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Reconstructing the phonon distribution of trapped ions out of the Lamb-Dicke regime
Christophe H. Valahu, Prachi Nagpal, Teerawat Chalermpusitarak, Maverick J. Millican, Cameron McGarry, Frank Scuccimarra, Vassili G. Matsos, Hon-Kwan Chan, Ting Rei Tan·September 21, 2026
Quantum Physics
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Abstract
Characterizing the phonon distribution of trapped-ion motional states is essential for many applications in quantum information processing, but existing methods become ill-conditioned beyond the Lamb-Dicke regime. We overcome this limitation by recasting phonon-state reconstruction as a filter-function inversion problem. Using composite pulses on the carrier and multiple sidebands, we engineer well-conditioned filters in phonon space to characterize pure and mixed states, study heating dynamics, and reconstruct Fock states up to $n=250$.