Hong-Ou-Mandel (HOM) interference of multi-mode frequency entangled states plays a crucial role in quantum metrology. However, as the number of modes increases, the HOM interference pattern becomes increasingly complex, making it challenging to comprehend intuitively. To overcome this problem, we present the theory and simulation of multi-mode-HOM interference (MM-HOMI) and compare it to multi-slit interference (MSI). We find that these two interferences have a strong mapping relationship and are determined by two factors: the envelope factor and the details factor. The envelope factor is contributed by the single-mode HOM interference (single-slit diffraction) for MM-HOMI (MSI). The details factor is given by sin ( Nx )/sin ( x ) ([sin ( Nv )/sin ( v )] 2 ) for MM-HOMI (MSI), where N is the mode (slit) number and x ( v ) is the phase spacing of two adjacent spectral modes (slits). As a potential application, we demonstrate that the square root of the maximal Fisher information in MM-HOMI increases linearly with the number of modes, indicating that MM-HOMI is a powerful tool for enhancing precision in time estimation. We also discuss multi-mode Mach-Zehnder interference, multi-mode NOON-state interference, and the extended Wiener-Khinchin theorem. This work may provide an intuitive understanding of MM-HOMI patterns and promote the application of MM-HOMI in quantum metrology.
Hong-Ou-Mandel (HOM) interference of multi-mode frequency entangled states plays a crucial role in quantum metrology. However, as the number of modes increases, the HOM interference pattern becomes increasingly complex, making it challenging to comprehend intuitively. To overcome this problem, we present the theory and simulation of multi-mode-HOM interference (MM-HOMI) and compare it to multi-slit interference (MSI). We find that these two interferences have a strong mapping relationship and are determined by two factors: the envelope factor and the details factor. The envelope factor is contributed by the single-mode HOM interference (single-slit diffraction) for MM-HOMI (MSI). The details factor is given by sin ( Nx )/sin ( x ) ([sin ( Nv )/sin ( v )] 2 ) for MM-HOMI (MSI), where N is the mode (slit) number and x ( v ) is the phase spacing of two adjacent spectral modes (slits). As a potential application, we demonstrate that the square root of the maximal Fisher information in MM-HOMI increases linearly with the number of modes, indicating that MM-HOMI is a powerful tool for enhancing precision in time estimation. We also discuss multi-mode Mach-Zehnder interference, multi-mode NOON-state interference, and the extended Wiener-Khinchin theorem. This work may provide an intuitive understanding of MM-HOMI patterns and promote the application of MM-HOMI in quantum metrology.
Quantum entanglement is a vital resource in quantum information processing. High-dimensional quantum entanglement offers advantages that classical systems cannot surpass, particularly in enhancing channel capacity, improving system noise resilience, and increasing sensitivity to external environments. The construction of multimode entanglement in the spectral domain is well-suited for fiber-optic systems. Here, we present a straightforward scheme for generating multimode frequency-bin entanglement using a semiconductor chip through a simple mode conversion. A general model for Hong–Ou–Mandel (HOM) interference with a multimode frequency-bin entangled state is presented and applied to the experiments. The multimode entangled photons we produced exhibit HOM interference with a high-visibility beating pattern, demonstrating a strong relationship with the mode number, mode spacing, and the profile of the single mode. Building on the Fisher information analysis, we explore the relationship between the features in multimode entangled state interference traces and the precision of interferometric measurements even in the presence of experimental nonidealities. This work may deepen the understanding of multimode frequency-bin entanglement and advance the application of multimode HOM interference in quantum sensing.
The Hong-Ou-Mandel (HOM) effect ranks among the most notable quantum interference phenomena, and is central to many applications in quantum technologies. The fundamental effect appears when two independent and indistinguishable photons are superimposed on a beam splitter, which achieves a complete suppression of coincidences between the two output ports. Much less studied, however, is when the fields share coherence (continuous-wave lasers) or mode envelope properties (pulsed lasers). In this case, we expect the existence of two distinct and concurrent HOM interference regimes: the traditional HOM dip on the coherence length time scale, and a structured HOM interference pattern on the pulse length scale. We develop a theoretical framework that describes HOM interference for laser fields having arbitrary temporal waveforms and only partial overlap in time. We observe structured HOM interference from a continuous-wave laser via fast polarization modulation and time-resolved single photon detection fast enough to resolve these structured HOM dips.
The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons - those with complex spatial profiles - under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions.
The Hong-Ou-Mandel (HOM) interference in the multimode frequency domain has been explored for precision metrology, with several experimental demonstrations exploiting its robustness against dispersion and phase noise, as well as its large dynamic range and compatibility with fragile samples. Conventional multimode HOM metrology exploits frequency-entangled states, which naturally satisfy bosonic exchange symmetry under any centered symmetric joint spectral distribution, to provide these advantages. However, these entangled states are typically generated via spontaneous parametric down-conversion (SPDC), requiring strong pump lasers that hinder practical implementation. In this paper, we employ frequency product states, which do not possess entanglement or path-mode exchange symmetry, as the probe state and post-select measurement outcomes exhibiting frequency anti-correlation. Our results demonstrate that these advantages,peak narrowing, dispersion cancellation, phase-noise immunity, a large dynamic range, and compatibility with fragile samples, arise neither from entanglement nor from bosonic exchange symmetry, but rather from spectral anti-correlation. We further show that entanglement is not the source of the measurement precision: the entanglement-free approach attains the same quantum Fisher information as the entangled-state scheme, indicating that the fundamental precision limit does not originate from entanglement.
Abstract Quantum interference is known to become extinct with distinguishing information, as illustrated by the ubiquitous double-slit experiment or the two-photon Hong–Ou–Mandel effect. In the former case single particle interference is destroyed with which-path information while in the latter bunching interference tails-off as photons become distinguishable. It has been observed that when more than two particles are involved, these interference patterns are in general a non-monotonic function of the distinguishability. Here we perform a comprehensive characterization, both theoretically and experimentally, of four-photon interference by analyzing the corresponding correlation functions, contemplating several degrees of distinguishability across different parameters. This study provides all the necessary tools to quantify the impact of multi-photon interference on precision measurements of parameters such as phase, frequency, and time difference. We apply these insights to quantify the precision in the estimation of an interferometric phase in a two-port interferometer using a four-photon state. Our results reveal that, for certain phase values, partially distinguishable multi-photon states can achieve higher Fisher information values compared to the two-photon experiment. These findings highlight the potential of distinguishable multi-photon states for enhanced precision in quantum metrology and related applications.
Earth, Moon and Sun unite when they star together in the three-body problem, whose intricate plot still baffles us today. For some reason, the factorization of the two-body problem into two one-body problems does not, in general, cross the N=2 border. Is computational irreducibility responsible for this emergence of complexity, as Stephen Wolfram likes to think? We don't know. The introduction to this thesis in Chapter 1, however, makes it clear that the history of science is marked by intermittent encounters of sudden complexities when the number 2 is left behind. In Chapter 2, I present an experiment that is quite similar in spirit, for my colleagues and I observe three-photon interference without two-photon and single-photon interference. We had to overcome significant experimental challenges that are typical for most quantum interference experiments involving more than two photons. Next in line is the three-slit interference experiment. Again a deceptively simple extension of the famous double-slit experiment, we are faced with questions that are difficult to access experimentally: the existence of genuine three-slit interference was first denied and then affirmed, though no experiment has decided yet. My contribution to the study of this problem is outlined in Chapter 3, where I use symmetry of measurement settings in such interference experiments to theoretically derive higher-order interference terms. In Chapter 4, I take a step back in one sense, for we study a two-photon phenomenon, but we also leap forward and discover entirely new interference landscapes. Theoretically and experimentally, I demonstrate how to use a polarization-modulated lasers to go beyond the standard Hong-Ou-Mandel (HOM) dip, and generate both triangular and square wave HOM interference patterns. Two-photon interference is also subject of Chapter 5, but with an interesting twist. While laser HOM interference relies on two independent photons, here we endow the pair with the strongest known correlations, namely entanglement. More specifically, we entangle a polarization and a time-bin qubit and use this hybrid to assess the viability of a rather special interferometer for quantum communication purposes.