Can Intense Quantum Light Beat Classical Uncertainty Relations?

Abstract

Uncertainty relations are fundamental to quantum mechanics, encoding limits on the simultaneous measurement of conjugate observables. Violations of joint uncertainty bounds can certify entanglement -- a resource critical for quantum information protocols and increasingly relevant in strong-field physics. Here, we investigate the pairwise time-delay and frequency-bandwidth uncertainties for arbitrary multimode quantum states of light, deriving a general lower bound for their joint product. We find that the nonclassical correction scales inversely with the average photon number, a behavior rooted in the so-called ``monogamy of entanglement''. These results clarify the intensity scaling of quantum advantages in nonclassical light states and highlight the interplay between entanglement and photon statistics.

Figures (2)

• Figure 1: Minimum uncertainty values of the joint time-bandwidth uncertainty product calculated with the uncertainty Hamiltonian method opatrny1995 for states with $n\in[2,5]$ photons and Hermite-Gauss mode expansions with $m\in [2,15]$ modes. Dashed lines correspond to fits up to 6th order in $m^{-1}$, with $R_n^{(\infty)}$ the estimated value for infinite basis set size.
• Figure 2: Scaling analysis. (a) Representation of a superposition of two- and three-photon states highlighting the fact that there are overall more uncorrelated than correlated pairs even when each state is individually totally entangled. (b) Negative of the nonclassical correction to the joint time-frequency uncertainty product for the minima of the BSV, with a linear asymptotic fit $\log{(1-\Delta\tau^2\Delta\Omega^2)}=\log{c}-k\log{\langle n\rangle}$ ($k\approx1,c\approx0.18$) and the general nonclassical bound of \ref{['eq:global_bound']} for comparison.