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Complementarity in single photon interference – the role of the mode function and vacuum fields
(2017)
Background
In earlier experiments the role of the vacuum fields could be demonstrated as the source of complementarity with respect to the temporal properties (Heuer et al., Phys. Rev. Lett. 114:053601, 2015).
Methods
Single photon first order interferences of spatially separated regions from the cone structure of spontaneous parametric down conversion allow for analyzing the role of the mode function in quantum optics regarding the complementarity principle.
Results
Here the spatial coherence properties of these vacuum fields are demonstrated as the physical reason for complementarity in these single photon quantum optical experiments. These results are directly connected to the mode picture in classical optics.
Conclusion
The properties of the involved vacuum fields selected via the measurement process are the physical background of the complementarity principle in quantum optics.
An external volume Bragg grating (VBG) is used for transverse and longitudinal mode stabilization of a broad area diode laser (BAL) with an on-chip transverse Bragg resonance (TBR) grating. The internal TBR grating defines a transverse low-loss mode at a specific propagation angle inside the BAL. Selection of the TBR mode was realized via the angular geometry of an external resonator assembly consisting of the TBR BAL and a feedback element. A feedback mirror provides near diffraction limited and spectral narrow output in the TBR mode albeit requiring an intricate alignment procedure. If feedback is provided via a VBG, adjustment proves to be far less critical and higher output powers were achieved. Moreover, additional modulation in the far field distribution became discernible allowing for a better study of the TBR concept. (C) 2015 Optical Society of America
Entangled photons generated by spontaneous parametric downconversion are ubiquitous in quantum optics. In general, they exhibit a complex spatial photon count distribution. This spatial structure is responsible for seemingly surprising results concerning, e.g., complementarity such as the apparent simultaneous observation of interference fringes V and which-way information D at a double slit, as recently reported by Menzel et al. [Proc. Natl. Acad. Sci. USA 109, 9314 (2012)]. We implement a complete quantitative model of the SPDC interaction that fully incorporates the effects of crystal anisotropies, phase matching, and the pump beam structure and allows for arbitrary manipulations of the SPDC light in the near and far fields. This enables us to establish an upper bound D-2 + V-2 <= 1.47 for the experimental parameters reported by Menzel et al. We report new experimental results that agree excellently with these theoretical predictions. The new model enables a detailed quantitative analysis of this surprising result and the fair sampling interpretation of biphotons passing a double slit. (C) 2015 Optical Society of America
Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.
Stabilized multi-wavelength emission from a single emitter broad area diode laser (BAL) is realized by utilizing an external cavity with a spectral beam combining architecture. Self-organized emitters that are equidistantly spaced across the slow axis are enforced by the spatially distributed wavelength selectivity of the external cavity. This resulted in an array like near-field emission although the BAL is physically a single emitter without any epitaxial sub-structuring and only one electrical contact. Each of the self-organized emitters is operated at a different wavelength and the emission is multiplexed into one spatial mode with near-diffraction limited beam quality. With this setup, multi-line emission of 31 individual spectral lines centered around and a total spectral width of 3.6 nm is realized with a 1000 mu m wide BAL just above threshold. To the best of our knowledge, this is the first demonstration of such a self-organization of emitters by optical feedback utilizing a spectral beam combining architecture.
The emission characteristics of a novel, specially designed broad area diode laser (BAL) with on-chip transversal Bragg resonance (TBR) grating in lateral direction were investigated in an off-axis external cavity setup. The internal TBR grating defines a low loss transversal mode at a specific angle of incidence and a certain wavelength. By providing feedback at this specific angle with an external mirror, it is possible to select this low loss transverse mode and stabilize the BAL. Near diffraction limited emission with an almost single lobed far field pattern could be realized, in contrast to the double lobed far field pattern of similar setups using standard BALs or phase-locked diode laser arrays. Furthermore, we could achieve a narrow bandwidth emission with a simplified setup without external frequency selective elements. (C) 2014 Optical Society of America
Spontaneous parametric down-conversion (SPDC) in a nonlinear crystal generates two single photons (signal and idler) with random phases. Thus, no first-order interference between them occurs. However, coherence can be induced in a cascaded setup of two crystals if, e.g., the idler modes of both crystals are aligned to be indistinguishable. Due to the effect of phase memory it is found that the first-order interference of the signal beams can be controlled by the phase delay between the pump beams. Even for pump photon delays much larger than the coherence length of the SPDC photons, the visibility is above 90%. The high visibilities reported here prove an almost perfect phase memory effect across the two interferometers for the pump and the signal photon modes.
Multi-wavelength, high spatial brightness operation of a phase-locked stripe-array diode laser
(2012)
Stable continuous wave multi-wavelength operation of a stripe-array diode laser with an externalcavity spectral beam combining geometry is presented. In this setup each emitter of the stripe-array is forced to operate at a different wavelength, which leads to a decoupling between the usually phase-locked emitters. With a reflective diffraction grating with a period of 300 lines per mm, 33 equidistant laser lines around a center wavelength of 978 nm were realized, spanning a spectral range of 26 nm. With this novel approach near-diffraction limited emission with a beam quality of M (2) < 1.2 and an output power of 450 mW was achieved. This laser light source can be used for applications requiring low temporal but high spatial coherence.
The precise knowledge of one of two complementary experimental outcomes prevents us from obtaining complete information about the other one. This formulation of Niels Bohr's principle of complementarity when applied to the paradigm of wave-particle dualism-that is, to Young's double-slit experiment-implies that the information about the slit through which a quantum particle has passed erases interference. In the present paper we report a double-slit experiment using two photons created by spontaneous parametric down-conversion where we observe interference in the signal photon despite the fact that we have located it in one of the slits due to its entanglement with the idler photon. This surprising aspect of complementarity comes to light by our special choice of the TEM01 pump mode. According to quantum field theory the signal photon is then in a coherent superposition of two distinct wave vectors giving rise to interference fringes analogous to two mechanical slits.
Cell-to-cell diversity in a synchronized chlamydomonas culture as revealed by single-cell analyses
(2012)
In a synchronized photoautotrophic culture of Chlamydomonas reinhardtii, cell size, cell number, and the averaged starch content were determined throughout the light-dark cycle. For single-cell analyses, the relative cellular starch was quantified by measuring the second harmonic generation (SHG). In destained cells, amylopectin essentially represents the only biophotonic structure. As revealed by various validation procedures, SHG signal intensities are a reliable relative measure of the cellular starch content. During photosynthesis-driven starch biosynthesis, synchronized Chlamydomonas cells possess an unexpected cell-to-cell diversity both in size and starch content, but the starch-related heterogeneity largely exceeds that of size. The cellular volume, starch content, and amount of starch/cell volume obey lognormal distributions. Starch degradation was initiated by inhibiting the photosynthetic electron transport in illuminated cells or by darkening. Under both conditions, the averaged rate of starch degradation is almost constant, but it is higher in illuminated than in darkened cells. At the single-cell level, rates of starch degradation largely differ but are unrelated to the initial cellular starch content. A rate equation describing the cellular starch degradation