Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1703.00251 · Physical Review Letters

Cross-Kerr Nonlinearity for Phonon Counting

Shiqian Ding, Gleb Maslennikov, Roland Hablützel, Dzmitry Matsukevich

Published Nov 8, 2017• 59 citations
arXivHTMLPDF

Abstract

State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions. We spectroscopically resolve the frequency shift of the motional sideband of the first mode due to the presence of single phonons in the second mode and use it to reconstruct the phonon number distribution of the second mode.

DOI
10.1103/physrevlett.119.193602

Related papers

Quantum Parametric Oscillator with Trapped Ions

Shiqian Ding, Gleb Maslennikov, Roland Hablützel +2 more

A strong nonlinear coupling between harmonic oscillators is highly desirable for quantum information processing and quantum simulation, but is difficult to achieve in many physical systems. Here, we exploit the Coulomb interaction between two trapped ions to achieve strong nonlinear coupling between normal modes of motion at the single-phonon level. We experimentally demonstrate phonon up- and down-conversion and apply this coupling to directly measure the parity and Wigner functions of the ions' motional states. Our results represent the fully quantum operation of a degenerate parametric oscillator and hold promise for quantum computation schemes that involve continuous variables.

arXiv:1512.01670•Physical Review Letters•Oct 12, 2017•70 citations

Nonlinear coupling of continuous variables at the single quantum level

Christian F. Roos, Thomas Monz, Kihwan Kim +4 more

We experimentally investigate nonlinear couplings between individual quanta of the vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian $H=\ensuremath{\hbar}\ensuremath{\chi}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{r}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{s}$, where ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{r}$, ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{s}$ are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment over a range of trap frequencies. With $2.97\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ stretch mode and $3.61\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ rocking mode frequencies, we observed a coupling of $20.5\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}∕\mathrm{phonon}$. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.

arXiv:0705.0788•Physical Review A•Apr 29, 2008•75 citations

Quantum parameter estimation of nonlinear coupling in a trilinear Hamiltonian with trapped ions

Peter A. Ivanov

I propose an efficient method for measuring nonlinear 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 nonlinear coupling either by measuring the phonon probability distribution or by directly observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of nonlinear 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 nonlinear 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 state between the two collective modes.

arXiv:2112.12487•Physical Review A•Mar 28, 2022•6 citations

Coherent coupling and non-destructive measurement of trapped-ion mechanical oscillators

Pan‐Yu Hou, Jenny J. Wu, Stephen D. Erickson +10 more

Abstract Coupled harmonic oscillators are ubiquitous in physics and play a prominent role in quantum science. They are a cornerstone of quantum mechanics and quantum field theory, where second quantization relies on harmonic oscillator operators to create and annihilate particles. Descriptions of quantum tunneling, beamsplitters, coupled potential wells, ``hopping terms'', decoherence, and many other phenomena rely on coupled harmonic oscillators. However, the ability to couple separate quantum harmonic oscillators directly, with coupling rates that substantially exceed decoherence rates, has remained elusive. Here, we realize high-fidelity coherent exchange of single motional quanta between harmonic oscillators -- in this case, spectrally separated harmonic modes of motion of a trapped ion crystal -- where the timing, strength, and phase of the coupling are controlled through an oscillating electric potential with suitable spatial variation. The coupling rate can be made much larger than the decoherence rates, enabling demonstrations of high-fidelity quantum state transfer, entanglement of motional modes, and Hong-Ou-Mandel-type interference. We also project a harmonic oscillator into its ground state by measurement and preserve that state during repetitions of the projective measurement, an important prerequisite for non-destructive syndrome measurement in continuous-variable quantum error correction. Controllable coupling between harmonic oscillators has potential applications in quantum information processing with continuous variables, quantum simulation, and precision measurements. It can also enable cooling and quantum logic spectroscopy involving motional modes of trapped ions that are not directly accessible.

arXiv:2205.14841•Nature Physics•Jul 29, 2024•22 citations

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

Marion Mallweger, Milena Guevara-Bertsch, Boyan T. Torosov +7 more

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

arXiv:2402.10041•Physical Review A•Nov 7, 2024•7 citations

Measure of phonon-number moments and motional quadratures through infinitesimal-time probing of trapped ions

Thierry Bastin, von Zanthier, J., Solano, E.

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.

•Jan 1, 2006•8 citations
State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions. We spectroscopically resolve the frequency shift of the motional sideband of the first mode due to the presence of single phonons in the second mode and use it to reconstruct the phonon number distribution of the second mode.
A strong nonlinear coupling between harmonic oscillators is highly desirable for quantum information processing and quantum simulation, but is difficult to achieve in many physical systems. Here, we exploit the Coulomb interaction between two trapped ions to achieve strong nonlinear coupling between normal modes of motion at the single-phonon level. We experimentally demonstrate phonon up- and down-conversion and apply this coupling to directly measure the parity and Wigner functions of the ions' motional states. Our results represent the fully quantum operation of a degenerate parametric oscillator and hold promise for quantum computation schemes that involve continuous variables.
We experimentally investigate nonlinear couplings between individual quanta of the vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian $H=\ensuremath{\hbar}\ensuremath{\chi}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{r}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{s}$, where ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{r}$, ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{s}$ are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment over a range of trap frequencies. With 2.97MHz2.97\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}2.97MHz stretch mode and 3.61MHz3.61\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}3.61MHz rocking mode frequencies, we observed a coupling of 20.5Hz∕phonon20.5\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}∕\mathrm{phonon}20.5Hz∕phonon. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed.
I propose an efficient method for measuring nonlinear 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 nonlinear coupling either by measuring the phonon probability distribution or by directly observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of nonlinear 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 nonlinear 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 state between the two collective modes.
Abstract Coupled harmonic oscillators are ubiquitous in physics and play a prominent role in quantum science. They are a cornerstone of quantum mechanics and quantum field theory, where second quantization relies on harmonic oscillator operators to create and annihilate particles. Descriptions of quantum tunneling, beamsplitters, coupled potential wells, ``hopping terms'', decoherence, and many other phenomena rely on coupled harmonic oscillators. However, the ability to couple separate quantum harmonic oscillators directly, with coupling rates that substantially exceed decoherence rates, has remained elusive. Here, we realize high-fidelity coherent exchange of single motional quanta between harmonic oscillators -- in this case, spectrally separated harmonic modes of motion of a trapped ion crystal -- where the timing, strength, and phase of the coupling are controlled through an oscillating electric potential with suitable spatial variation. The coupling rate can be made much larger than the decoherence rates, enabling demonstrations of high-fidelity quantum state transfer, entanglement of motional modes, and Hong-Ou-Mandel-type interference. We also project a harmonic oscillator into its ground state by measurement and preserve that state during repetitions of the projective measurement, an important prerequisite for non-destructive syndrome measurement in continuous-variable quantum error correction. Controllable coupling between harmonic oscillators has potential applications in quantum information processing with continuous variables, quantum simulation, and precision measurements. It can also enable cooling and quantum logic spectroscopy involving motional modes of trapped ions that are not directly accessible.
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
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.