{"product_id":"t-edu-qop1-quantum-optics-educational-kit-imperial","title":"T-EDU-QOP1 - Quantum Optics Educational Kit, Imperial","description":"\u003cp\u003eT-EDU-QOP1 - Quantum Optics Educational Kit, Imperial\u003c\/p\u003e\n\u003cp\u003e\u003ca href=\"https:\/\/cdn.shopify.com\/s\/files\/1\/1026\/4509\/files\/EDU-QOP1-Manual.pdf?v=1688066771\"\u003e\u003cstrong\u003eProduct Manual\u003c\/strong\u003e\u003c\/a\u003e\u003c\/p\u003e\n\u003cul class=\"SGBullet\"\u003e\n\u003cli\u003eIncludes Components to Investigate Quantum Properties of Light (Computer Not Included)\u003c\/li\u003e\n\u003cli\u003e\u003cspan\u003eRequires a User-Supplied Optical Table or Breadboard with Damping Feet\u003c\/span\u003e\u003c\/li\u003e\n\u003cli\u003e\u003cspan\u003eRecommended Optical Breadboard and Damping Feet Sold Separately\u003c\/span\u003e\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cspan\u003eT-EDU-QOP1(-M) Quantum Optics Educational Kit includes components to investigate quantum properties of light. This educational kit is offered in both an imperial and metric version.\u003c\/span\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cspan\u003eThis kit must be mounted on an optical table or breadboard, which is not included in this kit. If your lab does not already have a suitable one, we recommend the T-B2448FX (T-B60120AX) optical breadboard with the AV5(\/M) damping feet, which are available for purchase separately below.\u003c\/span\u003e\u003c\/p\u003e\n\u003ch3\u003eQuantum Description of Light\u003c\/h3\u003e\n\u003cp\u003eIn quantum mechanics, light is described by quantized excitation of the electromagnetic field, where the smallest possible excitation is a single photon (with quantum number n = 1). Fock states are non-classical light states with a well-defined photon number (see the left graph of Figure 2).\u003c\/p\u003e\n\u003cp\u003eClassical light, on the other hand, does not exhibit such a well-defined photon number. For example, light generated by a laser is in a coherent state. For a given mean photon number, the actual photon number follows a Poisson distribution (see the middle graph of Figure 2). Attenuation of the laser can only reduce the mean photon number while the underlying statistic remains Poissonian. Hence, an attenuated laser can never be used as a single photon source for quantum experiments.\u003c\/p\u003e\n\u003cp\u003eOther classical light sources, such as LEDs or blackbody radiation, are described by thermal states, which are mixed quantum states, and exhibit an even larger variance of in photon number compared to laser light (see the right graph of Figure 2).\u003c\/p\u003e\n\u003ch3\u003eGeneration of Single Photons\u003c\/h3\u003e\n\u003cp\u003eThe term “single photons” refers to Fock states with photon number n = 1. A range of different sources can be used to generate single photons. Nowadays, most experiments use a process called Spontaneous Parametric Down-Conversion (SPDC) to generate photon pairs. The EDU-QOP1(\/M) kit makes use of such a source, as it is rather simple to set up and offers stable operation, which makes it ideal for lab courses.\u003c\/p\u003e\n\u003cp\u003eIn SPDC, pump light generates two photons inside a nonlinear crystal, as seen in Figure 3. These photons are created virtually simultaneously, so that one of the photons can be used to signal the existence of the other, making it possible to perform measurements on single photons. For this reason, such a source is also called a heralded single photon source.\u003c\/p\u003e\n\u003cp\u003eThe T-EDU-QOP1 kit uses a β-Barium borate (BBO) crystal designed for a pump wavelength of 405 nm and a degenerate pair wavelength of 810 nm. The crystal is designed for a pair opening angle of 6° for spatially separated detection of both photons.\u003c\/p\u003e\n\u003ch3\u003eCoincidence Detection\u003c\/h3\u003e\n\u003cp\u003eThree\u003cspan\u003e SPDMA\u003c\/span\u003e\u003cspan\u003e \u003c\/span\u003esingle photon detectors are used in the kit, as seen in the schematic in Figure 4. Similar to a Geiger-Müller counter, an incoming photon creates an electron avalanche in the detector, which is detected and converted into a TTL level output signal.\u003c\/p\u003e\n\u003cp\u003eThese three signal channels are analyzed by an educational-grade time tagger for coincidences between the detected events, as shown in Figure 5: for each event on the Trigger channel T it checks whether there is another event on channel A or B within a few nanoseconds wide window before or after. This time period is called the coincidence window. If the condition is met, a coincidence event is generated at the coincidence channels T\u0026amp;A or T\u0026amp;B. A triple coincidence occurs if all three detectors register a photon within the coincidence window.\u003c\/p\u003e\n\u003cp\u003eFor a pair source, the coincidences measured between both arms occur more often than for an uncorrelated light source. This can be characterized by the second order correlation function,\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eg\u003c\/em\u003e\u003csup\u003e(2)\u003c\/sup\u003e, which compares the expected coincidences for an uncorrelated light source with the measured coincidences:\u003c\/p\u003e\n\u003cp\u003e\u003cimg src=\"https:\/\/www.thorlabs.com\/Images\/TabImages\/EDU_QOP1_g2_eq_A1.gif\" border=\"0\" alt=\"\"\u003e\u003c\/p\u003e\n\u003cp\u003ewhere\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eA\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eand\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eB\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eare the average count rates of detectors A and B, respectively,\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eAB\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eis the count rate of coincidences, and Δ\u003cem\u003et\u003c\/em\u003e\u003cspan\u003e \u003c\/span\u003eis the time window.\u003c\/p\u003e\n\u003cp\u003eIn the Grangier-Roger-Aspect experiment (see the\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eExperiments\u003c\/em\u003e\u003cspan\u003e \u003c\/span\u003etab), the triple coincidences are compared to the rate expected for an uncorrelated (classical) light source by using the second order correlation function\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eg\u003csup\u003e(\u003c\/sup\u003e\u003c\/em\u003e\u003csup\u003e2)\u003c\/sup\u003e\u003csub\u003eGRA\u003c\/sub\u003e:\u003c\/p\u003e\n\u003cp\u003e\u003cimg src=\"https:\/\/www.thorlabs.com\/Images\/TabImages\/EDU_QOP1_g2GRA_eq_A1.gif\" border=\"0\" alt=\"\"\u003e\u003c\/p\u003e\n\u003cp\u003ewhere\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eTAB\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eis the triple coincidence rate,\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eT\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eis the count rate of the trigger detector T, and\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eTA\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eand\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eR\u003c\/em\u003e\u003csub\u003eTB\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003eare the coincidendence rates of detectors T and A and T and B, respectively. As a single photon pair is not able to trigger events on all three detectors, the triple coincidence rate is close to zero for a heralded single photon source and thus\u003cspan\u003e \u003c\/span\u003e\u003cem\u003eg\u003c\/em\u003e\u003csup\u003e(2)\u003c\/sup\u003e\u003csub\u003eGRA\u003c\/sub\u003e\u003cspan\u003e \u003c\/span\u003e\u0026lt;\u0026lt; 1.\u003c\/p\u003e\n\u003ch3\u003eEasy Alignment\u003c\/h3\u003e\n\u003cp\u003eThe kit uses two iris apertures to define a common beam path for the pump and alignment lasers. For each laser, two mirrors are used for beam walking, ensuring fast and repeatable alignment of the system using visible light.\u003c\/p\u003e\n\u003cp\u003eAn axicon is placed at the position of the BBO crystal to generate a cone of red light from the alignment laser, which mimics the cone of photon pairs from the BBO. Using this visible indicator, the detectors can be reliably aligned at the correct positions and orientations. The laser light cone can further be used for demonstration purposes.\u003c\/p\u003e","brand":"Fosco Connect","offers":[{"title":"Default Title","offer_id":49083774468352,"sku":"T-EDUQOP1","price":78193.2,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0388\/5331\/2557\/files\/MTN036012-xl.jpg?v=1785204785","url":"https:\/\/alotechparts.com\/products\/t-edu-qop1-quantum-optics-educational-kit-imperial","provider":"Alo Tech Solutions","version":"1.0","type":"link"}