Transcript Document 7343754

Low-Light-Level Cross Phase Modulation
with Cold Atoms
J.H. Shieh, W.-J. Wang and Ying-Cheng Chen
Institute of Atomic and Molecular Sciences, Academia Sinica,
NTHU AMO Seminar, March 3, 2009
IAMS
Outline
•
•
•
•
•
•
Introduction to Cross Phase Modulation (XPM)
Briefs on Electromagnetically induced transparency (EIT)
Introductions on EIT-based XPM schemes
Considerations on few-photon-level XPM
Our experimental progress towards the goal
Prospective
Cross Phase Modulation
Probe light
Control light
Photon-photon has no coupling in
free space, at least at low field strength
where QED effect is not significant.
atoms
Photon can couple to photon via the
media (e.g. atoms).
φ
Without control light
With control light
Kerr effect: n=n0+n2I
Cross phase modulation: Phase change of the probe pulse under the presence
of control pulse and media. The Kerr effect.
•
One of the holey grail in nonlinear optics is to observe the π radian mutual
phase shift for two single photon pulses with small absorption loss.
XPM Application: Controlled-NOT gate for
Quantum Computation
•
•
CNOT and single qubit gates can be used to implement an arbitrary unitary
operation on n qubits and therefore are universal for quantum computation.
Single photon XPM can be used to implement the quantum phase gate and
CNOT gate
Truth table for CNOT gate
0 C 0T
 0 C 0T ; 0 C1T
1C 0T
 1C1T ; 1C1T
PBS
Control qubit
1  
0 or 1
 1C 0T
PBS
Signal
0  
Probe
 0 C1T
Atoms



Target qubit
For a good introductory article, see 陳易馨&余怡德 CPS Physics Bimonthly, 524, Oct. 2008
XPM in Generation of Entangled Photon Pairs
• Single photon π phase shift XPM can be implemented to generate
entangled photon pairs which are important in quantum teleportation.
• For a close look at quantum teleportation, see e.g. 2008 AMO
summer school presentation file in NCTS website given by 陳岳男.
PBS
0
PBS
Signal
450 linear polarization
(0
C
 1
C
Probe
1  
)/
Entangled photon pairs
2
Atoms
(0


C
1T 1
C
0 T)/ 2
XPM in Quantum Nondemolition Measurement
Signal beam
Meter beam
• QND measurement of the photon number by dispersive atom field
coupling. See. e.g. Scully, Quantum Optics, Sec.19-3.
Electromagnetically Induced Transparency (EIT),
the Phenomena
|3>
p
Atomic sample
Attenuated
31
Attenuated
31
Probe laser
|1>
Optical density=2
Transparent!
|3>
Probe laser
Pass through
again
Coupling laser
32
p

32
c
2>
|1>
 c  0, c  0.53 ,   0
For a review, see Rev. Mod. Phys. 77, 633,2005
EIT, the Physical Explanation
•
•
•
Destructive interference between excitation pathways
Destructive interference between two dressed states
Dark state or resonance
|3>
probe
coupling
＋
＝
＋…
＋
2
Atot

|2>
|1>
|3>
probe
Path ii
|3>
coupling
Path iii
1( N )  sin  2, N  1  cos  3, N
c
2( N )  cos  2, N  1  sin  3, N
coupling
|2>
probe
Path i
probe
tan 2  
c
c
 
 
1( N ) d  E p 1  2( N ) d  E p 1  0
|1>
Diagonalize the
HA+HAC+HAP
dark  cos  1  sin  2
tan  
p
c
A limiting case of coherent
population trapping effect
where
c
p
 
EIT and the Slow Light
• Group velocity of the probe pulse
 p (k p )  ck p / n( p )
vg 
•
d p
dk p
| p 0 
1
dk p
d p

| p 0
c
n   p (dn / d p ) | p 0
The steep dispersion in addition with no loss has
important effect on the probe propagation in EIT
medium : the lossless slow light.
Vg<17m/s, Hau et.al.
Nature397,594,1999
More on Slow Light
3N3 231 p
2
Re(  ) 

O
(

p)
2
2
4
c
•
If γ/Γ3<<1 & δc=0,
•
Higher order dispersion and finite
EIT bandwidth still cause slightly
pulse spreading.
At δp=0, one obtains (N: atom
density)
vg
•
•
•
n  1 
c
32 31

, ng  N
c 2
1  ng
2  c
Group delay for a sample with
length L
Lng

1 1
32 31
 d  L(  ) 
 N(
) L 2  OD 312
The slow light has practical
vg c
c
2
c
c
applications as optical delay line.
 c2   c2  31
considering the decoherence
Line Narrowing Effect with Large OD Gas
•
•
Has been observed in warm gas,
PRL 79,2959,1997.
T  exp( kL Im(  ))
Intensity transmission
•
For medium and large OD,
i  ( p   c )
3N3

31
8 2 (3 2  i p )(  i ( p   ))
EIT 
•
Delay Bandwidth product ~
OD
 c2
OD 3
Slow Light : Dark-State Polariton
coupling
coupling
probe
coupling
probe
|2>
|2>
|2>
1>
|3>
|3>
|3>
1>
1>
Light component
 ( z , t )  cos E p ( z , t )  sin 
tan   n g ; k  k c  k p
N  21 ( z , t )e ikz
Matter component:
atomic spin coherence


 c cos 2 
] ( z , t )  0
t
z
v g  c cos 2 
Lukin&Fleischhauer, PRL 84,5094,2000
[
EIT and the Photon Storage
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By adiabatically turn off the coupling light, the probe pulse can completely
transfer to atomic spin coherence and stored in the medium and can be
retrieved back to light pulse later on when adiabatically turn on the coupling.
This effect can be used as a quantum memory for photons.
The photon storage and retrieved process has been proved to be a phase
coherent process by Yu’s team.
coupling
probe
Hau et.al. Nature, 409,490,2001
Y.F. Chen et.al. PRA 72, 033812, 2005
Basic EIT-based XPM scheme: N-type system
4
3
probe
signal
coupling
With signal beam
Without
signal
2
1
• The scheme was proposed by Schmidt & Imamoğlu (Opt. Lett. 21,1936,1996).
• The signal beam cause ac Stark shift on state 2 and introduce a cross phase
modulation on probe.
• The EIT guarantee low probe loss with the transparency window if choosing
larger enough coupling field.
• The scheme was firstly demonstrated by Yi-Fu Zhu’s team (PRL91,093601,2003).
Dual Slow Light Scheme for Weak Field XPM
Lukin & Imamoğlu
PRL 84,1419,2000
Both signal and probe are slow-light pulses
•
•
Use a second species atom and a second coupling pulse to allow signal
pulse becoming a slow light pulse.
Both signal and probe pulses are tuned to the same slow group velocity.
This allow long interaction time between these two weak pulses to gain
Tightly
significant mutual phase shift.
focusing
Long interaction time
1. Long delay time -> high OD
2. Avoid loss due to absorption by decreasing the decoherence rate
Single Species Dual Slow Light Weak Field XPM
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The symmetric arrangement guarantee the
matched group velocity for the two weak
probe pulses for long interaction length.
Each probe pulse is the signal pulse of the
N-type system for the other EIT system.
The Zeeman shift >> Natural linewidth for
dispersive coupling in the N-type system.
Two coupling fields are needed.
The orthogonal coupling and probe
requires very cold sample to minimize the
residual Doppler broadening.
The two probe pulses can be used to
implement the quantum phase gate with
the qubit as polarization states.

qi   i     i   , i  ( S , P )
PRA 65,033833,2002



probe
signal
C
C
C
C




 e  i (0 0 )  
C
P
P
e
i (0C

C
C
P
C

P


 e i (lin lin n lin n lin )  
C
P
P
lin
)
 e i (lin 0 )  
C
P
P
P
C
P
P
P
C

P
N-Tripod Scheme XPM
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•
•
Both signal and probe form EIT with single
coupling beam and can be tuned with coupling
intensity and detuning and population difference
to match the group velocity.
Both signal and probe can be on exact EIT
resonance but still experience XPM.
Signal beam cause a cross phase modulation on
probe but also a self phase modulation.
Utilize Zeeman shift such that signal beam is
mainly dispersive coupling in the N-type system
Similar to previous scheme, one can implement
the quantum phase gate with polarization state
as qubits..
c
s
p
2
3
1
m=1
6P3/2,F=
3
6S1/2,F=4
6S1/2,F=3
PRL 97,063901,2006 & Opt. Comm. 681,2040,2008
4
5
m=3
m=0
m=2
m=0
Cs
N-Tripod
Probe
Signal
Im(χ)
Linear
susceptibility
Nonlinear
susceptibility
Re(χ)
The Light-Storage XPM Scheme
• Proposed and demonstrated by Yu’s team, PRL 96,043603,2006.
• Convert and store probe light into atomic spin coherence. Signal
beam is applied during the storage time to interact with atom.
• A phase shift of 440 for probe pulse was obtained with a 2-μs signal
pulse of Rabi frequency 0.32Γ with 65% transmission.
• The energy per unit area of signal beam, Ω2τ,affect the phase shift
at a fixed detuning.
• To increase the phase shift, one has to tightly focus the probe and
signal beam to increase the interaction strength and also to
increase the interaction time of signal with atoms.
Phase shift
Probe attenuation e-α

2
  2


2
  4

2
 2


2
  4
coupling
probe
signal
τ
Few-Photon-Level XPM
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•
•
1.
2.
3.
•
Large Kerr Nonlinearity
Low loss
Strong focusing to increase the atomlaser interaction strength
Long atom-laser interaction time
Possible schemes
Using the high-finesse cavity
Couple atoms and Light into the hollow
core fiber
Using the EIT-based stationary light
scheme together with transverse
waveguiding effect
All are challenging !
High-finesse cavity
cold atom
Coupling&
probe
Signal beam
Experimental Progress : Dense atomic medium
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•
•
In all EIT-based applications, the large optical density together with small
decoherence rate are crucial requirements.
We have obtained optical density > 100 using 2-dimensional MOT.
To obtain atomic sample with even larger OD, the optical dipole trapping is
required and is underway.
7cm
trapping
Coils&cell
Absorption Spectrum
Atom cloud
probe
trapping
trapping beam
Optics Express. Chen & Yu 16,3754(2008)
Optical density=105
Small Decoherence Rate
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To obtain small decoherence rate, good
mutual coherence between coupling and
probe lasers and small inhomogeneity in
magnetic field are crucial.
We obtained phase locking via the
modulation with vertical-cavity surfaceemitting laser (VCSEL) and injection
locking.
Obtained phase locking between
coupling and VCSEL with 13dBm
modulation power at ~9 GHz with
sideband power ratio ~ 15%.
Checked with beatnote by spectrum
analyzer showing that the linewidth
between coupling and probe to be <
10Hz, the instrument resolution limit.
Has been applied in the EIT experiments.
Coupling
ECDL
RF
Bias-Tee
Idc
VCSEL
PBS
λ/2
Probe
DL
coupling
~9GHz
VCSEL
Probe
frequency
Compensation of Stray Magnetic Field
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•
•
•
•
•
•
Three pairs of compensation coils with relative
large size (~50 cmφ) are used with 6
independent current channels applied to null
the stray field and gradients.
Stary field is minimized to < 30mG level by the
linewidth of EIT spectrum.
Non-metal support for MOT magnetic coils is
used to avoid the induced eddy current when
the MOT coils are turned off.
Current through MOT coils is rapidly turned off
(~30 μs) by field-effect-transitors together with
large damping resistor in parallel with coils.
Two layers of mu-metal are used to shield the
ion pump nearby the MOT.
Even with all of these, we observed that the
MOT inhomogeneous magnetic field decay
completely after 2 ms possibly due to the
induction of nearby metal stuffs.
We are using Faraday rotation effect to allow a
fast and quantitative diagnosis of stray field
situations.
~3GHz away
from resonance
L  B
PRA, 59,4836,1999
Typical EIT Spectrum
• Obtained EIT with ~50% transmission at 200kHz FWHM for OD~70
with coupling intensity ~5 mW/cm2.
Line Narrowing Effect with Large OD Gas
•
•
Has been observed in warm gas,
PRL 79,2959,1997.
T  exp( kL Im(  ))
Intensity transmission
•
For medium and large OD,
i  ( p   c )
3N3

31
8 2 (3 2  i p )(  i ( p   ))
EIT 
Increasing the
OD of atom cloud
 c2
OD 3
The Slow Light
• The typical delay time is 5-10 μs.
• Delay time > 10μs is observed at the expense of higher loss.
The Light Storage
• Observed the light storage signal. However, the storage time is still
short. Better compensation on the stray magnetic field is underway
to decrease the decoherence rate further.
Prespectives
• Short term:
1. Study the oscillatory effect of transverse magnetic field on slow light.
2. Realize the N-Tripod XPM in the two-dimensional MOT
• Middle term:
1. Obtain even higher OD gas in the optical dipole trap.
2. Study the transverse waveguiding effect and XPM enhancement
• Long term
1. Use the optical cavity with the light-storage XPM scheme to reach
the few-photon-level XPM.
2. …
Oscillatory Behavior on Slow Light with Transverse
Magnetic Field
• Why the oscillating behavior in
transverse magnetic field?
• What does the period
corresponding to?
• Does this behavior exist in Cs?
• If yes, what is the value of the
period?
• Preliminary experiment on Cs
do suggest similar transverse
magnetic field effect on delay
time. Better calibration on
compensation coils using
Faraday rotation is underway.
87Rb,
Yu’s team
N-Tripod XPM Scheme
• Optical pumping and/or microwave
transitions to prepare the population.
• Magnetic field ~ 30 Gauss to allow
dispersive coupling for N-type
system (Δ~4Γ)
• Beatnote interferometer proposed by
Yu’s team will be utilized to see the
XPM phase shift.
• The experiment should be quite
straightforward!
m=1
6P3/2,F=
3
6S1/2,F=4
6S1/2,F=3
m=3
m=0
m=2
m=0
Cs
PRA 72,033812,2005