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arXiv:2610.12579

Correlated Pair Creation with Positive- and Negative-Frequency Oscillators in a Trapped-Ion Quantum Simulator

Visal So, Mingjian Zhu, Han Pu, Guido Pagano

quant-phcond-mat.quant-gasphysics.atom-phSubmitted Oct 8, 2026• Announced Oct 12, 2026• 0 citations
arXivHTMLPDF

Abstract

Spin-dependent forces enable independent control over the effective frequencies of bosonic motional modes and their coupling strengths to spins in trapped-ion spin-boson quantum simulators. We show that the relative signs of these effective frequencies provide an important programmable resource for engineering distinct multimode dynamics. Focusing on a two-mode quantum Rabi model, changing the frequencies of the two modes from the same sign to opposite signs reorganizes the resonance structure of the spin-mediated bosonic interaction, converting the dominant resonant process from excitation exchange to correlated pair creation. In the dispersive regime, the resulting effective interaction realizes a two-mode parametric amplifier with stable oscillatory, critical, and exponentially amplifying regimes separated by a spin-dependent instability threshold. Across these regimes, the dynamics generate collective-quadrature squeezing and bipartite motional entanglement. Preparing the spin in a coherent superposition further allows different spin components to experience distinct stability regimes, generating tripartite spin-boson entanglement, while spin postselection can coherently combine the conditional bosonic branches to generate non-Gaussian entangled bosonic states. Finally, we outline an implementation using parameters within reach of current trapped-ion platforms.

Comments
14 + 10 pages, 7 + 5 figures, 1 table

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Abstract We propose protocols for the creation of useful entangled states in a system of spins collectively coupled to a bosonic mode, directly applicable to trapped-ion and cavity QED setups. The protocols use coherent manipulations of the resonant spin-boson interactions naturally arising in these systems to prepare spin squeezed states exponentially fast in time. The resonance condition harnesses the full spin-boson coupling and thus avoids the slower timescales when operating in the off-resonance regime. We demonstrate the robustness of the protocols by analyzing the effects of natural sources of decoherence in these systems and show their advantage compared to more standard slower approaches where entanglement is generated with off-resonant spin-boson interactions.
Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on two-dimensional crystal arrays of approximately 100 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and enhance the spin-motion coupling while maintaining spin coherence. With a stroboscopic protocol, we measure $5.4\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.28em}{0ex}}\mathrm{dB}$ of motional squeezing below the ground-state motion, from which theory predicts a 10-dB enhancement in the sensitivity for measuring small displacements using a recently demonstrated protocol [K. A. Gilmore et al., Science 373, 673 (2021)]. With a continuous squeezing protocol, we measure and accurately calibrate the parametric coupling strength. Theory suggests this protocol can be used to improve quantum spin squeezing, limited in our system by off-resonant light scatter. We illustrate numerically the trade-offs between strong parametric amplification and motional dephasing in the form of center-of-mass frequency fluctuations for improving quantum spin squeezing in our setup.
Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins.While native interactions between trapped-ion spins are typically pairwise, many quantum algorithms and quantum spin models naturally feature couplings between triplets, quartets, or higher orders of spins.Here, we formulate and analyze a mechanism that extends the standard Mølmer-Sørensen pairwise entangling gate and generates a controllable and programmable coupling between N spins of trapped ions.We show that spin-dependent optical parametric drives applied at twice the motional frequency generate a coordinate transformation of the collective ion motion in phase space, rendering displacement forces that are nonlinear in the spin operators.We formulate a simple framework that enables a systematic and faithful construction of high-order spin Hamiltonians and gates, including the effect of multiple modes of motion, and characterize the performance of such operations under realistic conditions.
A quantum oscillator always carries vacuum fluctuations, and modulating its parameters converts them into correlated pairs of real quanta. This vacuum amplification underlies squeezed light and Hawking radiation. In a closed quadratic system, pair creation competes with the energy splitting of the modes, and growth turns exponential only once pairing overcomes the splitting. Here we realize this competition in two motional modes of a trapped-ion chain. A two-mode-squeezing drive creates the pairs, and a beam-splitter coupling splits the motion into two coupled modes at different frequencies. The two rates are tuned and calibrated independently. Starting near the motional ground state, we cross the stability boundary in two ways. First, with the drive at the sum of the two bare-mode frequencies, the phonon number stays bounded until the pairing rate exceeds the splitting and grows exponentially beyond it. Second, tuning the drive into resonance with one coupled mode lowers the threshold to zero, and only that mode is amplified into a squeezed vacuum. Separate control of the two interactions makes the threshold for vacuum amplification programmable. This control can be used to simulate particle creation and quantum phase transitions, and to operate parametrically driven bosonic devices close to their stability limit.
Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins. While native interactions between trapped ion spins are typically pairwise, many quantum algorithms and quantum spin models naturally feature couplings between triplets, quartets or higher orders of spins. Here we formulate and analyze a mechanism that extends the standard Mølmer-Sørensen pairwise entangling gate and generates a controllable and programmable coupling between NNN spins of trapped ions. We show that spin-dependent optical forces applied at twice the motional frequency generate a coordinate-transformation of the collective ion motion in phase-space, rendering displacement forces that are nonlinear in the spin operators. We formulate a simple framework that enables a systematic and faithful construction of high-order spin Hamiltonians and gates, including the effect of multiple modes of motion, and characterize the performance of such operations under realistic conditions.