Physics 721: Homework # 5
Due Wednesday, Nov. 26
Questions or assistance: Dan Campbell dlcamp@umd.edu (maybe)
Dans Oce Hours: M 4:00-6:00pm, PSC Study nook.
1. Beam splitter transformations
An ideal beam splitter transforms two input eld modes a, b accord
Physics 721: Homework # 5 Solutions
1. Beam splitter transformations
bU
Part 1: Show that aout = U 1 aU and out = U 1 .
b
+
a b)
a
Unitarity implies U 1 = U = ei(b
. Therefore
+
a b)
a
U 1 aU = ei(b
+
a b)
aei(b
a
.
(1)
Using the equality
eA BeA = B [
Physics 721: Homework # 6
Due Wednesday Dec. 10, 2014
Questions or assistance: Seiji Sugawa, seiji.sugawa@nist.gov
Oce Monday 4-6 PM, usual place in PSC
Do any 3 (out of 4) problems for full credit. The remaining problem can be done for extra credit.
1. C
Physics 721: Homework # 4 Solution Set
1. Bragg scattering
a. Derive the equations of motion for the probability amplitudes c1,p and c2,p .
The Hamiltonian describing the interaction of two elds of dierent frequencies and wavevectors (but the
same Rabi fr
Physics 721: Homework # 2 Solutions
1. Interference in spontaneous emission and quantum beats
a. Derive evolution equations for the amplitudes of the upper states c2 (t) and c3 (t).
In this problem we will work in the interaction picture where i | = V | .
Physics 721: Homework # 4
Due Wednesday Nov. 12
Questions or assistance: Ana Valds Curiel (anavaldesc@gmail.com)
1. Bragg scattering
In this problem we will study how optical elds can be used to coherently transfer momentum to atoms.
Consider a two-level
Physics 721: Homework # 1 Solution Set
1. Optical transitions and angular momentum
(a) In abbreviated form, the Wigner Eckart theorem states that for an angular
(k)
momentum spherical tensor of rank 1, Jq , any set of operators Tq labeled by q that
satisf
Physics 271: Homework # 3
Due Wednesday Oct. 29
Questions or assistance: Andika Putra aputra@umd.edu
Oce Hours: Mondays, 3:50-6:00 (PSC, same place)
1. Raman uorescence
In this problem we investigate uorescence from a driven 3-level system, as illustrated
Physics 721: Homework # 1
Due Sept. 29
Questions or assistance: Dina Genkina, dgenkina@umd.edu
Oce Hours: Mondays, 4:00-6:00 (PSC, contact Dina for location)
1. Optical transitions and angular momentum
This problem reviews some aspects of atomic transitio