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Quantum Electronics and Laser Science Conference

Fourth-order interference for two independent quasi-thermal sources

Maria V. Chekhova, S. P. Kulik, Alexander N. Penin

Published Jun 7, 1996• 0 citations
OpenAlex

Abstract

Summary form only given. To demonstrate classical fourth-order interference, we used a He-Cd laser beam scattered in a sample of fused silica by an acoustic wave with quasi-thermal statistics. The acoustic wave was excited by means of a piezoelectric element, into which electric quasi-Gaussian noise with central frequency 50 MHz and bandwidth 3 MHz was fed.

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A new fourth-order interference experiment based on detecting photon pairs in coincidence has been carried out. A Mach-Zehnder type of interferometer is used, with the two photons generated simultaneously in the process of down-conversion as inputs and two photon counting detectors at the two outputs. The optical path difference can be varied piezoelectrically. It is found that the coincidence counting rate, after subtraction of accidentals, exhibits a sinusoidal variation with the optical path difference as predicted by quantum mechanics, but in violation of the laws of classical optics. This is another non-classical interference effeet. By contrast, two light beams derived from a He:Ne laser used as inputs to the interferometer, do not produce any fourth order interference.

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Fourth-order interference between two independent sources of stimulated Raman scattering

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Stimulated Raman scattering (SRS) produces Stokes light pulses that originate from quantum noise and exhibit macroscopic amplitude and phase fluctuations from one shot to another.1 By using transient stimulated Raman scattering, we generated light pulses with macroscopic energy and temporal coherence times that were long compared to their duration. Stokes pulses were generated independently in each arm of an interferometer and were interfered together at the output. The position, modulation depth, and brightness of the interference fringes fluctuated randomly from one shot to the next. We obtained both the ensemble-averaged intensity and the fourth-order intensity correlation function of the interfered Stokes light. The average has a smooth envelope and shows no modulation, whereas the intensity correlation function has a depth of modulation of 0.35 for Stokes generation in the unsaturated (thermal-like) regime and 0.46 in the saturated (laser-like) regime. This is in agreement with predicted values of 0.33 and 0.5.2

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Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.

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Interference Fringes with Maximal Contrast at Finite Coherence Time

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Interference fringes can result from the measurement of four-time fourth-order correlation functions of a wave field. These fringes have a statistical origin and, as a consequence, they show the greatest contrast when the coherence time of the field is finite. A simple acoustic experiment is presented in which these fringes are observed, and it is demonstrated that the contrast is maximal for partial coherence. Random telegraph phase noise is used to vary the field coherence in order to highlight the problem of interpreting this interference; for this noise, the Gaussian moment theorem may not be invoked to reduce the description of the interference to one in terms of first-order interference.

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We present the design, fabrication, and characterization of a monolithic, segmented, three-dimensional linear Paul ion trap for quantum science applications. The trap is fabricated from a single fused-silica block using selective laser-induced etching (SLE) and is subsequently metallized, forming electrodes isolated by self-shadowing trench structures without the need for layer alignment or external shadow masks. The segmented electrodes allow for shaping of the axial potential, enabling the creation of anharmonic potential wells, such as those required for equidistant ion strings. In addition, they enable shuttling and splitting of ion chains. We discuss key design choices and SLE-imposed constraints on achievable feature sizes, and evaluate electron-beam evaporation and magnetron sputtering as metallization approaches. Across two independent experimental setups, we demonstrate stable trapping and control of linear chains of up to 33 $^{40}$Ca$^+$ ions, including approximately equally spaced configurations. The measured secular frequencies in both traps agree with boundary-element simulations at the percent level, with residual deviations attributed to stray electric fields in the presence of anharmonic axial potentials, rather than fabrication imperfections. We measure axial micromotion field strengths on the order of 100 V/m along the trap axis, in approximate agreement with simulations. For radial mode frequencies near 2 MHz and an ion-electrode distance of 300 um, we measure heating rates of the order of 10 quanta/s in all but one motional mode, which is elevated by a technical noise source. The presented trap design is thus suitable for a wide range of quantum science applications and demonstrates the viability of SLE for the fabrication of finely segmented, monolithic, three-dimensional ion traps.

physics.atom-phCross-listedarXiv:2609.01694•Sep 2, 2026•0 citations
Summary form only given. To demonstrate classical fourth-order interference, we used a He-Cd laser beam scattered in a sample of fused silica by an acoustic wave with quasi-thermal statistics. The acoustic wave was excited by means of a piezoelectric element, into which electric quasi-Gaussian noise with central frequency 50 MHz and bandwidth 3 MHz was fed.
A new fourth-order interference experiment based on detecting photon pairs in coincidence has been carried out. A Mach-Zehnder type of interferometer is used, with the two photons generated simultaneously in the process of down-conversion as inputs and two photon counting detectors at the two outputs. The optical path difference can be varied piezoelectrically. It is found that the coincidence counting rate, after subtraction of accidentals, exhibits a sinusoidal variation with the optical path difference as predicted by quantum mechanics, but in violation of the laws of classical optics. This is another non-classical interference effeet. By contrast, two light beams derived from a He:Ne laser used as inputs to the interferometer, do not produce any fourth order interference.
Stimulated Raman scattering (SRS) produces Stokes light pulses that originate from quantum noise and exhibit macroscopic amplitude and phase fluctuations from one shot to another.1 By using transient stimulated Raman scattering, we generated light pulses with macroscopic energy and temporal coherence times that were long compared to their duration. Stokes pulses were generated independently in each arm of an interferometer and were interfered together at the output. The position, modulation depth, and brightness of the interference fringes fluctuated randomly from one shot to the next. We obtained both the ensemble-averaged intensity and the fourth-order intensity correlation function of the interfered Stokes light. The average has a smooth envelope and shows no modulation, whereas the intensity correlation function has a depth of modulation of 0.35 for Stokes generation in the unsaturated (thermal-like) regime and 0.46 in the saturated (laser-like) regime. This is in agreement with predicted values of 0.33 and 0.5.2
Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.
Interference fringes can result from the measurement of four-time fourth-order correlation functions of a wave field. These fringes have a statistical origin and, as a consequence, they show the greatest contrast when the coherence time of the field is finite. A simple acoustic experiment is presented in which these fringes are observed, and it is demonstrated that the contrast is maximal for partial coherence. Random telegraph phase noise is used to vary the field coherence in order to highlight the problem of interpreting this interference; for this noise, the Gaussian moment theorem may not be invoked to reduce the description of the interference to one in terms of first-order interference.
We present the design, fabrication, and characterization of a monolithic, segmented, three-dimensional linear Paul ion trap for quantum science applications. The trap is fabricated from a single fused-silica block using selective laser-induced etching (SLE) and is subsequently metallized, forming electrodes isolated by self-shadowing trench structures without the need for layer alignment or external shadow masks. The segmented electrodes allow for shaping of the axial potential, enabling the creation of anharmonic potential wells, such as those required for equidistant ion strings. In addition, they enable shuttling and splitting of ion chains. We discuss key design choices and SLE-imposed constraints on achievable feature sizes, and evaluate electron-beam evaporation and magnetron sputtering as metallization approaches. Across two independent experimental setups, we demonstrate stable trapping and control of linear chains of up to 33 40^{40}40Ca+^++ ions, including approximately equally spaced configurations. The measured secular frequencies in both traps agree with boundary-element simulations at the percent level, with residual deviations attributed to stray electric fields in the presence of anharmonic axial potentials, rather than fabrication imperfections. We measure axial micromotion field strengths on the order of 100 V/m along the trap axis, in approximate agreement with simulations. For radial mode frequencies near 2 MHz and an ion-electrode distance of 300 um, we measure heating rates of the order of 10 quanta/s in all but one motional mode, which is elevated by a technical noise source. The presented trap design is thus suitable for a wide range of quantum science applications and demonstrates the viability of SLE for the fabrication of finely segmented, monolithic, three-dimensional ion traps.