Nonquantum Information Gain from Higher-order Correlation Functions

Abstract

Nonlinear correlation functions are at the heart of quantum theory. The second-order correlation function $g^{(2)}(\tau )$ has been a cornerstone of quantum optics since over half a century and a myriad of quantum and classical applications has been discovered. In contrast, higher-order correlation functions have so far only been used to reveal the nonclassical character of the emitted fields. In this paper, we study the relation between the $k$th-order correlation function $g^{(k)}(0)$ and the projection of the underlying quantum state of light onto the subspace of Fock states with photon number less than $k$. We show, that when $g^{(k)}(0)$ falls below a critical value, lower bounds for the projection on this subspace can be concluded as well as on the ratio of the subspace with one upto $k-1$ photons and $k$ to infinity. These bounds are at face value only valid for nonclassical quantum states. However, when the quantum state includes a nonzero projection on the vacuum state, the value of $g^{(k)}(0)$ is artificially enhanced, potentially covering these projections. We derive an effective $k$th-order correlation function, which accounts for the effect of vacuum. We show that the information gained from the effective correlation function is not limited to nonclassical quantum states and thus constitute a quantum- and classical application of higher-order correlation functions.

8 pages, 3 figures

References in corpus (13)

• Engineered Quantum Dot Single Photon Sources
• Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator
• Accessing higher order correlations by time-multiplexing
• Giant optical nonlinearities from Rydberg-excitons in semiconductor microcavities
• Non-classical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity
• Two-photon blockade and photon-induced tunneling generated by squeezing
• Universal measurement of quantum correlations of radiation
• Effective second-order correlation function and single-photon detection
• Evaluating Performance of Photon-Number-Resolving Detectors
• Higher-order sub-Poissonian-like nonclassical fields: Theoretical and experimental comparison
• Comparison of lower order and higher order nonclassicality in photon added and photon subtracted squeezed coherent states
• Structure of the Harmonic Oscillator in the space of $n$-particle Glauber correlators
• Direct experimental observation of nonclassicality in ensembles of single photon emitters

Cited by in corpus (3)

• Nonclassicality detection from few Fock-state probabilities
• Coherence-based operational nonclassicality criteria
• Optimized higher-order photon state classification by machine learning