Observing the Heisenberg Uncertainty Principle in the Laboratory
The Cindy Regal group is so skillful at using laser light to track the position of a tiny drum that researchers have been able to observe a limit imposed by the Heisenberg Uncertainty Principle. In one experiment, the researchers measured the motion of the drum by sending light back and forth through it many times. During this measurement, however, 100 million photons from the laser beam struck the drum at random, making it vibrate. The extra vibration obscured the motion of the drum at exactly the level of precision predicted by the uncertainty principle.
Two aspects of the experiment made it possible to observe very small vibrations due to quantum mechanical effects. First, the experiment was done at the very low temperature of 5 K (-451 °C). The temperature was sufficiently low to reduce the amount of vibration caused by heating of the experiment by the surrounding environment. Second, the researchers used special drums that lose vibrational energy very slowly. Thus, when they measured vibrations during the experiment, they were able to determine that quantum fluctuations of light were causing about half of them.
The detection of the extra vibration indicated that the experimenters had reached a limit on successive measurements imposed by the uncertainty principle. This principle dictates that the closer someone comes to measuring the exact position of an object, the less that can be known about how fast the object is moving. In other words, this law recognizes that it is not possible to both precisely measure the position of an object and how fast it is moving at the same instant. Of course how fast something is moving has a whole lot to do with its exact position in the future. This paradox results in a conundrum for the experiment physicist like Regal: Do we make the best position measurement now or obscure the motion later?
Regal says the easiest way to get the best precision is to give up precise knowledge of an initial position to balance the combined uncertainty in position and velocity. However, there may exist ways to work around quantum limits. The challenge of trying to do so has a particular fascination for Regal.
Using measurements to solve the Schrödinger equation
The Steve Cundiff group has developed a new technique to measure key parameters needed to solve the Schrödinger equation, which describes the time-dependent evolution of quantum states in a physical system. For the equation to work, it’s necessary to figure out a key part of this equation known as the Hamiltonian, which describes the total energy of the system. However, this is not an easy task for theorists since Hamiltonians for real-life systems must characterize a multitude of quantum states and quantum pathways that inevitably exist inside a roiling quantum world.
For experiments involving many atoms or other particles that interact with each other and the environment, the only hope of determining the correct Hamiltonian may be to do it experimentally, as has been demonstrated by the group. The group used a technique know as optical three-dimensional (3D) Fourier-transform spectroscopy to acquire detailed spectra of hot (180 ºC) potassium (K) atoms. The spectra provided a window into the quantum world of the atoms in the experiment.
Using the spectra, the researchers were able to disentangle all possible pathways between specific initial conditions of the K atoms (typically ground states) and final conditions (including excited and superposition states). Once they had identified all possible pathways, they were able to make the measurements necessary for describing the pathways. This information allowed them to figure out some pieces of the Hamiltonian they needed.
This work is a big step towards being able to experimentally determine a Hamiltonian for an even more complex system. It could even lead one day to the ability to coherently control chemical reactions.
Reducing quantum noise in precision measurement
The James Thompson group has come up with a creative way to measure the spins in a collection of a million atoms: Premeasure the quantum noise in the experiment and then subtract out the quantum noise at the end of the precision measurement. The secret is to avoid doing anything that detects and measures the spins of individual atoms in the ensemble. If states of individual atoms are measured, then those atoms stop being part of the collective superposition of all the atoms, and any subsequent precision measurement will be ruined. So regardless of what measurement technique is used, it must not alter the quantum state of specific atoms.
Details on this clever technique can be found in Working around the Quantum Limits to Precision Measurement.