Coherent Absorption of N00N States

Thomas Roger, Sara Restuccia, Ashley Lyons, Daniel Giovannini, Jacquiline Romero, John Jeffers, Miles Padgett, and Daniele Faccio

Phys. Rev. Lett. 117, 023601 – Published 6 July 2016

Abstract

Recent results in deeply subwavelength thickness films demonstrate coherent control and logical gate operations with both classical and single-photon light sources. However, quantum processing and devices typically involve more than one photon and nontrivial input quantum states. Here we experimentally investigate two-photon N00N state coherent absorption in a multilayer graphene film. Depending on the N00N state input phase, it is possible to selectively choose between single- or two-photon absorption of the input state in the graphene film. These results demonstrate that coherent absorption in the quantum regime exhibits unique features, opening up applications in multiphoton spectroscopy and imaging.

Received 3 March 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.023601

Physics Subject Headings (PhySH)

Quantum foundations Quantum optics Second order nonlinear optical processes

Graphene

Atomic, Molecular & Optical

Authors & Affiliations

Thomas Roger¹, Sara Restuccia², Ashley Lyons¹, Daniel Giovannini^2,*, Jacquiline Romero^2,†, John Jeffers³, Miles Padgett², and Daniele Faccio¹

¹School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh, United Kingdom
²School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
³Department of Physics, University of Strathclyde, Glasgow, G4 0NG Scotland, United Kingdom

^*Present address: The Edward S. Rogers Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario M5S 3G4, Canada.
^†Present address: School of Mathematics and Physics, University of Queensland, Brisbane 4072, Australia.

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Vol. 117, Iss. 2 — 8 July 2016

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Images

Figure 1
Experimental layout. A frequency tripled Nd:YAG laser is used to pump a type 1 BBO crystal producing correlated biphotons. The biphotons ( $P 1$ , $P 2$ ) are separated by a knife-edge prism (KEP) and coupled to single-mode polarization maintaining fibers. One of the fiber couplers is mounted on a translation stage in order to control the relative delay between the two photons. The photons are recombined on a $50 ∶ 50$ fiber beam splitter ${BS}_{1}$ within their coherence length in order to produce bunched photon pairs which exit the beam splitter in the quantum state $| 2, 0 ⟩ - e^{2 i ϕ} | 0, 2 ⟩$ . The phase $ϕ$ of the quantum state is tuned by a mirror mounted to a piezoelectrically transduced stage. The quantum state is combined once again onto a second beam splitter ${BS}_{2}$ , which is either a lossless $50 ∶ 50$ beam splitter or an absorptive graphene beam splitter. The output states from the second beam splitter are measured with four single-photon avalanche diodes (SPADs), $A$ , $B$ , $C$ , and $D$ after two further $50 ∶ 50$ beam splitters, ${BS}_{3}$ and ${BS}_{4}$ . Inset (a) shows a schematic drawing of the output beam splitter ${BS}_{2}$ with the input and output states, as referred to in the text. The HOM interference measured at the output of ${BS}_{1}$ with a depth of 89% is shown in inset (b).
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Figure 2
Lossless $50 ∶ 50$ beam splitter. (a) Raw experimental data showing the coincidence counts per second measured between detectors $A$ and $B$ as a function of interferometer mirror position. We note that the nonperfect visibility of the fringes presented is due to imperfections in the lossless beam splitter as well as a background contribution to the coincidence rate from $| 11 ⟩$ states at the input to ${BS}_{2}$ . (b) Blue curve, Fourier transform of the single detector counts showing an oscillation peak at $k_{1} = 1 / λ$ . Green shaded area curve, Fourier transform of the coincidence counts showing a peak at frequency $k_{2} = 2 / λ$ . Dashed black curve, Gaussian fit to the peak at $k_{2}$ used to filter the raw data. (c) Fourier-filtered data for all six detection pairs as a function of mirror position. Same-side detection pairs ( $A B$ and $C D$ ) are $π$ out of phase with respect to opposing-side detector pairs (e.g., $B C$ and $A D$ ).
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Figure 3
Experimental data from a lossy beam splitter. (a) Raw data showing the coincidence counts per second measured between detectors $A$ and $B$ as a function of interferometer mirror position. (b) Blue curve, Fourier transform of the single detector counts showing an oscillation at $k_{1} = 1 / λ$ . Green shaded curve, Fourier transform of the coincidence counts showing a peak at frequency $k_{2} = 2 / λ$ . Dashed black curve, Gaussian fit to the peak at $k_{2}$ used to filter the raw data. (c) Fourier-filtered data for all six detection pairs as a function of mirror position. All six coincidence traces are in phase, suggesting a coherent absorption effect. The slight phase shift seen here is due to the asymmetry of the air-graphene-substrate beam splitter.
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Figure 4
Experimentally measured total coincidence rates. Sum of coincidence counts for all six detection pairs as a function of interferometer mirror position measured for (i) no sample (black curve), (ii) $50 ∶ 50$ lossless beam splitter (purple curve), and (iii) lossy graphene beam splitter (red curve). The blue curve is a three-parameter fit to the data using $A \sin (k_{2} . Δ x_{2} + ϕ) + B$ , where $A$ , $B$ , and $ϕ$ are free parameters. In (iii), the minima and maxima are related to a switching between input photon states $| 2_{+} ⟩$ and $| 2_{-} ⟩$ , respectively, and, therefore, to switching in the output states from single- to two-photon absorption.
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