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arXiv:2403.14017

Linearized analysis of dissipative Two Axis Counter Twisting (TACT) squeezing for Metrology

Garry Goldstein

Published Mar 20, 2024• 0 citations
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Abstract

In this work we analyze two axis twisting in the presence of depolarizing channel dissipation. We find that spin squeezing is only possible if the dissipation is parametrically weaker than the squeezing coupling. Squeezing may be used for meteorologically useful decrease of spin noise but only in the case where the squeezing occurs before measurement, in the case one squeezes as one measures one also squeezes the signal thereby making spin squeezing ineffective for metrological gain. The key mathematical advance made in this work is the observation that TACT in the presence of depolarizing noise is equivalent to TACT with reduced polarization and no noise. We find an exponential gain in signal to noise with the exponent proportional to the ratio between the squeezing strength and the depolarization rate.

DOI
10.48550/arxiv.2403.14017

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In this work we analyze two axis twisting in the presence of depolarizing channel dissipation. We find that spin squeezing is only possible if the dissipation is parametrically weaker than the squeezing coupling. Squeezing may be used for meteorologically useful decrease of spin noise but only in the case where the squeezing occurs before measurement, in the case one squeezes as one measures one also squeezes the signal thereby making spin squeezing ineffective for metrological gain. The key mathematical advance made in this work is the observation that TACT in the presence of depolarizing noise is equivalent to TACT with reduced polarization and no noise. We find an exponential gain in signal to noise with the exponent proportional to the ratio between the squeezing strength and the depolarization rate.
Squeezed spin states possess unique quantum correlation or entanglement and are significantly promising for advancing quantum information processing and quantum metrology. In recent back-to-back publications [C. Gross et al., Nature (London) 464, 1165 (2010) and Max F. Riedel et al., Nature (London) 464, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at -8.2 and -2.5 dB, respectively, in two-component atomic condensates exhibiting one-axis-twisting interactions. The noise reduction limit for the one-axis twisting scales as ∝1/N(2/3), which for a condensate with N∼10(3) atoms is about 100 times below the standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the one-axis-twisting spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction ∝1/N or an extra tenfold improvement for N∼10(3).
In this work we study One Axis Twisting (OAT) spin squeezing for metrology in the presence of decoherence. We study Linbladian evolution in the presence of both T_1 and T_2 (longitudinal and transverse relaxation processes). We show that spin squeezing can be an effective way to improve metrological accuracy even in the presence of decoherence for OAT squeezing. We show our results are not sensitive to inhomogeneity of the squeezing strength of the many spin OAT Hamiltonian and that very general squeezed states do not have entanglement enhanced decoherence. We also extend the Kitagawa-Ueda OAT squeezing formula to finite polarization.
Spin squeezing can increase the sensitivity of interferometric measurements of small signals in large spin ensembles beyond the standard quantum limit. In many practical settings, the ideal metrological gain is limited by imperfect readout of the sensor. To overcome this issue, protocols based on time reversal of unitary one-axis-twist (OAT) spin-squeezing dynamics have been proposed. Such protocols mitigate readout noise and, when implemented using cavity feedback, have been argued to also be robust against dissipation as long as the collective cooperativity of the system is sufficiently large [Davis et al., Phys. Rev. Lett. 116, 053601 (2016)]. Here, we perform a careful systematic study of dissipative effects on three different implementations of a OAT twist-untwist sensing scheme (based on symmetric as well as asymmetric cavity feedback and on a Tavis-Cummings interaction). Our full treatment shows that the three approaches have markedly different properties and resilience when subject to dissipation. Moreover, the metrological gain for an implementation using symmetric cavity feedback is more sensitive to undesired dissipation than was previously appreciated.
We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state ∣θ0,ϕ0⟩|\theta_{0}, \phi_0\rangle∣θ0​,ϕ0​⟩ with the polar angle θ0=π/2\theta_0=\pi/2θ0​=π/2. If the dephasing rate γ≪S−1/3\gamma\ll S^{-1/3}γ≪S−1/3, where SSS is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely ξ2∝S−2/3\xi^2\propto S^{-2/3}ξ2∝S−2/3. While for a moderate dephasing, the achievable squeezing obeys the power rule S−2/5S^{-2/5}S−2/5, which is slightly worse than the ideal case. When the dephasing rate γ>S1/2\gamma>S^{1/2}γ>S1/2, we show that the squeezing is weak and neglectable.
Squeezed spin states have important applications in quantum metrology and sensing. It has been shown by S\o{}rensen and M\o{}lmer [Phys. Rev. A 66, 022314 (2002)] that an effective one-axis-twisting interaction can be realized in a cavity setup via a double off-resonance stimulated Raman scattering, resulting in a noise reduction scaling $\ensuremath{\propto}1/{N}^{2/3}$ with NNN being the atom number. Here, we show that, by making an appropriate change of the initial input spin state, it is possible to produce a one-axis-twisting spin squeezing via a single off-resonance stimulated Raman scattering, which thus can greatly simplify the realistic implementation. We also show that the one-axis-twisting interaction can be transformed into a more efficient two-axis-twisting interaction by rotating the collective spin while coupling to the cavity, yielding a Heisenberg limited noise reduction $\ensuremath{\propto}1/N$. Considering the noise effects due to atomic decoherence and cavity decay, we find that substantial squeezing is still attainable with current laboratory techniques.