# Quantum Optics - transition from pure to mixed state

Hello guys,

I am trying to understand the following experiment:

1. Prepare a 2 level atom in state |0>
2. Shine in a Pi/2 pulse --> atom goes to 1/√2 (|0>+|1>)
3. Wait time T
4. Shine in second Pi/2 pulse
a) if the state is pure: atom will go to state |1>, p1=1
b) if the state is mixed: p1=1/2, p2=1/2

And below a plot of p1 with respect to T. It starts at p1=1 and decreases with T to 1/2.

I don't understand point 4.
What I understand:
If T=0, the state is a pure superposition and gets to |1> via the second Pi/2 pulse
But as soon as time T passes after the first pulse, I am losing information, since the atom interacts with the vacuum fields (who are also responsible for spontaneous emission).

But what does that mean? Does the interaction with the vacuum 'destroy' my superposition and force the atom into either state |0> or state |1>?
Because if I then apply my second light pulse, it would go either from |0> to 1/√2 (|0>+|1>) or from |1> to 1/√2 (|0>+|1>), and then I would have my probabilities at 1/2.

Regards

## Answers and Replies

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DrClaude
Mentor
But as soon as time T passes after the first pulse, I am losing information, since the atom interacts with the vacuum fields (who are also responsible for spontaneous emission).
Yes, but you also have to consider the lifetime of the state with respect to the duration of the experiment. Using a long-lifetime excited state, one can neglect any effect due to spontaneous emission. It can also become simply a source of uncertainty (for instance, in an atomic clock).

Ok, lets assume it has a short enough average lifetime to play a role.
How exactly is the vacuum field 'destroying' the superposition? Is it possible to understand it intuitively?

vanhees71
Gold Member
2019 Award
The vacuum is not a field but a specific state of quantum fields.

Lord Jestocost
I am trying to understand the following experiment:

1. Prepare a 2 level atom in state |0>
2. Shine in a Pi/2 pulse --> atom goes to 1/√2 (|0>+|1>)
3. Wait time T
4. Shine in second Pi/2 pulse
a) if the state is pure: atom will go to state |1>, p1=1
b) if the state is mixed: p1=1/2, p2=1/2
I am not sure whether the interpretation is correct. Do you have a reference where the experiment is described?

jim mcnamara