On-chip interaction-free measurements via the quantum Zeno effect

Although interference is a classical-wave phenomenon, the superposition principle, which underlies interference of individual particles, is at the heart of quantum physics. An interaction-free measurement (IFM) harnesses the wave-particle duality of single photons to sense the presence of an object via the modification of the interference pattern, which can be accomplished even if the photon and the object have not interacted with each other. By using the quantum Zeno effect, the efficiency of an IFM can be made arbitrarily close to unity. Here we report an on-chip realization of the IFM based on silicon photonics. We exploit the inherent advantages of the lithographically written waveguides (excellent interferometric phase stability and mode matching) and obtain multipath interference with visibility above $98\%$. We achieved a normalized IFM efficiency up to $68.2\%$, which exceeds the $50\%$ limit of the original IFM proposal.

Figure 1

Interaction-free measurement. (a) An optical MZI is formed by two beam splitters (BS1 and BS2) and two mirrors. The MZI is aligned such that all the photons will go to detector U and none will go to detector L. (b) If the bomb is inserted, its presence will destroy the destructive interference at detector L. Each detection event by L indicates the presence of the bomb, and IFM succeeds. (c) The efficiency of the successful IFM ${\eta }_{\mathrm{IFM}}$, the probabilities of successful IFM $\left(\mathrm{P}\left(\mathrm{IFM}\right)\right)$ and absorption of the photon by the bomb $\left(\mathrm{P}\left(\mathrm{abs}\right)\right)$ are shown as black, red (dark gray), and green (light gray) curves, respectively.

Figure 2

Quantum-Zeno-effect-enabled interaction-free measurement. (a) A photon entering the cMZI from the lower input will coherently and gradually evolve to the upper half of the cMZI and will then be detected by U. (b). If bombs are inserted in the upper arm of the cMZI, the multistage interference is destroyed, and L will detect a large portion of the input photons due to the quantum Zeno effect. (c) By increasing the number of the beam splitters, both ${\eta }_{\mathrm{IFM}}$ (black triangles) and $\mathrm{P}\left(\mathrm{IFM}\right)$ (red squares) can be made arbitrarily close to 1, and $\mathrm{P}\left(\mathrm{abs}\right)$ (green circles) is reduced to close to 0.

Figure 3

Design of directional couplers. (a) The normalized power distribution of the propagating transverse electric (TE) mode confined by a single Si waveguide that is 400 nm wide and 220 nm thick. The effective refractive index $n_{\mathrm{eff}}$ of this mode is about 2.1129. In the coupling region, two waveguides are brought close to each other, and mode hybridization occurs due to the evanescent coupling. Therefore new compound modes become the new eigenmodes. (b) and (c) The simulated TE-like electric-field component $E_x$ of the symmetric and the antisymmetric compound modes. In this simulation, we choose the gap between the two waveguides to be 270 nm. For the symmetric (antisymmetric) mode, the electrical fields distributed in the two silicon waveguides are in (out) of phase, i.e., the relative phase is zero $\left(\pi \right)$. The effective refractive index $n_{\mathrm{eff}}$ is about 2.1232 and 2.1036 for the symmetric and antisymmetric modes, respectively. The power and electrical field distributions in (a)–(c) are shown in linear color scale. (d) The effective refractive indexes of these two compound modes as functions of the gap between the two waveguides. The black curve is the effective index of the symmetric mode $n_s$, and the red curve is that of the antisymmetric mode $n_a$. See text for details on how the coupling length of these two waveguides $l_c$ can be derived. As we increase the gap, the difference of the effective refractive indexes of these two modes becomes smaller, and hence the coupling length becomes larger. (e) The reflectivity and transmissivity of a directional coupler composed of the above-mentioned waveguides for a design length of 20 $\mu \text{m}$.

Figure 4

The optical micrograph and schematic setup of a device with 10-stage QZIFM circuitry. There are five grating couplers (GC, labeled by numbers). GC 2 is used as the input. GC 1 couples out half of the total input power, which is measured by detector T. GCs 3 and 5 couple out the lower and upper outputs of the MZI circuit, which are then measured by detectors L and U, respectively. A tunable diode laser (TDL) is used as the light source, and a variable optical attenuator (VOA) is used to attenuate the laser to the single-photon level. A fiber polarization controller (FPC) is used to rotate the polarization of the input light so that it is TE. A set of the same TDL, VOA, and FPC provides a light source to GC 4 for measuring the output coupling differences between GCs 3 and 5. Scale bar is 250 $\mu \text{m}$.

Figure 5

Experimental data of IFM. (a) The transmission spectra of the lower and upper outputs of a device without an absorber [corresponding to Fig. 1]. (b) The transmission spectra with a full absorber present in the upper arm of the interferometer. (c) The result of the two-stage IFM as a function of the reflectivity of the first directional coupler. The black curve is the theoretical prediction as in Fig. 1.

Figure 6

Experimental data of the QZIFM. (a) The transmission spectra of the lower and upper outputs of a ten-stage device without an absorber. (b) The transmission spectra with nine full absorbers present in the upper arm of the interferometer. (c) The results of the 5-, 10-, and 20-stage QZIFMs. The solid black curve is the theoretical prediction of a lossless device. The red dashed and green dotted curves are the predictions with $7.4\%$ and $21.2\%$ loss per stage, respectively. Data for $N=5$ (measured at the wavelength of 1539.75 nm) and 10 (measured at the wavelength of 1527.25 nm) are in good agreement with the red dashed curve. Data for $N=20$ (measured at a wavelength of 1538.645 nm) show higher loss and are in agreement with the green curve [37].

Figure 7

The optical micrographs of (a) a typical two-stage device for IFM and (b) a typical five-stage device for QZIFM.

Figure 8

(a) The optical micrograph of a 20-stage device for a QZIFM. (b) The transmission spectra of the lower and upper outputs of a 20-stage device without an absorber, which corresponds to the situation shown in Fig. 2. (c) The normalized transmission spectra in logarithm scale. (d) The transmission spectra with 19 full absorbers present in the upper arm of the interferometer. Note that this device has the same design as (b), except the gaps between the absorbers and the upper arm of connected interferometers have changed from 10 $\mu \text{m}$ to 190 nm. (e) The normalized transmission spectra in logarithm scale. It is clear that the interference disappeared, which is the signature of QZIFM.