Rate and depth of two-axis twisting by pair exchange under the self-Kerr constraint
Abstract
In this paper, we study two bosonic modes that exchange pairs of quanta, which realize two-axis twisting exactly: within a sector of fixed particle number the exchange operator is proportional to the two-axis twisting generator, with a fixed factor of two. Because any real nonlinear medium supplies a local Kerr nonlinearity alongside this operator, the two merge into one twisting Hamiltonian governed by a single dimensionless ratio r=χs/χe of the Kerr strength to the exchange strength. Two conditions then decide how much of the ideal behavior survives this constraint, and they must be met separately. The first concerns speed: the exponential squeezing rate follows in closed form, vanishes exactly at r=±1, and recovers as the square root of the distance from that point. The second concerns depth: the smallest attainable squeezing parameter depends only on the anisotropy of the mean-field saddle, attaining the full two-axis-twisting value at r=0 and r=±3 regardless of the rate, so that settings sharing the same anisotropy but differing twofold in rate reach the same depth. The two conditions address different targets, and a system may squeeze quickly yet terminate at a shallow optimum; only r=0 is optimal in both respects. The closed-form Gaussian solution reveals a further systematic bias: because the early-time decay rate of the variance exceeds twice the exponential rate, a fit to short-time data overestimates the rate by more than a factor of two. Since an isotropic cubic nonlinearity imposes r=1, the value at which the rate vanishes, the two strengths must be mismatched, and a moderate mismatch already restores most of the optimal depth. Finally, the constraint is invisible at low excitation: at two quanta the Kerr term shifts both coupled states equally, so the two Hamiltonians are indistinguishable until four quanta.
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BibTeX
@misc{yu2026rate,
title = {{Rate and depth of two-axis twisting by pair exchange under the self-Kerr constraint}},
author = {Qing Yu and Ying Li and Cuilu Zhai and Shiqing Tang and Wangjun Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15774},
eprint = {2610.15774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15774},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rate and depth of two-axis twisting by pair exchange under the self-Kerr constraint
AU - Qing Yu
AU - Ying Li
AU - Cuilu Zhai
AU - Shiqing Tang
AU - Wangjun Lu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.15774
UR - https://arxiv.org/abs/2610.15774
AB - In this paper, we study two bosonic modes that exchange pairs of quanta, which realize two-axis twisting exactly: within a sector of fixed particle number the exchange operator is proportional to the two-axis twisting generator, with a fixed factor of two. Because any real nonlinear medium supplies a local Kerr nonlinearity alongside this operator, the two merge into one twisting Hamiltonian governed by a single dimensionless ratio r=χ_s/χ_e of the Kerr strength to the exchange strength. Two conditions then decide how much of the ideal behavior survives this constraint, and they must be met separately. The first concerns speed: the exponential squeezing rate follows in closed form, vanishes exactly at r=±1, and recovers as the square root of the distance from that point. The second concerns depth: the smallest attainable squeezing parameter depends only on the anisotropy of the mean-field saddle, attaining the full two-axis-twisting value at r=0 and r=±3 regardless of the rate, so that settings sharing the same anisotropy but differing twofold in rate reach the same depth. The two conditions address different targets, and a system may squeeze quickly yet terminate at a shallow optimum; only r=0 is optimal in both respects. The closed-form Gaussian solution reveals a further systematic bias: because the early-time decay rate of the variance exceeds twice the exponential rate, a fit to short-time data overestimates the rate by more than a factor of two. Since an isotropic cubic nonlinearity imposes r=1, the value at which the rate vanishes, the two strengths must be mismatched, and a moderate mismatch already restores most of the optimal depth. Finally, the constraint is invisible at low excitation: at two quanta the Kerr term shifts both coupled states equally, so the two Hamiltonians are indistinguishable until four quanta.
ER -