[Paper Review] Stokes--anti-Stokes Correlations in Raman Scattering from Diamond Membranes

Mark Kasperczyk, Ado Jório+3 more|arXiv (Cornell University)|Mar 2, 2015

Mechanical and Optical Resonators18 references3 citations

TL;DR

This study investigates Stokes–anti-Stokes photon correlations in Raman scattering from diamond membranes, demonstrating that Stokes-induced anti-Stokes (SaS) scattering dominates at low laser powers, leading to strong quantum correlations. The second-order cross-correlation $g_{\rm S,aS}^{(2)}(0)$ decreases as $1/P_{\rm L}$, revealing highly nonclassical superbunching and confirming the phonon-mediated quantum memory mechanism in diamond.

ABSTRACT

We investigate the arrival statistics of Stokes (S) and anti-Stokes (aS) Raman photons generated in diamond membranes. Strong quantum correlations between the S and aS signals are observed, which implies that the two processes share the same phonon, that is, the phonon excited by the S process is consumed in the aS process. We show that the intensity cross-correlation $g_{ m S,aS}^{(2)}(0)$, which describes the simultaneous detection of Stokes and anti-Stokes photons, decreases steadily with laser power as $1/{ m P_L}$. Contrary to many other material systems, diamond exhibits a maximum $g_{ m S,aS}^{(2)}(0)$ at very low pump powers, implying that the Stokes-induced aS photons outnumber the thermally generated aS photons. On the other hand, the coincidence rate shows a quadratic plus cubic power dependence, which indicates a departure from the Stokes-induced anti-Stokes process.

Motivation & Objective

• To investigate the quantum correlations between Stokes and anti-Stokes Raman photons in diamond membranes.
• To determine the conditions under which Stokes-induced anti-Stokes (SaS) scattering dominates over thermally generated anti-Stokes processes.
• To quantify the power-dependent behavior of second-order intensity cross-correlations $g_{\rm S,aS}^{(2)}(0)$ for identifying nonclassical photon pair generation.
• To evaluate the role of phonon-mediated processes in enabling quantum memory and heralded single-photon sources in diamond.
• To analyze the impact of sample thickness and laser pulse repetition rate on correlation visibility and background suppression.

Proposed method

• Measure Stokes and anti-Stokes Raman signals in a 50 μm thick freestanding diamond membrane using 785 nm laser excitation with 130 fs pulses at 76 MHz repetition rate.
• Use spectral line fitting to extract Stokes and anti-Stokes signal intensities as functions of average laser power $P_{\rm L}$.
• Calculate the second-order intensity cross-correlation $g_{\rm S,aS}^{(2)}(0)$ from coincidence counts at zero time delay, normalized by accidental coincidences.
• Model the power dependence of coincidence rates, including quadratic and cubic terms to account for multi-pulse correlations.
• Analyze time-resolved coincidence histograms to separate intra-pulse ($\Delta t = 0$) and inter-pulse ($\Delta t \neq 0$) contributions.
• Use the ratio of $\Delta t = 0$ to $\Delta t \neq 0$ coincidence peaks to derive the $P_{\rm L}^{-1}$ dependence of $g_{\rm S,aS}^{(2)}(0)$, confirming phonon-mediated correlation.

Experimental results

Research questions

• RQ1 How does the second-order cross-correlation $g_{\rm S,aS}^{(2)}(0)$ vary with laser pump power in diamond membranes?
• RQ2 What is the relative contribution of thermally generated anti-Stokes photons versus Stokes-induced anti-Stokes photons at low excitation powers?
• RQ3 Why does $g_{\rm S,aS}^{(2)}(0)$ decrease as $1/P_{\rm L}$, and how does this relate to inter-pulse correlations?
• RQ4 To what extent do inter-pulse correlations distort the measurement of true quantum correlations at $\Delta t = 0$?
• RQ5 Can diamond membranes be engineered to maximize $g_{\rm S,aS}^{(2)}(0)$ for quantum memory and single-photon source applications?

Key findings

• The Stokes signal exhibits a linear dependence on laser power, confirming spontaneous Raman scattering behavior.
• The anti-Stokes signal shows a linear power dependence at low intensities (dominated by thermal phonons) and a quadratic dependence at high intensities (indicative of Stokes-induced anti-Stokes scattering).
• The second-order cross-correlation $g_{\rm S,aS}^{(2)}(0)$ decreases as $1/P_{\rm L}$, indicating strong nonclassical correlations that violate classical bounds.
• At very low pump powers, $g_{\rm S,aS}^{(2)}(0)$ reaches a maximum, confirming that Stokes-induced anti-Stokes photons outnumber thermally generated ones.
• Coincidence rates show a quadratic plus cubic power dependence, revealing contributions from inter-pulse correlations that scale with $P_{\rm L}$.
• Thinner diamond membranes reduce inter-pulse correlation peaks more than intra-pulse peaks, enhancing $g_{\rm S,aS}^{(2)}(0)$ beyond the classical limit of 2.