Quantum erasing against the time stream (part 2): How to outsmart photons

Contents

Anyone who has ever had to make a difficult choice between two alternatives and unfortunately opted for the one that turned out to be less favorable in retrospect will have wished they could simply turn back time to revise their decision. Unfortunately, this is not possible in everyday life. But in the world of the very smallest, the quantum, there is an effect that some claim would allow us to retrospectively make a decision about the outcome of an event that is already in the past.

In the first part of the article, we introduced the concept of quantum erasing of light: As long as photons are allowed to take multiple paths to a projection surface or detector, such as through a double slit, even single emitted photons reveal their wave nature and create an interference pattern of light and dark fringes. This phenomenon can only be explained by the fact that the possible paths influence each other, even if only a single particle passes through each of them. However, as soon as an attempt is made to determine the exact path of individual photons, the interference pattern disappears and gives way to a disdainful diffraction pattern, as if each photon had actually only ever taken one specific path. The light is then no longer capable of interference.

Quantum erasing of light means modifying the experimental setup set up to measure the light path in such a way that the information about the path is "erased" again before it is evaluated. This restores the interference capability of the light. This is achieved by superimposing the separated light paths in such a way that the photons have several possibilities of reaching the detector or projection screen. As shown in the first part, this can even be done in a home experiment with polarizing filter foils, or – with considerably more effort, but also persuasiveness – with a Mach-Zehnder interferometer.

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Quantum erasing in retrospect

So far, so amazing. The whole thing becomes even more interesting if quantum erasing is only carried out after the photons have already been registered by the detectors. Can the interference pattern still be influenced afterwards? That seems completely absurd – Either the photons on the screen interfere or they don't. But quantum physics says that as long as the photons can take several unobserved paths to the target, they will interfere. However, as soon as you measure the path, they will not. Can photons be tricked by delaying the measurement of the path? And how can such a measurement be carried out without influencing the photons if the measurement of the path changes the result?

The physicists Marlan O. Scully and Kai Drühl had already proposed a thought experiment in 1982 with which the "which-path" information could be obtained retrospectively: the "quantum eraser with delayed selection".

In their work, instead of a double slit, Scully and Drühl proposed two neighboring atoms whose electrons are pumped to a higher energy level a by a laser pulse λ. Excited electrons spontaneously fall back to the ground state b and emit photons γ, which interfere on a screen or detector. In general, not both atoms are excited at the same time, but sometimes one and sometimes the other emits a photon. As it is not possible to determine afterwards which atom emitted the photon, the impressions of (very) many photons add up to an interference pattern.

The situation is different if atoms with three possible energy levels a, b and c are used, of which b and c are stable, while a is unstable, which can be ensured by choosing the right type of atom. If an electron is pumped from the ground state c to the unstable state a by the laser pulse, then the electron spontaneously falls back either to the ground state c or to the intermediate state b. Jumps to the ground state c can be ignored, as they emit light of a different (shorter, as the energy difference between a and c is greater than between a and b) wavelength than the transition a🠒b. If you look at the two atoms afterwards exactly when a photon γ testifies to such a transition. Then, in the vast majority of cases, you will find exactly one of the atoms in state b and thus know the source of the photon afterwards. The case in which both atoms are found in state b, which in turn would obscure the origin of the photon, is disproportionately rarer and hardly distorts the result.

So if you only look at light from transition a🠒b and filter out light from transition a🠒c (which is easy to do with a color filter), you should not see any interference pattern, although the setup of the experiment is practically identical to the one mentioned at the beginning. However, the atoms in state b now reveal the path taken by the photon and thus destroy the interference pattern.

However, this information can also be deleted again. If a second laser pulse λ₂ is sent, which raises the electron from energy level b to a fourth unstable level b', from which it immediately falls back to c, it again becomes indistinguishable from an atom whose electron has never left c and has not emitted a photon γ. However, it emits another photon Φ of a different wavelength at the transition b'🠒c. And it is precisely this photon that can be used to subsequently erase the information about the origin of the photon γ or not, as it reveals whether an atom was in state b or not.

Scully and Drühl proposed the following setup for evaluating the photon Φ: The two atoms are each hit in parallel in quick succession by two laser pulses λ₁ and λ₂ with precisely matched energies: The first causes the transition c🠒a, emitting a photon γ at the spontaneously occurring transition a🠒b; the second causes the transition of b🠒b', emitting a photon Φ at the relapse b'🠒c. The photons γ are detected by a movable detector D₀, which can scan the superposition pattern of the photons, while most of the photons Φ produced when the b state is deleted are focused on a second detector D₁. As long as D₁ can register Φ photons from both atoms, it remains unclear which atom was the source of a photon γ.

An electro-optical shutter between the atoms with the detector on one side can specifically prevent the Φ-photons of the atom on the other side of the shutter from reaching D₁. Each photon Φ registered by D₁ must therefore originate from the other atom located on the same side of the detector. In this case, it should no longer be possible to observe interference for γ-photons that arrive at the same time as the Φ-photons registered at D₁. With an electronic switch that can open and close the electro-optical shutter, it would be possible to switch between the two modes at lightning speed and thus select whether the origin of the γ photon is known or not. Accordingly, the interference pattern at D₀ could be switched off, depending on whether Φ photons from both atoms are allowed to pass through to D₁ or only from one of the two.

However, the experiment only becomes really exciting if the evaluation of the Φ-photons is significantly delayed. In principle, you could first send them to Alpha Centauri for 4.3 years and then send them back again before evaluating them, as long as you know the approximately 8.6-year transit time precisely enough to draw conclusions about the γ-photons that hit the screen when the associated Φ-photon was created. Thus, after 8.6 years, it should be possible to retrospectively influence whether a sequence of photons has generated an interference pattern or not!