Engineering multi-mode bosonic squeezed states using Monte-Carlo optimization

TL;DR

This paper introduces a Monte-Carlo optimization method to engineer multi-mode bosonic squeezed states in ultracold atomic systems, enabling quantum-enhanced sensing beyond classical limits with feasible experimental setups.

Contribution

The authors develop a novel Monte-Carlo based optimization technique to efficiently generate multi-mode squeezed states in bosonic systems, advancing quantum metrology capabilities.

Findings

Intermediate QFI scaling between SQL and HL identified.

Monte Carlo optimization successfully produces states with desired QFI scaling.

Feasible experimental parameters can achieve near-Heisenberg limit in gravimetry.

Abstract

Bosonic systems, such as photons and ultracold atoms, have played a central role in demonstrating quantum-enhanced sensing. Quantum entanglement, through squeezed and GHZ states, enables sensing beyond classical limits. However, such a quantum advantage has so far been confined to two-mode bosonic systems, as analogous multi-mode squeezed states are non-trivial to prepare. Here, we develop a Monte-Carlo based optimization technique which can be used to efficiently engineer a Hamiltonian control-sequence for multi-mode bosonic systems to prepare multi-mode squeezed states. Specifically, we consider a Bose-Einstein condensate in an optical lattice, relevant for applications in gravimetry and gradiometry, and demonstrate that metrologically useful squeezed states can be generated using the Bose-Hubbard Hamiltonian which includes on-site atomic interactions, tunable via Feshbach resonances. By analyzing the distribution (density) of the quantum Fisher information (QFI) over the Hilbert space, we identify a characteristic \textit{intermediate scaling} of the QFI: $\mathcal{O}(N^2 L+L^2 N)$, which lies between the standard quantum limit (SQL) and the Heisenberg limit (HL) for $N$ atoms in $L$ modes. We show that in general, within the Hilbert space there is a finite, $\mathcal{O}(1)$ measure subset of Hilbert space with an intermediate QFI scaling. Therefore, one can find a Hamiltonian control sequence using a Monte Carlo optimization over random control sequences, that produces a state with intermediate scaling of the QFI. We assume an experimentally accessible range of the control parameters in the Hamiltonian resources and show that the intermediate scaling can be readily achieved. Our results indicate that the HL can be approached in quantum gravimetry using realistic experimental parameters for systems with $L=\mathcal{O}(1)$ and $N\gg L$.