# Tag Info

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### Is the vacuum state a coherent state?

The coherent state $\vert \alpha\rangle$ is just a vacuum state $\vert 0\rangle$ translated in $x$ and $p$ space so $\alpha=x_0+ip_0$. Thus the vacuum state is a coherent state that has not been ...
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### Eigenstates of the creation operator

Well, here is a seat-of-the pants "lark" formal answer, going to "rigged" Fock spaces and places you (or anybody else) shouldn't really be at; except you may already have been ...
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### Countable basis of coherent states used to express coherent states

A more detailed investigation of the completeness of an arbitrary countable subset $\lvert \alpha_i\rangle$ of coherent states can be found in "On the completeness of a system of coherent states" by ...
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### What does coherent superposition mean?

The word "coherent" is used in Physics in a rather sloppy way. Your first state is a linear combination of harmonic oscillator eigenvectors that turns into a gaussian in momentum/position ...
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### Calculating free energy from coherent state path integral

The extra term you are missing can be interpreted as an error in the zero point energy. This error comes from the regularization of the infinite product for the partition function. Take for example ...
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### Finding the wavefunction of coherent state in 2D oscillator

@Abezhiko has done the bulk of the crucial combinatorics, up to the first line of his multi-level formula. Set $m\omega/\hbar= 1$, nondimensionalizing, and reinstate it only in the end if you must, ...
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### Time evolution of squeezed states

It is a very good question with a subtle answer! Let me give you a short answer and then recommend a good paper that you can take a look. The time evolution of a squeezed states defined as you ...
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### Time Evolution of Coherent State (Gerry and Knight)

\begin{align} e^{-i\omega t/2}e^{-i\omega t \hat n}\vert\alpha\rangle&= e^{-i\omega t/2}\sum_{N}e^{-i\omega t \hat n}e^{-\vert\alpha\vert^2/2} \frac{\alpha^n}{\sqrt{n!}}\vert n\rangle\\ &=e^{-...
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### Why are coherent states of harmonic oscillators called "coherent"?

Coherent States of Harmonic Oscillator are Quantum Mechanical states which have definite phase and Minimum Uncertainty. The Quantum Mechanical states of Harmonic Oscillator do not have definite phase ...

### Definition of spatial and temporal coherence in QM?

To talk about lasers specifically we need to discuss the quantization of the electromagnetic field, i.e. quantum field theory (QFT). In order to avoid that subject for the moment and to build ...
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### Why use coherent state path integral? What is its motivation or goal?

The coherent state path integral is basically a recipe for converting a Hamiltonian into a Lagrangian. In condensed matter, we often start with a "microscopic" Hamiltonian description of a material ...
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### Basic question on holomorphic formalism in QM

The reason that you can pass from the holomorphic representation to the real representation and vice versa is the existence of a unitary transformation between the two representations. This ...
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### Coherent states of Quantum harmonic oscillator

A good way to think of $\lambda$ is to consider the coherent state as a displaced harmonic oscillator ground state. Writing $\lambda=\lambda_r+i\lambda_i$ with $\lambda_{r,i}$ the real and imaginary ...
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### Can we derive the classical beam-splitter theory from the quantum beam-splitter Fock state picture?

The cleanest way to understand beam splitters in quantum optics is via their action on the creation and annihilation operators, which is the same as their action on the classical field amplitudes: if ...
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### Laser power and coherent state amplitude

You can look at the details in the Wikipedia article on the quantization of the electromagnetic field, but I will sum up some relevant bits below. First, you seem to take the analogy with the massive ...
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### Projective measurement using two mode squeezed state?

If you are happy with destructive measurements, this can be done in principle in the lab. Let $\rho$ be the input state, and write $|\xi\rangle = S|n,0\rangle$. Undo the squeezing transformation $S$, ...
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### Why don't the oscillator coherent states disperse in time?

The coherent structure of the state is not preserved by a general quantum evolution. It is preserved only in very special cases, i.e. when the evolution is generated by the second quantization of a ...
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### It seems that expectation value of $H$ on coherent states is independent of time? But why?
As the Hamilton operator $H$ and the time-evolution operator $U(t)=e^{-iHt/\hbar}$ commute, the expectation value of $H$ in any state $|\psi(t)\rangle = U(t) | \psi(0)\rangle$ is independent of $t$. ...