Quantum optics Flashcards
Photon wavefuncitons must be
symmetric because they are bosons
Why can ladder operators be used on E and B fields?
Because the oscillation between E and B energy is mathematically equivalent to the oscillation between potential and kinetic energy in a harmonic oscillator
[a, a+] =
1
Electric field operator
E_o (a + a+) sin kz
where E_o = (h_bar w /epsilon_o L)^1/2
Magnetic field operator
-i E_0/c (a - a+) cos kz
Hamiltonian of light field
h_bar w (a+a + 1/2)
Creation operator acting on a number state
a+ |n> = sqrt(n+1) |n+1>
Anihilation operator acting on a number state
a|n> = sqrt(n) |n-1>
Number operator is
a+a
Why are E and B fields of a number state not well defined?
Because they depend on (a + a+) which has a non-zero standard deviation
Variance of E and B fields
2n+1
Thermal state =
inchoherent mixture of number states
Coherent state =
Action of the annihilation operator on a coherent state
a|alpha> = alpha|alpha>
Show that coherent states are minimally uncertain
Mean photon number of coherent state
alpha^2
Find the normalisation of the coherent state
How does coherent state evolve with time?
Remains same coherent state but with accumulated phase
Variance of E and B fields of coherent state
1
How can a generic number state be expressed in terms of the vacuum state?
Action of a beam splitter
What is photon bunching/the Hong-Ou-Mandel effect?
When two photons with identical polarisation are incident on different inputs of a beamsplitter, both photons will exit through the same port.
What is the displacement operator?
exp(alpha a+ - alpha*a)
D|0> = |alpha>
It is a unitary operator
Can displacement operators be combined by adding arguments?
No
What are squeezed states?
States where the variance in E is not the same as the variance in B
What is the squeeze operator?
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.
How else can a squeezed state be created?
Squeeze magnitude at the expense of phase and vice-versa. Limiting case is a number state - has perfectly defined photon number and undefined phase
2 applications of squeezed states?
- Improved interferometer sensitivity
- Atomic clocks - more sensitive
What is the Jaynes-Cummings Hamiltonian?
Which terms can be droppped from the Hamiltonian and why?
The two outer terms - takes a lot more energy to add a photon and excite an atom in one go
What is the JC Hamiltonian in a cavity if we neglect outer terms and assume perfect frequncy matching?
What are the dressed states and what are their energies?
Why do coherent states not become entangled with atoms when they interact?
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.
How can spotanteous emission be suppressed?
By separating the cavity modes such that non appear near resonance
How does Rabbi flopping cause exponential population decay?
If the cavity lifetime is short compared to the timescale of Rabbi flopping population will be lost.
What is the Casimir effect?
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.
What is the Lamb shift?
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.
How can a global phase be relacent?
Pass a quantum state through a beam splitter. Add a global phase to one branch. Recombine them. Now there is a relative phase.
What is a Berry phase?
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.
What is a Parcharatname state?
Doesn’t depend on global phases and is not a modulus squared.
What is the Aharanov-Bohm effect?
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.
