August 13, 2022

# Atomic cloud key to controlling a quantum state without measuring it

Way back when I was still working in the lab, there was a lot of buzz about something called “coherent control.” The basic idea was to take the principles of traditional control theory—the same theory that makes things like cruise control work—and apply them to quantum systems.

Some very cool ideas and insights came out of that early work, but it has taken a while to put them into practice. Now, we might be starting to see some practical applications emerging, with researchers demonstrating in a new paper the active cooling of a membrane using coherent control.

## Measurement is bad

A traditional control system has something like a desired state, such as the target speed of a car. By repeatedly measuring the speed of a car and accelerating or decelerating, the control system can bring the car to the target speed.

Deciding how much acceleration or deceleration to apply at any given moment is the actual art of building a control system. But the key to the entire process is that measurement. Without it, the control system falls apart.

To give you an idea of where we are heading, we’ll look at how a quantum control system must differ from a classical control system. Let’s imagine that I have a quantum system with two possible states that we will call “up” and “down.” My goal is to develop a control system for my quantum system. I choose a target state for the system—up.

My system starts in a balanced superposition of up and down, meaning that if I measure the state of the system, I have a 50 percent chance of getting “up.” The other half of the time, I get “down.” Once measured, however, the state is set, and any further measurements will produce the same results. There is no chance to alter the system from then on.

In other words, my control system will not work half the time, and the other half, it will have nothing to do.

## State of change

However, a quantum system is not static. Left to itself, the initial superposition state will evolve—after a few seconds, the probability of measuring “up” will not be 50 percent. If I understand my quantum system, I can drive that evolution with a light, a magnetic field, or some other kick in the quantum pants. If my kick is timed right—and of just the right amount—when I measure, I will find the system in the up state 100 percent of the time.

What I’ve described is only half a control system, as I’m only using a model (my understanding) of the quantum system to choose the timing and intensity of the kick I give it. The loop can be completed by allowing the quantum system to interact in some way with the kick that I apply so that it switches itself on and off at the correct times. My simple example doesn’t immediately suggest a way to do that, however.

In a more complicated quantum system, the effect of a measurement is more subtle. It introduces a back action that can limit your ability to reach the target state. In the coming example, the goal is to cool a membrane, which basically means extracting all the thermal energy from it so that the membrane vibrates in its lowest energy state—a state with just a single quanta of energy.

Now imagine that my control system measures the vibration of the membrane to adjust my energy extraction tool (whatever that might be). The measurement will add at least one quanta of energy, so even if I hit the target state, my measurement will remove the membrane from the target state by adding energy. Avoiding this measurement step is the magical ingredient to the researcher’s control system.

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