Beating the Standard Quantum Limit With Single‐Photon‐Added Coherent States

ABSTRACT

The standard quantum limit (SQL), also known as the shot‐noise limit, defines how quantum fluctuations of light constrain measurement precision. In a benchmark experiment using the Mach–Zehnder interferometer (MZI), where a coherent state with the average photon number is combined with an ordinary vacuum input, the SQL for the phase uncertainty is given by the well‐known relation . Using a single‐photon‐added coherent state and a weak coherent state as inputs, we report enhanced phase sensitivity in an MZI that surpasses the SQL. In stark contrast to conventional approaches, we focus on the low‐photon‐number regime () and show that this scheme achieves better phase sensitivity than the SQL. Furthermore, the phase offset can serve as a control parameter to tailor the photon statistics of the output beam. We further show that this enhancement does not arise from the single‐mode Wigner negativity of SPACS which persists even when paired with vacuum, yet never beats the SQL but rather from non‐classical cross‐correlations in the joint two‐mode Wigner function generated when the SPACS interferes with a coherent field. Beating the SQL at low photon numbers may find applications in “photon‐starved” quantum sensing, spectroscopy, and metrology.