Quantum Memory for Pedestrians – Niels Bohr Institutet - Københavns Universitet

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Here we will give a short explanation on how a quantum memory works. It is not assumed that the reader has pre-knowledge in the field.

 




First we explain about light the fact that light behaves like waves. Next we consider a property of atoms called spin. With this knowledge at hand we demonstrate similarities between light and matter in some respects. As a consequence it is possible to store some information carried by light in atoms. We will also explain a little quantum mechanics and its consequences. This is necessary for the understanding of the fact that a "quantum memory" is better than a "classical memory" (we explain these concepts below). Properties of Light:

Light travels with the speed of light which is 300.000 km per second in vacuum. This makes light a very good information carrier for transport. For instance optical fibers are often used in the communication industry. The radio waves received by an ordinary FM-radio are also a kind of light (with a slower oscillation frequency than visible light).

Light behaves like waves. It travels precisely as waves on the surface of the ocean or sound waves through the air - only a lot faster.

Light bulb movie

Example of a traveling light wave.

Colour movie Strength movie Phase movie

There are different important properties of a light wave. The colour of the light is decided by the wavelength as illustrated by the first picture. Blue light has a shorter wavelength than red light. The strength of the light is set by the magnitude of the wave excursion (second picture). Finally there is a property called phase. This property decides when the wave is at the top or bottom. In the last picture the phase is varied continuously.

Atoms as small spinning tops:

Atoms have the property that they can be at rest. This is not the case for light. To store some information for an amount of time atoms are a good choice, contrary to light.

There are many different properties characterizing atoms. One of these is called spin. You may think of a little spinning top (hence the name). The spinning top behavior may be caused by an electron moving around the atomic nucleus. The direction of the axis around which the top is spinning can be anywhere in space.

Spinning top movie

Sometimes atoms behave like spinning tops.

Atoms as memory for a state of light:

As we discussed above, light is good for transporting information at atoms are good for storage of information. Now take some light with a chosen colour. We assume that some information has been encoded in the strength and the phase of this light. We would like to transfer this information to atoms and hence we must find a method to represent the strength and phase of the light in the spinning top. This representation is explained pictorially below.

Light/spin movie

Here we picture different states of light and atoms which correspond to each other. If the spinning top is pointing in the vertical direction the light is off (has strength zero). The stronger the light, the more the top is rotated away from vertical. The phase is encoded in the direction in which the top is rotated away from vertical.

Now let us turn to an actual procedure of storing the information carried by light in a spinning top. For instance one can simply measure the strength and phase of the light and note the result on a piece of paper. Then we know how much and in which direction to rotate the spinning top.

Classical mapping

The light hits a detector which measures the strength and phase of light. Then the spinning top can be rotated by the proper amount in the right direction and the information has been transfered. In the next section we denote this procedure "classical memory".

There is a slight problem, though. We have forgotten to check with the laws of nature whether this is at all possible! The method explained above actually only works with a certain precision. This is a consequence of quantum mechanics. We will explain more below.

Quantum Mechanics for Light and Atoms:

Quantum mechanics is the physical theory which is necessary to describe the smallest parts of nature. The word "quantum" arises from the fact that nature contains a kind of smallest building blocks (a smallest quantum) of literally everything. For instance light can be considered as a collection of a lot of small particles as shown below.

The photon

The smallest parts of light: We consider a pulse of light and we dim the strength to see how weak the light can be. With a very thorough look one will discover that there is a smallest building block of light - a light particle which physicists call a photon. This particle cannot be divided further.

A single photon represents very, very weak light in an everyday sense. For instance a red bulb with 60W light power emits roughly 2*1020 (a one with twenty zeros) photons every second. You have to look very carefully to see the effect of a single photon. However, this is possible in modern physics experiments.

The fact that nature is a collection of smallest building blocks has strong consequences, especially for systems of a size so small that only a few building blocks are present. In fact, a single photon only has space available to carry "a certain amount of information". Hence the total amount of information in a weak pulse of light has to be small. This may be compared to a book so small that there is only space for e.g. five letters. Evidently not much information can be written in such a book. Practically all this means that a weak pulse of light will seem to be quite noisy, see the figure below.

Light noise Atomic noise

Left: A weak pulse of light is noisy - it contains so-called quantum noise. This kind of noise is in principle similar to noise on an FM-radio or to "snow" on a TV-screen. There is just one difference; you cannot get rid of the noise. It will always be there to some extent. Right: It is not only light which becomes noisy as a consequence of quantum mechanics. A spinning top consisting of few atoms will also contain a considerable amount of noise. This may be visualized as if the direction of the spinning top is not exactly defined.

The fact that the direction of the spinning top cannot be precisely defined can be viewed from another perspective. You can say that the spinning top both points a little to the left and a little to the right at the same time. Within quantum mechanics physical systems can easily be in different states at the same time. This is commonplace for quantum physicists but nonsense for non-physicists. But whether you are a quantum physicist or not, this just has to be accepted without further explanation. This is the way nature works!

Quantum mechanics has consequences for the method of information transfer which we denoted "classical memory" above. The quantum noise prevents us from measuring the incoming state of light precisely - it is simply not possible. Below we explain pictorially what happens if one attempts anyway to measure the state of light.

Strength/phase movie

During a measurement we can only extract a certain amount of information about the state of light since the light particles that we will detect each has a maximum amount of information. Pictorially this can be thought of as if we are only allowed to detect the light wave at a few points - here next to the six arrows. We are showing two cases. In one we obtain good information about the strength of the light state but we must accept that we do not know much about the phase. The other case is opposite, we detect the phase with good accuracy but now it is hard to estimate the strength of the light.

The above example represents a well-known phenomenon in quantum mechanics, the so-called complementarity principle. The strength and phase of light are complementary. They cannot both be precisely defined at the same time.

For atoms, or our spinning top, there is also a complementarity principle. When the spinning top is pointing roughly in the vertical direction (within some allowed precision) you may e.g. ask one of two questions. (1) How much does the spinning top point in/out of the picture? (2) How much is the spinning top pointing left/right? These two questions cannot be answered precisely at the same time. The two directions are complementary, just like the strength and phase was for light.

Now we may understand why the "classical memory" is not entirely precise. In this case we would like to transfer both the strength and the phase of light to atoms. So instead of making a very precise measurement of either the strength or the phase, we have to compromise and make a half-precise measurement on both.

But now let us see how to transfer a state of light to atoms with a method better than "classical memory". This is what we call "quantum memory" (classical as opposed to quantum).

Quantum mapping

A transfer method of information better than the classical method: The light is sent through atoms. The laws of physics will describe what is going on in this case. If the experiment is carried out correctly, a part of the light information (e.g. the phase) will be transfered to atoms. With a careful look at the illustration it can be seen that the spinning top is rotated slightly out of the picture while the light is passing by. Next we may concentrate on measuring the remaining information about the light (e.g. the amplitude). We will not obtain information about the phase of the light but this is not important since this information is already stored in atoms. The measured information of the light strength can now be used to rotate the spinning top into the correct position.

The above procedure works better than "classical memory". The incoming light state is unknown for us, and quantum mechanics actually forbids us to obtain a complete picture of the incoming state. Anyway it is possible to design a procedure of information transfer from light to atoms which works better than if we had tried to measure on the light directly.