Study of Quantum InterferencePhenomena in Cold Atoms

余怡德清華大學物理系

陳應誠 廖彥安林重維 陳韻文 蘇蓉容 邱馨瑩 潘冠錡

陳泳帆 蔡仁祥 楊致芸 劉昱辰陳德鴻

— from Reduction of the Light Speed to Quantum Entanglement

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speedreduction to 17 metres per second in an ultracold atomic gas,” Nature397, 594-598 (18 February 1999).

Measure Light Speed in a Medium

DetectorLaser

t

DetectorLaser

t + td

atoms

l

v l / td

Chromatic dispersion

ωω

ωω1

ωk1

kω

v,cω

nk g

ddn

n

c

ddn

ccn

ddd

d

The index refraction of fused quartz. 01.0

ddn

The Phenomenon ofElectromagnetically Induced Transparency (EIT)

probe laser

probe lasercoupling laser

atoms

atoms

|3

|2

|1

Coupling

Probe

= + + + .......

path i path ii path iii .......

Transition amplitudes: Ai Aii Aiii.......

Transition probability of |1 |2 = | Ai + Aii + Aiii + ....... |2

EIT is the destructive interference between Ai , Aii , Aiii , .......

The probe absorption is suppressed.

Quantum Interference

Experimental Setup

CouplingLaser

Probe Laser

PDT

T

T

T

T

T

z

y

x

AO

M

AO

M

Quadrupole Magnet

Quadrupole Magnet

T: trapping beam

Typically, we trap 4×107 87Rb atoms in a vapor-cell MOT. All fieldsof the MOT are shut off during the measurement of spectra.

The coupling and probe fields propagate nearly in the same directionand they are switched by AOMs.

Probe

|g1 |g2

|e

Coupling

Experimental Spectrum without the Coupling Laser

Experimental Spectrum in the Presence of the Coupling Laser

Ultrahigh Contrast near the Resonance

ωω

vg

ddn

n

c

Group Velocity Predicted from the Experimental Data

吸收率

折射率

色散

Photon Switching by Quantum Interference

Probe

|1 |2

|3|4

Coupling

Switching

A weak probe field and a strong coupling field form the EIT configuration.

Presence of the switching field enables the probe absorption and induces thethree-photon transition from the ground state |1 to the excited state |4.

One switching photon is enough to cause one probe photon absorbed underthe ideal condition. (Harris and Yamamoto, PRL81, 3611)

The Three-Fold Entangled State

|1 |2

|3 |4

Coupling

Switching

Probe

50/50 BS

,0111002

1fpsfps

where 1 or 0 in the | s, | p, and | f denotes presence or absence of the switching, probe, and fluorescence photons measured by the detectors.

Requirements: OD 10 and 10-3.

Einstein-Podolsky-Rosen (EPR) Paradox

Particle 1 in spin or is 50% and so is particle 2. The two particles must have opposite spin states. Their spin states won’t be known until measurements.

QM: 212112 2

1

S0

S1/2 S1/2

Information Propagation Cannot Exceed c

After the two particles travel far away, their spin states aremeasured.

If cttL )( 12 , it is not possible for the two to exchangethe information of their spin states.

The probabilism concept of QM is wrong.

1

S

N

Stern-Gerlach at t1

S

N

Stern-Gerlach at t2

L

2

Quantum Non-locality The wavefunction 12

is everywhere.

Particles 1 and 2 do not need to exchange any information.

Since the two particles must have opposite spin states,they are entangled.

An EPR or entangled pair.

Down-conversion by a BBO crystal to generate two entangled photons along the intersecting directions of the cones.

Teleportation

An EPR source generates thousands of entangled pairs.

Bob keeps one of the entangled pair and the counterpart issent to Alice.

Once Alice receives all her particles, Bob starts to transmitinformation based on the measurements of his particles.

public communication

EPRSource

Bob Alice

secure channel

Information Encoding and Decoding

Data transmitted through the public communication do notreveal real information.

Only the random numbers are sent in the secure channel.

The information can only be known by Bob and Alice.

......... .........

0 1 1 0 ...............

.........R R R x Rx

0 1 1 0 ...............

Bob Alice

EPR1: EPR2:

Information: