity of the radiation field considered, it is found that the values of the cross sections calculated by using the field-free bound state are not significantly modified when the corrections to the wavefunction of the bound state due to the driving action of the low-frequency field are accounted for.
Some many-body theories of optical transitions in solids were examined from projection and population criteria. The results showed that state-independent projection methods cannot be applied to electron systems with non-uniform energy spectra. Moreover, neglecting some important terms in a second-order approximation leads to invalidation of the population criterion. In addition, a valid theory satisfying these two criteria can be obtained using a proper state-dependent projection operator and Kang-Choi reduction identity, and the result can be interpreted using a diagram, which can model the quantum dynamics of electron in solids.
The present Rapid Communication makes two points. (1) The exact matrix elements for the transitions between two hydrogenic states accompanied by the emission or absorption of one photon has been calculated in closed form without resorting to multiple expansions. Thus, retardation is taken into account exactly. (2) In addition to using these exact matrix elements to calculate transition probabilities, one can make estimates of the contribution to second-order processes of these matrix elements. In particular, it can be shown that the total contribution of bound-state matrix elements to the electromagnetic shift of the ground state is finite without renormalization.
This study proposes a scalable pre-processing method that incorporates crosstalk effects in quantum devices, with a focus on mitigating measurement errors. Measurement errors are modeled as a transition probability matrix between ideal and noisy distributions. However, the size of this matrix grows exponentially with the number of qubits, posing a major challenge for large systems. To overcome this, we exploit two empirical observations obtained from experiments on an 8-qubit superconducting quantum device: (i) error correlations are strongly influenced by the topology of the qubit connectivity, and (ii) the mitigated observable exhibits locality, with dominant contributions from low-order terms. Based on these features, we introduce an approximation scheme that restricts attention to observables with limited locality and to qubits within a bounded distance on a device graph. Transition probabilities are efficiently estimated using parallel measurements based on a perfect hash family, reducing the required number of measurements from polynomial to quasi-linear in system size. We validate our approach on a 32-qubit device and demonstrate that it achieves a 50 % reduction in error compared to unmitigated data and a 10 % improvement over a conventional method that neglects crosstalk. Our results highlight the potential of topology-aware, locality-preserving error mitigation for enhancing quantum computations on near-term devices.