Two-Color Pump-Probe Measurement of Photonic Quantum Correlations Mediated by a Single Phonon

We propose and demonstrate a versatile technique to measure the lifetime of the one-phonon Fock state using two-color pump-probe Raman scattering and spectrally resolved, time-correlated photon counting. Following pulsed laser excitation, the $n=1$ phonon Fock state is probabilistically prepared by projective measurement of a single Stokes photon. The detection of an anti-Stokes photon generated by a second, time-delayed laser pulse probes the phonon population with subpicosecond time resolution. We observe strongly nonclassical Stokes–anti-Stokes correlations, whose decay maps the single phonon dynamics. Our scheme can be applied to any Raman-active vibrational mode. It can be modified to measure the lifetime of $n\ge 1$ Fock states or the phonon quantum coherences through the preparation and detection of two-mode entangled vibrational states.

Figure 1

(a) Concept of the experiment: The first (write) laser pulse probabilistically prepares the phonon in state $|n=1⟩$ upon detection of a Stokes photon. The second (read) pulse, after a time delay $\mathrm{\Delta }t$ converts this phonon into an anti-Stokes photon. (b) Schematics of the photon counting in the frequency domain [single-photon avalanche photodiode (SPAD)]. The choice of ${\omega }_1$ and ${\omega }_2$ is completely free, as long as the Stokes and anti-Stokes photons can be efficiently isolated by spectral filtering.

Figure 2

Schematic drawing of the experimental setup. Half-wave plate (HW); polarizing beam splitter (PBS); spatial filter (SF); short-, long, band-pass filters (SP,LP,BP) (tunable filters are highlighted in green); delay line (DL); dichroic mirror (DM); objective lens (OL) ($\text{numerical aperture}=0.8$); single-mode fiber (SMF) (HP780, Thorlabs); graded index multimode fiber (MMF) ($100\mu \mathrm{m}$ core, NA 0.29, OZ Optics); flip mirror (FM). A video camera is used to overlap the beams.

Figure 3

(a) S–aS coincidence histogram (20 min integration). The S (aS) count rates were $<2.5\times {10}^4\mathrm{Hz}$ ($<8\times {10}^2\mathrm{Hz}$), with a dark count rate $<5\times {10}^2\mathrm{Hz}$. The OPO (Ti:sapphire) powers just after the sample were $\sim 1.5\mathrm{mW}$ ($\sim 3.5\mathrm{mW}$). Inset: representative Raman spectrum; the pass bands of the filters placed before the S and aS detectors are overlaid in blue. (b) Write-read delay dependence of the measured S–aS correlation (open circles) and fit (dashed line) using an exponential decay ($\text{time constant}=3.9\pm 0.7\mathrm{ps}$) convoluted with the instrument response (Gaussian with standard deviation $\sigma =223\mathrm{fs}$, see the Supplemental Material [21]). The gray area marks the classical bounds. Inset: coincidence histograms at different delays. (c) Measured S–aS correlations at zero delay vs pulse energy in the write beam (symbols) for different pulse energies in the read beam. Solid lines are the result of the simplified analytical model presented in the Supplemental Material [21], Sec. 4. It has two free parameters: the overall collection and detection efficiency $\eta$ (probability of registering a S or aS photon emitted in the right spatial mode) and a factor $\alpha$ accounting for the nonideal phonon-photon conversion in the read pulse, which we relate to imperfect mode overlap. The best fit to the data is obtained with $\eta =0.07$ and $\alpha =0.3$.

Figure 4

(a) Decay of the normalized S–aS correlation $[g_{\mathrm{S},\mathrm{aS}}^{(2)}(\mathrm{\Delta }t)-1]/[g_{\mathrm{S},\mathrm{aS}}^{(2)}(0)-1]$ (symbols) as a function of write-read delay $\mathrm{\Delta }t$ for two configurations of laser wavelengths (red and black colors), yielding S and aS peaks as shown in the inset. The fitted exponential decays (solid lines) have time constants $4.2\pm 0.5$ (red line) and $4.0\pm 0.3\mathrm{ps}$ (black line).