An atomic clock based on a fountain of atoms. NSF
Physics, as you may have read before, is based around two wildly successful theories. On the grand scale, galaxies, planets, and all the other big stuff dance to the tune of gravity. But, like your teenage daughter, all the little stuff stares in bewildered embarrassment at gravity’s dancing. Quantum mechanics is the only beat the little stuff is willing get down to. Unlike teenage rebellion, though, no one claims to understand what keeps relativity and quantum mechanics from getting along.
Because we refuse to believe that these two theories are separate, physicists are constantly trying to find a way to fit them together. Part and parcel with creating a unifying model is finding evidence of a connection between the gravity and quantum mechanics. For example, showing that the gravitational force experienced by a particle depended on the particle’s internal quantum state would be a great sign of a deeper connection between the two theories. The latest attempt to show this uses a new way to look for coupling between gravity and the quantum property called spin.
I’m free, free fallin’
One of the cornerstones of general relativity is that objects move in straight lines through a curved spacetime. So, if two objects have identical masses and are in free fall, they should follow identical trajectories. And this is what we have observed since the time of Galileo (although I seem to recall that Galileo’s public experiment came to an embarrassing end due to differences in air resistance).
The quantum state of an object doesn’t seem to make a difference. However, if there is some common theory that underlies general relativity and quantum mechanics, at some level, gravity probably has to act differently on different quantum states.
To see this effect means measuring very tiny differences in free fall trajectories. Until recently, that was close to impossible. But it may be possible now thanks to the realization of Bose-Einstein condensates. The condensates themselves don’t necessarily provide the tools we need, but the equipment used to create a condensate allows us to manipulate clouds of atoms with exquisite precision. This precision is the basis of a new free fall test from researchers in China.
Surge like a fountain, like tide
The basic principle behind the new work is simple. If you want to measure acceleration due to gravity, you create a fountain of atoms and measure how long it takes for an atom to travel from the bottom of the fountain to the top and back again. As long as you know the starting velocity of the atoms and measure the time accurately, then you can calculate the force due to gravity. To do that, you need to impart a well-defined momentum to the cloud at a specific time.
Superposition is nothing more than addition for waves. Let’s say we have two sets of waves that overlap in space and time. At any given point, a trough may line up with a peak, their peaks may line up, or anything in between. Superposition tells us how to add up these waves so that the result reconstructs the patterns that we observe in nature.
Then you need to measure the transit time. This is done using the way quantum states evolve in time, which also means you need to prepare the cloud of atoms in a precisely defined quantum state.
If I put the cloud into a superposition of two states, then that superposition will evolve in time. What do I mean by that? Let’s say that I set up a superposition between states A and B. Now, when I take a measurement, I won’t get a mixture of A and B; I only ever get A or B. But the probability of obtaining A (or B) oscillates in time. So at one moment, the probability might be 50 percent, a short time later it is 75 percent, then a little while later it is 100 percent. Then it starts to fall until it reaches zero and then it starts to increase again.
This oscillation has a regular period that is defined by the environment. So, under controlled circumstances, I set the superposition state as the atomic cloud drifts out the top of the fountain, and at a certain time later, I make a measurement. Each atom reports either state A or state B. The ratio of the amount of A and B tells me how much time has passed for the atoms, and, therefore, what the force of gravity was during their time in the fountain.
Once you have that working, the experiment is dead simple (he says in the tone of someone who is confident he will never have to actually build the apparatus or perform the experiment). Essentially, you take your atomic cloud and choose a couple of different atomic states. Place the atoms in one of those states and measure the free fall time. Then repeat the experiment for the second state. Any difference, in this ideal case, is due to gravity acting differently on the two quantum states. Simple, right?
Practically speaking, this is kind-a-sorta really, really difficult.
I feel like I’m spinnin’
Obviously, you have to choose a pair of quantum states to compare. In the case of our Chinese researchers, they chose to test for coupling between gravity and a particle’s intrinsic angular momentum, called spin. This choice makes sense because we know that in macroscopic bodies, the rotation of a body (in other words, its angular momentum) modifies the local gravitational field. So, depending on the direction and magnitude of the angular momentum, the local gravitational field will be different. Maybe we can see this classical effect in quantum states, too?
However, quantum spin is, confusingly, not related to the rotation of a body. Indeed, if you calculate how fast an electron needs to rotate in order to generate its spin angular momentum, you’ll come up with a ridiculous number (especially if you take the idea of the electron being a point particle seriously). Nevertheless, particles like electrons and protons, as well as composite particles like atoms, have intrinsic spin angular momentum. So, an experiment comparing the free fall of particles with the same spin, but oriented in different directions, makes perfect sense.
Except for one thing: magnetic fields. The spin of a particle is also coupled to its magnetic moment. That means that if there are any changes in the magnetic field around the atom fountain, the atomic cloud will experience a force due to these variations. Since the researchers want to measure a difference between two spin states that have opposite orientations, this is bad. They will always find that the two spin populations have different fountain trajectories, but the difference will largely be due to variations in the magnetic field, rather than to differences in gravitational forces.
So the story of this research is eliminating stray magnetic fields. Indeed, the researchers spend most of their paper describing how they test for magnetic fields before using additional electromagnets to cancel out stray fields. They even invented a new measurement technique that partially compensates for any remaining variations in the magnetic fields. To a large extent, the researchers were successful.
So, does gravity care about your spin?
Short answer: no. The researchers obtained a null result, meaning that, to within the precision of their measurements, there was no detectable difference in atomic free falls when atoms were in different spin states.
But this is really just the beginning of the experiment. We can expect even more sensitive measurements from the same researchers within the next few years. And the strategies that they used to increase accuracy can be transferred to other high-precision measurements.
Physical Review Letters, 2016, DOI: 10.1103/PhysRevLett.117.023001
See the full article here .
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