This experiment is the delayed-choice quantum eraser.
The experiment was first performed in 1998 and repeated in Brazil in 2008 with a slightly different setup (see the Literature section), more similar to ours. On one path, a double slit produces interference for non-entangled photons. With entangled photons, detector $D_1$ alone never shows interference, even though the photons pass through the double slit. This is the purple curve in the animation.
However, when we examine coincidences between $D_1$ and $D_2$, the results depend on the polarizer angles. By rotating the idler polarizer $P_2$, we can make interference fringes appear or disappear in the coincidence data. This is the pink curve in the animation.
At first glance, it may appear that a measurement made in the present can alter one made in the past.
The key insight is that the which-path information is encoded in the idler photon. Measuring the idler at $0°$ or $90°$ preserves this information, yielding no interference. Measuring at $\pm45°$ erases the information, and interference reappears in the coincidences.
Use the animation to explore the experiment:
Curious about what an entanglement optical setup looks like? Here are photos of our apparatus:
The below image shows a schematic of the apparatus. All components are shown, but not to scale.
The BBO crystal produces photon pairs in the Bell state:
Signal path (path 1): A double slit ($b = 200\,\mu\text{m}$ slit width, $d = 400\,\mu\text{m}$ separation) with polarizers $P_A = 0°$ and $P_B = 90°$ covering each slit. A 500 mm focal length lens is placed midway between the slits and detector (500 mm from each). A third polarizer $P_1$ at $45°$ acts as the eraser. Detector $D_1$ is mounted on a linear actuator with a $200\,\mu\text{m}$ slit in front.
Idler path (path 2): A 500 mm lens (500 mm from the detector) and a rotatable polarizer $P_2$.
Detection system: Single-photon detectors coupled to optical fibers. Each fiber input requires a collimator and bandpass filter. The detectors count photons over a fixed integration time. We scan $D_1$ across the beam to reconstruct the spatial pattern. $D_2$ remains stationary since the idler beam has no spatial structure. Components before the BBO (beam preparation optics) are described in Experiment 4.
Data files for each $P_2$ configuration:
To reconstruct each pattern, we scanned the actuator across the beam. At each position, we recorded multiple samples to compute an average and standard deviation. We performed several sweeps to further reduce noise. Each file contains 7 columns:
- Polarizer angle 1 (fixed in this experiment)
- Polarizer angle 2 (fixed in this experiment)
- Actuator position ($\mu$m)
- Sweep number
- Counts at $D_1$ (signal path)
- Counts at $D_2$ (idler path)
- Coincidences between $D_1$ and $D_2$
Singles (left column): All four curves are identical (within experimental error). The $D_1$ singles show only diffraction, regardless of $P_2$. This confirms that no local measurement at $D_1$ can reveal interference.
Coincidences (right column):
- $P_2 = \pm 45°$: Clear interference fringes. The two patterns are complementary (peaks and troughs swap).
- $P_2 = 0°$ or $90°$: No interference, only diffraction. The two curves are slightly shifted because each selects photons from a different slit. The diffraction maxima are centered on each slit.
This is the quantum eraser effect: interference appears only in coincidences, and only when $P_2$ is set to erase which-path information.
The BBO crystal generates entangled photon pairs in the Bell state:
The photons travel along two paths:
Signal path: A double slit where each slit is covered by a polarizer ($P_A = 0°$, $P_B = 90°$). This encodes which-path information in the polarization. A third polarizer $P_1$ at $45°$ projects both polarizations onto the diagonal basis.
Idler path: A single rotatable polarizer $P_2$ at angle $\gamma$. The key physics:
- After the slit polarizers, measuring the idler's polarization reveals which slit the signal passed through (vertical $\Rightarrow$ slit $A$, horizontal $\Rightarrow$ slit $B$).
- If $P_2 = 0°$ or $90°$, it selects one polarization, preserving which-path information. Coincidences show only diffraction.
- If $P_2 = \pm 45°$, it projects onto the diagonal basis, erasing which-path information. Coincidences show interference.
- Singles at $D_1$ never show interference, regardless of $P_2$. The which-path information exists in the idler, even if we choose not to access it.
The "delayed choice'' aspect: the idler can be measured after the signal is detected. The choice of $P_2$ angle determines whether interference appears in the coincidence record, even though the signal detection already occurred.
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The delayed-choice quantum eraser follows the same logic as Experiment 3, but with entangled photons. The idler polarizer $P_2$ plays the role that $P_1$ played before: it chooses which basis to use, and that choice determines whether interference appears.
The state after the slit polarizers
The BBO produces entangled pairs. After the signal passes through the double slit (with $P_A = 0°$ on slit $A$, $P_B = 90°$ on slit $B$) and the eraser polarizer $P_1$ at $45°$, the state is:
The signal polarization is now diagonal for both paths — $P_1$ has done its job. But the idler polarizations are still orthogonal: $\ket{\updownarrow}_2$ vs $\ket{\leftrightarrow}_2$.
This is why $D_1$ alone sees no interference: the two paths are still distinguishable via the idler.
Choosing a basis
Here is the key insight: the idler polarizer $P_2$ chooses which basis to express the idler in.
In the H/V basis ($P_2 = 0°$ or $90°$): The idler states $\ket{\updownarrow}_2$ and $\ket{\leftrightarrow}_2$ are orthogonal $\rightarrow$ the two terms cannot combine $\rightarrow$ no interference.
Setting $P_2 = 0°$ selects only $\ket{\updownarrow}_2$ photons (from slit $A$). Setting $P_2 = 90°$ selects only $\ket{\leftrightarrow}_2$ photons (from slit $B$). Either way, we know which slit.
In the diagonal basis ($P_2 = \pm 45°$): We can rewrite the idler states as:
Now both paths contribute to $\ket{\diag}_2$ and both contribute to $\ket{\adiag}_2$. When $P_2$ selects one diagonal component, it mixes amplitudes from both slits $\rightarrow$ interference is possible.
What $P_2$ does
The idler polarizer projects onto angle $\gamma$. The coincidence intensity is:
Why does $\pm 45°$ restore interference?
At $0°$ or $90°$, the polarizer selects idler photons from one slit only. The coincidence record contains only single-slit photons $\rightarrow$ no interference.
At $45°$, the polarizer accepts idler photons from both slits with equal amplitude. A coincidence event could have come from either path — we cannot tell. The which-way information has been erased, and interference reappears.
This is the delayed-choice quantum eraser: the choice of $P_2$ can be made after the signal is detected, yet it determines whether interference appears in the coincidence record.
Complementary pairs
The $45°$ and $-45°$ patterns are opposite (maxima $\leftrightarrow$ minima). The $0°$ and $90°$ patterns are shifted copies of each other (centered on each slit).
In all cases, summing the complementary pair recovers the same diffraction envelope. The idler polarizer does not create or destroy photons — it picks a decomposition.
Why no interference in singles?
The $D_1$ singles count all signal photons, regardless of what happens to the idler. This is equivalent to averaging over all possible $P_2$ angles:
The interference terms cancel. Only by selecting a specific idler outcome (via coincidences) can interference appear.
If you want to check out some papers that did the same experiment, here are the two best resources we have found:
If you want a more interactive resource, here are some Youtube videos we found to be accurate and insightful.
