# Understanding Squeezed States: Explanations & Evolution

• rudocurtir
In summary, the S states are solutions of the harmonic oscillator in a quantum optics setting and are generalizations of coherent states. They can be constructed by applying squeeze operators to coherent states and satisfy the Heisenberg uncertainty relation. For a more thorough understanding, one can refer to the chapters on coherent states and squeezed light in "Optical coherence and quantum optics" by Mandel and Wolf.
rudocurtir
Hello. I'm posting here for the first time.

Can somebody give a short explanation on what the S states are?
How do we construct them? How do they take evolution in time?
I know that they are some sort of generalization of the coherent states, but do they come from the same Hamiltonian?

PS: My name is Pablo, I study Physics at Santiago de Compostela (Spain).
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Would you mind if you were a bit more clear...?I mean,in what context did you meet these concepts...?What form does the Hamiltonian have...?

Daniel.

rudocurtir said:
Can somebody give a short explanation on what the S states are?
How do we construct them? How do they take evolution in time?
I

I'm no expert on this. What I vaguely know is the following: these are states that are solutions of the harmonic oscillator (usually in a quantum optics setting, where the harmonic oscillator is a mode of the EM field).
You know that coherent states are eigenstates of the annihilation operator, and they have particular properties (like the satisfy exactly the Heisenberg uncertainty relation: minimum uncertainty). Coherent states are in fact displacements of the vacuum state (if you apply the finite translation operator to the vacuum state, you obtain a coherent state).
But you can do more bricolage: you can also apply "squeeze" operators, which transform coherent states in other states (eh, squeezed states) ; these states also satisfy the HUP exactly.

If you want to have a very thorough reading on this, look at the chapter on coherent states, and the chapter on squeezed light (I think it is the last chapter) in Mandel and Wolf, the bible of quantum optics: "Optical coherence and quantum optics".

cheers,
Patrick.

## 1. What are squeezed states?

Squeezed states are quantum states of light or matter that have reduced quantum noise in one of the quadratures (position or momentum) at the expense of increased noise in the other quadrature. This means that the uncertainty in one of the quadratures is reduced, while the uncertainty in the other quadrature is increased.

## 2. How are squeezed states created?

Squeezed states can be created through a process called parametric down-conversion, where a strong laser beam is passed through a nonlinear crystal, resulting in two weaker beams with a specific phase relationship that creates the squeezed state.

## 3. What are the applications of squeezed states?

Squeezed states have a variety of applications in quantum information processing, quantum metrology, and quantum sensing. They can also be used in gravitational wave detectors to improve their sensitivity.

## 4. How do squeezed states evolve over time?

The evolution of squeezed states is governed by the Schrödinger equation, which describes the time evolution of quantum systems. Squeezed states can be manipulated and controlled through various techniques, such as using optical elements to change the phase or amplitude of the squeezed state.

## 5. What are the benefits of using squeezed states in quantum systems?

Squeezed states offer several advantages in quantum systems, including improved precision in measurements, enhanced sensitivity in detectors, and increased information-carrying capacity in communication systems. They also allow for more efficient use of resources in quantum information processing tasks.

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