Undergrad 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 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
View full post »

Similar threads

Undergrad Delayed Choice Quantum Eraser with altered beam splitter
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Use of the Beam Splitter Operator
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Interference of signal photons entangled with idlers
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Bell tests: Changing detector settings "just before photon arrives"
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Generation of polarization-squeezed beams
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Delayed choice quantum eraser setup with no beam splitter
  • · Replies 14 ·
Replies
14
Views
2K
Graduate Two Different Fock State Inputs into a Beam Splitter
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Does x affect the value of [a^2,(a^†)^2×e^2ikx]
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How does the thickness of a beam splitter affect the phase shift produced?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Does Causality in QFT Require Commuting Field Operators Outside the Light Cone?
  • · Replies 18 ·
Replies
18
Views
2K