All Questions
Tagged with coherent-states density-operator
9
questions
1
vote
0
answers
31
views
Existence of Glauber-Sudardhan $P$-representation of arbitrary given density operator for light field
In all textbooks on quantum optics I can reach (Scully, Leonhardt, Walls, etc), the Glauber-Sudardhan $P$-representation $P(\alpha)$ is introduced in the following two ways:
Fourier transform of $\...
- 695
0
votes
0
answers
129
views
Coherent states and thermal properties
I am reading a paper called Thermodynamics of Coherent States and Black Hole Entropy, written by Bashkirov and Sukhanov. If I understand correctly, they define a coherent state by the equation
$$a|d\...
- 3,992
1
vote
1
answer
216
views
Master equation with a coherent bath
When we consider an oscillator $a$ acting with a bath of oscillators $b_i$ with the interaction Hamiltonian reads
$$H_{int}=\sum_{i}g_ia b_i^{\dagger}+g_i^*a^{\dagger}b_i,$$ with the free Hamiltonian:
...
- 442
3
votes
1
answer
134
views
Off-diagonal elements of density matrix in three-level system
In a three-level system, let's say an atom with three possible states, $|1\rangle$ being the lowest and $|3\rangle$ the highest ($E_1<E_2<E_3$), where
$$\Psi(t)= C_1(t)|1\rangle+C_2(t)|2\rangle+...
- 381
3
votes
1
answer
2k
views
Is the density matrix corresponding to a state $|\alpha\rangle$ simply $\rho =| \alpha \rangle \langle \alpha \mid$?
The eigenstate of the annihilation operator $a$ is given by the state $a\mid \alpha \rangle = \alpha \mid \alpha \rangle$. In the Fock state basis, we can expand this state as
$$\mid \alpha \rangle = ...
- 330
1
vote
0
answers
168
views
How to represent the square root of a density matrix via the Glauber-Sudarshan representation?
I am trying to calculate the quantum Fisher Information of some quantum states which are represented via their P (Glauber-Sudarshan) representation,
$$\rho = \int P_\rho(\alpha) |{\alpha}\rangle \...
- 11
2
votes
0
answers
50
views
Diagonalisation of quasi-thermal state
I have the following density operator $$\frac{1}{t \pi N} \int_{\mathbb{C}} \mathrm{d}^2\gamma \exp
\left[
-\frac{|\gamma+r\alpha|^2}{t^2 N}
\right]
|{\gamma}\rangle\langle{\gamma}|,$$
where $0\leq t,...
- 143
2
votes
0
answers
110
views
Expansion of an arbitrary density matrix in terms of coherent states?
It is well-known that any pure state can be expanded in terms of coherent states namely
$$\left|\psi\right>=\frac{1}{\pi}\int d^2\alpha\left<\alpha|\psi\right>\left|\alpha\right>$$ due to ...
- 67
7
votes
4
answers
2k
views
Derivation of $P$ representation of the thermal density operator
I'm trying to derive the P representation for the thermal state
$$
\rho = \sum_{n=0}^\infty \frac{\mathrm{e}^{-\beta \omega n}}{Z} |n\rangle \langle n |
$$
where $\beta$ is the inverse temperature, $...
- 455