Summary form only given. Consider an experiment where a single photon is split into two wave-packets by a beam splitter and where the two wave packets are made to overlap in a specific region in space. If the two wave-packets arrive at the same time, an interference pattern can be recorded by a classical detector such as a photographic plate. If however, the difference in arrival time between the two wave-packets is made to be larger than the coherence time of the wave packets, the interference pattern, as recorded by the detector, will disappear. It has been argued that if the classical detector is replaced by a material that can remember the phase of the electromagnetic field, i.e. a material with a long homogeneous dephasing time, it would be possible to record the interference between the two wave-packets even if the time difference between them is much larger than the coherence time. We denote this single-photon self-interference. The interference pattern would take the form of a frequency dependent population grating in the material and could be detected by diffracting a light pulse on this grating. The delayed single-photon self-interference experiment has several unique features. It is a four-wave mixing experiment where the two first pulses share a total of only one photon. Thus interaction between these two pulses and the material, normally considered as a nonlinear multiphoton process, is here carried out by a single photon. We have performed experiments with multiphoton excitation pulses and extrapolated the data to the single photon level. These experiments support the conclusion from the theoretical calculations that delayed single-photon self-interference could be observed.
Summary form only given. Consider an experiment where a single photon is split into two wave-packets by a beam splitter and where the two wave packets are made to overlap in a specific region in space. If the two wave-packets arrive at the same time, an interference pattern can be recorded by a classical detector such as a photographic plate. If however, the difference in arrival time between the two wave-packets is made to be larger than the coherence time of the wave packets, the interference pattern, as recorded by the detector, will disappear. It has been argued that if the classical detector is replaced by a material that can remember the phase of the electromagnetic field, i.e. a material with a long homogeneous dephasing time, it would be possible to record the interference between the two wave-packets even if the time difference between them is much larger than the coherence time. We denote this single-photon self-interference. The interference pattern would take the form of a frequency dependent population grating in the material and could be detected by diffracting a light pulse on this grating. The delayed single-photon self-interference experiment has several unique features. It is a four-wave mixing experiment where the two first pulses share a total of only one photon. Thus interaction between these two pulses and the material, normally considered as a nonlinear multiphoton process, is here carried out by a single photon. We have performed experiments with multiphoton excitation pulses and extrapolated the data to the single photon level. These experiments support the conclusion from the theoretical calculations that delayed single-photon self-interference could be observed.
It has been suggested that a single photon can interfere with itself even if the difference between the two paths in the interferometer is larger than the ``length'' of the photon [Kessel' and Moiseev, JETP Lett. 58, 81 (1993)]. The interference is regained by detecting the photons using a photon-echo process, where the absorbing atoms will, effectively, act as narrow-band filters. Such an experiment has several unique features. For example, single photons are used to carry out what is generally regarded as a multiphoton process; the absorption of a single photon can be regarded as separated into two different moments in time; the fact that the single-photon interference is regained using atoms acting as narrow-band filters as the detector means that the control of the detection process is quite different from cases where electronic (or possibly photographic) detection is used to register the interference etc. In general, interference and absorption are combined and intertwined in the experiment, which is discussed in this paper, in a way that has not been done before. In the present paper the possibility to carry out such an experiment in practice is investigated in some detail. The signal strength is explicitly calculated and the results are compared with our experimental data for the case of many interfering photons. We imply that this result can readily be extrapolated to the single-photon situation. We analyze the material parameters that are important for carrying out the experiment and give specific examples of some suitable materials.
A photon echo experiment has been performed using accumulated highly attenuated laser pulses. We show experimentally that the photon echo process can be performed with, on the average, less than one photon in each pair of excitation pulses. The results support an interpretation where this nonlinear process can be performed with, on the average, less than one photon shared between two of the optical fields involved in the degenerate four-wave-mixing process. Further, we argue that the experiment can be interpreted as a form of delayed self-interference for photon wave packets that do not overlap in both space and time.
For centuries Young’s double-slit interference continues to be a hot discussion subject about whether light is waves or particles. This work unravels the self-interference parados, and sheds light on such a concept that assumes a photon can split, self-interfere, and recombine. This work elucidates how coherent photons from a laser source could produce a double-slit interference pattern without the hypothesis of unphysical splitting and recombination of a single photon. Unlike the conventional single wave-function description for the whole ensemble of particles, we develop a pilot-wave trajectory approach to track every photon’s wave-packet propagation and calculate the evolution of the interference intensity in time. We demonstrate how wave packets and phase coherence affect the interference pattern. To resolve the century-old self-interference paradox, we show that such an hypothesis is unnecessary, and the illusion is due to the long coherence length of laser photons and overlaps of delocalized light wave packets.
Abstract The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon wave packets, like the decomposition into single-frequency field modes or spatio-temporal modes matching the photonic wave packets. Both representations lead to equivalent results, and a photon-by-photon analysis reveals that the quantum-mechanical two-photon interference can be interpreted as a classical one-photon interference once a first photon is detected. A novel time-dependent quantum-beat effect is predicted if the interfering photons have different frequencies. The calculation also reveals that full two-photon fringe visibility can be achieved under almost any circumstances by applying a temporal filter to the signal. PACS 42.50.Dv, 42.50.Ct 1
Within the framework of the ‘Pairwise Interference Model’ of light–matter interaction, it is postulated that light particles follow definite trajectories, and thus, for example, in the double-slit experiment, a particle can pass through only one of the two slits. On this premise, the interference of two photons is examined in greater detail. It is hypothesized that the interference of a photon pair requires the involvement of matter and, initially, that both molecular excitations and photons oscillate at the same frequency and that the continuity of the oscillation is not disrupted by absorption and emission. The molecular excitations in the light source are supposed to oscillate synchronously. Both photons arrive at the same point on the detector but may travel along different paths and therefore arrive at different times. Under these conditions, their phase difference, φ(2) – φ(1), is always zero. Consequently, no interference pattern can form on the detector screen and therefore the assumptions made are incorrect. Alternatively, one may assume that only the photon oscillates, whereas the excitation stores the phase, φ, possessed by the photon at the instant of absorption. In this case, φ(2) – φ(1) corresponds to the difference in travel times modulo the oscillation period, and an interference pattern can form. However, this assumption is problematic for some reasons: the nature of the matter-based memory remains unclear; according to the special theory of relativity, no time elapses for a particle travelling at the speed of light, meaning that it cannot oscillate; and the assumption contradicts Bohr’s correspondence principle. In a classical wave, the phase information propagates away from the source at the wave velocity without changing. This leads to the alternative possibility that the excitations oscillate, whereas the photons do not. Instead, the photons transport information about the phase of the excitation at the instant of emission. As can be shown, in this case, φ(2) – φ(1) likewise corresponds to the difference in travel times modulo the oscillation period. However, this hypothesis contradicts the de Broglie postulate, according to which all particles exhibit wave properties, and the relation ε = hν must therefore be interpreted differently. It also raises the question of how the dimensions of a laser, specifically the mirror separation, can influence the wavelength of the amplified light if a photon has no wavelength. Using replicator dynamics and the ‘Pairwise Interference Model’ of light–matter interaction, a simulation demonstrates that, in a simplified laser model, assuming that photons do not oscillate whereas excitations do, self-organisation gives rise to a phase pattern in the sequence of photons within the emitted light beam that corresponds to the pattern obtained by discretising a classical wave. Thus, coherent light can exhibit wave properties even if photons themselves do not. Finally, the possibility of how incoherent light acquires wave properties is briefly discussed.
We present time-resolved diffraction and two-slit interference experiments using a streak camera as a detector for femtosecond pulses of photons. These experiments show how the diffraction pattern is built by adding frames of a few photons to each frame. It is estimated that after 300 photons the diffraction pattern emerges. With time resolution we can check the speed of light and put an upper limit of 2 ps at our resolution to the time for wave function collapse in the quantum measurement process. We then produce interference experiments with photons of different energies impinging on the slits, i.e. we know which photon impinges on each slit. We show that for poor time resolution, no interference is observed, but for high time resolution, we have interference that is revealed as beats of 100 GHz frequency. The condition for interference is that the two pulses should overlap spatially at the detector, even if the pulses have different energies but are generated from the same pulse of the laser. The interference seems to be in agreement with classical theory at first sight. However, closer study and analysis of the data show deviations in the visibility of the interference fringes and of their phase. These experiments are discussed in connection with quantum mechanics and it may be concluded that the time resolution provides new data for understanding the longstanding and continuing arguments on wave-particle duality initiated by Newton, Young, Fresnel, Planck and others. A thought experiment is presented in the appendix to try to distinguish the photons at the detector by making it sensitive to colour.