EQuAL Student Seminar: Bharath Hebbe Madhusudhana

Identical bosons in quantum sensing: in-situ error detection and squeezing from scrambling

With great sensitivity comes great fragility. While entangled quantum states are powerful tools for sensing, their inherent fragility typically limits the scalability and practicality of quantum advantage. In this talk, I will show how in-situ error detection can mitigate these effects, allowing us to retain metrological gains even in noisy, unshielded environments [1, 2]. By leveraging the symmetric wave functions of identical bosons, we can ensure that environmental errors are symmetrized across the system, enabling a unique form of real-time error detection and post-correction [2]. In particular, we consider a system of N identical bosons in a lattice with L sites governed by a Bose-Hubbard Hamiltonian. The quantum many- body states in this system are naturally sensitive to linear potentials along the lattice such as those induced by gravity—allowing for high-precision gravimetry. While the sensitivity to gravity of separable quantum states is restricted to the Standard Quantum Limit (SQL), we demonstrate that "scrambling" dynamics, generated by randomly varying the Bose-Hubbard Hamiltonian in time, almost always yield many-body states with significant quantum advantage i.e., sensitivity beyond the SQL [3]. This provides a useful technique to prepare squeezed states with L>2. To harness this, we develop a Loschmidt echo sequence capable of sensing gravity at sensitivities approaching the Heisenberg scaling. We next consider gravimetry in the presence of noise. We show that for L>2, i.e., systems with more than two lattice sites, one can detect and post-correct some of the noise in gravimetry. The key insight is that one simultaneously reads out L occupancies in this system in each experimental shot and when L>2, this is more information than just the signal (i.e., gravity) and the "extra" information can be used to partially detect the noise. We show, interestingly, that after the post-correction, one can recover the quantum advantage even in the presence of noise [2]. We develop a Bayesian post-correction technique which uses the L occupancies to mitigate the shot-to-shot noise and generalize the Loschmidt echo sequence to include this noise mitigation.