Filtering Out Photonic Fock States

Unprecedented optical nonlinearities can be generated probabilistically in simple linear-optical networks conditioned on specific measurement outcomes. We describe a highly controllable quantum filter for photon number states, which takes advantage of such a measurement-induced amplitude nonlinearity. The basis for this filter is multiphoton nonclassical interference which we demonstrate for one- and two-photon states over a wide range of beam splitter reflectivities. Specifically, we show that the transmission probability, conditional on a specific measurement outcome, can be larger for a two-photon state than a one-photon state; this is not possible with linear optics alone.

Figure 1

Schematic setup for the quantum filter. An $n$-photon state in mode 1 and ancilla photon in mode 2 are incident on a beam splitter with reflectivity, $R$. The probability to find a single (i.e., one and only one) photon in mode 3, and hence $n$-photons in mode 4, is $P_{NL}=R^{n-1}[R-(1-R)n{]}^2$. When $R=n/(n+1)$, one never finds a single photon in the output mode 3. By the linearity of quantum mechanics, if the input state had contained a superposition of photon number states, and a single photon was found in mode 3, the $n$-photon component would be completely removed from the output state.

Figure 2

Experimental setup for the demonstration of a quantum filter. Input states containing one or two photons are produced using parametric down-conversion in a type-II phase-matched 2-mm BBO crystal pumped by ultraviolet laser pulses. Interference filters (F) select light with a center wavelength of 789 nm and bandwidth of 4 nm. (a) In the $n=1$ case, the input photon and ancilla photon originate from the same down-conversion pair. Polarization controllers (Pol Control) compensate unwanted polarization rotations in the optical fibers. (b) In the $n=2$ case, the two input photons came from one down-conversion pair on the forward pass of the pump. These photons were probabilistically combined into the same optical mode using a fiber beam splitter. This produces a horizontally polarized two-photon state. The vertically polarized ancilla is produced in a second down-conversion pair on the backward pass of the pump heralded by a detection event at $D_1$. The one- or two-photon states are contained in mode 1 and the ancilla photon in mode 2. (c) The photons were combined in a variable-reflectivity beam splitter constructed using two polarizing beam splitters (PBSs) and a half-wave plate (HWP). Their relative times of arrival were controlled by the delays on the fiber coupler and pump mirror. In output mode 3, a click at detector $D_2$ is required for the quantum filter to implement the desired transformation. In the $n=1$ case, the output photons were measured at detector $D_3$, while in the $n=2$ case photon pairs were detected by the cascaded detector pair $D_3$ and $D_4$.

Figure 3

Experimental results for one- and two-photon input states. (a) The twofold coincidences for the $n=1$ configuration [Fig. 2a] between detectors $D_2$ and $D_3$ are shown as a function of the relative delay introduced by the fiber coupler. Solid lines show Gaussian fits to the data. All cases show a decrease in the coincidence rate with a maximum measured visibility of $(83\pm 1)\%$ for $R=1/2$. (b) The fourfold coincidences as a function of delay for the $n=2$ source configuration [Fig. 2b] for the same $R$ values. In this case, the maximum visibility was measured to be $(78\pm 5)\%$ at $R=2/3$ not $1/2$. The experimental data for $R=1/6$ show an increase in coincidence rate at zero delay. (c) All experimentally measured visibilities are shown as a function of the $R$ for $n=1$ (open circles, dotted line theory) and $n=2$ (solid diamonds, solid line theory) input states. (d) Conditional transmission probabilities inferred from the experimental data are shown for both the $n=1$ (open circles, dotted line theory) and $n=2$ (solid diamond, straight line theory) cases for different $R$ settings.