What specifically are they talking about when they use the term “squeezed vacuum”? Can someone de-metaphor this for me, and explain it in more technical language?
Also, when I first read this, I imagined squeezing a photon into two to mean using a non-linear material to convert a high-energy photon into two entangled lower-energy photons, allowing them to get highly precise position information. But possibly I’m wrong, and they’re just referring to sending a photon through a partially silvered mirror. Or maybe something else entirely. So what do they mean there, as well?
Generally, a squeezed state is a state that saturates the uncertainty principle, i.e. for which ∆x∆p = ħ/2, and in such a way that ∆x doesn’t equal ∆p. The name derives from the fact that you can express the uncertainty in a state by an area in a diagram; for a state in which position and momentum uncertainty agree, that area is a circle, and if both don’t agree, it’s an ellipse—i.e. the uncertainty region has been ‘squeezed’.
A squeezed vacuum is a squeezed state such that the average amplitude of the light is zero (but not, in general, the average photon number).
It is easiest to think about this in terms of a harmonic oscillator. The generalization from harmonic oscillators to the modes of oscillation in an optical resonator is straightforward (for a physicist).
The “vacuum state” of a harmonic oscillator (and the modes of an optical resonator) is the lowest energy state. For the oscillator, it does NOT represent a state of no motion, it is represented by a gaussian wave packet with a characteristic width in which delta x and delta p are equal in the natural dimensionless units for the system.
In the oscillator, we can excite the system to higher energy states by adding energy in units of twice the vacuum state energy. The same is true in the optical case, but we have a special name for these extra boosts of energy. We call them photons. It is just terminology, which can lead to confusion.
Now, it is possible to imagine infinitely many other excited states, which are not in general energy states (states with a well-defined energy). For example, in the oscillator, imagine that you squeeze the ground state gaussian wave function so delta x is smaller. In this case delta p will be bigger, preserving the product of delta x and delta p. We call this a squeezed state of the vacuum. You can squeeze any state in this fashion. If you squeeze the vacuum (ground state) or any other energy state, it will no longer be a stationary state, it will evolve in time. For a squeezed vacuum state, if it is very narrow in position at time zero (and broad in momentum), it will be very narrow in momentum (and broad in position) a quarter cycle later.
I’ve probably only confused you further, but the important thing is not to get confused by terms like “vacuum” and “photon” that tend to obscure the simple picture of what is going on here.
In atoms, the energy states of the electron are of prime importance, because electrons are electrically charged and will radiate their energy away until they decay into an energy state, which is stationary. For light, no such thing occurs, so optical states are usually far away from being energy states characterized by a fixed number of photons.
OK, yes, that was too much of a gloss. Effectively, you can make both dimensionless, by measuring position in units of √(ћ/(ωm)), and momentum in units of √(ћωm) (I’ve heard this called ‘natural oscillator units’). In terms of those, the uncertainty relation for a squeezed state should then be ∆x∆p = 1/2, of course.
