Verifying continuous-variable entanglement of intense light pulses

Three different methods have been discussed to verify continuous variable entanglement of intense light beams. We demonstrate all three methods using the same setup to facilitate the comparison. The nonlinearity used to generate entanglement is the Kerr effect in optical fibers. Due to the brightness of the entangled pulses, standard homodyne detection is not an appropriate tool for the verification. However, we show that by using large asymmetric interferometers on each beam individually, two noncommuting variables can be accessed and the presence of entanglement verified via joint measurements on the two beams. Alternatively, we witness entanglement by combining the two beams on a beam splitter that yields certain linear combinations of quadrature amplitudes which suffice to prove the presence of entanglement.

Figure 1

(Color online) Schematic representation of entanglement generation in a phase space diagram. Two bright amplitude squeezed beams interfere with relative phase $\theta$ at a $50∕50$ beam splitter. Note that the plotted situation corresponds to nonideal entanglement generation where $\theta \ne \pi ∕2$, the resulting uncertainty areas are elliptical and the uncertainty in amplitude and phase is different for the two modes. Throughout this paper, the amplitude quadrature $\widehat{X}$ is defined to point along the direction of the classical excitation, the phase quadrature $\widehat{Y}$ is perpendicular (see inset).

Figure 2

(Color online) Setup for entanglement generation. Two squeezed beams of orthogonal polarization are generated in an asymmetric fiber Sagnac interferometer and are brought to interference at a polarizing beam splitter (PBS) together with a $\lambda ∕2$ wave plate. To control the relative phase of the two pulses and to compensate their relative delay due to the birefringence of the fiber, a Michelson interferometer is placed in front of the Sagnac loop. G: Gradient index lens, Det A and B: DC detectors for phase lock, BS: beam splitter.

Figure 3

(Color online) (a) Experimental setup of the phase-measuring interferometer. The orientation of the first $\lambda ∕2$ plate determines the type of measurement: amplitude measurement (AM) or phase measurement (PM). PBS, polarizing beam splitter; $50∕50$, beam splitter. (b) Schematic of the setup to verify entanglement using two phase-measuring interferometers.

Figure 4

(Color online) Correlations of the (a) amplitude quadrature and (b) phase quadrature of the entangled beam pair measured with the unbalanced Mach-Zehnder interferometer. In each graph, the noise level (trace 1) of the correlation signal is shown together with the corresponding shot-noise level (trace 2), the noise level of the individual beams (traces 3), and the signal with the anticorrelations (traces 4). The traces were corrected by subtracting the electronic noise, which was at $-84.4\mathrm{dB}\mathrm{m}$. The measurement frequency was $20.5\mathrm{MHz}$. Similar results were presented in Ref. 20, however, the results shown here were obtained in a setup with improved performance.

Figure 5

(Color online) Schematic setup for correlation measurements by interference of the entangled beam pair at a $50∕50$ beam splitter and direct detection.

Figure 6

(Color online) Correlations of the (a) amplitude quadrature and (b) phase quadrature of the entangled beam pair measured via interference and direct detection. In the graph the noise level of the correlation signal is shown together with the corresponding shot-noise level. The traces were corrected by subtracting the electronic noise, which was at $-87.8\mathrm{dB}\mathrm{m}$. The measurement frequency was $17.5\mathrm{MHz}$.

Figure 7

(Color online) Direct detection of nonseparability. Both entangled beams were brought to interference, the noise power is measured in the individual output ports. Amplitude squeezing of $2.8\mathrm{dB}$ and $2.6\mathrm{dB}$ below the shot-noise level is observed. the measurement frequency was $17.5\mathrm{MHz}$, the electronic noise level was at $-87.8\mathrm{dB}\mathrm{m}$.