Quantum optical coherence: From linear to nonlinear interferometers

Kai-Hong Luo, Matteo Santandrea, Michael Stefszky, Jan Sperling, Marcello Massaro, Alessandro Ferreri, Polina R. Sharapova, Harald Herrmann, and Christine Silberhorn

Phys. Rev. A 104, 043707 – Published 21 October 2021

Abstract

Interferometers provide a highly sensitive means to investigate and exploit the coherence properties of light in metrology applications. However, interferometers come in various forms and exploit different properties of the optical states within. In this paper, we introduce a classification scheme that characterizes any interferometer based on the number of involved nonlinear elements by studying their influence on single-photon and photon-pair states. Several examples of specific interferometers from these more general classes are discussed, and the theory describing the expected first-order and second-order coherence measurements for single-photon and single-photon-pair input states is summarized and compared. These theoretical predictions are then tested in an innovative experimental setup that is easily able to switch between implementing an interferometer consisting of only one or two nonlinear elements. The resulting singles and coincidence rates are measured in both configurations and the results are seen to fit well with the presented theory. The measured results of coherence are tied back to the presented classification scheme, revealing that our experimental design can be useful in gaining insight into the properties of the various interferometeric setups containing different degrees of nonlinearity.

Received 16 March 2021
Revised 7 September 2021
Accepted 27 September 2021

DOI:https://doi.org/10.1103/PhysRevA.104.043707

Physics Subject Headings (PhySH)

Nonlinear optics Optical coherence Quantum optics

Optical interferometry

Atomic, Molecular & Optical

Authors & Affiliations

Kai-Hong Luo ^1,*, Matteo Santandrea ¹, Michael Stefszky¹, Jan Sperling ¹, Marcello Massaro ¹, Alessandro Ferreri ², Polina R. Sharapova², Harald Herrmann¹, and Christine Silberhorn¹

¹Integrated Quantum Optics Group, Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
²Department of Physics and CeOPP, Paderborn University, Warburger Strasse 100, 33098 Paderborn, Germany

^*khluo@mail.uni-paderborn.de

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 104, Iss. 4 — October 2021

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
General scheme of an optical interferometric setup, showing that the setup can be decomposed into its constituent parts. The decomposition into generation, manipulation, and detection stages for many systems is somewhat arbitrary and is explored in this paper.
Reuse & Permissions
Figure 2
Schematic of various interferometeric systems. (a) Single-photon input state in a linear interferometer. (b) Single-photon pair input state in a linear interferometer, which may exhibit entanglement. (c) Vacuum-seeded seminonlinear interferometer, producing identical signal and idler photons from a parametric downconversion (PDC) process. (d) Vacuum-seeded nonlinear interferometer with PDC stages as the nonlinear elements. For each interferometer configuration, both mean photon number from each output, $n_{a}$ and $n_{b}$ , and coincidence probability, $P_{a b}$ , are illustrated to the right of the setup. The inserts show details of the fringing pattern around the region of maximum interference. The dashed box indicates what is considered as the generation stage in each optical interferometer.
Reuse & Permissions
Figure 3
Experimental setup (a) and corresponding conceptual overview of seminonlinear (b) and folded, nonlinear interferometer (c) based around a single nonlinear waveguide. Full details of the setup are provided in the text. The delay stage used in both experimental geometries is identical. (b) Illustration of a seminonlinear interferometer. When the reflected pump beam in the backward direction is blocked, i.e., only the forward pump is present, the QWP is turned to $45^{\circ}$ and the HWP is turned to $22 . 5^{\circ}$ , we have the HOM interference occurring at PBS2. (c) Schematic diagram of folded nonlinear interferometer. When the QWP is set at $0^{\circ}$ , we directly and individually count the number of signal and idler photons because of the polarization-dependent splitting.
Reuse & Permissions
Figure 4
Measured singles (black and red for photons $a$ and $b$ , respectively) and coincidence (blue) count rates for seminonlinear (a) and nonlinear (b), (c) interferometer configurations as a function of the varied position of the movable mirror (MM) from Fig. 3. Tick labels on top are the corresponding time delays. The reduction in count rates in (a) and (b) at larger translation stage positions are caused by a slight misalignment of the stage. Graph (c) shows a magnified view of the interference fringes at the time delay corresponding to maximum visibility ( $- 4.50$ ps). Connecting solid lines are provided as a guide for the eye.
Reuse & Permissions
Figure 5
Comparison of theory and measured results from the reconfigurable experimental setup for a 19-mm-long sample with 1-nm-broad spectral filters. The experiment is first configured for seminonlinear HOM-type interference (cyan), before being reconfigured to realize a nonlinear interferometer (orange). Solid lines correspond to the measured experimental results while dashed lines correspond to the theoretical envelopes given by Eqs. (12) and (16).
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information