Quantum Eraser

## Introduction

With our next experiment we now encounter a new topic. This is the topic of measurement. Measurement in the quantum world plays a very different role than it does in the classical world. In the quantum world measurements are no longer passive, their role is much more active [1]. To explore this topic of measurements we employ what is known as the Quantum Eraser. The goal of this experiment is to show that the visibility of observed fringe pattern is affected by making measurements.

The visibility of the fringe pattern is dependent on the amount of path information available. If we are able to determine which path the photon takes, then there is no interference. On the other hand, if we cannot tell which path the photon takes then interference can be observed.

In our experiment it is possible to switch between having full path information to having no path information. When the path information is no longer available, the information is said to be erased.

We were able to demonstrate quantum erasure in a Mach-Zehnder interferometer using an entangled-state source, which exhibits quantum mechanical correlations. We found that the visibility of the measured interference pattern does indeed depend on the path information available. We found that interference is lost when which-path information for the signal beam can be obtained by tagging the photon using polarization.

## Parts of Experiment:

1. Regular Interference - this was done with no polarizer in place and with both half wave-plates set to the same polarization. The prediction for this part of the experiment is the same as that for the single photon interference exeriment
2. The second experiment was the "tagged" photon experiment . In this experiment we had no polarizer. One wave-plate was rotated by 45o, which rotated the polarization by 90o. A rotation of the half-wave plate by $\phi$ rotates the polarization by $2{\phi}$ The state of the photon emerging from arm 1 is [2]:

(1)
\begin{align} |l_1> = AB[cos2{\phi}|V> + sin2{\phi}|H>] \end{align}

and the probability of detecting is defined by

(2)
\begin{align} P = RT{|e^{i{\delta}_1}|l_1> + e^{i{\delta}_2}|V>|}^2 = {1 \over 2}(1 + cos2{\phi}cos{\delta}) \end{align}

for $R = T = {1 \over 2}$

3. The Quantum Eraser. Kept the wave-pates rotated, but put the polarizer in, which effectively "erases" the path information. By putting the polarizer in we erase the "which-path" information by projecting two orthogonal states using the polarizer set to ${\pi} \over 4$. The state of the photon after the polarizer is now [2]:

(3)
\begin{align} |S_{{\pi} \over 4}>(<S_{{\pi} \over 4}|H>e^{i{\delta}_1} + <S_{{\pi} \over 4}|V>e^{i{\delta}_2}) \end{align}

## Experimental Setup:

The setup for this experiment was simple after we had our interferometer aligned. We simply had to insert two half wave plates (one in each arm or our interferometer), and one polarizer after the second beam splitter as shown below.

## Results:

In the first part of the experiment we have basically the same set up we did when we were simply measuring interference. Therefore we expect to see result that are the same, and we do!

In part two of our experiment we have two "tagged" paths. This gives us the unexpected result of no interference. The figure shows measured coincidence counts when the polarizers are at different values. In this case no interference is observed.

In the last part we have tagged the photons, and then effectively "untagged" them using the polarizer. That means after the polarizer we have no way of measuring which path the photon has taken. The figure shows measured coincidence counts between entangled photon pairs when the path information is erased. In this case our interference pattern returns and high visibility interference is observed.

We can see how these change relative to each other if we create a composite of all three graphs:

We can see that the polarizer takes out some of the photons. This is why the third experiment is significantly lower than the first.

The mystery of the Quantum Eraser is that when we tag the photon so that we can determine which path the photon travels it seems to know that we are watching and only travels one way. However when we erase path information and we can no longer determine which path the photon travels the interference returns!

To say it simply: The photon seems to know when we are watching and behaves differently when we can say where it has traveled.

This is a problem, if we observe we destroy the interference pattern. But, if we don’t tag the paths then it is impossible to know which way the particle goes.

References
1. Greenstein and Zajonc. The Quantum Challenge. Jones and Bartlett Publishers: Massachusetts. (2006)
2. E. J. Galvez, C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, "Interference with correlated photons: Five quantum mechanics experiments for undergraduates," Am. J. of Phys. 73, 127-140 (2005)
page revision: 30, last edited: 01 May 2009 19:48