Phonon-phonon interactions due to non-linear effects in a linear ion trap

Abstract

We examine in detail the theory of the intrinsic non-linearities in the dynamics of trapped ions due to the Coulomb interaction. In particular the possibility of mode-mode coupling, which can be a source of decoherence in trapped ion quantum computation, or, alternatively, can be exploited for parametric down-conversion of phonons, is discussed and conditions under which such coupling is possible are derived.

25 pages, 4 figures

Cited by in corpus (57)

• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Quantum absorption refrigerator with trapped ions
• Trapped ion quantum computation with transverse phonon modes
• Quantum thermal absorption machines: refrigerators, engines and clocks
• Multiple membrane cavity optomechanics
• EIT ground-state cooling of long ion strings
• Normal modes of trapped ions in the presence of anharmonic trap potentials
• Trapped ions in optical lattices for probing oscillator chain models
• Quantum Engines and Refrigerators
• Quantum non-demolition state detection and spectroscopy of single trapped molecules
• Nonlinear coupling of continuous variables at the single quantum level
• A quantum parametric oscillator with trapped ions
• Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal
• Cross-Kerr nonlinearity for phonon counting
• A single-ion nonlinear mechanical oscillator
• Theory of Cross Phase Modulation for the Vibrational Modes of Trapped Ions
• Structure, dynamics and bifurcations of discrete solitons in trapped ion crystals
• Quantum computation and simulation with vibrational modes of trapped ions
• Phonon mediated quantum spin simulator employing a planar ionic crystal in a Penning trap
• Entanglement and Quantum Noise Due to a Thermal Bosonic Field
• Tuning heat transport in trapped-ion chains across a structural phase transition
• Quantum Simulations with a Trilinear Hamiltonian
• Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions
• Coherent rotations of qubits within a multi-species ion-trap quantum computer
• Finite temperature spectrum at the symmetry-breaking linear-zigzag transition
• Two-dimensional spectroscopy for the study of ion Coulomb crystals
• Quantum Thermometry with Trapped Ions
• Exact calculation of phonon effects on spin squeezing
• Motional heating of spatially extended ion crystals
• Practical Entanglement Estimation for Spin-System Quantum Simulators
• Quantum nanofriction in trapped ion chains with a topological defect
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Relationship between the transverse-field Ising model and the XY model via the rotating-wave approximation
• First principle simulation of ultra-cold ion crystals in a Penning trap with Doppler cooling and a rotating wall potential
• Catching, trapping and in-situ-identification of thorium ions inside Coulomb crystals of ${}^{40}$Ca${}^{+}$ ions
• Toward hybrid quantum simulations with qubits and qumodes on trapped-ion platforms
• Intrinsic anharmonic effects on the phonon frequencies and effective spin-spin interactions in a quantum simulator made from trapped ions in a linear Paul trap
• Theoretical basis for quantum simulation with a planar ionic crystal in a Penning trap using a triangular rotating wall
• Entanglement growth via splitting of a few thermal quanta
• Single-shot measurements of phonon number states using the Autler-Townes effect
• Linear Mode-Mixing of Phonons with Trapped Ions
• Sculpting bosonic states with arithmetic subtractions
• Bespoke Pulse Design for Robust Rapid Two-Qubit Gates with Trapped Ions
• Interaction graph engineering in trapped-ion quantum simulators with global drives
• Quantum parameter estimation of nonlinear coupling in trilinear Hamiltonian with trapped ions
• Dynamics of quantum discommensurations in the Frenkel-Kontorova chain
• Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap based quantum simulator
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• Adiabatically controlled motional states of a ground-state cooled CaO${}^{+}$ and Ca${}^{+}$ trapped ion chain
• Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature
• The role of higher-order terms in trapped-ion quantum computing with magnetic gradient induced coupling
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Quantum computing architecture with Rydberg gates in trapped ions
• Entanglement across sliding-pinned transition of ion chains in optical cavities
• Laser-free method for creation of two-mode squeezed state and beam-splitter transformation with trapped ions
• Doubling Qubits in a Trapped-Ion System via Vibrational Dual-Rail Encoding