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Polarization-Controlled Temporal-Mode Interference with Quantum States of Light

Tayyab Yahya

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

Spatial double-slit experiments have been central to understanding wave-particle duality, demonstrating how single photons interfere in transverse momentum when given two spatially separated alternatives. Analogue demonstrations have shown the corresponding relationship in the time-frequency domain with classical electric fields. Extending this to quantum states of light reveals how different photon states acquire different phases through the same temporal separation, producing distinct spectral interference signatures. In this work, we investigate temporal interference with three different quantum states of light — a single-photon state, a separable two-photon state, and a two-photon NOON state — all on the same physical platform and with the same temporal delay. Experimentally, we prepare ultrafast pulses of photon states in polarization and use the birefringent delay of beta-barium borate (BBO) crystals to introduce a femtosecond temporal separation between the orthogonal polarization components. A polarization projection in a superposition basis then removes the which-time information and produces spectral interference, providing an analogue of the temporal double slit. The photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a Sagnac interferometer, tuned to produce all three quantum states by adjusting the pump polarization, with the NOON state reaching a measured visibility of (88.99 ± 0.21)%. The spectra are recorded through dispersive Fourier transform using a long single-mode fiber and single photon detectors. The measured spectra show that single-photon and separable two-photon states both oscillate at the same rate, consistent with a phase given by the photon frequency multiplied by the temporal delay, with the two-photon spectral pattern being the product of the individual single-photon spectra. The NOON state, in contrast, oscillates twice as fast, governed by the collective phase of the two photons, which depends on the sum of their frequencies rather than on the individual photon spectral modulations, and which reduces to twice the single-photon phase along the equal-frequency diagonal. This doubled phase accumulation makes NOON-state temporal interference directly relevant to quantum-enhanced sensing and metrology. Different polarization projections further allow tuning of the interference patterns across all three states.

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Spatial double-slit experiments have been central to understanding wave-particle duality, demonstrating how single photons interfere in transverse momentum when given two spatially separated alternatives. Analogue demonstrations have shown the corresponding relationship in the time-frequency domain with classical electric fields. Extending this to quantum states of light reveals how different photon states acquire different phases through the same temporal separation, producing distinct spectral interference signatures. In this work, we investigate temporal interference with three different quantum states of light — a single-photon state, a separable two-photon state, and a two-photon NOON state — all on the same physical platform and with the same temporal delay. Experimentally, we prepare ultrafast pulses of photon states in polarization and use the birefringent delay of beta-barium borate (BBO) crystals to introduce a femtosecond temporal separation between the orthogonal polarization components. A polarization projection in a superposition basis then removes the which-time information and produces spectral interference, providing an analogue of the temporal double slit. The photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a Sagnac interferometer, tuned to produce all three quantum states by adjusting the pump polarization, with the NOON state reaching a measured visibility of (88.99 ± 0.21)%. The spectra are recorded through dispersive Fourier transform using a long single-mode fiber and single photon detectors. The measured spectra show that single-photon and separable two-photon states both oscillate at the same rate, consistent with a phase given by the photon frequency multiplied by the temporal delay, with the two-photon spectral pattern being the product of the individual single-photon spectra. The NOON state, in contrast, oscillates twice as fast, governed by the collective phase of the two photons, which depends on the sum of their frequencies rather than on the individual photon spectral modulations, and which reduces to twice the single-photon phase along the equal-frequency diagonal. This doubled phase accumulation makes NOON-state temporal interference directly relevant to quantum-enhanced sensing and metrology. Different polarization projections further allow tuning of the interference patterns across all three states.
Creating and controlling well-defined single-photon states is important for many quantum enhanced technologies. Information can be encoded in any degree of freedom associated with a single-photon field excitation, for example in the polarization or transverse spatial mode structure. The ability to encode multiple qubits in these states is desirable for high data transmission rates and increased information processing capacity. The spectral-temporal domain offers a large Hilbert space for encoding information, well suited to integrated optical architectures owing to the low cross-talk between channels. Indeed, time-frequency encoding is an integral component of existing information technologies infrastructure. Thus, complete, coherent control of the spectral-temporal mode structure of light is essential to advancing optical quantum technologies. Arbitrary control of single-photon states has been demonstrated in the polarization and spatial-momentum degrees of freedom however, is yet to be established in the spectral-temporal domain. Recently it was shown that spectral-temporal pulse shaping is experimentally feasible using nonlinear optical methods. However, such techniques can introduce noise photons, are challenging to implement deterministically and require specially prepared auxiliary pump pulses. Furthermore, they are typically only possible at relatively low repetition rates to avoid damage of nonlinear optical materials. Here, we demonstrate deterministic pulse shaping of single-photon wave packets by introducing a time-varying phase. Applying linear or quadratic phase to the wave packet introduces a spectral shift or spectral broadening, respectively. Achieving significant spectral manipulation requires temporal-phase modulation on the order of π. The phase must also vary on the same time scale as the optical pulses, approximately 1 ps in duration here. This relatively rapid phase variation is achieved using a fast electro-optic phase modulator. The modulator is driven by a time-varying voltage that is synchronized with a pulse train of single-photon wave packets for accurate temporal phase control. In this thesis, we experimentally demonstrate control of the spectral-temporal state of single-photon wave packets using this method. Heralded single-photon wave packets are generated by spontaneous parametric down conversion pumped by a frequency-doubled Titanium-Sapphire laser oscillator with 80 MHz repetition rate. To achieve significant modulation of single-photon pulses a 10 V peak-to-peak radio-frequency signal of 40 GHz drives the phase modulator, which requires approximately 3.6 V to achieve a π phase shift. The signal is synchronized with the oscillator pulse train using custom designed electronics. Details of these electronics are presented, resulting in a robust phase and amplitude controllable 40 GHz voltage source, phase locked to the single-photon pulse train. To demonstrate the utility of this pulse-shaping method we experimentally show spectral shearing of almost 1 nm for single-photon wave packets with 830 nm central wavelength and 1 nm bandwidth. Measurement of the second-order intensity correlation before and after the wave-packet manipulation remains constant within uncertainty of the measurement, showing that the quantum nature of the single-photon source is not deteriorated by the modulator. Preservation of the wave-packet coherence is verified by two-photon interference between spectrally sheared and non-modulated single-photons.
We propose theoretically a quantum interferometer in which the NOON state interferometer is combined with the Hong-Ou-Mandel interferometer. With this interferometer, the temporal interference patterns associated with biphoton frequency sum and difference can be shown in different parts of a single interferogram. It is thus possible to simultaneously obtain the spectral correlation information of biphotons in both frequency sum and difference by taking the Fourier transform from such an interferogram. This provides a method for complete spectral characterization of an arbitrary two-photon state with exchange symmetry and might be useful in quantum Fourier-transform spectroscopy where direct spectral measurement is difficult. Furthermore, as it can realize the measurement of time intervals on three scales at the same time, we expect that it can provide a method in quantum metrology. Finally, we discuss another potential application of such an interferometer in the generation and characterization of high-dimensional and phase-controlled frequency entanglement.
Abstract Wave–particle duality is a counterintuitive nature of quantum physics that challenges many common-sense assumptions, and Young’s double-slit interference is a prototypical example. While most quantum erasure experiments emphasized the choice of erasing or marking the which-path information of one quantum system, we use frequency entanglement to report a nonlocal temporal double-slit interferometer such that the which-time information determines the wave-like or particle-like behaviors. Since frequency-entangled photons are created simultaneously by using spontaneous parametric down conversion, the mark of temporal distinguishability is readily prepared by delaying one of the entangled photons, and its quantum eraser is implemented by using spectrally resolved detection with a tunable delayed choice. These results may provide an alternative aspect and insight into the role of the temporal degree in quantum-light complementarity and photon interference.
This thesis concerns the role of polarization, coherence, and geometric phase in both quantum and classical light interference.In the quantum domain, the thesis analyzes vector-light interference in a doubleslit geometry for single-photon and multiphoton states.Using a coherence Stokes formalism, a unified description of polarization modulation, geometric phase, and wave-particle duality is established.Single-photon interference is shown to exhibit a fundamental complementarity relation that directly links the geometric phase at the observation screen to which-path information at the slits.This framework is further extended to higher-order interference of multimode N00N states, where Nth-order polarization modulation and geometric-phase accumulation scale linearly with photon number and lead to new higher-order vector-light complementarity relations.In the classical domain, the thesis explores beam and pulse shaping enabled by polarization gratings.Spatial polarization gratings are shown to provide control over the profiles, coherence, diffraction orders, and polarization of partially coherent and partially polarized pulsed beams.The analysis is further extended to ultrafast pulse shaping, where spectral polarization gratings generate multiple temporally shifted pulses with distinct polarization states.Furthermore, a novel Poincaré pulse in the spatiospectral domain is presented.
The double-slit experiment strikingly demonstrates the wave-particle duality of quantum objects. In this famous experiment, particles pass one-by-one through a pair of slits and are detected on a distant screen. A distinct wave-like pattern emerges after many discrete particle impacts as if each particle is passing through both slits and interfering with itself. Here we present a temporally- and spatially-resolved measurement of the double-slit interference pattern using single photons. We send single photons through a birefringent double-slit apparatus and use a linear array of single-photon detectors to observe the developing interference pattern. The analysis of the buildup allows us to compare quantum mechanics and the corpuscular model, which aims to explain the mystery of single-particle interference. Finally, we send one photon from an entangled pair through our double-slit setup and show the dependence of the resulting interference pattern on the twin photon's measured state. Our results provide new insight into the dynamics of the buildup process in the double-slit experiment, and can be used as a valuable resource in quantum information applications.
Quantum entanglement enables a wide range of fundamental studies and practical applications in quantum optics, computing, and communication. In this work, we investigate two-photon interference using position-momentum entangled photons generated via Type-II Spontaneous Parametric Down-Conversion (SPDC). By employing a double-slit setup, we explore two distinct quantum interference phenomena: the Hanbury Brown and Twiss (HBT) effect, where the photons pass through different slits, and NOON-state interference, where both photons traverse the same slit. We deterministically separate the two photons based on their orthogonal polarizations and demonstrate that both interference effects persist despite their distinguishability at the detectors. This result goes beyond the conventional understanding of two-photon interference and reveals a novel nonlocal HBT effect, where interference occurs even in the absence of spatial overlap, and is rooted in entanglement. Our findings deepen the understanding of quantum interference and open new avenues for applications in quantum optics and precision measurement.