Temporal Quantum Correlations in Inelastic Light Scattering from Water

Water is one of the most prevalent chemicals on our planet, an integral part of both our environment and our existence as a species. Yet it is also rich in anomalous behaviors. Here we reveal that water is a novel—yet ubiquitous—source for quantum correlated photon pairs at ambient conditions. The photon pairs are produced through Raman scattering, and the correlations arise from the shared quantum of a vibrational mode between the Stokes and anti-Stokes scattering events. We confirm the nonclassical nature of the produced photon pairs by showing that the cross-correlation and autocorrelations of the signals violate a Cauchy-Schwarz inequality by over 5 orders of magnitude. The unprecedented degree of violating the inequality in pure water, as well as the well-defined polarization properties of the photon pairs, points to its usefulness in quantum information.

Figure 1

(a) $\mathrm{S}(+)$ and $\mathrm{AS}(-)$ Raman spectrum of liquid water, including the three intramolecular ${\mathrm{H}}_2\mathrm{O}$ vibrations (${\nu }_1$, ${\nu }_2$, and ${\nu }_3$; see the schematics). The spectrometer charge coupled device camera is not capable of distinguishing the AS signal from the readout noise in this 1h-accumulation spectrum. Intermolecular vibrations appear at lower frequencies [16], and the peak at zero is leakage from laser through the notch filter (cuts from $-200$ up to $+400{\mathrm{cm}}^{-1}$). These unwanted signals are removed in the temporal correlation measurements by bandpass filters [17]. (b) Schematics explaining the production of correlated photons within the ${\nu }_2$ mode. In the S process, at time $t$, an incident photon from the laser (${\omega }_{\text{laser}}$) is converted into a photon with smaller energy (${\omega }_{\mathrm{S}}$), and the remaining energy is transferred to the molecule as a quantum of vibration. At time $t^{\prime }$, another photon from the laser is converted into a photon with higher energy (${\omega }_{\mathrm{AS}}$) in the AS process by absorbing the quantum of vibration. The time for the energy exchange between S and the AS processes is shown by $\mathrm{\Delta }t=t^{\prime }-t$. (c) Histogram of measured $\mathrm{\Delta }t$ values from ${\nu }_2$. The corresponding cross-correlation function at zero delay is $g_{\mathrm{S},\mathrm{AS}}^{(2)}(0)=915$, the highest value we achieved. The signal (peak at $\mathrm{\Delta }t=0$) is 3 orders of magnitude higher than the background (peaks at $\mathrm{\Delta }t\ne 0$); see the inset [17].

Figure 2

(a) and (b) plot, respectively, the Raman spectra from diamond and the ${\nu }_2$ bending mode of liquid water. (c) and (d) plot, respectively, the histogram of coincidences for diamond [$g_{\mathrm{S},\mathrm{AS}}^{(2)}(0)=33$] and for water [$g_{\mathrm{S},\mathrm{AS}}^{(2)}(0)=549$]. The uncertainties in all the measured cross-correlations and the spectra are due primarily to Poissonian noise in the photon counting [17]. (a) and (b) or (c) and (d) were measured with the same experimental apparatus for direct comparison.

Figure 3

(a) Calculated dependence of the SAS correlation [$g_{\mathrm{S},\mathrm{AS}}^{(2)}(0)$] on the number of incident photons (${\alpha }^2$) [19], for water (blue) and diamond (red). (b) Low photon fluency saturation values as a function of the ratio between the vibrational energy and the thermal energy ($E_{\text{vibration}}/k_{B}T$). Calculations here are for $T=290\mathrm{K}$. More details are in Refs. [17, 19].

Figure 4

Polarized nature of the $1640{\mathrm{cm}}^{-1}$ quantum correlated SAS emission from water. (a) Both polarizers are oriented parallel to the excitation electric field. (b) The correlation is largely unchanged and still shows highly nonclassical correlation. The measured value of the cross-correlation is $g_{\mathrm{S},\mathrm{AS}}^{(2)}(0)=513$. (c) The AS polarizer is parallel to the excitation, while the S polarizer is perpendicular. (d) The coincidence rate is very weak, and the measured value of the cross-correlation is at least 2 orders of magnitude smaller. The observed value of $g_{\mathrm{S},\mathrm{AS}}^{(2)}(0)\sim 6$ can be attributed to leakage through the polarizers.