Quantum Trick Boosts Measurement Accuracy by Cancelling Out Signal Interference

Scientists are continually seeking methods to enhance the precision of metrology, and recent work demonstrates a novel approach utilising quantum entanglement to surpass conventional limitations. Jihao Ma, Jiahao Huang (from the Institute of Quantum Precision Measurement, State Key Laboratory of Radio Frequency Heterogeneous Integration, College of Physics and Optoelectronic Engineering, Shenzhen University), and Chaohong Lee et al. present a new scheme employing alternating in-phase and quadrature modulation (AIQM) to mitigate the detrimental effects of nonlinear interactions which typically hinder signal accumulation in entanglement-enhanced metrology. This research is significant because it achieves improved metrological performance, especially under conditions of strong nonlinearity and extended signal accumulation, without requiring active control of these interactions. By strategically eliminating and then utilising nonlinear effects, the AIQM scheme offers a pathway towards robust, high-precision quantum measurements.

Mitigating nonlinear interactions for enhanced quantum measurement precision

Scientists have developed a new technique to enhance the precision of quantum measurements beyond conventional limitations. This breakthrough centres on a method for suppressing detrimental nonlinear interactions that typically hinder the performance of entanglement-enhanced quantum metrology. The research introduces an alternating in-phase and quadrature modulation (AIQM) scheme, designed to operate under a fixed nonlinear interaction, thereby eliminating its adverse effects during signal accumulation.
By selectively eliminating and utilising these interactions, the study enables high-precision and high-accuracy sensing without requiring complex active control of the nonlinear interaction itself. The work addresses a central challenge in quantum metrology, where nonlinear interactions, while essential for generating entanglement, often degrade precision during the crucial signal accumulation phase.

Conventional approaches demand precise control, activation, deactivation, and reversal, of these interactions, a task that proves experimentally demanding. This new AIQM scheme circumvents this need by sequentially applying in-phase and quadrature driving fields, effectively cancelling the impact of nonlinear interactions on signal accumulation.
The time-interleaved approach demonstrates improved metrological performance, particularly under strong nonlinear interaction and prolonged signal accumulation, exhibiting pronounced robustness against parameter variations. Researchers propose the AIQM protocol to suppress the one-axis twisting (OAT) interaction during signal accumulation in entanglement-enhanced quantum metrology.

By periodically alternating between in-phase and quadrature driving fields, the protocol suppresses the detrimental effects of the OAT interaction. The AIQM scheme exhibits enhanced performance under strong OAT and long accumulation times, alongside robustness to parameter variations. Furthermore, the AIQM can be used for both entanglement preparation and interaction-based readout, presenting a full-stage protocol that outperforms conventional methods and demonstrates strong robustness against detection noise.

This advancement introduces a protocol that advances quantum metrology without requiring control of the nonlinear interaction, opening a door to high-precision, detection-noise-robust sensing in interacting multiparticle quantum systems. The study considers a general OAT system for N interacting identical particles occupying two distinct energy levels, mathematically characterised by a collective spin vector.

An arbitrary state can be expressed as |ψ⟩= PJ m=−J Cn|J, m⟩, where the Dicke states |J, m⟩ satisfy J2|J, m⟩= J(J +1)|J, m⟩and Jz|J, m⟩= m|J, m⟩ with m = −J, −J + 1, ., +J. The system is driven by an in-phase field DI(t) = ΩI cos [(ωc + ωm)t] + ΩI cos [(ωc −ωm)t] and a quadrature field DQ(t) = −ΩQ sin [(ωc + ωm)t] −ΩQ sin [(ωc −ωm)t], where ωc is the carrier frequency, ωm is the modulation frequency, and ΩI and ΩQ are the respective Rabi frequencies.

Selective elimination of nonlinear interactions via alternating in-phase and quadrature modulation

An alternating in-phase and quadrature modulation (AIQM) scheme was developed to enhance measurement precision beyond the standard quantum limit. This technique addresses the detrimental effects of nonlinear interaction during signal accumulation by sequentially applying in-phase and quadrature driving fields.

The AIQM scheme operates under a fixed nonlinear interaction, eliminating its impact on signal accumulation through a time-interleaved approach. The research employed a methodology focused on selectively eliminating and utilizing nonlinear interactions via AIQM, enabling high-precision and high-accuracy entanglement enhancement without active control of the nonlinear interaction.

Performance was assessed by comparing estimation precision, denoted as ∆ω0, under AIQM with conventional schemes, particularly under strong nonlinear interaction and prolonged signal accumulation times. Results demonstrate that AIQM achieves superior metrological performance, exhibiting pronounced robustness against parameter variations.

To further investigate robustness, the study examined the estimation precision under varying modulation frequency ωm, the ratio of Rabi frequencies Ω/ωm, and the phase α in the second period. Increasing ωm caused the rescaled estimation precision to converge towards values obtained from an effective time-independent Hamiltonian, indicating efficient suppression of the nonlinear interaction when ωm/(2πNχ) exceeded 5, where N is the particle number and χ represents the interaction strength.

Analysis of the ratio Ω/ωm revealed that AIQM maintained estimation precision better than the standard quantum limit over the interval Ω/ωm ∈[0.62, 0.87]. The full-stage AIQM protocol integrates entanglement preparation, signal accumulation, and interaction-based readout. Initially, a spin-coherent state along the z-axis was prepared, followed by the generation of a spin-squeezed state using effective time-dependent Hamiltonians.

A rotation UR was then applied to prepare an entangled state along the x-axis, minimizing squeezing along the y-axis, before signal accumulation using the effective Hamiltonian. Subsequent rotations U†R and UR′ facilitated encoding and recovery of the signal, ultimately leading to a significant displacement for enhanced detection.

AIQM protocol delivers sub-SQL precision in frequency estimation with suppressed off-axis transverse interaction

Estimation precision reached below the standard quantum limit (SQL) through an alternating in-phase and quadrature modulation (AIQM) scheme. This work demonstrates improved metrological performance, particularly under strong nonlinear interaction and prolonged signal accumulation, achieving robustness against parameter variations.

The study successfully suppresses the off-axis transverse (OAT) interaction, enabling high-precision and high-accuracy entanglement-enhanced measurements without active control of the nonlinear interaction. Calculations of the population imbalance uncertainty, ∆Jz, revealed strong suppression when employing the AIQM protocol.

This suppression yielded a high precision ∆ω0, demonstrably below the SQL, as confirmed by numerical results aligning with analytical predictions based on an effective Hamiltonian. Analysis of the estimation precision ∆ω0 against rescaled signal accumulation time χts showed that without AIQM, precision initially decreased before increasing due to detrimental OAT effects.

Conversely, with AIQM, estimation precision decreased monotonically with ∆ω0 proportional to 1/(χts), consistently remaining better than the SQL. This indicates the potential to utilize signal accumulation time as a scalable resource for enhancing measurement sensitivity by efficiently suppressing the OAT interaction.

Examining the dependence of ∆ω0 on interaction strength χ for accumulation times of ts = 0.01δ−1 and ts = 0.1δ−1, the research found that without AIQM, ∆ω0 increased with χ. However, under AIQM, ∆ω0 remained unchanged across all χ values, demonstrating robustness even with strong interaction. Even with weak OAT interaction, long accumulation times degraded precision in the absence of AIQM, while the AIQM scheme maintained high estimation precision.

Further analysis revealed that the AIQM scheme efficiently suppresses the OAT interaction when the modulation frequency ωm exceeds 2π × 5Nχ, enhancing estimation precision. Over the interval Ω/ωm ∈[0.62, 0.87], the estimation precision under AIQM remained superior to the SQL. The study also demonstrated that the AIQM protocol maintains high estimation precision across a phase range of α/π ∈[0.28, 0.72]. Finally, the full-stage AIQM protocol, combining entanglement preparation, signal accumulation, and interaction-based readout, showed precision scaling with the particle number N, indicating potential for further enhancement.

Mitigating nonlinearities improves precision in extended quantum metrology

Scientists have developed an alternating in-phase and quadrature modulation (AIQM) scheme to enhance the precision of quantum metrology, surpassing the standard quantum limit. This new approach effectively mitigates the detrimental effects of nonlinear interactions that typically hinder measurement accuracy during signal accumulation.

By sequentially applying in-phase and quadrature driving fields, the AIQM scheme eliminates the impact of these nonlinear interactions without requiring active control over them. The research demonstrates improved metrological performance, particularly under conditions of strong nonlinear interaction and extended signal accumulation times, alongside notable robustness against variations in control parameters.

Experiments indicate that the AIQM protocol consistently outperforms conventional methods, approaching the Heisenberg scaling limit for precision and maintaining accuracy even with increased detection noise. The authors acknowledge that the scheme’s performance is contingent upon specific experimental parameters and system characteristics.

Furthermore, the periodic modulations inherent in AIQM extend beyond metrology, offering potential applications in versatile Floquet engineering for quantum manipulation and providing a means to investigate complex quantum phenomena like out-of-time-order correlations. The AIQM protocol is readily implementable across diverse experimental platforms, including Bose-condensed atoms, cavity-QED systems, and trapped ions, with analysis confirming that required parameters are currently achievable. This work therefore establishes a pathway towards high-precision, noise-resilient quantum metrology without the need for complex nonlinear interaction control, and opens avenues for exploration in broader areas of quantum information science.