====== Single Photon Interference - Spring 2022 ====== ---- {{ :phylabs:lab_courses:phys-211-wiki-home:wave-particle-duality:optical_table.png?400 |}} There are only two known physical phenomena for which classical physics fails to provide an explanation of the experimental results: //Wave-Particle Duality// and //Quantum Entanglement//.  For both of these phenomena, attempts to explain the results of experiment using only classical physics concepts leads to nonsensical contradictions. Quantum mechanics, however, correctly predicts the outcomes of these experiments. In this experiment you will investigate the behavior of individual photons interacting with beam splitters and passing through an interferometer. The results of the measurements illustrate the nature of wave-particle duality as well as quantum mechanical concepts such as the behavior of wave packets, distinguishability of paths, and the effects of observation on experimental outcomes. ====== Prep Meeting Research ====== In this experiment you will learn how to use quantum optics and single photon counting techniques to investigate the phenomena of //single photon interference//. The optical setup allows us to send photons one at a time through a Mach-Zhender interferometer. Your task will be to think of as many ways as possible to use the apparatus to conduct experiments which show evidence for the quantum mechanical phenomena of single photon interference and draw parallels with classical interference of electro-magnetic waves. **Before** your //Prep Meeting// make sure that you are familiar with the following: * Single Photon Interference. This wikipedia article is a good starting point. [[https://en.wikipedia.org/wiki/Double-slit_experiment#Mach-Zehnder_interferometer]] * What is a Mach-Zhender interferometer and how does it differ from the more common Michelson interferometer. Again, a wikipedia search is a good place to start. * The quantum mechanical concept of //which way information// and the //quantum eraser//. * What a half-waveplate is and what it does to linearly polarized light which passes through it. **WARNING:** The pump laser beam **WILL** cause permanent eye damage, including possible blindness, if used without protection. Laser safety goggles **MUST** be worn at all times and the door **MUST** be closed when the laser is on, even when the table is covered. Wait for instructions before turning on the pump laser. ====== Introduction ====== ---- The concept of wave particle duality is perhaps best expressed by the following quote:  //"But what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light by a choice of only one of the two languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do."// -- A.  Einstein and I. Leopold. //The evolution of physics: the growth of ideas from early concepts to relativity and quanta.// CUP Archive, 1961. Experimentally, light can be shown to have the properties of both waves and particles. Furthermore, whether light behaves as a wave or a particle depends on the nature of the measurement being made and the information available to the observer. For purposes of this discussion, we will define something as being a particle or a wave based on the following criteria: - **Localization:** Particles have well defined discrete locations in space at any particular time, whereas waves extend continuously throughout space.   - **Interference:** Waves can superimpose at a given location and exhibit interference effects, whereas particles do not.   In this experiment you will make measurements to show that single photons of light, passing through an interferometer one at a time can exhibit interference behavior. ====== Apparatus ====== ---- Figure 2 gives an overview of the optical table. Note that positioning and alignment of the various components must be done with great precision. (The overlap of paths must be within a few wavelengths of light, a precision on the order of microns!) Due to time constraints, the optical components have been aligned on the table for you. You will perform only a limited number of manipulations during the experiment. **IMPORTANT**: Accidentally knocking a single optical component out of alignment by the slightest amount could result in a full day's delay. Think about where you are putting your hands. Take care not to bump into things. Don't adjust the optics yourself except where explicitly instructed.
| {{ :phylabs:lab_courses:phys-211-wiki-home:wave-particle-duality:wpd_layout_full.png |}} | | **Figure 2**: Layout of components on the optical table. |
For simplicity we can break the whole setup down in to three parts based on function – a photon source, and two separate experimental setups. Let us look at each part and describe the components within each section. The optical components are described in more detail on [[phylabs:lab_courses:phys-211-wiki-home:single-photon-interference-spring:wpd_optics|this page]]. ===== Computer data acquisition ===== ==== Data acquisition hardware ==== The APD signals are collected and the piezo voltage is controlled by a computer data acquisition (DAQ) system. A National Instruments PCIe-6341 multifunction DAQ card (NI-DAQ), installed in the computer tower, connects to an SCB-68A interface as shown in Fig. 6. | {{ :phylabs:lab_courses:phys-211-wiki-home:wave-particle-duality:worddav032d73a252dceb03ec496ae072c2e2e0.png?400 |}} | | **Figure 6**: Computer data acquisition system. | Signals from the APDs and to the ThorLabs piezo driver connect to the SCB-68A through a BNC connector plate as shown schematically in Fig. 7. | {{ phylabs:lab_courses:phys-211-wiki-home:single-photon-interference:bnc_plate_oct-2021.png?400 |}} | | **Figure 7a**: Layout of interface connections. | | {{ phylabs:lab_courses:phys-211-wiki-home:single-photon-interference:wiring_diag_v3.png?400 |}} | | **Figure 7b**: Wiring diagram for making connections to the NI interface. | The DAQ card is capable of both generating and collecting a variety of analog and digital signals. For this experiment we use one analog voltage output to control the piezo voltage, and four digital counter inputs to record pulses from the APDs. The card is controlled by a LabView program called //SP_DAQ//. ==== Data acquisition software ==== //SP_DAQ// has three operating modes selectable by tabs in the interface window; //Singles Rates//, //Coincidence Rates// and //Coincidence Scan//. In //Singles Rates// mode the interface displays an analog and digital rate meter for each counter on the DAQ card. There is an input box for the user to set the //Count Time// which is the time, in seconds, for which the DAQ will count pulses from the APDs. Clicking the //Start// button initiates a measurement. While running the analog meters display the pulse rate for each counter. At the end of the measurement the average event rate and the total number of counts recorded are displayed along with the actual elapsed run time. The //Abort// button stops a measurement in progress. In _Coincidence Rates _mode the interface displays analog and digital rate meters for Idler singles rates, Idler/Port A coincidence rate, and Idler/Port B coincidence rate. This mode operates just like the singles rates mode. In //Coincidence Scan// mode the interface displays controls and readings for two photon coincidence counting while scaning over a range of piezo voltages. The user can set a //Starting Piezo Voltage//, an //Ending Piezo Voltage//, and the //Voltage Step// size for the piezo scan using the sliders. The //Run Length// can be set which determines how long the software spends counting at each voltage step. Clicking the //Start// button initiates a scan. The //Abort// button stops a scan in progress. A //Save// button allows the user to save the measurements from the most recent scan to a text file. ==== Coincidence counting ==== In order to count coincident hits on two different APD's we utilize the counters on the NI-DAQ card in a start/stop mode as shown in Fig. 8. In this mode each pulse from the Idler APD is split into two signals, one (prompt) going to the start input of a counter, the other (delayed) going through an additional 100 ns of delay before arriving at the stop input of the same counter. The signal from a second APD runs through a 50 ns delay before connecting to the counter input. Thus a photon detected by the Idler APD will cause the counter to run for a 100 ns interval of time. If a photon strikes the APD connected to the input of that counter within this 100 ns interval it will be recorded. If both APDs detect photons simultaneously, the signal from the second APD will arrive at the counter input 50 ns after the counter has been started by the signal from the Idler APD and will thus be counted. | {{ phylabs:lab_courses:phys-211-wiki-home:single-photon-interference:single_photon_coincidence.png?400 |}} | | **Figure 8**: NI-DAQ card counter connections. | Used this way, the counter increments only when the two APD's are hit within ±50 ns of one another. Note that when counting coincidences between two detectors where events arrive randomly but at a well defined average rate, there will always be some probability that the two detectors are struck within the coincidence time window due to purely random chance.  If the rate of detections at each detector is known ($R_1$ and $R_2$) and the coincidence window is given as $\Delta t$, then the rate of accidental coinsidences $R_{acc}$ is given by $R_{acc} = R_1 * R_2 * \Delta t$. ==== Data acquisition interface connections ==== The BNC side of the interface connector panel is labeled as shown in Fig. 7a. Verify that the connections are correct. The four APD's should all have 3 ft long BNC cables coming from the outputs on the APD modules. The APDs from Ports A and B each connect to an additional 50 ns long BNC cable before connecting to the interface connector panel. The 3 ft long BNC from the idler APD connects to the Idler Prompt input on the interface connector panel with a "T" adapter. The other end of the "T" adapter connects to a 100 ns long BNC cable the other end of which connects to the Idler Delay input. The Piezo voltage output on the interface connector panel should be connected to the voltage input for the //y//-axis of the ThorLabs 3-Axis Piezo Controller. Use the manual knob on the Piezo controller to set the y-axis voltage to 50 V. ===== Experimental procedure ===== ---- Use the apparatus to experimentally verify that a single photon can interfere with itself. Also show that if the photon carries with it information about which path the photon took through the interferometer, that interference no longer occurs. ====== Analysis and Final Report ====== ---- Your analysis is due 4 days after your second day in lab. The analysis is not a lab report, rather it is all of the data reduction, number crunching, calculations, curve fitting, error propagation etc. which is necessary for you to establish your final conclusions. Think of it as being more like an extended homework set where you have to show how you got your final results. Three days after your analysis submission your group will have a meeting with the TA to go over your analysis and make sure you are prepared to write your final report. The final report is due three days after the analysis meeting. Your graded analysis will be returned along with your graded final report. ===== Analysis Meeting ===== Three days after your analysis is due your group will meet with the TA to discuss the overall analysis and make clear what needs to go into your final report. //Note that this meeting is not for the purpose of discussing your grade on the analysis, you will receive the grade on the analysis along with the graded final report.// Instead this is an opportunity for the TA to have reviewed your analysis to identify where you may have short comings or misconceptions in your understanding of the experiment with the goal of improving what goes into your final report. It is also an opportunity for you to make sure that you understand what your TA is looking for in your report. You are expected to bring a detailed outline for your final report to this meeting. The outline should consist of section and sub-section headings which make clear what information you will put into the report as well as the order in which that information will appear. This should literally be a single page document. Having a meaningfully thought out outline will count towards your participation grade for the meeting. The expectation is that between feedback on your analysis and your outline you should leave this meeting with a clear idea of how you will write up your final report. ===== Analysis Rubric ===== Your analysis, like your reports, should be submitted as a single PDF. It is not expected that you will write narrative descriptions as you will in your final report. For the analysis it is acceptable to organize it into sections with one or two brief sentences of description. Things should be put in a sensible order so that the TA can follow what you are doing. For example plots, fits and calculations related to your energy calibration should be grouped together into a section, and that section should be placed before you apply the calibration to your data. For cases such as fitting and extracting peak locations for all of your scattering data it is sufficient to show one representative plot of a fit to the data along with a table containing all of the values. Scans or photographs of calculations done on paper or in your lab notebook are acceptable but absolutely MUST be clear and readable. Each item below is graded on a 0-4 point scale: * **(4) - Good (A):** Work is done correctly and covers everything in adequate detail. * **(3) - Adequate (B):** Minor mistakes were made. Misses one or more minor elements. * **(2) - Needs improvement (C):** Work is incomplete or incorrect in some significant way. * **(1) - Inadequate (D):** Work is mostly incomplete or incorrect. * **(0) - Missing (F):** omits all elements or makes no meaningful attempt. All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items. ;#; **Analysis Rubric Still Under Development. It will be finished by the end of third week.** ;#;
| Item | Good (4) | | | | | | | | | | | | | | Other specific items which may have been discussed with your TA. | Anything else which your TA has made clear they expect to see in your analysis. **Items in this category need to be discussed between the TA and Students before the end of their last day in lab and need to have been approved by the course instructor or a member of the lab staff.** |
===== Final Report ===== ---- The final report is due three days after your scheduled analysis meeting with the TA. It should be built around your final conclusions. Everything in your report should support your final result and conclusions. You need to make clear things you did, decisions you made in the lab which are important to understanding how you arrived at your results and conclusions. This might include: * Showing **quantitatively** that you are measurements involve single photons. * Showing as **quantitatively** and definitively as possible that you do see interference when single photons pass through an interferometer. * Showing that the information carried by the photon determines whether or not interference occurs. Your writeup of your analysis should be structured in a way that is clear and readable, there should be a logic to the flow of it. Your final report will be evaluated based on the following rubric. The rubric is not a format for your analysis, you are not expected to have a specific section on //Data Handling// or //Presentation of Data//. Elements of the different rubric categories will appear at different points through out your analysis writeup. Each item below is graded on a 0-4 point scale: * **4 – Good (A):** completes all listed tasks and provides appropriate context; thinks carefully about data and analysis; addresses all concerns raised by the results (where appropriate). * **3 – Adequate (B):** misses one or more minor element or lacks appropriate context; leaves a problem or ambiguity unaddressed; does not present analysis clearly enough. * **2 – Needs improvement (C):** omits or mishandles one or more item which renders the analysis fundamentally incorrect or incomplete; presents results in an incorrect or unclear way. * **1 – Inadequate (D):** omits or mishandles multiple items or treats them at an insufficient level; presentation is overall muddled or inaccurate; flaws in logic or process. * **0 – Missing (F):** omits all elements or makes no meaningful attempt. All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items. ===== Final Report Rubric =====
| Section | Good (4) | | Flow | The report is well organized and clearly written. The logical flow of how information is presented makes it easy for the reader to understand what is being communicated. Extraneous information unrelated to the conclusions is minimized. | | Presentation of Data | Presents plots of data as needed and uses them to support the narrative of the report. Properly labels plots, and makes presentation clean and clear. Uses error bars where appropriate. Includes captions that provide appropriate context. Presents all numerical values with appropriate units and significant figures. Clearly formats numbers, equations, tables, etc. | | Data Handling | Describes how the raw data was processed including with uncertainties. Details fit functions and provides sample fits (if appropriate). Details other calculations/considerations and provides sample calculations or reasoning (if appropriate). | | Discussion of Uncertainties | Identifies relevant sources of uncertainty in measured quantities, and quantifies values when possible. Describes how uncertainties were assessed and incorporated into the analysis. Identifies potential sources of systematic bias and describes how they are accounted for in the analysis or eliminated. | | Presentation of Results | Final results are presented clearly. Data tables and plots are used where appropriate and are properly labeled and annotated. Measured and calculated quantities include units and uncertainties where appropriate. | | Conclusions | Makes clear final conclusions that are fully supported by the experimental results and discusses the overall take-aways of the experiment appropriately. Properly accounts for or contextualizes measurement uncertainties and potential sources of systematic bias. |
===== References ===== ---- {{ :phylabs:lab_courses:phys-211-wiki-home:wave-particle-duality:interference_with_correlated_photons.pdf | |E.J. Galvez et. al. "Interference with Correlated photons: Five quantum mechanics experiments for undergraduates", Am. J. Phys. 73, 127-140 (2005)}}. [2] A.C. Melissinos, J. Napolitano, //Experiments in Modern Physics 2nd Ed//., Academic Press (2003). [3] [[http://www.feynmanlectures.caltech.edu/III_01.html |R. P. Feynman, R. B. Leighton, M. Sands. //The Feynman Lectures on Physics, Vol III,// (Ch. 1.), Addison-Wesley Publishing Company, 1971.]]