Quantum and Nano Optics Laboratory. Jacob Begis Lab partners: Josh Rose, Edward Pei

Transcription

1 Quantum and Nano Optics Laboratory Jacob Begis Lab partners: Josh Rose, Edward Pei

2 Experiments to be Discussed Lab 1: Entanglement and Bell s Inequalities Lab 2: Single Photon Interference Labs 3 and 4: Confocal Microscopy Imaging of Single Emitter Fluorescence and Hanbury, Brown, and Twiss Setup, Photon Antibunching

3 Lab 1: Entanglement and Bell s Inequalities In quantum mechanics, two particles are called entangled if their state cannot be factored into single-particle states:

4 Lab 1 Background A wavefunction represents a quantum particle s probability of having certain characteristics at any given time When a quantum particle is observed its wavefunction collapses

5 Entanglement If two quantum particles interact they may become entangled Entanglement is one inseparable state that is indefinite regardless of the distance between them If one member of an entangled pair s wavefunction collapses, so does its pair s

6 Entanglement Cont. This principle is central to many applications including quantum cryptography This is because measurements performed on the first particle gives reliable information about the state of its entangled pair.

7 Bell s Inequality The existence of quantum entanglement can be proved using Bell s inequalities He made a theorem containing simple inequalities which are always be valid under classical conditions A violation of these inequalities means non-classical phenomena such as entanglement may be present.

8 CHSH Inequality One method for calculating Bell s inequalities is the Causer, Horne, Shimony and Holt (CHSH) method. S = E α, β E α, β + E α, β E α, β E α, β = N α,β +N α,β N α,β N α,β N α,β +N α,β +N α,β +N(α,β) N α, β Is the coincidence count at with two polarizers set to angles α and β

9 Experimental Apperatus

10 BBO (Beta Barium Borate) Crystals Negative uniaxial nonlinear crystals (Type 1 cut) A type one cut leads to a non-linear effect called spontaneous parametric down-conversion An incident photon is converted into two photons of longer wavelength called the signal and idler photon. This process was used to generate two cones of light with entangled pairs.

11 Spontaneous Parametric Down Conversion When a horizontally polarized photon of a certain wavelength hits the BBO crystal, two photons of two times the wavelength leave the crystal with an vertical polarization state

12 Spontaneous Parametric Down Conversion Cont. We used two BBO crystals to generate the H and V-polarized cones Pump beam has both a horizontal and vertical component to its polarization, while each crystal transmits a different orthogonal polarization component. When one photon is split into two the two are entangled.

13 Overlapping Cones Overlapping cones on EM-CCD camera imaged directly after BBO crystals.

14 Fringe Visibility/Cosine Squared Dependence Coincidence count One polarizer has a constant angle constant (blue is 135, pink is 45) with other ranging from 0 to 360 degrees. Fringe visibility V = N mmm N mmm (N mmm N mmm ) =0.9987

15 Quartz Plate Alignment We varied the horizontal angle of the quartz plate looking for the optimal angles. The optimal orientation angle of the quartz plate is where the different lines intersect Coincidence Count Horizontle angle

16 Quartz Plate Alignment Con.t We checked for vertical alignment using the same method Coincidence Counts Counts Vertical Angle

17 CHSH Data Table for 16 coincidence count measurements Net coincidence is average coincidence minus accidental coincidence. Polarizer A Polarizer B Net coincidence

18 Results S was computed to be 2.47 > 2! We successfully violated the CHSH Bell inequality We also took coincidence count measurements and calculated S when the quartz plate was intentionally 5 degrees misaligned. S was about 1.57, far below 2.

19 Lab 2 Single Photon Interference

20 Wave Particle Duality The purpose of this experiment was to prove light may behave as either a particle or a wave depending on the situation

21 Which Way Information If a photon has a probability of taking two paths that recombine later, its wave function will split, taking both paths and interfere when the paths recombine If there is only one possible path the photon s wavefunction will collapse and there will be no interference

22 Young s Double Slit Experimental Setup and Theory Diagram of apparatus Diagram of double slit Interference Pattern

23 Young s Double Slit Experimental Setup and Theory Cont. We used an EM-CCD camera as the observation screen and a HE-NE laser with nm wavelength with an output power of 1 μw. We used neutral density filters to attenuate the beam to the single photon level. There was on average one photon per meter, so on average one photon in the system at a time

24 0.1 s exposure, and 4.66 order of magnitude attenuation. 0.1 s exposure, 4.66 order of magnitude attenuation, with 20 accumulations s exposure, 4.66 order of magnitude attenuation, 20 accumulations, with 255 gain. 0.1 s exposure time, and 3 order of magnitude attenuation.

25 Image with the Best Contrast second exposure, 120 accumulations, 4.66 order of attenuation with 255 gain.

26 Mach-Zehnder Experimental Setup

27 Setup Explained The polarizing beam splitter splits the laser beam such that photons with two orthogonal polarization states takes two different paths By rotating the second Polarizer different polarization components are transmitted, leading to which way information The neutral density filter attenuates the beam The spatial filter cleans the beam

28 Which Way Information Mach-Zehnder interferometer setup for single photon interference This allows us to analyze the effect on the fringe visibility by rotating the second polarizer. The following images were taken with 1 second exposure, no accumulations, no gain and 5 orders of attenuation Mach Zehnder interference pattern with second polarizer set to 0. Mach Zehnder interference pattern with second polarizer set to 60.

29 Fringe Visibility FFFFFF VVVVVVVVVV = I mmm I mmm I mmm +I mmm I max and I min the maximum and minimum intensities on a fringe Image J software was used to measure I max and I min values for the second polarizer s angles ranging from 0 to 360 in 10 increments.

30 Results 0.8 Visibility Fringe Visibility Polarizer 2 angle There were significant drops in Fringe Visibility every 90

31 Results Cont. The presence of interference fringes at some angles of the second polarizer, but not others demonstrates that photons can behave as either waves or particles depending on the situation

32 Labs 3 and 4 Confocal Microscopy Imaging of Single Emitter Fluorescence and Hanbury, Brown, and Twiss Setup, Photon Antibunching Purpose: To prove that a source of light can be a single-photon source and that a single-photon source exhibit antibunching

33 Single Photon Source A single photon source emits photons separated in time. This is called antibunching When these sources are excited by an external field only one photon is emitted per unit time. This time is the fluorescence lifetime τ. Examples of single photon sources include single atoms, quantum dots and nano-diomonds.

34 Antibunching Attenuated laser beams will have photons that can come in pairs or triplets. They only have one photon on average per some distance. Single emitters will exhibit antibunching, since they are only capable of emitting one photon at a time separated by fluorescence lifetime.

35 Confocal Microscopy Confocal Fluorescence microscopy can be used to irradiate a sample with focused light from a singlemode laser beam and direct the sample response through a pinhole. It is important that the light originating from the laser does not pass through the pinhole so only the sample response reaches the detector. This type of imaging has a shallow depth of focus but a high numerical aperture maximized using oil immersion.

36 Experimental Setup Hanbury, Brown and Twiss interferometer setup used to confirm antibunching using a confocal microscope.

37 Once the beam is focused and the system aligned the port selector directs the light to the APD s (which serve as a functional pinholes). The beam hits a 50/50 non-polarizing beam splitter which directs half the light toward APD 1 and half towards APD 2. We use two APD s to because one APD can not record consecutive photons. When APD 1 receives a photon, a TTL pulse is sent to the computer card that starts charging a capacitor. When APD 2 receives a photon, a second pulse is sent to the computer card and the capacitor stops charging. The time between these pulses is determined from the capacitor charge.

38 However there is a delay between these two pulses. To compensate for this physical limitation we create an intentional delay between the start and stop signal. The time difference of these two signals allows us to make an antibunching histogram. If two photons hit the detectors with 0 time separation they are not antibunched. A histogram of all recorded times should zero coincidence count at zero time separation if the photons are antibunched.

39 Quantum Dots We used quantum dots as our single photon source. Quantum dots are molecules with semiconductor like properties that fluoresce at various wavelengths. A problem with quantum dots is that they blink. This means that they stop emitting photons for brief amounts of time. A He-Ne laser was used to excite the quantum dots.

40 Antibunching Histogram Coincidence Count Time Delay 60 (ns) The center of the x-axis is 60 ns because that is the physical delay. So 60 can be thought of as the 0 point.

41 Florescence Lifetime y = ln(x) R² = Coincidence Count Series1 Log. (Series1) Time Delay The slope of this histogram s Logarithmic trend line was calculated to be the florescence lifetime

42 Results Antibunching was successfully observed from quantum dots The fluorescence lifetime was calculated to be nanoseconds

43 Summary Lab 1: We demonstrated polarization state entanglement photon pairs. This was achieved using the CHSH Bell inequality. We got a value a maximum value of S of 2.47 which convincingly violates the CHSH Bell inequality.

44 Summary Cont. Lab 2: This experiment confirmed the phenomenon of waveparticle duality. The photons interfered with themselves resulting in an interference pattern in both experimental setups. The dependence of polarization angle with the Mach-Zehnder setup demonstrates the power of which way information. If the photon knows its path then its wavefunction collapses. The presence of interference fringes at some angles of the second polarizer, but not others demonstrates that photons can behave as either waves or particles depending on the situation

45 Summary Cont. Lab 3 and 4: Antibunching of quantum dots was successfully observed. The fluorescence lifetime was calculated to be nanoseconds.