We show that a bimodal squeezed state leads to optimal precision in the estimation of loss, overcoming challenges in producing and detecting high photon number Fock states. Using a time-reversal procedure provides a precise estimation that approaches the bound for weak absorption.
Quantum estimation of parameters defining open-system dynamics may be enhanced by using ancillas that are entangled with the probe but are not submitted to the dynamics. Here we consider the important problem of estimation of transmission of light by a sample, with losses due to absorption and scattering. We show, through the determination of the quantum Fisher information, that the ancilla strategy leads to the best possible precision in single-mode estimation—the one obtained for a Fock-state input—through joint photon counting of probe and ancilla, which are modes of a bimodal squeezed state produced by an optical parametric amplifier. This proposal overcomes the challenge of producing and detecting high-photon-number Fock states, and it is quite robust in the presence of additional noise: We show that it is immune to phase noise and the precision does not change if the incoming state gets disentangled. Furthermore, the quantum gain is still present under moderate photon losses of the input beams. We also discuss an alternative to joint photon counting, which is readily implementable with present technology and approaches the quantum Fisher information result for weak absorption, even with moderate photon losses of the input beams before the sample is probed: a time-reversal procedure, placing the sample between two optical parametric amplifiers, with the second undoing the squeezing produced by the first one. The precision of estimation of the loss parameter is obtained from the average outgoing total photon number and its variance. In both procedures, the state of the probe and the detection procedure are independent of the value of the parameter. Published by the American Physical Society 2024
Absorption and gain processes are fundamental to any light-matter interaction and a precise measurement of these parameters is important for various scientific and technological applications. Quantum probes, specifically the squeezed states, have proved very successful, particularly in the applications that deal with phase shift and force measurements. In this paper, we focus on improving the sensitivity of the estimation of the photon-loss coefficient of a weakly absorbing medium as well as the estimation of the gain parameter using a two-mode bright squeezed state. The generation of this state combines the advantage of a coherent beam for its large photon number with the quantum properties of the two-mode squeezing operation in an optical parametric amplifier. We present two measurement schemes: balanced photodetection and time-reversed metrology, both utilizing two-mode bright squeezed light. The maximum quantum advantage we can achieve using two-mode bright squeezed light is 3.7 times for the absorption parameter $\ensuremath{\alpha}=0.05$ and 8.4 times for $\ensuremath{\alpha}=0.01$ as compared to using only the coherent state. Similarly, the maximum quantum advantage for the estimation of optical gain is found around 2.95 times for the gain coefficient G=1.05 and around 6.35 times for G=1.01. We discuss the significance of using one measurement scheme over the other under different squeezing conditions. We compare our results with the Cram\'er-Rao bound for a two-mode bright squeezed state to assess the quality of the proposed methodologies.
It is now well appreciated that quantum physics can be used to build better sensors. Such sensors can be based on unitary systems [1,2] like interferometers or open systems based on scattering and lossy transmission channels [3-5]. The framework of the quantum Fisher information enables one to obtain best estimates of the parameters and then one can design possible experiments that can reach Cramer- Rao bounds. I would bring out not only the importance of the quantum states used as probes, but also the importance of the ‘quantum’ measurement schemes especially the ones that depend on time reversed arrangements. I would illustrate the great usefulness of squeezed states of matter and light for metrology. [1] S. C. Burd et al., Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019). [2] G. S. Agarwal, and L. Davidovich, Quantifying quantum-amplified metrology via Fisher information, Phys. Rev. Res. 4, L 012014 (2022). [3] J. Wang, L. Davidovich, and G. S. Agarwal, Quantum sensing of open systems: Estimation of damping constants and temperature, Phys. Rev. Res. 2, 033389 (2020). [4] F. Li, T. Li, M. O. Scully, and G. S. Agarwal, Quantum advantage with seeded squeezed light for absorption measurement, Phys. Rev. Applied 15, 044030 (2021). [5] T.Li, F. Li, X. Liu, V. Yakovlev and G. S. Agarwal, Quantum-enhanced stimulated Brillouin scattering spectroscopy and imaging, OPTICA 9, 959 (2022).
We propose a protocol to overcome the shot noise limit and reach the Heisenberg scaling limit for parameter estimation by using quantum optimal control and a time-reversal strategy. Exemplified through the phase estimation, which can play an important role in quantum navigation and measurement, we show that the uncertainty arising from a photon number measurement of the system can saturate the assisted Creamér-Rao bound, independent of the phase being estimated. In a realistic case with photon loss, we show that the optimal estimation may still be attainable by optimal control and a projective measurement on an ancilla two-level system coupled to photonic modes.
We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T . The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T , whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T , as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.