July 5, 2022

# Quantum Zeno Effect

#### How DR WHO used it to freeze time

Image: ©unsplash: used for representational purposes only.

You all heard saying “a watched pot never boils”, but what if it actually boiled faster when you watched? Of course, in our macroscopic world, watching or not doesn’t make a difference. But in the quantum world, where we consider the energy levels of an atom, active measurement can make a huge difference. [1]

In Quantum Physics, it is possible to probabilistically slow down time for a split of seconds. Today, using the Quantum Zeno Effect, We will save Schrodinger’s cat, freeze the weeping angels of DR WHO, and take pictures without shining a light on a particle. Throughout this article, we will build upon a fairly good intuition into these phenomena using the notion and understanding of the Quantum Zeno Effect. But first, let’s start with the classical one.

Suppose, to reach the lab on the far side of the campus, a physicist first needs to cross half the width of the campus, which takes a finite time. Then, he needs to cross half of the remaining distance, which takes another finite time, and then half of the remaining distance, and so on. The distance across the campus is divided into an infinite number of half steps, each requiring a finite time to cross. “If you add together an infinite number of steps, each taking a finite time, it should take an infinite amount of time to cross the campus”. Thus, it should be impossible for the physicist to ever get all the way to his lab. read more

Image: ©ted-ed: used for representational purposes only.

But there is a mathematical solution to the apparent paradox — as the distance between the physicist and the lab decreases, the time required to cross it also decreases: If it takes one second to cross half the width of the campus, it takes half a second to cross the next quarter, and a quarter of a second to cross the next eighth, and so on.

Adding together all those times, we find that:

1s + 1/2s + 1/4s + 1/8s +…..=2s

The infinite sum gives a finite result — the physicist crosses the campus in two seconds. Motion is possible after all.

According to Chad Orzel’s book, The definitive quantum Zeno effect experiment was done in 1990 by Wayne Itano in Dave Wineland’s group at the US National Institute of Standards and Technology (NIST) in Colorado, using [Be]+ beryllium ions.[2] Ions are atoms with one electron removed, and they, like all atoms, they have a set of allowed energy states that can switch between by absorbing or emitting light. Itano’s experiment collected a few thousand beryllium ions and used microwaves to shift them slowly from one state to another.

The ions took 256 milliseconds to move from State 1 to State 2 while left unmeasured. Their state during this process was defined by a wavefunction with two parts, one for the probability of finding the atom in State 1 and the other for the probability of finding the atom in State 2. The atoms were 100% in State 1 at the beginning of the experiment, and 100% in State 2 by the end. Between those two places, the probability of State 2 steadily increased while the probability of State 1 steadily decreased.

The researchers used an ultraviolet laser with a frequency set, so that, an ion in State 1 would happily absorb light, whereas, ions in State 2 would not. State 1 ions absorbed laser photons and re-emitted them a few nanoseconds later, forming a bright spot on a camera pointed at the ions. Ions in State 2, on the other hand, produced no light when illuminated by the laser. Then, the total amount of light reaching the camera was a direct measurement of the number of ions in State 1.

To demonstrate the quantum Zeno effect, the NIST group trapped a large number of ions, all in State 1. Then they turned on the microwaves, waited for 256 milliseconds, and pulsed on the laser. None of the ions produced any light, indicating that 100% of the sample had moved to State 2, as expected. Then they repeated the experiment, with two laser pulses: one after 128 ms (halfway through the move to State 2), and one after 256 ms. In this case, they saw half as much light after 256 ms, indicating that only 50% of the sample had made the transition to State 2.

Image: ©wayne-Itano’s paper: used for representational purposes only.

As shown in the pictures above, the quantum Zeno effect explains the decreasing probability. The ions’ state was measured midway through the laser pulse. Many of these were discovered in State 1, and the measurement destroyed the State 2 part of the wavefunction. Because these atoms were now completely in State 1, the transition had to start over, with the probability of State 2 increasing slowly. After another 128 ms, the probability of finding the ions in State 2 was only 50%.

The probability of moving from State 1 to State 2 decreased further with more measurements. With four pulses (at 64, 128, 192, and 256 ms), only 35% of the atoms made the transition. With eight pulses, only 19% made the transition. With a total of 64 laser pulses over the full experimental interval (one every 4 ms), fewer than 1% of the atoms made the transition.

I understand that if we measure repeatedly, we can get our outcome in the state where we had began fisrt. But how do you slow down the time? is it really possible?well! at first it may seem absurd, but let me give you a mathematical explanation.

#### Mathematical Explanation:

Consider a quantum system in the state psi at t equals 0 we perform a measurement with some operators A:lambda which yields the eigenvalue lambda After such a measurement the wavefunction collapses to the corresponding eigenvector of A which we call psi-lambda.

Image: ©pretty-much-physics: used for representational purposes only.Image: ©pretty-much-physics: used for representational purposes only.

If we leave the system alone, then the wavefunction will change according to the time-dependent Schrodinger equation and it might yield a different eigenvalue at a later time, however, we don’t give the system enough time to do its time evolution. Instead, we perform another measurement at time t equals epsilon with the same operator A:lambda, such that, even if the wave function evolved a tiny bit, it will probably collapse to psi-lambda again. “more in this video.[3]

This means we can effectively freeze the quantum system.In 2014, a team of physicists led by Y.S. Patil at Cornell University successfully demonstrated that rapid repetitive measurements can effectively freeze a system in place. The potential implications of this are huge, as the paper asserts, “The techniques demonstrated here… … augur intriguing prospects of realizing novel many-body interactions such as a measurement-induced dynamic coupling between the internal, emotional and topological states of a quantum many-particle system.” [Patil 2014]

#### Saving Schrodinger’s cat:

To summarize, We can consider how this could affect Schrodinger’s cat. Say, we set up a box that contains a radioactive atom, a vile of poison, and a cat — such a way that if the atom decays the cat will be killed. The Zeno effect says that if we check on the cat, then we reset the atom’s decayed clock data, thereby preventing the vile from breaking and keeping the cat alive. “Learn how Felix Pollock saves the cat in this video.[4]

#### Freezing Weeping Angles of DR WHO:

In Dr WHO, a science fiction series, you can even lock and freeze the weeping angel, who turns people into stone and throws them back in time, by using Quantum Zeno Effect. All you have to do is follow Dr. Who’s advice, as he was warning his friends saying,

#### Other applications of Quantum Zeno Effect:

The quantum Zeno effect has been verified by experiments many times and one paper even suggests that the quantum Zeno effect is a key mechanism in the magnetoreception of birds that enables them to see magnetic fields.[5]

Moreover, it has been demonstrated experimentally using polarized photons, by physicists in Innsbruck, Los Alamos, and Illinois. Quantum Interrogation, a little like Quantum Zeno Effect, allows you to do some incredible things — taking pictures of objects without ever bouncing light off them, for example.

“If someone shoots you with a quantum arrow, don’t blink.”

If you liked this article, consider leaving some claps and follow the publication, Quantum London. We are going to publish a lot of resources for quantum Computing and Quantum Physics, from hardware to algorithms and many more. Stay tuned for our next article on quantum computing, see you then!

#### references

[1] Washington University in St. Louis — Zeno Effect

[2] Quantum Zeno effect — Wayne M. Itano 1990

[3] Pretty Much Physics — Mathematical Explanation

[4] My favorite physicist Dr. Felix Pollock’s cat saving talk

[5] The Radical-Pair Mechanism of Magnetoreception

[6] How to Teach [Quantum] Physics to Your Dog — Chad Orzel

#### The video that encouraged me to write this article:

PBS Space Time — https://youtu.be/SMPid7Sh0EEProfessor Cynthia Sue Larson — https://youtu.be/K5hkb3LR60c

#### Optional reading on Quantum Zeno Effect:

Quantum Zeno Effect was originally published in Quantum Computing on Medium, where people are continuing the conversation by highlighting and responding to this story.