| Summary: | The quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experimentally demonstrate tilt measurements using a higher-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>40</mn></msub></mrow></semantics></math></inline-formula> mode as the probe beam. Using the balanced homodyne detection with an optimal local beam, which involves the superposition of high-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>30</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>50</mn></msub></mrow></semantics></math></inline-formula> modes, we demonstrate the precision of the tilt measurement approaching the QCRB. The signal-to-noise ratio of the tilt measurement is enhanced by 9.2 dB compared with the traditional method using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>00</mn></msub></mrow></semantics></math></inline-formula> as the probe beam. This scheme is more practical and robust to losses, which has potential applications in areas such as laser interferometer gravitational-wave observatories and high-sensitivity atomic force microscopes.
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