Demonstration of Light-Matter Micro-Macro Quantum Correlations

Quantum mechanics predicts microscopic phenomena with undeniable success. Nevertheless, current theoretical and experimental efforts still do not yield conclusive evidence that there is or is not a fundamental limitation on the possibility to observe quantum phenomena at the macroscopic scale. This question prompted several experimental efforts producing quantum superpositions of large quantum states in light or matter. We report on the observation of quantum correlations, revealed using an entanglement witness, between a single photon and an atomic ensemble of billions of ions frozen in a crystal. The matter part of the state involves the superposition of two macroscopically distinguishable solid-state components composed of several tens of atomic excitations. Assuming the insignificance of the time ordering our experiment indirectly shows light-matter micro-macro entanglement. Our approach leverages from quantum memory techniques and could be used in other systems to expand the size of quantum superpositions in matter.

Figure 1

Experimental scheme. (a) Conceptual scheme for the creation and analysis of the light-matter micro-macro entangled state $|\mathrm{\Psi }⟩$. First, a displacement operation ${\mathcal{D}}_H^s(\alpha )$ is applied on the signal mode of the micro-micro polarization entangled state $|\psi ⟩$ using a beam splitter (BS) with high transmittance. The displaced signal photon of the micro-macro state $|\mathrm{\Psi }⟩$ is then mapped inside a solid-state quantum memory (QM) that has a storage and retrieval efficiency $\eta$. To characterize the state, it is first displaced back to $|\psi ⟩$ (in the ideal case) when it is retrieved from the memory using ${\mathcal{D}}_H^s(-\sqrt{\eta }\alpha )$, and is then analyzed using various entanglement witnesses. (b) Detailed setup. A polarization entangled pair of photons is created using spontaneous parametric down-conversion from two periodically poled nonlinear waveguides (PPLN and PPKTP) placed in the arms of a polarization interferometer [28] seeded by a continuous wave laser (532 nm wavelength). Dichroic mirror (DM) is used to separate two photons spatially. After the spectral filtering the idler photon is detected by one of the detectors ($D_1^{(i)}$ or $D_2^{(i)}$). This event heralds a single photon in the signal mode, and it triggers the generation of a coherent state pulse (CSP) using an electro-optical intensity modulator (EOM) that carves a pulse out of a continuous wave laser at 883 nm. The CSP is sent in the QM in a different spatial mode than the signal mode. This further allows preparing both the displacement and back-displacement pulses with the required delay and amplitudes (see text and [29] for details). The relative phase necessary for this is set by an electro-optic phase modulator (PM). The first displacement pulse ${\mathcal{D}}_H^s(\alpha )$ is synchronized with the heralded single photon on a BS that has a 99.5% transmittance. The resulting state $|\mathrm{\Psi }⟩$ is stored inside the QM and released after a predetermined time of ${\tau }_s=50\mathrm{ns}$. The second displacement ${\mathcal{D}}_H^s(-\sqrt{\eta }\alpha )$ is then applied on the state retrieved from the QM. The state is analyzed, together with the idler photon previously measured, using free-space polarization analyzers composed of quarter-wave ($\lambda /4$) and half-wave ($\lambda /2$) plates followed by polarizing beam splitters (PBS).

Figure 2

Measured values of the $S$ parameter of the CHSH-Bell inequality (dots) as a function of the size of the displacement before the QM (top $x$ axis) or as a function of the average number of atomic excitations inside the QM (bottom $x$ axis). CHSH violation values are above the local bound with up to 7 excitations on average, and above the entanglement bound with up to 23 excitations on average. The error bars are estimated assuming Poisson statistics for the detections. The solid line is obtained from a theoretical model based on independently measured parameters, and the shaded area represents a one standard-deviation uncertainty on the predictions of the model.

Figure 3

Quantum state characterization. (a) PPT and concurrence values (obtained from quantum state tomography) as a function of the size of the displacement before the QM (top $x$ axis) or as a function of the average number of atomic excitations inside the QM (bottom $x$ axis). The error bars are estimated from Monte Carlo simulations assuming Poisson noise. The PPT criteria remains negative and the concurrence value remains positive with up to 47 excitations on average. The solid lines in all graphs are obtained from a theoretical model based on the independently measured parameters, and the shaded areas are the uncertainty on these parameters. (b) Distribution of number of atomic excitations of the two macroscopically distinguishable components $\mathcal{D}(\alpha )|1⟩$ and $|\alpha ⟩$ when expressed in the $\{|0⟩+|1⟩,|0⟩-|1⟩\}$ basis.