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arXiv:2402.10041 · Physical Review A

Motional-state analysis of a trapped ion by ultranarrowband composite pulses

Marion Mallweger, Milena Guevara-Bertsch, Boyan T. Torosov, Robin Thomm, Natalia Kuk, Harry Parke, Christian F. Roos, Gerard T. Higgins, Markus Hennrich, Nikolay V. Vitanov

Published Nov 7, 2024• 7 citations
arXivHTMLPDF

Abstract

In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultranarrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence. Published by the American Physical Society 2024

DOI
10.1103/physreva.110.053103

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In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultranarrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence. Published by the American Physical Society 2024
The measurement of phonon numbers in laser-cooled ions is pivotal for determining whether an ion is in its ground state. Commonly employed experimental techniques include the analysis of red-to-blue sideband ratios and the adiabatic evolution on the red-sideband transition. We introduce a theoretical approach utilizing composite pulses that enables the direct measurement of the population in a specific Fock state, eliminating the need for state evolution fitting. This method offers a more straightforward quantification of higher Fock state populations compared to the red-sideband adiabatic evolution technique. By applying quantum optimal control strategies, we enhance the fidelity of the unitary operations executed by the composite pulses. By utilizing numerical calculation methods of quantum optimal control, we have overcome the limitations of analytical calculations that require weak coupling and first-order Lamb-Dicke expansion, allowing our method to achieve sufficient accuracy in strong coupling regime. Furthermore, we also present a data processing method that allows the estimated value of the phonon number to be closer to the true value. An illustrative example of its efficacy in high Fock state measurement is provided.
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime.It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time τ = 0.In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction times, remaining thus insensitive to decoherence processes.
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=250n=250n=250.
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime. It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time t=0. In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction times, remaining thus insensitive to decoherence processes.
Efficient preparation and detection of the motional state of trapped ions is important in many experiments ranging from quantum computation to precision spectroscopy. We investigate the stimulated Raman adiabatic passage (STIRAP) technique for the manipulation of motional states in a trapped ion system. The presented technique uses a Raman coupling between two hyperfine ground states in 25 Mg + , implemented with delayed pulses, which removes a single phonon independent of the initial motional state. We show that for a thermal probability distribution of motional states the STIRAP population transfer is more efficient than a stimulated Raman Rabi pulse on a motional sideband. In contrast to previous implementations, a large detuning of more than 200 times the natural linewidth of the transition is used. This approach renders STIRAP suitable for atoms in which resonant laser fields would populate nearby fluorescing excited states and thus impede the STIRAP process. We use the technique to measure the wavefunction overlap of excited motional states with the motional ground state. This is an important application for force sensing applications using trapped ions, such as photon recoil spectroscopy, in which the signal is proportional to the depletion of motional ground state population. Furthermore, a determination of the ground state population enables a simple measurement of the ion's temperature.
Trapped ion systems are at the forefront of the development of various forms of quantum technology. Continuing to improve and establish new devices and techniques for the control of trapped ions is a vital element of ongoing research. In this thesis, a range of experiments which aim to expand the quantum toolkit of trapped ion systems are presented. These results primarily focus on the control and detection of bound motional states of a single trapped 88Sr+ ion for the purposes of quantum simulation and computation. We demonstrate how the interference between motional modes can reveal an interesting new interpretation of the mechanism behind light-matter interaction and introduce two separate techniques for the detection of motional states, based on the Autler-Townes effect and the use of composite pulses respectively. Additionally, we introduce a novel method to perform micromotion compensation and build upon previous works studying the effects of trapping electric fields on a single trapped Rydberg ion, observing the second-order quadrupolar response of the ion with a highly precise sensitivity.