I Commutation of Beam splitter operator with Displacement operator

Click For Summary
The discussion focuses on the commutation relationship between a beam splitter operator and a displacement operator. The beam splitter operator is defined as (a†)b + (b†)a, while the displacement operator is expressed as exp(α↠- α*â). Participants suggest checking if the beam splitter operator commutes with the argument of the displacement operator's exponential. This involves evaluating the commutation relations between the creation and lowering operators. Understanding these commutation properties is crucial for applications in quantum optics and related fields.
deepalakshmi
Messages
95
Reaction score
6
TL;DR
Does Beam splitter operator and Displacement operator of coherent state commute with each other?
I have a beam splitter operator (a†)b +(b†)a. Does it commute with exp(αâ†-α*â). Here a and ↠are creation and lowering operator
 
Physics news on Phys.org
Well, just check, whether the BS operator commutes with the argument of the operator exponential!
 

Thread 'Angular Momentum Vector and Its Magnitude'

For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
View full post »

Similar threads

I Use of the Beam Splitter Operator
Replies
4
Views
2K
I Delayed Choice Quantum Eraser with altered beam splitter
Replies
8
Views
2K
I Generation of polarization-squeezed beams
Replies
2
Views
1K
I Delayed choice quantum eraser setup with no beam splitter
Replies
14
Views
1K
A Two Different Fock State Inputs into a Beam Splitter
Replies
1
Views
2K
I Counterfactual quantum computation on interferometer
Replies
1
Views
2K
I Interference of signal photons entangled with idlers
Replies
2
Views
2K
I Commutator of x and p in quantum mechanics
Replies
4
Views
388
I Bell tests: Changing detector settings "just before photon arrives"
Replies
4
Views
1K
I Photon states and interference in an Interferometer
Replies
12
Views
2K