Entanglement Enabled Intensity Interferometry of different wavelengths of light

Highlights

• We use quantum entanglement to erase the color of photons for a new imaging method.

• Can achieve higher resolution imaging by accessing hidden phase information.

• We detail practical experimental designs to implement our theoretical protocols.

Abstract

We propose methods to perform intensity interferometry of photons having two different wavelengths. Distinguishable particles typically cannot interfere with each other, but we overcome that obstacle by processing the particles via entanglement and projection so that they lead to the same final state at the detection apparatus. Specifically, we discuss how quasi-phase-matched nonlinear crystals can be used to convert a quantum superposition of light of different wavelengths onto a common wavelength, while preserving the phase information essential for their meaningful interference. We thereby gain access to a host of new observables, which can probe subtle frequency correlations and entanglement. Further, we generalize the van Cittert–Zernike formula for the intensity interferometry of extended sources, demonstrate how our proposal supports enhanced resolution of sources with different spectral character, and suggest potential applications.

Introduction

The Hanbury-Brown–Twiss (HBT) effect is a staple of multi-particle interferometry, with broad applications in experimental physics [1], [2], [3], [4], [5], [6]. It is generally considered that indistinguishability of particles is a central requirement for multi-particle interference, but in fact it is possible to generalize HBT to allow for the interference of distinguishable particles. Interference between potentially distinguishable particles can be observed by a using detection apparatus that does not, at a fundamental quantum mechanical level, distinguish the particles: a procedure we call “Entanglement Enabled Intensity Interferometry” (E${}^2$I${}^2$).

To enable interference between photons of different wavelength, it is not enough that the detector fail to read out the wavelength of an incoming photon. Rather, the detector must reach the same final quantum state in response to photons of either wavelength. To achieve that goal, one must exploit appropriate projections and/or entanglement between the incoming particles and the detector. In this paper, we explore several methods involving nonlinear crystals, coherent pumps, and filters to demonstrate intensity interferometry with photons of different wavelengths. Our methods potentially have applications in several fields, notably including astronomy and fluorescence microscopy, in which one might profit from improved resolution among sources with different spectral characteristics.

Nonlinear optical properties of crystals figure centrally in our practical proposals. Frequency upconversion and downconversion are forms of three-wave mixing in which the frequency of a photon is changed while its other quantum properties (including phase information) are preserved [7], [8], [9]. In these processes, an input photon as well as a coherent state (referred to as the pump) interacts in the nonlinear crystal in such a way that the frequency of the input photon is altered while a pump photon is created or annihilated, conserving energy. Quantum frequency upconversion has been used to bring the wavelength of a photon into a region where detectors are very efficient [10], [11], while quantum frequency downconversion may be used to convert photons from a wavelength convenient for information processing to a wavelength that is convenient for transmission [12], [13], [14], [15].

The possibility to perform frequency conversion on sources of different wavelength, thus producing indistinguishable photons which subsequently interfere, has been demonstrated experimentally. This was achieved in the context of the Hong–Ou–Mandel dip, where two photons of different wavelength were both upconverted before arriving simultaneously at a beamsplitter [16]. The quality of the resulting interference quantifies the success of the upconversion and its ability to preserve phase information. It is even possible to combine frequency conversion and beamsplitting into a single step [17].

In HBT, two detectors can receive photons from either of two distinct sources. The inability of the detectors to determine which photons come from which source is a necessary condition for two-photon interference. If the sources emit distinguishable photons, it becomes possible to determine which photons were emitted from which source. If our detectors are capable of making that determination, then interference becomes impossible. In many applications of interferometry, one only has access to light from a particular source after it has been spatially mixed with light from other sources. To address such applications we must modify the procedures of the previous paragraph. A major goal of this paper is to spell out how to do that.

In Section 2, we explain E${}^2$I${}^2$ in the context of HBT and describe the mechanism that allows one to perform intensity interferometry on sources of different wavelengths conceptually. Then in Section 3, we detail three different methods, of increasing complexity and generality, for implementing this mechanism for E${}^2$I${}^2$. Section 4 provides a detailed, concrete proposal for a proof-of-principle experiment demonstrating the first of the methods from Section 3. Applications are described mathematically in Section 5, where we generalize the classic van Cittert–Zernike formulae, and specific examples are given in Section 6. Additional protocols for E${}^2$I${}^2$ in more general settings are presented in theAppendix A Polarization, Appendix B Bosons and fermions, Appendix C General entanglement, Appendix D Single source of decaying particles.