Quantum optics

Question 1

Photon wavefuncitons must be

Answer 1

symmetric because they are bosons

Question 2

Why can ladder operators be used on E and B fields?

Answer 2

Because the oscillation between E and B energy is mathematically equivalent to the oscillation between potential and kinetic energy in a harmonic oscillator

Question 3

[a, a+] =

Answer 3

1

Question 4

Electric field operator

Answer 4

E_o (a + a+) sin kz

where E_o = (h_bar w /epsilon_o L)^1/2

Question 5

Magnetic field operator

Answer 5

-i E_0/c (a - a+) cos kz

Question 6

Hamiltonian of light field

Answer 6

h_bar w (a+a + 1/2)

Question 7

Creation operator acting on a number state

Answer 7

a+ |n> = sqrt(n+1) |n+1>

Question 8

Anihilation operator acting on a number state

Answer 8

a|n> = sqrt(n) |n-1>

Question 9

Number operator is

Answer 9

a+a

Question 10

Why are E and B fields of a number state not well defined?

Answer 10

Because they depend on (a + a+) which has a non-zero standard deviation

Question 11

Variance of E and B fields

Answer 11

2n+1

Question 12

Thermal state =

Answer 12

inchoherent mixture of number states

Question 13

Coherent state =

Answer 13

Question 14

Action of the annihilation operator on a coherent state

Answer 14

a|alpha> = alpha|alpha>

Question 15

Show that coherent states are minimally uncertain

Answer 15

Question 16

Mean photon number of coherent state

Answer 16

alpha^2

Question 17

Find the normalisation of the coherent state

Answer 17

Question 18

How does coherent state evolve with time?

Answer 18

Remains same coherent state but with accumulated phase

Question 19

Variance of E and B fields of coherent state

Answer 19

1

Question 20

How can a generic number state be expressed in terms of the vacuum state?

Answer 20

Question 21

Action of a beam splitter

Answer 21

Question 22

What is photon bunching/the Hong-Ou-Mandel effect?

Answer 22

When two photons with identical polarisation are incident on different inputs of a beamsplitter, both photons will exit through the same port.

Question 23

What is the displacement operator?

Answer 23

exp(alpha a+ - alpha*a)

D|0> = |alpha>

It is a unitary operator

Question 24

Can displacement operators be combined by adding arguments?

Answer 24

No

Question 25

What are squeezed states?

Answer 25

States where the variance in E is not the same as the variance in B

Question 26

What is the squeeze operator?

Answer 26

S(E) = exp (1/2E\*a^2 - 1/2 Ea+^2) where the real part of E squeezes E-field and the imaginary part the B-field.

Question 27

How else can a squeezed state be created?

Answer 27

Squeeze magnitude at the expense of phase and vice-versa. Limiting case is a number state - has perfectly defined photon number and undefined phase

Question 28

2 applications of squeezed states?

Answer 28

1. Improved interferometer sensitivity 2. Atomic clocks - more sensitive

Question 29

What is the Jaynes-Cummings Hamiltonian?

Answer 29

Question 30

Which terms can be droppped from the Hamiltonian and why?

Answer 30

The two outer terms - takes a lot more energy to add a photon and excite an atom in one go

Question 31

What is the JC Hamiltonian in a cavity if we neglect outer terms and assume perfect frequncy matching?

Answer 31

Question 32

What are the dressed states and what are their energies?

Answer 32

Question 33

Why do coherent states not become entangled with atoms when they interact?

Answer 33

Because when a photon is added to or removed from a coherent state the state created is not orthogonal to the orginal state, as it would be for a number state.

Question 34

How can spotanteous emission be suppressed?

Answer 34

By separating the cavity modes such that non appear near resonance

Question 35

How does Rabbi flopping cause exponential population decay?

Answer 35

If the cavity lifetime is short compared to the timescale of Rabbi flopping population will be lost.

Question 36

What is the Casimir effect?

Answer 36

Imagine two parallel conducting plates. More modes can exist in space around them than between them. This means the energy density between the plates is lower than outside the plates so there will be a force pushing them together.

Question 37

What is the Lamb shift?

Answer 37

A small energy differnece between 2s 2S1/2 and 2p 2P1/2 caused by a QED effect. Hard to detect as there are many other small effects such as nuclear volume interaction and nuclear hyperfine interactions.

Question 38

How can a global phase be relacent?

Answer 38

Pass a quantum state through a beam splitter. Add a global phase to one branch. Recombine them. Now there is a relative phase.

Question 39

What is a Berry phase?

Answer 39

A phase which accumulates when a system evolves under an adiabatically varying Hamiltonian. Imagine a spin-half particle in a magnetic field with an adiabatically varying direction. The Berry phase picked up will be m\*solid angle swept out by field vector.

Question 40

What is a Parcharatname state?

Answer 40

Doesn't depend on global phases and is not a modulus squared.

Question 41

What is the Aharanov-Bohm effect?

Answer 41

When two electrons pass on different sides of a solenoid they pick up differnt phases. This is because the solenoid acts as a singularity. The phase picked up depends on the current in the solenoid.