Broadening of the drumhead mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap

Abstract

Two-dimensional crystals of ions stored in Penning traps are a leading platform for quantum simulation and sensing experiments. For small amplitudes, the out-of-plane motion of such crystals can be described by a discrete set of normal modes called the drumhead modes, which can be used to implement a range of quantum information protocols. However, experimental observations of crystals with Doppler-cooled and even near-ground-state-cooled drumhead modes reveal an unresolved drumhead mode spectrum. In this work, we establish in-plane thermal fluctuations in ion positions as a major contributor to the broadening of the drumhead mode spectrum. In the process, we demonstrate how the confining magnetic field leads to unconventional in-plane normal modes, whose average potential and kinetic energies are not equal. This property, in turn, has implications for the sampling procedure required to choose the in-plane initial conditions for molecular dynamics simulations. For current operating conditions of the NIST Penning trap, our study suggests that the two dimensional crystals produced in this trap undergo in-plane potential energy fluctuations of the order of $10$ mK. Our study therefore motivates the need for designing improved techniques to cool the in-plane degrees of freedom.

arXiv comment17 pages, 10 figures

References in corpus (22)

• Quantum metrology with nonclassical states of atomic ensembles
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Measuring the scrambling of quantum information
• Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition
• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Near ground-state cooling of two-dimensional trapped-ion crystals with more than 100 ions
• Amplitude sensing below the zero-point fluctuations with a two-dimensional trapped-ion mechanical oscillator
• Spectroscopy and Thermometry of Drumhead Modes in a Mesoscopic Trapped-Ion Crystal using Entanglement
• Theory of robust multi-qubit non-adiabatic gates for trapped-ions
• Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment
• Phonon mediated quantum spin simulator employing a planar ionic crystal in a Penning trap
• Scalable arrays of micro-Penning traps for quantum computing and simulation
• Spin Dephasing as a Probe of Mode Temperature, Motional State Distributions, and Heating Rates in a 2D Ion Crystal
• Controlling the potential landscape and normal modes of ion Coulomb crystals by a standing wave optical potential
• Sideband cooling of the radial modes of motion of a single ion in a Penning trap
• Site-resolved imaging of beryllium ion crystals in a high-optical-access Penning trap with inbore optomechanics
• Perpendicular laser cooling with a rotating wall potential in a Penning trap
• Doppler Cooled Ions in a Compact, Reconfigurable Penning Trap
• Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals
• First principle simulation of ultra-cold ion crystals in a Penning trap with Doppler cooling and a rotating wall potential

Cited by in corpus (14)

• Quantum-enhanced sensing of displacements and electric fields with large trapped-ion crystals
• The physics and applications of strongly coupled plasmas levitated in electrodynamic traps
• Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals
• Finite temperature spectrum at the symmetry-breaking linear-zigzag transition
• Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals
• Bilayer crystals of trapped ions for quantum information processing
• Individual-Ion Addressing and Readout in a Penning Trap
• Equilibration of the planar modes of ultracold two dimensional ion crystals in a Penning trap
• Rapid cooling of the in-plane motion of two-dimensional ion crystals in a Penning trap to millikelvin temperatures
• In-situ-tunable spin-spin interactions in a Penning trap with in-bore optomechanics
• Numerical Simulations of 3D Ion Crystal Dynamics in a Penning Trap using the Fast Multipole Method
• Adiabatic Cooling of Planar Motion in a Penning Trap Ion Crystal to Sub-Millikelvin Temperatures
• Parametric Amplification of Spin-Motion Coupling in Three-Dimensional Trapped-Ion Crystals
• Efficient Three-Dimensional Sub-Doppler Cooling of ${}^{40}$Ca${}^{+}$ in a Penning Trap