Quantum and Nano Optics Laboratory · screen and a HE-NE laser with 632.8 nm wavelength with an output power of 1 μW. • We sed neutral density filters to attenuate the u beam to

Quantum and Nano Optics Laboratory

Jacob Begis Lab partners: Josh Rose, Edward Pei

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

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:

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”

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

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.

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.

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⊥,𝛽𝑁 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

Experimental Apperatus

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.

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

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.

Overlapping Cones

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

Fringe Visibility/Cosine Squared Dependence

-505

1015202530354045

Coincidence count

• Fringe visibility 𝑉 = 𝑁𝑚𝑚𝑚

−𝑁𝑚𝑚𝑚

(𝑁𝑚𝑚𝑚

−𝑁𝑚𝑚𝑚

) =0.9987

One polarizer has a constant angle constant (blue is 135, pink is 45) with other ranging from 0 to 360 degrees.

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.

0

20

40

60

80

100

120

140

160

180

-5 -4 -3 -2 -1 0 1 2 3 4 5

Coi

ncid

ence

Cou

nt

Horizontle angle

135

45

0

90

Quartz Plate Alignment Con.t

• We checked for vertical alignment using the same method

0

20

40

60

80

100

120

140

160

180

30 31 32 33 34 35 36 37 38 39 40

Cou

nts

Vertical Angle

Coincidence Counts

0-0

90-90

45-45

135-135

CHSH Data

Polarizer A Polarizer B Net coincidence

-45 -22.5 38.76

-45 22.5 3.64

-45 67.5 4.74

-45 112.5 42.71

0 -22.5 38.06

0 22.5 35.01

0 67.5 12.68

0 112.5 13.02

45 -22.5 7.72

45 22.5 39.34

45 67.5 52.00

45 112.5 12.00

90 -22.5 10.07

90 22.5 14.69

90 67.5 34.68

90 112.5 48.71

• Table for 16 coincidence count measurements • Net coincidence is average coincidence minus accidental coincidence.

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.

Lab 2 Single Photon Interference

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

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

Young’s Double Slit Experimental Setup and Theory

Diagram of apparatus

Diagram of double slit Interference Pattern

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 632.8 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

0.1 s exposure, and 4.66 order of magnitude attenuation.

0.1 s exposure, 4.66 order of magnitude attenuation, with 20 accumulations

0.0005 s exposure, 4.66 order of magnitude attenuation, 20 accumulations, with 255 gain.

0.1 s exposure time, and 3 order of magnitude attenuation.

Image with the Best Contrast

• 0.0005 second exposure, 120 accumulations, 4.66 order of attenuation with 255 gain.

Mach-Zehnder Experimental Setup

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’

Mach Zehnder interference pattern with second polarizer set to 0 °.

Mach Zehnder interference pattern with second polarizer set to 60 °.

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

Fringe Visibility

• 𝐹𝐹𝐹𝐹𝐹𝐹 𝑉𝐹𝑉𝐹𝑉𝐹𝑉𝐹𝑉𝑉 = 𝐼𝑚𝑚𝑚−𝐼𝑚𝑚𝑚𝐼𝑚𝑚𝑚+𝐼𝑚𝑚𝑚

• Imax and Imin the maximum and minimum intensities

on a fringe

• Image J software was used to measure Imax and Imin values for the second polarizer’s angles ranging from 0 ° to 360 ° in 10 ° increments.

Results

There were significant drops in Fringe Visibility every 90 °

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-40 10 60 110 160 210 260 310 360

Fringe Visibility

Polarizer 2 angle

Visibility

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

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

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.

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.

Confocal Microscopy • Confocal Fluorescence microscopy can be used to

irradiate a sample with focused light from a single-mode 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.

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

Experimental Setup

• 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.

• 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.

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.

Antibunching Histogram

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.

0

10

20

30

40

50

0 20 40 60 80 100 120

Coincidence Count

Time Delay (ns)

Florescence Lifetime

y = 34.319ln(x) - 124.97 R² = 0.3335

0

10

20

30

40

50

60

55 75 95 115

Coincidence Count

Time Delay

Series1

Log. (Series1)

The slope of this histogram’s Logarithmic trend line was calculated to be the florescence lifetime

Results

• Antibunching was successfully observed from quantum dots

• The fluorescence lifetime was calculated to be 34.32 nanoseconds

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.

Summary Cont.

• Lab 2: This experiment confirmed the phenomenon of wave-

particle 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

Summary Cont.

• Lab 3 and 4:

• Antibunching of quantum dots was successfully observed.

• The fluorescence lifetime was calculated to be 34.32 nanoseconds.