Quantum parameter estimation of nonlinear coupling in trilinear Hamiltonian with trapped ions
arXiv:2112.12487 · doi:10.1103/PhysRevA.105.032617
Abstract
I propose an efficient method for measuring non-linear coupling between the collective axial breathing mode and the radial rocking mode induced by the mutual Coulomb repulsion in linear ion crystal. The quantum sensing technique is based on the laser induced coupling between one of the vibrational modes and the internal ion's spin states which allows to estimate the non-linear coupling either by measuring the phonon probability distribution or directly be observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of non-linear phonon coupling the off-resonance interaction between the ion spin states and the axial breathing mode leads to spin-dependent phonon squeezing of the radial rocking mode. Thus the non-linear coupling can be estimated by measuring population distribution of the motional squeezed state. Furthermore, I show that the off-resonance interaction between the spin and the radial rocking mode creates a spin-dependent beam splitter operation between the two vibrational modes. Thus, the parameter estimation can be carried out by detecting the ion spin populations. Finally, I show that the measurement uncertainty precision can reach the Heisenberg limit by using an entangled states between the two collective modes.
arXiv comment7 pages, 4 figures
References in corpus (28)
- Quantum sensing
- Quantum metrology with nonclassical states of atomic ensembles
- Quantum computing with trapped ions
- Quantum dynamics of cold trapped ions, with application to quantum computation
- Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement
- Quantum absorption refrigerator with trapped ions
- Trapped-ion quantum logic gates based on oscillating magnetic fields
- Quantum-enhanced sensing of displacements and electric fields with large trapped-ion crystals
- Quantum amplification of mechanical oscillator motion
- Ultrasensitive force and displacement detection using trapped ions
- Absolute frequency measurement of the 40Ca+ S1/2 - D5/2 clock transition
- Quantum simulation of the quantum Rabi model in a trapped ion
- EIT ground-state cooling of long ion strings
- Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions
- Ultrasensitive Magnetometer Using a Single Atom
- Phonon-phonon interactions due to non-linear effects in a linear ion trap
- Measurement of the magnetic interaction between two electrons
- Nonlinear coupling of continuous variables at the single quantum level
- A quantum parametric oscillator with trapped ions
- Entanglement-based dc magnetometry with separated ions
- Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
- Hybrid quantum computation gate with trapped ion system
- Cross-Kerr nonlinearity for phonon counting
- Quantum Lock-in Force Sensing using Optical Clock Doppler Velocimetry
- Theory of Cross Phase Modulation for the Vibrational Modes of Trapped Ions
- One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons
- Quantum Simulations with a Trilinear Hamiltonian
- Adiabatic Sensing Technique for Optimal Temperature Estimation using Trapped Ions