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1. Spin Squeezing as a Probe of Emergent Quantum Orders

   https://doi.org/10.7566/JPSCP.38.011149  

   Nikolov, Ilija K.; Carr, Stephen; Del Maestro, Adrian G.; Ramanathan, Chandrasekhar; Mitrović, Vesna F. (May 2023, Proceedings of the 29th International Conference on Low Temperature Physics (LT29))

   Nuclear magnetic resonance (NMR) experiments can reveal local properties in materials, but are often limited by the low signal-to-noise ratio. Spin squeezed states have an improved resolution below the Heisenberg limit in one of the spin components, and have been extensively used to improve the sensitivity of atomic clocks, for example [1]. Interacting and entangled spin ensembles with non-linear coupling are a natural candidate for implementing squeezing. Here, we propose measurement of the spin-squeezing parameter that itself can act as a local probe of emergent orders in quantum materials. In particular, we demonstrate how to investigate an anisotropic electric field gradient via its coupling to the nuclear quadrupole moment. While squeezed spin states are pure, the squeezing parameter can be estimated for both pure and mixed states. We evaluate the range of fields and temperatures for which a thermal-equilibrium state is sufficient to improve the resolution in an NMR experiment and probe relevant parameters of the quadrupole Hamiltonian, including its anisotropy. 

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2. Adaptive Phase Estimation with Squeezed Vacuum Approaching the Quantum Limit

   https://doi.org/10.22331/q-2024-09-25-1480  

   Rodríguez-García, M A; Becerra, F E (September 2024, Quantum)

   Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0,\pi /2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0,\pi )$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology. 

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3. Non-Gaussian and Gottesman–Kitaev–Preskill state preparation by photon catalysis

   https://doi.org/10.1088/1367-2630/ab5330  

   Eaton, Miller; Nehra, Rajveer; Pfister, Olivier (November 2019, New Journal of Physics)

   Abstract Continuous-variable quantum-computing is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman–Kitaev–Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states andM-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states (M= 2). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states. 

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4. Effect of imperfect homodyne visibility on multi-spatial-mode two-mode squeezing measurements

   https://doi.org/10.1364/OE.379033  

   Gupta, Prasoon; Speirs, Rory_W; Jones, Kevin_M; Lett, Paul_D (January 2020, Optics Express)

   We study the effect of homodyne detector visibility on the measurement of quadrature squeezing for a spatially multi-mode source of two-mode squeezed light. Sources like optical parametric oscillators (OPO) typically produce squeezing in a single spatial mode because the nonlinear medium is within a mode-selective optical cavity. For such a source, imperfect interference visibility in the homodyne detector couples in additional vacuum noise, which can be accounted for by introducing an equivalent loss term. In a free-space multi-spatial-mode system imperfect homodyne detector visibility can couple in uncorrelated squeezed modes, and hence can cause faster degradation of the measured squeezing. We show experimentally the dependence of the measured squeezing level on the visibility of homodyne detectors used to probe two-mode squeezed states produced by a free space four-wave mixing process in⁸⁵Rb vapor, and also demonstrate that a simple theoretical model agrees closely with the experimental data. 

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5. Non-Gaussian Quantum State Engineering with Squared-Quadrature Quantum Nondemolition Measurements

   https://doi.org/10.1364/CLEO_FS.2023.FM3E.4  

   Nehra, Rajveer; Yanagimoto, Ryotatsu; Mabuchi, Hideo; Marandi, Alireza (January 2023, Optica Publishing Group)

   We present a method for generating squeezed Schr¨odinger cat states and cubic phase states via quantum nondemolition measurement of the squared-quadrature operator, offering a realistic route to fault-tolerant universal continuous-variable quantum computation. 

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